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ZnO-based thermoelectrics : modelling, electrochemical thick film growth, and characterization Sielmann, Christoph 2016

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ZnO-based Thermoelectrics:Modelling, Electrochemical Thick FilmGrowth, and CharacterizationbyChristoph SielmannB.Sc., University of Alberta, 2005M.A.Sc., The University of British Columbia, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2016c© Christoph Sielmann 2016AbstractThe thermoelectric performance of electrodeposited, aluminum doped zincoxide was assessed. In this work, wurtzite ZnO was first modelled usingMueller-Plathe to compare the effectiveness of different nanostructured con-figurations on reducing thermal conductivity. A new analysis technique, Lo-cal Vibrational Density of States Equilibrium Molecular Dynamics (LVDOS-EMD), was created to study localized lattice vibrations around nanostruc-tural features of silicon and ZnO, and was used to predict thermal propertiesin materials of similar composition 17× faster than conventional thermalmodelling methods. A 30% void density was determined to yield the bestreduction in thermal conductivity by volume of voids in bulk Al:ZnO witha computed thermal conductivity of 0.77 W m−1 K−1 at room temperature,3× below the threshold achieved through established experimental meanswith high electrical conductivity Al:ZnO.Thick film, electrodeposited Al:ZnO was grown using a nitrate system.Experiments on solution pH using various counter electrodes demonstratedthat inert electrodes caused acidification of the growth solution, limiting filmthickness. Chloride contamination from commonly used Ag/AgCl referenceelectrodes was also determined to affect thick film opacity, morphology, crys-tallinity, and electrical properties. Aluminum integration and activation wasexplored by adding Al(NO3)3 to the growth solution during film synthesis,yielding aluminum integration molar ratios of up to 1.72% (Al.034Zn.966O).Partially doped films in excess of 95 µm thick, 4× the thickness reported else-where, were electrochemically grown and characterized. Sub-micron voidswere integrated into the films using sacrificial material and annealing. A newelectrochemical chromium etching methodology was developed and success-fully used to free 20 films from their growth substrates for thermoelectriccharacterization.A new, reusable thermoelectric test apparatus for thin film thermoelec-tric testing was designed, implemented, calibrated, and successfully de-ployed to characterize ZnO and Al:ZnO thin films grown 79 - 95 µm inthickness. Extremely low thermal conductivity of 11 mW m−1 K−1 at roomtemperature was demonstrated concurrently with a Seebeck coefficient ofiiAbstract−88 µV K−1. Polycrystallinity and poor dopant activation yielded a lowelectrical conductivity of 0.75 mS/cm and corresponding low room temper-ature ZT of 1.3× 10−5 for the Al:ZnO films.iiiPrefaceStatement of ContributionsSome energy dispersive x-ray spectroscopy results discussed in Section 3.4were performed by Dr. Suresha Mahadeva. Ms. Valerie Siller per-formed some experimental work under my supervision, including Al:ZnOfilm growth, microscope photographs, electrical resistance measurements offilms and interface materials, and chromium etching experiments presentedin Sections 3.4, 3.5, and 4.1.List of Publications or SubmissionsSome of the work presented throughout this dissertation has text and/orfigures derived from the following papers:• Section 2.1: Christoph Sielmann, Boris Stoeber, and Konrad Walus.Rapid Approximation of Nanowire Thermal Conductivity UsingMolecular Dynamics Simulations. Submitted, 2014• Section 3.2: Christoph Sielmann, Konrad Walus, and Boris Stoeber.Zinc exhaustion in ZnO electrodeposition. Thin Solid Films, 592, PartA:76–80, October 2015. ISSN 0040-6090. doi: 10.1016/j.tsf.2015.08.041• Section 3.3: Christoph Sielmann, Boris Stoeber, and Konrad Walus.Chloride Contamination of Electrochemically Grown Zinc Oxide ThickFilms. Accepted, Journal of Applied Electrochemistry, 2016• Section 3.4: Christoph Sielmann, Valerie Siller, Boris Stoeber, andKonrad Walus. Thick Film Electrochemical Growth of Al-Doped ZincOxide. Submitted, 2016• Section 3.5: C. Sielmann, V. Siller, K. Walus, and B. Stoeber. Acid-Free Electrochemical Chromium Etch and Release of Nanoscale GoldFilms. Journal of Microelectromechanical Systems, 25(4):701–707, Au-gust 2016. ISSN 1057-7157. doi: 10.1109/JMEMS.2016.2576924ivList of Publications or Submissions• Chapter 4 and Appendix 4.3: Christoph Sielmann, Konrad Walus, andBoris Stoeber. Direct Thermoelectric Measurements of Electrochemi-cally Grown Al:ZnO Thin Films. In Preparation. 2016vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxivAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Thermoelectric Theory . . . . . . . . . . . . . . . . . Ideal Materials . . . . . . . . . . . . . . . . Low Dimensional Materials . . . . . . . . . 81.2.2 Zinc Oxide . . . . . . . . . . . . . . . . . . . . . . . . 91.2.3 Al:ZnO Thermoelectrics . . . . . . . . . . . . . . . . 111.2.4 Electrochemistry . . . . . . . . . . . . . . . . . . . . . 121.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1 LVDOS-EMD . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1.1 Formulation of Theory . . . . . . . . . . . . . . . . . Boltzmann Transport Equation . . . . . . . Vibrational Density of States . . . . . . . . Survival Equation . . . . . . . . . . . . . . . 22viTable of Contents2.1.1.4 Determination of Mean Free Path . . . . . . 282.1.2 Validation of Theory . . . . . . . . . . . . . . . . . . Monte Carlo Simulation . . . . . . . . . . . 302.1.2.2 Lattice Dynamics Density of States . . . . . 332.1.2.3 Lattice Dynamics Group Velocity . . . . . . 352.1.2.4 Normal Mode Decomposition . . . . . . . . 352.1.2.5 LVDOS of Straight Segments . . . . . . . . 382.1.2.6 LVDOS Sampling Window Size . . . . . . . 392.1.3 Methodology and Performance on Silicon Nanostruc-tures . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.1.4 Discussion of Validation . . . . . . . . . . . . . . . . . 492.2 Zinc Oxide Nanostructures . . . . . . . . . . . . . . . . . . . 492.2.1 Molecular Dynamics Simulation of ZnO . . . . . . . . 512.2.2 Extrapolating from Nanostructures to Bulk . . . . . . 542.2.3 Electronic Modelling . . . . . . . . . . . . . . . . . . 542.2.4 Structural Thermoelectric Enhancement Factor . . . 562.2.5 Intrastructural LVDOS-EMD . . . . . . . . . . . . . . 562.2.6 Straight Nanowires . . . . . . . . . . . . . . . . . . . 572.2.7 Hollow Nanowires . . . . . . . . . . . . . . . . . . . . 602.2.8 Heterostructured Nanowires . . . . . . . . . . . . . . 622.2.9 Nanovoided Nanostructures . . . . . . . . . . . . . . . 642.2.10 HCP-Voided Nanostructures . . . . . . . . . . . . . . 672.3 Comparison and Summary of ZnO Nanostructures . . . . . . 692.3.1 Comparison of Modelling Results . . . . . . . . . . . 692.3.2 Summary of Modelling Results . . . . . . . . . . . . . 723 Experimental Growth and Release of Al:ZnO . . . . . . . . 753.1 Equipment and Methodology . . . . . . . . . . . . . . . . . . 763.2 Counter Electrode Selection . . . . . . . . . . . . . . . . . . 773.2.1 Experimental Methods . . . . . . . . . . . . . . . . . 793.2.2 Single Potential Deposition . . . . . . . . . . . . . . . 803.2.3 Multiple Potential Deposition . . . . . . . . . . . . . 833.2.4 Summary of Counter Electrode Effects . . . . . . . . 843.3 Reference Electrode Effects . . . . . . . . . . . . . . . . . . . 853.3.1 Experimental Methods . . . . . . . . . . . . . . . . . 873.3.2 Results and Discussion . . . . . . . . . . . . . . . . . 873.3.2.1 Chloride Concentration in ZnO . . . . . . . 883.3.2.2 Crystallinity of ZnO . . . . . . . . . . . . . 903.3.2.3 Morphology of ZnO . . . . . . . . . . . . . . 923.3.2.4 Resistance of ZnO . . . . . . . . . . . . . . . 93viiTable of Contents3.3.3 Summary of Reference Electrode Effects . . . . . . . 943.4 Growing and Characterizing Al:ZnO Films . . . . . . . . . . 943.4.1 Experimental Methods . . . . . . . . . . . . . . . . . 953.4.2 Results and Discussion . . . . . . . . . . . . . . . . . 963.4.2.1 ZnO Film Base Composition . . . . . . . . . 963.4.2.2 Aluminum Absorption . . . . . . . . . . . . 983.4.2.3 Dopant Integration . . . . . . . . . . . . . . 1023.4.2.4 Annealing . . . . . . . . . . . . . . . . . . . 1073.4.3 Summary of Al:ZnO Growth . . . . . . . . . . . . . . 1083.5 Release of Films from the Substrate . . . . . . . . . . . . . . 1093.5.1 Chemical Etching of Chromium . . . . . . . . . . . . 1103.5.2 Electrochemical Etching of Chromium . . . . . . . . . 1103.5.3 Procedure and Equipment . . . . . . . . . . . . . . . 1113.5.3.1 Slide Preparation . . . . . . . . . . . . . . . 1113.5.3.2 Solution Selection . . . . . . . . . . . . . . . 1123.5.3.3 Apparatus . . . . . . . . . . . . . . . . . . . 1123.5.3.4 Procedure . . . . . . . . . . . . . . . . . . . 1133.5.4 Results and Conclusions . . . . . . . . . . . . . . . . 1153.5.4.1 Characterization of Blank Slides . . . . . . . 1153.5.4.2 Etching and Characterization of CoatedSlides . . . . . . . . . . . . . . . . . . . . . . 1213.5.4.3 Summary of Slide Release . . . . . . . . . . 1233.6 ZnO Nanostructural Growth . . . . . . . . . . . . . . . . . . 1253.6.1 Nanovoided Bulk Growth . . . . . . . . . . . . . . . . 1263.6.1.1 Zinc Hydroxide Method . . . . . . . . . . . 1263.6.1.2 Eosin Y Dye Method . . . . . . . . . . . . . 1293.7 Growth and Release Summary . . . . . . . . . . . . . . . . . 1294 Thermoelectric Characterization of ZnO Films . . . . . . . 1324.1 Interface Materials . . . . . . . . . . . . . . . . . . . . . . . . 1344.1.1 Material Electrical Characterization . . . . . . . . . . 1344.1.2 Interfacing to ZnO Films . . . . . . . . . . . . . . . . 1354.2 Themoelectric Tester . . . . . . . . . . . . . . . . . . . . . . 1374.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 1374.2.1.1 Test Apparatus Enclosure . . . . . . . . . . 1384.2.1.2 Test Apparatus Heater Probe . . . . . . . . 1394.3 Thermoelectric Tester Calibration and Validation . . . . . . 1424.3.1 Calibration Methodology . . . . . . . . . . . . . . . . 1424.3.2 Repeatability and Calibration . . . . . . . . . . . . . 1454.3.2.1 Calibration Measurements . . . . . . . . . . 146viiiTable of Contents4.3.2.2 Silicon Measurements . . . . . . . . . . . . . 1504.4 ZnO Thermoelectric Measurements . . . . . . . . . . . . . . 1514.4.1 Experimental Preparation . . . . . . . . . . . . . . . 1524.4.2 Annealing Process . . . . . . . . . . . . . . . . . . . . 1524.4.3 Performance of Annealed Films . . . . . . . . . . . . 1564.5 Characterization Summary . . . . . . . . . . . . . . . . . . . 1605 Conclusions and Future Work . . . . . . . . . . . . . . . . . . 1635.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 1645.1.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . 1645.1.2 Experimental Growth and Etching . . . . . . . . . . . 1655.1.3 Thermoelectric Characterization . . . . . . . . . . . . 1655.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169AppendicesA Supplemental Results . . . . . . . . . . . . . . . . . . . . . . . 196A.1 Electronic Quantum Modelling . . . . . . . . . . . . . . . . . 196A.2 Other ZnO Growth Considerations . . . . . . . . . . . . . . . 197A.2.1 Solution Stirring During Growth . . . . . . . . . . . . 197A.2.2 Bubble Formation on Film Integrity . . . . . . . . . . 199A.2.3 Substrate Orientation and Location . . . . . . . . . . 200A.2.4 ZnO Growth Denouement and Cooling . . . . . . . . 200A.3 Alternative ZnO Substrate Release Methods . . . . . . . . . 201A.3.1 Mechanical Removal . . . . . . . . . . . . . . . . . . . 201A.3.2 Growth on Graphite . . . . . . . . . . . . . . . . . . . 202A.4 Experimental Synthesis of Additional ZnO Structures . . . . 203A.4.1 Template Assisted Growth . . . . . . . . . . . . . . . 203A.4.2 Heterostructural Growth . . . . . . . . . . . . . . . . 205B Thermoelectric Tester Design . . . . . . . . . . . . . . . . . . 209B.1 Front Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209B.2 Labview Programming . . . . . . . . . . . . . . . . . . . . . 211B.3 Plate Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 215B.4 Microheater Design . . . . . . . . . . . . . . . . . . . . . . . 217ixTable of ContentsC Thermoelectric Tester Source . . . . . . . . . . . . . . . . . . 226C.1 Firmware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226C.2 Front Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234C.3 Labview Programming . . . . . . . . . . . . . . . . . . . . . 235D Matlab Source Files . . . . . . . . . . . . . . . . . . . . . . . . 239D.1 Nanowire Area Calculation . . . . . . . . . . . . . . . . . . . 239D.2 Extract Single Time Frame from LAMMPS Data . . . . . . 243D.3 Thermal Conductivity Using Muller-Plathe . . . . . . . . . . 245D.4 Si Nanowire/Bulk Creation . . . . . . . . . . . . . . . . . . . 250D.5 ZnO Nanowire/Bulk Creation . . . . . . . . . . . . . . . . . 255D.6 Generate LDOS-EMD LAMMPS Script for Void Structures . 266D.7 Generate VAF Slices for Simple LDOS-EMD . . . . . . . . . 269D.8 Generate VAF Slices for Advanced LDOS-EMD . . . . . . . 273D.9 Thermal Conductivity Using Simple LDOS-EMD . . . . . . 279D.10 Thermoelectric Calibration and Analysis . . . . . . . . . . . 282E Potentiostat Source Files . . . . . . . . . . . . . . . . . . . . . 297E.1 Front Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297E.2 Labview Programming . . . . . . . . . . . . . . . . . . . . . 299F LAMMPS Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . 303F.1 Silicon Bulk . . . . . . . . . . . . . . . . . . . . . . . . . . . 303F.2 Silicon Nanowire . . . . . . . . . . . . . . . . . . . . . . . . . 305F.3 ZnO Bulk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307F.4 ZnO Nanowire . . . . . . . . . . . . . . . . . . . . . . . . . . 309F.5 ZnO LDOS-EMD Void Simulation . . . . . . . . . . . . . . . 311xList of Tables2.1 MD NEMD results for simulations of 8 × 8 × 200 unit cell,fully periodic ZnO bulk simulations showing relaxation lat-tice constants and calculated thermal conductivity for threedifferent force field models. . . . . . . . . . . . . . . . . . . . 512.2 Results of ZnO heterostructure simulations showing effec-tive area, simulated thermal conductivity, and the normal-ized effect of changing the periodicity of Zn-ZnO superlatticenanowires for superlattice configurations involving differentsizes of zinc and zinc oxide segments. . . . . . . . . . . . . . . 642.3 Summary of the area calculations used to estimate classicalelectronic conductivity, thermal reverse NEMD conductivitycalculations, and STEF for each modelled nanostructure. . . 713.1 Etching Times for Coated Slides . . . . . . . . . . . . . . . . 1224.1 Summary of IV test results for characterizing the measuredresistance, R, and IV curve shape of different interface pastes,glues, liquids, and greases. Values should only be consideredaccurate within an order of magnitude and are intended forthe comparison of different possible interface materials ratherthan providing data on the absolute electrical performance ofthe tested materials. Contact area between the material andsubstrate was regulated to 5± 2 mm2. . . . . . . . . . . . . . 1354.2 Pre-calibration and post-calibration silicon wafer measure-ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1514.3 A room temperature comparison of the thermoelectric prop-erties of ZnO and Al:ZnO grown electrochemically (this work)and using other methods (other publications). . . . . . . . . . 162xiList of Figures1.1 Plot showing the conversion efficiency of a variety of heat toelectricity conversion systems[6]. The dimensionless thermo-electric figure of merit, ZT , is also shown, representing theZT required for a thermoelectric module to achieve compa-rable efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Simplified thermoelectric power generation module showingelectrical connections on either side. Commercial modulestypically consist of many such pairs. . . . . . . . . . . . . . . 41.3 a) Illustration of a wurtzite ZnO unit cell, b) A slice of awurtzite ZnO nanowire used for modelling in Chapter 2 withthe c-axis aligned vertically, rendered using VMD[49]. Redspheres represent zinc atoms and grey atoms represent oxygenatoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 A standard, three electrode potentiostat is shown. . . . . . . 132.1 A visual representation of a Si lattice structure showingroughening parameters is shown. This figure shows the struc-ture prior to relaxation and is intended to highlight the pa-rameters varied in the notching in advance of executing thesimulation. Nanowires are structured along the 〈001〉 direction. 202.2 LVDOS along the z-axis of a 4.9 × 4.9 × 27nm3 (a) straightand (b) notched silicon nanowire. The roughened nanowire in(b) has 1.6 nm deep, 0.54 nm diameter notches every 5.4 nmalong its length. Slices were made every 0.135 nm along thenanowire and are labeled along the x-axis. . . . . . . . . . . . 232.3 Illustration of a particle (bullet) travelling through a sliceof gas for the purpose of solving the survival equation. ∆xrepresents the thickness of the slice and L is the length of theslice in this two dimensional representation. . . . . . . . . . . 24xiiList of Figures2.4 Illustration of the transport of wavelets within a multi-segmented structure, where red particles are travelling withinthe same mode along the structure, and blue particles origi-nate from intermode scattering in the same segment. . . . . . 272.5 A plot of the cumulative particle density across 200 segmentsof a 1,000 segment structure where each segment has a 100%survival rate except for each 10th segment, which has an 80%survival rate. The simulation assumes an instantaneous par-ticle density expectation value of 10 particles/segment andruns over 2,000 simulation time steps. . . . . . . . . . . . . . 312.6 Calculated MFP as a function of time window size using(2.35) applied to simulations with segments of 10% surviv-ability (lowest curve) through 80% survivability (highest curve). 322.7 MFP results showing simulation MFP, calculated MFP usingparticle density mean approximation, and calculated MFPusing particle density max approximation results. Shown arecurves for a mean free path of 20 (top), 10 (middle), and 5(bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.8 The vibrational density of states calculated using VAF for a2.7 nm (5 unit cells) diameter silicon nanowire notched everytwo unit cells and a 3.8 nm straight nanowire, and the totalphonon density of states calculated using a dynamical matrixfor a similar 〈001〉 periodic 2.7 nm diameter straight nanowire. 342.9 The k-averaged group velocity calculated from lattice disper-sion for a 2.7 nm (5 unit cells) silicon nanowire notched everytwo unit cells, a 2.7 nm (5 unit cells) straight nanowire, anda 3.8 nm (7 unit cells) straight nanowire periodic along the〈001〉 plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.10 The vibrational wavelet mean free path calculated usingLVDOS-EMD of a 2.7 nm (5 unit cells) silicon nanowirenotched every two unit cells is shown and compared with thephonon mean free path of an identical structure calculatedusing normal mode decomposition. . . . . . . . . . . . . . . . 382.11 MFP calculated using LVDOS-EMD for straight, siliconnanowires from 1.6 nm to 4.9 nm in width. The MFP dis-played represents the mean average and standard deviationof all calculated spectral components from 0 - 25 THz for eachwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39xiiiList of Figures2.12 Studies using the MD results of simulations based on 3.8 nm(top), 2.7 nm straight and notched (middle), and 1.6 nm (bot-tom) silicon nanowires. a) Average frequency-dependent LV-DOS, and b) coefficient of determination showing how wellthe spatially-averaged LVDOS for each segment increases lin-early with FFT time window size. . . . . . . . . . . . . . . . 412.13 Comparison of MFP calculation of a straight (top) and aroughened/notched (bottom) silicon nanowire 4.9 nm diam-eter. The roughened nanowire has 1.6 nm deep, 0.54 nm di-ameter notches every 5.4 nm along the length of the nanowire.The straight nanowire is shown as a mean average (black line)of four simulations with different starting conditions (greyoverlay). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.14 LVDOS profile for k = 4.9 nm (a,b) and k = 1.6 nm (c,d)silicon nanowires generated from EMD (a,b) or NEMD (c,d)simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.15 Thermal conductance using LVDOS-EMD as a function of ex-ported silicon nanowire a) length data and b) time data basedon 4.9 nm nanowires. Time data is normalized by calculatedthermal conductance at 1 ps for each nanowire. . . . . . . . . 452.16 Normalized thermal conductance of silicon nanowires by a)variable nanowire thickness of smooth nanowires, b) variablenotch depth for k = 4.89 nm, p = 5.43 nm, w = 0.543 nm,c) variable notch period for k = 2.72 nm, D = 0.543 nm,w = 0.543 nm, and d) variable notch width for k = 3.80 nm,D = 0.543 nm, p = 5.43 nm. Calculated thermal conductanceis normalized to a) a 3.26 nm thick straight nanowire, b-d) anunnotched nanowire of similar thickness. The error bars showthe variation in Mueller-Plathe simulation results for thermalconductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.17 Comsol model of a notched nanowire where each segment isdesignated a thermal conductivity from Mueller-Plathe re-sults of straight nanowires of identical thickness. . . . . . . . 482.18 The 5 × 5 unit cell (5 unit cells along the long, outsideedge) ZnO nanowire configuration used for MD simulations isshown. Red atoms are zinc and grey atoms are oxygen. Theimage is rendered using VMD[49]. . . . . . . . . . . . . . . . 50xivList of Figures2.19 A plot of inverse, simulated, bulk ZnO thermal conductivityusing Mueller-Plathe against inverse simulation cell length.The lengths simulated range from 50 unit cells (26 nm) to 300unit cells (156 nm). Two thermal conductivities were calcu-lated per length with the results being averaged. Uncertaintyat each length is within 0.5 W m−1 K. . . . . . . . . . . . . . . 532.20 Cross-sectional slice of a hexagonal nanowire consisting ofirregular voids showing the grid of squares used to deter-mine occupation for area calculations. Points representingthe atoms were first overlayed onto the grid squares and thenlines were drawn between nearest and next nearest neighboursto fill in the space between atoms. . . . . . . . . . . . . . . . 552.21 The cross-section of a variety of ZnO nanostructured materi-als post simulation. Red dots are zinc atoms and blue dotsare oxygen atoms. . . . . . . . . . . . . . . . . . . . . . . . . 592.22 An image showing the LVDOS of a straight, 104 nm long, 5×5unit cell, hexagonal ZnO nanowire oriented along the z-axis. . 602.23 An image showing the LVDOS of a hollow, 104 nm long, 5×5unit cell, hexagonal ZnO nanowire oriented along the z-axis. . 612.24 A plot showing the effective area, simulated thermal conduc-tivity, and normalized STEF of hollow nanowires as a functionof etching radius. . . . . . . . . . . . . . . . . . . . . . . . . . 622.25 An image showing the LVDOS of a superlattice, 104 nm long,5 × 5 unit cell, hexagonal ZnO nanowire oriented along thez-axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632.26 An image showing the LVDOS of a randomly voided nanos-tructure with spherical voids 3.0± 1.5 A˚ in size and repre-senting 20% of the total volume of the 104 nm long, 5×5 unitcell, hexagonal ZnO nanowire oriented along the z-axis. . . . 652.27 A chart plotting the NEMD, simple LVDOS-EMD, and ad-vanced (intrastructural) LVDOS-EMD thermal conductivitiesas a function of void density for ZnO nanowires. The voidsare 3.0± 1.5 A˚ in radius and 2600 voids represents 50% of thevolume of the nanowire. . . . . . . . . . . . . . . . . . . . . . 672.28 A chart plotting the NEMD, simple LVDOS-EMD, and ad-vanced (intrastructural) LVDOS-EMD thermal conductivitiesas a function of void density for ZnO nanowires. The voidsare 5.0± 2.5 A˚ in radius and 525 voids represents 40% of thevolume of the nanowire. . . . . . . . . . . . . . . . . . . . . . 68xvList of Figures2.29 A plot showing the effective area, simulated thermal conduc-tivity, and normalized STEF of voided nanowires as a functionof void density for R = 3.0± 1.5 A˚ voids. . . . . . . . . . . . 692.30 An image showing the LVDOS of a 104 nm long, 5×5 unit cell,hexagonal ZnO nanowire with 3 A˚ radius spheres removed inhexagonal closely packed configuration with sphere centers10 A˚ apart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.31 A plot showing simple and advanced (intrastructural)LVDOS-EMD and NEMD results for a variety of structures.The intrastructural LVDOS-EMD results show the thermalconductivity determined for each thin segment as well as theaverage and standard distribution. . . . . . . . . . . . . . . . 723.1 Example EDX spectrum of a galvanostatically grown, Al-doped (5 µmol/L growth solution concentration), chloridecontaminated Al:ZnO thin film. . . . . . . . . . . . . . . . . . 783.2 pH of 20 mL, 0.1 M Zn(NO3)2 solutions grown on2.54 cm×3.1 cm of exposed gold-coated glass using differentcounter electrode materials where a) shows pH as a functionof deposition time and b) shows pH as a function of totalapplied charge. Uncertainty in pH measurement is ±0.3. . . . 813.3 Deposition current density of 20 mL, 0.1 M Zn(NO3)2 solu-tions grown using different counter electrode materials at aVset = −1.2 V. Growth conditions were otherwise identical tothose in Figure 3.2. . . . . . . . . . . . . . . . . . . . . . . . . 823.4 SEM images at identical scales of uncoated ZnO films grownusing a) Zn-grown film viewed overhead, b) Zn-grown filmviewed at 45◦, c) Pt-grown film viewed overhead, and d) Pt-grown film viewed at 45◦. . . . . . . . . . . . . . . . . . . . . 833.5 XRD measurements of films grown using either zinc or plat-inum counter electrodes under otherwise similar conditions.Counts have been normalized by intensity of (002) crystalorientation. The peak near scattering angle 38◦ is due to thegold substrate beneath the film. No unexpected out-of-bandspikes were noted from 0-90◦. . . . . . . . . . . . . . . . . . 843.6 Deposition currents of 100 mL, 0.1 M Zn(NO3)2 solutionsgrown using zinc counter electrodes at different reference po-tentials (Vset). Normalization currents (A0) used are 19.6 mA,21.2 mA, and 22.0 mA for Vset = −1.10, −1.05, and −1.00 V,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85xviList of Figures3.7 Deposition pH and transferred charge of a 100 mL, 0.1 MZn(NO3)2 solution grown using a zinc counter electrode withpotential (Vset) varying throughout the deposition. Uncer-tainty in pH measurement is ±0.3. . . . . . . . . . . . . . . . 863.8 EDX measurements performed at 15 kV on the cross-sectionof a ZnO film. EDX measurements were performed as dis-cussed in Section 3.1 except for the beam mode which wasset to point to increase spatial resolution. At least three sam-ples were taken at different points throughout the film todetermine the standard deviation as shown by the errors bars. 893.9 XRD results comparing peaks of a ZnO film grown withand without an Ag/AgCl reference electrode over 11 hours.The inset shows higher resolution results from 2θ = 30◦ to38◦ which is the region of greatest interest for assessing thecrystallinity of ZnO film. Crystal orientations apply to ZnOunless indicated otherwise. . . . . . . . . . . . . . . . . . . . . 913.10 SEM results taken at a 45◦ angle showing low (a,c,e,g) andhigh magnification (b,d,f,h) comparisons of ZnO films gal-vanostatically grown at 1 mA/cm2 (a,b,e,f) and 3 mA/cm2(c,d,g,h) until 40 C/cm2 of charge had exchanged. Films inthe top row were grown without an Ag/AgCl reference elec-trode, whereas films in the bottom row were grown with anAg/AgCl reference electrode. . . . . . . . . . . . . . . . . . . 923.11 Optical microscope images using yellow light to facilitatequalitative contrast between ZnO film crystallinity and yel-low light transmission. Both ZnO films were galvanos-tatically grown a) using an Ag/AgCl reference electrodeand b) without using a reference electrode. The chloride-contaminated film (a) appeared optically grey, translucent,and non-homogenous when visually compared to the filmgrown without the reference electrode. . . . . . . . . . . . . . 933.12 Quantitative EDX results showing a molar concentrationcomparison between a commercially purchased ZnO refer-ence powder and galvanostatically grown ZnO films preparedat different current densities and aluminum concentrations.EDX measurements were performed as described in Sec-tion!3.1. Error bars represent the maximum and minimumof at least three measurements across the surface of the ma-terial. Accuracy should be considered within 5%. . . . . . . . 97xviiList of Figures3.13 45◦ SEM cross-section of an undoped ZnO sample galvano-statically grown on gold at Iset = 2.0 mA/cm2 for 5.5 h atT = 80 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.14 XRD spectrum of ZnO and gold substrate showing high (002)(c-axis) orientation of the film. . . . . . . . . . . . . . . . . . 993.15 A plot showing voltammograms of 0.1 M Zn(NO3)2 and 0.1 MAl(NO3)3 taken on identical gold substrates and at identicaltemperatures of 80◦C. Each test was performed three timesconsecutively with all six curves shown in the plot. . . . . . . 1003.16 A plot showing the Ag/AgCl reference voltage response to theintroduction of varying concentrations of Al(NO3)3. 100 µLto 1 mL volumes of Al(NO3)3 were introduced to a 100 mLsolution of 0.1 M Zn(NO3)2 undergoing galvanostatic depo-sition at 1.0 mA/cm2 to raise the solution concentration ofAl3+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013.17 A plot showing quantitative EDX measurements of Al3+ mo-lar concentration within the film as a function of sustaineddopant concentration within the electrochemical growth so-lution. The molar quantity of aluminum is compared to thatof zinc, oxygen, and chloride also found in the film. The solidline represents a logarithmic fit. . . . . . . . . . . . . . . . . . 1023.18 A plot showing film thickness measurements as a functionof sustained aluminum dopant concentration within the elec-trochemical growth solution. All films were grown at identi-cal current densities of 1 mA/cm2 for identical durations of11.1 hours. The solid line represents a logarithmic fit. . . . . . 1033.19 45◦ SEM images of an Al:ZnO sample grown with 30 µmolAl(NO3)3 solution where a) shows both the ZnO film surface(below) and the layer of caked Al(OH)3 (above), and b/c)shows closer images of the Al(OH)3 layer. . . . . . . . . . . . 1043.20 45◦ SEM images of ZnO samples galvanostatically grownat Iset = 1.0 mA/cm2 with approximately a) no dopant,b) 1 µmol/L Al(NO3)3, c) 3 µmol/L Al(NO3)3, d) 5 µmol/LAl(NO3)3, e) 10 µmol/L Al(NO3)3, and f) 30 µmol/L Al(NO3)3.1053.21 An XRD spectrum comparing 2θ angle of ZnO galvanostat-ically grown at Iset = 1.0 mA/cm2 with different concentra-tions of Al(NO3)3 with a) showing the primary range of inter-est for ZnO structures and b) emphasizing the slight differencein peak position between the doped films. . . . . . . . . . . . 106xviiiList of Figures3.22 ZnO film resistivity as a function of estimated Al(NO3)3dopant concentration in the growth solution. Measurementsrepresent c-axis resistivity. . . . . . . . . . . . . . . . . . . . . 1073.23 A sample configuration, not shown to scale. 2.0 cm x 1.5 cmgold coated slides were procured and then partially electro-chemically coated with a 1.0 cm×1.0 cm×20 µm thick layer ofZnO or a 1.0 cm×1.0 cm×76 µm thick layer of polyimide tape.Copper adhesive tape, protected by polyimide, was used toelectrically connect the slides to a potentiostat. . . . . . . . . 1123.24 Schematics of the setup for etching the chromium from theslide and releasing the gold film. The optional reference elec-trode is not shown but would be located in close proximityto the glass slide. . . . . . . . . . . . . . . . . . . . . . . . . . 1133.25 Illustrations of a) how latent stress in the deposited film cancause the gold layer to deform against the glass, preventingetching solution access to the remaining chromium, and b)how increasing solution height creates new paths to etchedtrapped regions of chromium. Illustrations are not to scale. . 1153.26 Photo through the glass of a 1.0 cm×1.0 cm slide showing afully chromium etched gold surface. The outline of the ZnOlayer on the front of the slide can also be seen as reducingwrinkling in the gold layer. . . . . . . . . . . . . . . . . . . . 1163.27 A plot showing mean etching distance as a function of timefor solutions containing hydroxide or phosphate. The etchingwas performed on blank gold slides under normal conditions.Etching time was measured along one axis when the etchingprocess crossed marked distance threshold on the slides. Thehorizontal error bars represent one standard deviation fromthe average, and vertical bars represent uncertainty in dis-tance measurements due to the line widths of the markingson the slides. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1173.28 Electrochemical voltammogram showing a) current vs.Ag/AgCl reference electrode for hydroxide and phosphate-based solutions, and b) Ag/AgCl reference electrode poten-tial vs. total applied potential when sweeping the appliedpotential to produce a reference potential from 0 - 1 V at arate of 1 mV/s. The samples under test were smaller Au/Cr/-glass slides approximately 1.0 cm×1.5 cm in dimension. Thechromium was not completely removed from the sample bythe end of this experiment. . . . . . . . . . . . . . . . . . . . 118xixList of Figures3.29 A plot showing total etching time as a function of electro-chemical reference potential for solutions containing hydrox-ide or phosphate. The etching was performed on blank goldslides under otherwise normal conditions. Error bars indicateuncertainty in determining completion of the etch. . . . . . . 1193.30 A plot showing total etching time as a function of etchingsolution concentration for solutions containing hydroxide orphosphate. The etching was performed on blank gold slidesunder otherwise normal conditions. Error bars indicate un-certainty in determining completion of the etch. . . . . . . . . 1203.31 Total etching time as a function of solution temperature forsolutions containing hydroxide or phosphate. The etchingwas performed on blank gold slides under otherwise normalconditions. Error bars indicate uncertainty in determiningcompletion of the etch. . . . . . . . . . . . . . . . . . . . . . . 1213.32 Shown are etching times as a function of distance of 1) a sam-ple with only glass/Au/Cr etched in phosphate under normalconditions, 2) a sample covered with a 1 cm wide strip ofpolyimide tape beginning 2.5 mm from the edge etched inphosphate under normal conditions, and 3) a sample coveredwith a 1 cm2 ZnO layer beginning 4 mm from the edge etchedvertically in hydroxide (did not complete) under normal con-ditions. Time was measured as the etching process crossedmarked distances on the slides. . . . . . . . . . . . . . . . . . 1233.33 SEM images taken at 20 kV showing a ZnO film grown at3 mA/cm2 current density a) before and b) after etching thechromium layer in pH = 11 sodium hydroxide. . . . . . . . . 1243.34 SEM images taken at 20 kV showing the effect of a 90 minutesodium phosphate etch on the surface morphology of ZnOwhere a) is the edge of the film exposed after etching andtaken at 45◦to the horizontal and b) is a similar image of apristine, unetched ZnO film. The effect appears confined tothe surface and does not change the morphology of the bulk. 1253.35 SEM images taken at 20 kV showing Zn(OH)2 particles gen-erated in solution by adding small quantities of NaOH analo-gous to hydroxide formation during electrochemical deposition.127xxList of Figures3.36 SEM images taken at 15 kV showing 200◦C annealed, un-doped ZnO where a) shows the cross-section of the film, b)shows a higher zoom section of the cross-section covered insmall voids, c) shows another section of the film also coveredin holes, and d) magnifies the voids themselves which rangefrom 50 nm to 400 nm in diameter. . . . . . . . . . . . . . . . 1284.1 SEM images taken 20 kV at 45◦ angles showing a) gold sideZnO film surface and cross-section, b) gold side ZnO filmsurface (close up), c) solution side ZnO film surface and cross-section, and d) solution side ZnO film surface (close up). . . . 1364.2 Overview diagram of thermoelectric test apparatus. . . . . . . 1394.3 Close up diagram of the thermoelectric test apparatus heatingelement, interface, and DUT. . . . . . . . . . . . . . . . . . . 1414.4 Circuit analog for heat flow through the heater probe, inter-face, and device. . . . . . . . . . . . . . . . . . . . . . . . . . 1424.5 Probe and plate temperature as a function of time for twomeasurements of a ZnO film (see Section 4.4). . . . . . . . . . 1464.6 Induced temperature gradient between heater probe and baseplate as a function of applied thermal power. The fit shown isa purely 4th order fit using (4.2). Three separate calibrationsare shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1474.7 Temperature difference as a function of thermal power for aseries of closed calibrations. . . . . . . . . . . . . . . . . . . . 1484.8 Electrical conductance as a function of average temperaturefor a series of closed calibrations. . . . . . . . . . . . . . . . . 1494.9 Induced voltage as a function for temperature difference aseries of closed calibrations. . . . . . . . . . . . . . . . . . . . 1494.10 Temperature as a function of applied thermal power beforeand after calibration of a 500 µm thick silicon wafer n-typedoped to a resistivity of 0.002 Ωcm. . . . . . . . . . . . . . . . 1504.11 Induced voltage as a function of the temperature differencebetween the probe and the plate before and after calibrationof a 500 µm thick silicon wafer n-type doped to a resistivityof 0.002 Ωcm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 151xxiList of Figures4.12 Temperature differential across the film of a 3 mA/cm2 cur-rent density ZnO sample showing ramp up and annealing aswell as ramp down. Both ramp up and ramp down are pro-grammed with the same thermal power step configurationand, without changes in film properties, should converge toidentical temperature plateaus. . . . . . . . . . . . . . . . . . 1534.13 Pre-annealed thermal conductivity as a function of averagetemperature for a variety of ZnO-based samples. . . . . . . . 1554.14 Pre-annealed electrical conductivity as a function of averagetemperature for a variety of ZnO-based samples. . . . . . . . 1554.15 Pre-annealed Seebeck coefficient vs. Pt as a function of aver-age temperature for a variety of ZnO-based samples. . . . . . 1564.16 Pre-annealed figure of merit as a function of average temper-ature for a variety of ZnO-based samples. . . . . . . . . . . . 1574.17 Annealed thermal conductivity as a function of average tem-perature for a variety of ZnO-based samples. . . . . . . . . . 1584.18 Annealed electrical conductivity as a function of average tem-perature for a variety of ZnO-based samples. . . . . . . . . . 1594.19 Annealed Seebeck coefficient vs. Pt as a function of averagetemperature for a variety of ZnO-based samples. . . . . . . . 1594.20 Annealed figure of merit as a function of average temperaturefor a variety of ZnO-based samples. . . . . . . . . . . . . . . . 160A.1 Bandstructures from LDA+SIC simulations of a) bulk ZnO,and b) a hexagonal nanowire composed of ZnO segments of 4unit cell length. The inset in a) shows bulk ZnO bandstruc-ture calculated using LDA+SIC as a reference[47]. . . . . . . 198A.2 Microscope image showing a chloride-contaminated (for bet-ter contrast) ZnO film where bubbles were no longer removedonce the deposition reached 50% completion. . . . . . . . . . 199A.3 XRD measurements of a ZnO-on-graphite film along withgold and ZnO reference patterns are shown. . . . . . . . . . . 203A.4 SEM measurements of a) the graphite surface, b) ZnO grownon graphite, and c) anomalous structures embedded into thefilm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204A.5 SEM images taken at 20 kV showing ZnO nanowires poten-tiostatically grown at Vref = −1.0 V emerging from the topof a polycarbonate template. The nanowires were then elec-trochemically coated with copper in a Cu(SO4) solution in anattempt to develop a film. . . . . . . . . . . . . . . . . . . . . 206xxiiList of FiguresA.6 XRD plot comparing conventionally electrochemically grownZnO with a ZnO heterostructure grown by swapping appliedcurrent density from 1 mA/cm2 to 10 mA/cm2 every 10 C ofcharge transferred. . . . . . . . . . . . . . . . . . . . . . . . . 207A.7 SEM images taken at 15 kV showing the cross-section of aheterostructured ZnO/Zn film. The object seen in the figureis a protrusion from the film and is representative of manyother protrusions along the surface. . . . . . . . . . . . . . . . 208B.1 Labview Front Panel of Thermoelectric Tester Application. . 210B.2 Drawing of Thermoelectric Test Apparatus enclosure baseplate. 1/4a¨luminum was used. . . . . . . . . . . . . . . . . . . 216B.3 Concept mock-up of a thin film heating element based on amicrofabricated silicon wafer. A thermocouple is inserted intothe back grove of the substrate. . . . . . . . . . . . . . . . . . 218C.1 Labview Front Panel of Thermoelectric Tester Application. . 234E.1 Labview Front Panel of Potentiostat Application. . . . . . . . 298xxiiiList of Symbolsα Seebeck Coefficient [V/K]β Proportional velocity analogous to group velocityκ Thermal conductivity tensor∇T Temperature gradientD(q) Dynamical matrixe(q,m) Eigvenvectors of the Dynamical MatrixQ Heat flux vectorq Phonon wavevectorr0(j) Initial position of a unit cellu(j, i; t) Displacement of an atom from its mean average positionη Efficiencyγ Adjustment factor for efficiency calculationκ Thermal conductivity [W/mK]ω Angular frequencyρ Electrical resistivity [Ωcm]σ Electrical conductivity [S/cm]σ Stefan-Boltzmann constantτ(q,m) Phonon lifetimeξ Structural Thermoelectric Enhancement Factor (STEF)ζ Proportional rate of scattering into a segmentxxivList of SymbolsA Cross-sectional area [m2]a Atom iterator or overlap-corrected width of a segmentAclosed Total contact surface area between the heater element and the baseplateADUT Device under test cross-sectional areab General purpose iteratorC(q,m) Modal heat capacity of the materialD Density of statesD Notch depthd DistanceE Energye Emissivityf Regression linear fitI Electric current Ai General purpose iteratorj General purpose iteratorK Thermal conductance[W/K]k General purpose iterator or nanowire diameterL Length [m]l Mean free pathM Massm Phonon modeN Number of particles or objects within the specified systemp Notch periodPs(ω) Probability of a wavelet surviving segment sxxvList of SymbolsQ Thermal power [W]QH Thermal power from a heater [W]Qs(ω) Probability of a wavelet surviving exactly s segmentsR Electrical resistance [Ω]RHIratio Ratio between heater element thermal resistance and interfacethermal resistanceS Total number of segments along a materials Segment of a larger whole, or general purpose iteratorT Temperature [K]T (q,m; t) Kinetic energy for the given mode and timeU(q,m; t) Potential energy for the given mode and timeV Volumevg(q,m) Modal phonon group velocityVac Alternating current voltage [V]Vdc Direct current voltage [V]W Available work/power [W]w Notch width or time window sizeZ Thermoelectric figure of merit [1/T]Za Velocity autocorrelation function to atom aZs Probability of a particle surviving segment s without collisionZT Unitless thermoelectric figure of meritxxviAcknowledgementsI wish to thank my supervisors, Dr. Konrad Walus and Dr. Boris Stoe-ber, for taking a chance on a hypothesis with great potential and moderaterisk. Their insights, patience, support, and understanding have been in-strumental in every success throughout the project. I wish to thank ValerieSiller for her experimental contributions, rigorous scientific standards, andgeneral enthusiasm for the work. Her willingness to travel overseas anddedicate herself fully to a challenging project in a foreign language demon-strates outstanding character. I wish to thank Dr. Suresha Mahadeva andDr. Lisheng Wang, who both provided insights into the material scienceinvolved in the project and assisted with some of the characterization mea-surements. I would like to acknowledge funding, equipment, and facilitiesprovided by Natural Sciences and Enginereing Research Council (NSERC),the Canadian Foundation for Innovation (CFI) and the Univeristy of BritishColumbia through the Four Year Fellowship Program. Simulation time wasprovided by Computing Canada Westgrid clusters. I wish to thank my labcolleagues, particularly Anas Bsoul, Simon Beyer, and Andrew Cavers, allof whom provided advice or a sympathetic ear depending on the complexityor persistence of the problem. Finally, I wish to thank my family for theirsupport and unwavering patience, and my wife, Sara, without whom thiswork would not have been possible.xxviiDedicationIn dedication to my exceptionally patient and endlessly supportive wife,Sara.xxviiiChapter 1Introduction1.1 MotivationAn ongoing challenge today is the pursuit of greater quantities of clean, us-able energy. Transportation, manufacturing, heating and cooling, medicalservices, and primary resource extraction are critical, energy-intensive en-deavours that continue to demand significant power. Many of the currentmethods employed to extract usable energy from resources such as fossilfuels yield waste heat during the process. As an example, average fossil-fueldriven power plants only extract 40% of the available chemical energy fromtheir fuel, relegating the remainder as waste heat expelled through steamor as heated water into heat sinks such as lakes[3]. If all industries are con-sidered then approximately 70% of the world’s energy is wasted as heat[4].Limitations in existing technology limit efficiency, portability, longevity, andsafety in large-scale energy production facilities that depend on heat to pro-duce usable power. New, solid state technology that can scale cost effectivelywith power demand could see applications ranging from portable waste heatrecovery to large scale power generation[5]. A comparison between commonheat to power conversion technologies can be found in Figure 1.1.Thermoelectric materials convert a thermal gradient into an electric po-tential through the Seebeck effect. It is an old technology which is used inapplications including small-scale nuclear thermoelectric generators, such asthose found on the Voyager I and II spacecraft, solid state cooling througha related Peltier effect, and temperature sensing through the ubiquitousthermocouple. Research in the 1990s spurred a renaissance in the field ofthermoelectrics as researchers determined that small-dimensional structuressuch as quantum dots and nanowires have the potential to yield far moreefficient thermoelectric materials[7].Active thermoelectric companies, such as Alphabet Energy, GMZ En-ergy, and Laird Technologies are developing thermoelectric devices based onnanostructured materials for thermoelectric power generation[8, 9], automo-tive energy recovery[10, 11], military waste heat recovery[12], diesel genera-tors, industrial machines, and the oil and gas sector[13]. Alphabet Energy11.1. Motivation0%10%20%30%40%50%60%70%80%90%300 500 700 900 1100 1300 1500Module Efficiency (%)Hot Temperature (K)0.51351015InfZTCarnotSolar/Nuclear BraytonSolar/NuclearRankineCoal RankineGeothermalThermoelectricsEmergingThermoelectricsFigure 1.1: Plot showing the conversion efficiency of a variety of heat toelectricity conversion systems[6]. The dimensionless thermoelectric figure ofmerit, ZT , is also shown, representing the ZT required for a thermoelectricmodule to achieve comparable efficiency.recently commercialized a 25 kW electrical output per 1000 kW waste heatthermoelectric generator (TEG) targeting oil and gas applications and is fo-cusing their research and development on low cost thermoelectric materialsthat do not require exotic elements[8]. Laird Technologies has commercial-ized a series of low power thin film thermoelectric modules for commercialapplications. Although they still operate at low efficiencies compared to me-chanical methods of power generation, their small scale and flexible designopens up new markets for waste heat recovery[5].The performance of a thermoelectric module is determined by its di-mensionless figure of merit, ZT , where module efficiency approaches Carnotefficiency as ZT approaches infinity. A recent study on the economics ofthermoelectrics suggest that modules demonstrating ZT > 1 are alreadycost competitive in some sectors for power generation, provided that themodules can be scaled up appropriately[14]. With the increase in thermo-electrics research, there have been numerous publications within the last10 years highlighting materials with ZT > 2, although these experiments21.2. Backgroundare often difficult to reproduce, which complicates integrating these newmaterials into commercializable modules[15]. One of the best performingthermoelectric modules has a reported ZT = 1.96 and is based on superlat-tice nanomaterials[14].With increasing industrial and academic interest, international fundinghas increased as well. The global thermoelectric market was worth $364.1million USD in 2014 and is expected to reach $763.5 million USD by 2022[5].Zervos and Harrop have proposed that integration of thermoelectric modulesin vehicles for waste heat recovery may happen as soon as 2020, and withthe continued growing interest in clean energy technologies, it is likely thatinterest in low cost, environmentally friendly, high efficiency thermoelectricmaterials will continue to expand. Further advances in thermoelectrics couldlead to solid state replacements for many mechanical systems associatedwith power generation, such as steam turbines, as solid state alternativesthat require less maintenance and operate more safely. Smaller scale sys-tems for heat recovery and personal power generation could also be realized,affording greater independence from central power generation and reducingwasted energy from transmitting power long distances. Developing theseopportunities through the design and fabrication of efficient, cost-effectivethermoelectric materials primarily motivate this work.1.2 Background1.2.1 Thermoelectric TheoryThermoelectricity involves the conversion of a thermal flux into electricity.Typical thermoelectric power generation and cooling modules comprise ofnumerous thermocouples connected thermally in parallel and electrically inseries or parallel depending on the desired operating voltage of the module.Thermocouples consist of a hot junction and a cold junction, with dissim-ilar materials, typically n-doped and p-doped semiconductors, as shown inFigure 1.2. Electronic majority charge carriers, electrons and holes for n-type and p-type materials, respectively, diffuse with the thermal gradient toproduce a net current through the device. Concurrently, heat propagatesfrom the hot junction (x = Lp,n) to the cold junction (x = 0), reducing theoverall efficiency of the module. As the electrons travel through each legof the thermocouple, electrical resistance in the material dissipates electronenergy, also reducing the overall efficiency of the module.The heat power into the module from the surface of the thermoelectricmodule, Qp and Qn, for the p-type and n-type legs respectively, consumed31.2. BackgroundHot sideCold sidep-type n-typee-e-e- e-e-e- e- e-e-e- e- +-Current flowh+h+ h+h+ h+h+ h+h+h+h+h+CarrierDiffusionElectrical Terminal Interconnectsx = Lp,nx = 0Figure 1.2: Simplified thermoelectric power generation module showing elec-trical connections on either side. Commercial modules typically consist ofmany such the module are[16]Qp = αpITH + κpApdTdL, (1.1)Qn = αnITH + κnAndTdL, (1.2)where αx is the Seebeck coefficient, I is the electrical current, TH is thetemperature at the hot end of the device, κx is thermal conductivity, Axis the cross-sectional area, L is the length of the leg, and x represents theleg material (typically n or p type). The Seebeck coefficient of the mate-rial is the open circuit (zero current density) induced voltage per degreeof temperature difference between the points of measurement. The coef-ficient is conventionally determined with respect to another material usedin the measurement, and is thus generally known as the relative Seebeckcoefficient. The relative Seebeck coefficient is typically expressed relative toplatinum, and values reported in this work are thus adjusted. It is possible41.2. Backgroundto determine the absolute Seebeck coefficient of a material by measuring itscoefficient using a superconducting measurement lead near absolute zero intemperature, but performing this measurement was considered out of scopefor this work.The heat consumption of the device is a sum of 1.1 and 1.2 integratedover the length of the thermocouple, yieldingQH = K∆T + (αp − αn) ITH − 12I2R, (1.3)where R is the electrical resistance of the module, K is the thermal con-ductance, and ∆T is the difference in temperature along the length of thedevice. The electrical power produced under ideal conditions isW = I [(αp − αn) ∆T − IR] , (1.4)where W is the electrical power available from the module. The moduleefficiency isη =WQH=I [(αp − αn) ∆T − IR]K∆T + (αp − αn) ITH − 12I2R. (1.5)If the module is operated at peak efficiency by selecting a matching loadRload = γR, (1.6)whereγ =(1 + Z(TH + TC)2) 12, (1.7)then the maximum electrical current, I, electrical power, W , and efficiency,η, areI =(αp − αn) ∆TR(γ + 1), (1.8)W =γ [(αp − αn) ∆T ]2R (γ + 1)2, (1.9)ηmax =(γ − 1) ∆T[(γ + 1)TH −∆T ] . (1.10)The figure of merit in units of 1/K, Z, can be determined independently foreach leg material usingZp,n =α2p,nρp,nκp,n, (1.11)51.2. Backgroundand for the entire module usingZ =(αp − αn)2(√ρnκn +√ρpκp)2, (1.12)where ρx is the electrical resistivity for leg material x. The more conventionaldimensionless figure of merit, ZT , can be determined by multiplying Z,which varies with temperature, by the average temperature of the device,T . The module figure of merit is maximized when the product of RK isminimized, which occurs when leg dimensions are defined using[16]LnApLpAn=(ρpσnρnσp)0.5. (1.13)If the module is optimized for maximum power output rather than max-imum efficiency then the load resistance,Rload = R, (1.14)and the resulting current, power, and efficiency areI =(αp − αn) ∆T2R, (1.15)W =[(αp − αn) ∆T ]24R, (1.16)andηmax =Z∆T4 + ZTH + Z(TH+TC)2. (1.17)Ideal Carnot efficiency can be represented byη = 1− TCTH, (1.18)and the efficiency of a thermoelectric module as a function of its ZT , repre-senting the dimensionless figure of merit using the average temperature ofthe device, isη =(1− TCTH) √1 + ZT − 1√1 + ZT + TCTH. (1.19)From (1.19), module efficiency approaches (1.18) as ZT approaches infinity.A high ZT can only be achieved by maximizing the Seebeck coefficient andelectrical conductivity while minimizing thermal conductivity as shown by(1.11) and (1.12).61.2. Background1.2.1.1 Ideal MaterialsThe characteristics of an ideal thermoelectric material have been welldefined[17], with entropic reversibility being a critical factor for high ZTmaterials. Highly entropically reversible thermoelectric materials are struc-tured to keep electrons within a very narrow energy range, thereby mini-mizing entropic losses (heat) when the electrons arrive at the cold junction.The Seebeck coefficient of the material must be non-zero and as large aspossible. Similarly, the electrical conductivity of the material must be verylarge such that no induced electrical power is lost to heat before it leavesthe module. Of exceptional importance is the manner in which heat travelsthrough the module. Heat can propagate from the hot junction to the coldjunction through phononic or electronic energy transfer. The former is a re-sult of lattice vibrations within the material whereas the latter results fromexcess energy stored within electrons as they reach the cold junction[16].While the electronic contributions to thermal conductivity are often ig-nored as the phonon contributions are much greater, as thermoelectric mate-rials continue to improve by reducing phonon transport, the electronic con-tribution becomes more important. Minimizing the electronic contributionto thermal conductivity requires reducing the energy variability of the elec-trons as they reach the cold junction while concurrently selecting the tem-perature gradient and vacuum energy, or work function, of the cold electrodeto prevent the formation and transmission of hot electrons[17]. These con-ditions are necessary for the thermoelectric process to be reversible, whichis required to minimize non-Carnot entropic losses resulting from the con-version of thermal energy to electrical energy. For example, if the phononcontribution to thermal conductivity is less than 0.5 W m−1 K−1 then anorder of magnitude reduction in electron energy variation from 250 meV to25 meV can increase ZT from 3 to 6[17]. Lower phonon contribution tothermal energy increases the significance of this effect, meaning that highefficiency thermoelectric materials exceeding ZT = 3 must seriously con-sider mitigating electronic contributions to thermal conductivity in the ma-terial. Some experimental evidence exists to support this model proposedby Humphrey and Linke, reinforcing these conclusions[17–19].Reducing electron energy spread is possible using nanostructured ma-terials with reduced dimensionality such as quantum dots (0D), nanowires(1D), and quantum wells (2D)[7]. These materials increase the spread be-tween energy bands available to electrons. Some materials, such as superlat-tice nanostructures use bandgap tailoring to mask off electrons with lowerenergy levels by imposing periodic electronic band energy barriers[20]. Prac-71.2. Backgroundtical materials must also emphasize a reduction of thermal conductivity byinterfering with phonon transport and minimizing the spread of electronenergy while still demonstrating a large Seebeck coefficient and electricalconductivity. Low Dimensional MaterialsA large variety of structures and structural modifications have been exploredexperimentally and theoretically in an effort to improve performance. Zerodimensional devices such as quantum dots have a delta function electronicdensity of states, and have been shown in highly controlled environmentsto have amenable thermoelectric properties[21–23]. One dimensional (1D)structures such as nanowires are easier to fabricate, present a density ofstates with narrow peaks, and have received the bulk of experimental andtheoretical exploration. A subset of nanowires, superlattice nanowires, ben-efit in that they can provide both zero dimensional (0D) and 1D confinement(depending on size) while also further reducing lattice thermal conductivitythrough enhanced phonon boundary scattering[18, 21–25]. Surface modifica-tions to nanowires have also been a subject of great interest since the exper-imental work of Hochbaum et al. revealed a 100× reduction in room temper-ature silicon lattice thermal conductivity[26]. This reduction was achievedby using a wet etch technique to roughen the surface of the nanowires with2 - 4 nm diameter cavities of unknown depth[26, 27]. 2D devices such asquantum wells have been considered, although their performance has yetto compete with devices with greater quantum confinement[19, 28, 29]. Aninteresting hybrid material classification is nanobulk materials. These mate-rials are fabricated by fusing nanoscale pellets into bulk structures througha process such as sintering[30, 31]. Recent publications using this methodhave shown very promising results using Al-doped zinc oxide (Al:ZnO)[32].Companies such as Alphabet Energy, GMZ Energy, and Laird Technolo-gies are pursuing nanostructured thermoelectric materials, with nanobulkand thin film technologies demonstrating the greatest commercial viabilityin this category at present[9, 12, 14]. For large-scale power generation appli-cations, one dimensional structures such as nanowires do not have the crosssectional area necessary to achieve the desired power density for a generator,resulting in a reduction in cost competitiveness for the material[14]. Onedimensional structures are also very difficult to integrate into modules andwithout a filler material must contend with radiative heat transfer throughthe device. Many publications favourably model the thermoelectric perfor-mance of nanowires and superlattice structures, but very little experimental81.2. Backgroundevidence exists to support these models on the scales necessary to achieverealizable, repeatable quantum effects.Nanobulk and thin film technologies incorporate nanostructural featureswithin the materials primarily to impede phonon transport without sig-nificantly reducing electronic transport by creating scattering sites withimpurities or nanovoids embedded into the material[30, 32]. Other meth-ods are also currently under examination to improve thermoelectric per-formance by introducing nanostructural features to bulk materials, such asinducing mechanical deformations in silicon through the application of highpressure[33], producing nanoscale precipitates in bulk materials[34], form-ing multi-phase or unstable materials[35], introducing new crystal struc-tures into the material lattice[36], enhancing disorder in the material forphonon band tailoring[37, 38], or increasing the effect of defects on phononpropagation[39]. Some methods, such as the addition of dislocation ar-rays in bulk bismuth antimony telluride have produced materials withZT = 1.86[38].1.2.2 Zinc OxideZinc oxide (ZnO) is a common, semiconducting, crystalline materialwith many desirable properties including a large bandgap, optical trans-parency, high melting temperature, and piezoelectricity. ZnO is a natu-rally n-doped semiconductor with established and upcoming applicationsin photovoltaics, microelectromechanical systems, piezoelectric devices, andthermoelectrics[40–44]. Additional doping of ZnO can have significant ef-fects on the structural morphology, optical transparency, and thermal andelectrical conductivity of the material[45]. For example, chloride doping ofnitrate-based, electrochemically grown ZnO can cap the formation of ZnOnanowires, allowing for the formation of complex tree-like structures[46].ZnO has a typical electronic bandgap of 3.3 eV and adopts either azinc blende or wurtzite structure. A wurtzite ZnO unit cell and an or-thographic image of a ZnO nanowire are shown in Figure 1.3. The distancebetween zinc atoms along 〈100〉 (a) is 3.25 A˚ and the distance between zincatoms along 〈001〉 (c) is 5.20 A˚[47]. The ratio, u, is ideally 3/8 for an idealwurtzite structure. ZnO can form atomically thin layers while retainingstability and can also be formed into hexagonal nanowires, plates, and pil-lared structures[40]. Zinc oxide is environmentally friendly, extremely lowcost, and is considered to be one of the economically fastest growing oxidematerials in industry[12, 48].Metal oxide thermoelectrics form a material system based on one or91.2. Backgroundcab = u×c[0 0 0 1]a)b)Figure 1.3: a) Illustration of a wurtzite ZnO unit cell, b) A slice of a wurtziteZnO nanowire used for modelling in Chapter 2 with the c-axis aligned verti-cally, rendered using VMD[49]. Red spheres represent zinc atoms and greyatoms represent oxygen atoms.multiple cations bonded with oxygen. Example oxide materials with goodthermoelectric properties include zinc oxide (ZnO) (n-type), NaxCoO2 (p-type), Ca3Co4O9 (p-type), SrTiO3 (n-type), and CaMnO3 (n-type)[50]. Ox-ides have gained substantial interest as thermoelectric materials due to theirhigh temperature chemical stability, low thermal conductivity, chemical re-sistance, ease of synthesis, high mechanical strength, and moderate to highbandgap[51]. Though not a viable thermoelectric material on its own dueto a low electrical conductivity, when doped with aluminum (Al), gallium(Ga), or a mixture of both, bulk zinc oxide can exceed a ZT of 0.3 at1000◦C[52, 53]. Aluminum-doped zinc oxide (Al:ZnO) shows particularlyhigh promise and is considered to be one of the best performing oxide ther-101.2. Backgroundmoelectric materials[44, 52–55].1.2.3 Al:ZnO ThermoelectricsAl doping of ZnO has been successfully performed using a variety of meth-ods including electrochemical deposition[56–61], RF plasma and magnetronsputtering[43, 60, 62, 63], ball mill grinding of ZnO and Al2O3 pow-der followed by sintering[53], pyrolytic and thermal decomposition[64–66],and laser ablation[44]. Al doping is desirable for many applications, in-cluding dye-sensitized solar collectors[60], thermoelectrics[43, 44, 53, 62],nanostructures[59], and light emitting diodes[56]. The moderate bandgapand high electrical conductivity of 2% (molar ratio of Al to Zn) dopedAl:ZnO contributes to its excellent thermoelectric performance, whileits high thermal conductivity is its greatest detractor for thermoelectricapplications[44, 53]. It is an excellent candidate for microstructuring toreduce thermal conductivity.Aluminum can be integrated into the film using a variety of fabrica-tion techniques[55, 64, 65, 67–69]. The preferred type of integration in-volves substitution doping of ZnO where zinc ions are replaced by alu-minum ions in a predominantly ZnO crystal lattice. The replacement re-sults in localized distortions in the lattice structure and serves as an n-typedopant, in some cases yielding extremely high electrical conductivity ex-ceeding 2000 S/cm[54]. Aluminum has also demonstrated p-type doping ef-fects when co-doped with nitrogen[70]. The ideal methodology for growingAl:ZnO thermoelectrics would• allow for the introduction of nanostructural features such as voids orheterostructures,• permit gradient or controlled doping for electronic band tailoring andreducing electronic contribution to thermal conductivity,• support a rapid rate of growth,• be scalable to large surface areas,• and require a minimum of energy to help reduce fabrication costs.Most methods for fabricating Al:ZnO involve either vacuum depositionor sintering a powder at temperatures above 900◦C, both of which demandsignificant energy and equipment[44, 52, 62]. Hydrothermal and electro-chemical (wet) growth of ZnO thin films and nanostructures are both well es-tablished in literature and resolve some of these limitations[40, 66]. Growth111.2. Backgroundof ZnO in solution occurs at low temperatures, is scalable, and providesample flexibility to modify the properties of the material during growththrough the introduction of dopant chemicals and capping agents[40, 58].Some work has also been performed on growing Al:ZnO thin films elec-trochemically by adding dopant agents into the growth solution, but thethermoelectric properties of electrochemically grown Al:ZnO have not beeninvestigated[56–59, 61, 65]. Due to the versatility, low cost, and scalabilityof the electrochemical deposition of Al:ZnO, electrodeposition was chosenas the fabrication methodology for this work.1.2.4 ElectrochemistryElectrodeposition involves the use of electrochemistry to deposit materialonto a substrate. In a standard three electrode configuration, a substrate(cathode) onto which the desired material is to be deposited is connected toa wire and is placed within a solution containing ions. A counter electrode,or anode, is chosen to complete the circuit and allow a site where oxidationcan take place. An optional reference electrode is typically included for moreaccurate measurement of solution potential relative to the substrate. Elec-trodeposition can occur potentiostatically, where applied potential betweenanode and cathode is adjusted to maintain a constant reference potential,or galvanostatically, where a constant current between anode and cathodeis applied. A basic potentiostatic setup is shown in Figure 1.4. Depositionsnecessarily operate below the boiling point of the process fluid, typically wa-ter, and are historically ubiquitous for plating metals, including aluminum,gold, and chromium[71]. Recent work with electrochemistry has enabled thedeposition of more complex materials such as ZnO[72, 73].Electrochemistry offers very versatile control of the material forma-tion, permitting variations in solution temperature, applied potential, andsolution chemical composition as methods for varying the properties ofthe films during growth, enabling the formation of a large variety ofnanostructures[40, 74]. The anion groups typically used in ZnO electrode-position are nitrates, sulphates, acetates, and chlorides[72, 73, 75]. Of theseanion groups, nitrates and chlorides have been most explored within theliterature[72, 73, 76–88]. Depositing ZnO with chloride anions requiresthe addition of gaseous oxygen to the growth solution to form the ox-ide, whereas the nitrate anion provides the oxygen through electrochem-ical decomposition of nitrate into hydroxide as shown by the followingreaction[40, 77, 80, 82, 84, 89]:Zn2+ + NO −3 + 2 e− −−→ ZnO ↓ + NO −2 (1.20)121.3. ObjectivesSubstrateCathodeAnodeReferenceIonic solutionReferenceSignalPower Supply Note that appliedvoltage is negativeFigure 1.4: A standard, three electrode potentiostat is shown.The nitrate system was chosen for the electrodeposition of ZnO exploredin this work due to a lower reagent cost and simpler electrochemical setup.A significant limitation in the available literature for producing Al:ZnO elec-trochemically involves the study of Al-doping in thicker Al:ZnO films basedon the nitrate growth system. Existing experiments generally limit growthtimes to under two hours and focus primarily on potentiostatically grownfilms[45, 46, 59]. The thermoelectric performance of thin films (<10 µm) isdifficult to characterize and requires higher cost interface materials, neces-sitating the development of thicker film growth. Reference material on theelectrochemical growth of Al:ZnO using the nitrate system is also limited,with doping being demonstrated but not very well characterized[40, 58, 59].1.3 ObjectivesThe overarching objective of the work is to produce a low cost, environmen-tally friendly n-doped thermoelectric material suitable for integration into athermoelectric module. This objective is separated into the following tasks:131.3. Objectives1. Develop a modelling methodology to rapidly approximate the relativethermal conductivity of similar nanostructures.2. Use modelling to qualitatively assess the thermal behaviour of nanos-tructured ZnO and choose structures for experimental synthesis.3. Synthesize high quality, thick film Al:ZnO with the desired structuresusing electrochemistry.4. Test the thermoelectric properties of the synthesized Al:ZnO struc-tures.14Chapter 2ModellingThere exists a wide range of nanostructures with the potential for syn-thesis with the Al:ZnO material system that may augment the thermo-electric performance of the material[90, 91]. Since the thermal conductiv-ity of unmodified bulk Al:ZnO is approximately 20-40 W m−1 K−1 at roomtemperature[53], finding nanostructures that reduce lattice thermal conduc-tivity proportionately more than electronic conductivity was the focus ofthis work. To determine which structures warrant experimental examina-tion, a consistent, primarily qualitative mechanism that takes into accountspecial phonon scattering mechanisms that are difficult to describe throughexisting analytical theory was developed to enable the rapid comparisonof the thermoelectric performance of various nanostructures. To simplifythe modelling of the materials, undoped ZnO was used in all simulations.It is assumed that thermoelectrically beneficial nanostructural features willapply similarly to both ZnO and Al:ZnO material systems for low dopingdensities.The behaviour of phonons within nanostructured materials has beena subject of intense study using a remarkable variety of numericaland analytical modelling techniques. For example, to model the be-haviour of roughness on silicon nanowires, which has experimentally pro-duced a 100× reduction in thermal conductivity[26], models have beenconstructed using Monte Carlo simulations[92, 93], atomistic Green’sfunction[94–96], the Boltzmann Transport Equation (BTE)[97, 98], per-turbation theory[99], scattering-matrices[100], molecular dynamics[98, 101,102], phonon hydrodynamics[103], and finite element analysis[104]. Othershave assembled tools for estimating phonon propagation through nanostruc-tures based on various classical and quantum assumptions[105, 106]. Thesemodels are often designed to favour a small subgroup of nanostructures, suchas surface roughness features, or they make assumptions about the behaviourof phonons that neglect their wave-like behaviour around nanometre-scaledobstacles[4].To minimize the risk of bias in phonon modelling, molecular dynamicswas chosen. Molecular dynamics uses either experimentally or theoreti-15Chapter 2. Modellingcally derived force fields to model the interaction between small subsets ofatoms within a large lattice. The simulation runs iteratively with a con-stant time step, allowing for the natural evolution of phonon behaviour as amesoscopic culmination of the interactions between all of the atoms in themodel. Molecular dynamics has been successful in modelling the behaviourof nanostructures, but it is generally limited in that significant computa-tional resources are required to run the simulations[101, 107, 108]. To helpprovide better insight into the phonon behaviour around nanostructures, amethod for rapidly simulating and producing phonon density maps usinglocal vibrational density of states (LVDOS) was developed. LVDOS equi-librium molecular dynamics (LVDOS-EMD) simulations could also providerelative thermal conductivities between similar nanostructures, enabling thestudy and comparison of many different structures using significantly fewerresources.All thermal conductivity modelling was performed assuming a system at300 K. This temperature was selected for many reasons: 1) The cold side of athermoelectric device will be near this temperature in most applications; 2)The force field chosen for modelling ZnO, ReaxFF, was characterized at thistemperature[109]; 3) At 300 K, calculated vibrational (occupied) density ofstates will closely match material density of states; 4) Temperatures above600 K would prevent studying the Zn/ZnO heterostructure.ZnO is a very stable material over a wide range of temperatures andexperimentally demonstrates good adherence to the Callaway model for lat-tice thermal conductivity[16, 110]. It is therefore assumed that reductionsin thermal conductivity at room temperature will lead to corresponding re-ductions in thermal conductivity at all temperatures. No nanostructureswere chosen specifically to create temperature-dependent phonon interfer-ence patterns, although such structures do exist[111]. The effect of thealuminum dopant was also neglected in the models as each model was ex-pected to be doped identically, and dopants provide defect scattering siteswhich are expected to reduce thermal conductivity in all cases.Of the variety of nanostructures available, unmodified nanowires, hollownanowires[40], surface roughened nanowires[112], nanovoided bulk[31, 32],and superlattice nanowires[113, 114] were chosen for primary investigationthrough modelling. Some additional structures were briefly considered fortheir viability as well, such as zinc-filled ZnO tubes, but were found to bechemically unstable and were thus not explored in further detail.162.1. LVDOS-EMD2.1 LVDOS-EMDThis section discusses the methods used for determining thermal conduc-tivity of silicon and ZnO nanostructures, including the development of lo-cal density of states equilibrium molecular dynamics (LVDOS-EMD). Themethodology is first illustrated using silicon due to the comparatively rapidMD simulation of silicon over ZnO and its well established force fields forthermal conductivity calculation.Thermal conductivity in an anisotropic material can be defined usingFourier’s equationQ = −κ∇T, (2.1)where Q is the heat flux vector, κ is the thermal conductivity tensor, and∇T is the temperature gradient. κ includes the effects of both electronsand phonons, where the former can generally be neglected in high thermalconductivity (>20 W m−1 K−1) dielectric and semiconducting materials. As-suming no radiative transfer, heat transfer occurs primarily through latticevibrations in wavelets called phonons.Several means exist for using molecular dynamics (MD) for determiningthe thermal conductivity of a nanostructured material. Most commonly,MD simulations using equilibrium molecular dynamics (EMD) and non-equilibrium molecular dynamics (NEMD) are performed. Molecular dy-namics discretely simulates the motion of a collection of atoms under spec-ified conditions based on pre-calculated or empirically determined poten-tials. EMD simulations using methods such as Green-Kubo involve relaxingthe atomic structure under study at thermal equilibrium [115, 116]. InGreen-Kubo, correlations are used to examine the decay of coherent phononwavelets as they traverse the structure[117]. Simulations must typically ex-ecute > 1× 106 iterations depending on the material thermal conductivity,and multiple simulations must be executed and the results averaged to con-verge at a reasonable thermal conductivity[118]. This method is useful fordetermining the thermal conductivity of a material at a specified tempera-ture and is often used to estimate thermal conductivity in many directionsconcurrently. Substantial computing time is required to execute the simu-lations, and they may not converge if the structure is complex with manyinterstitial and surface features[119, 119, 120].Reverse NEMD (herein also referred to simply as NEMD) involves in-ducing a thermal flux within the material by swapping kinetic energy andmomentum between two groups of atoms. The Mueller-Plathe (MP), a di-rect method, swaps the energy and momentum of the hottest atom in the172.1. LVDOS-EMD“cold” region and the coolest atom in the “hot” region thereby graduallyforming a temperature gradient between “hot” and “cold” regions [107, 121].Once the gradient reaches steady state, the energy flux and temperaturegradient across the structure are both acquired and used to determine thethermal conductivity. This method has a high probability of success forstable structures, but it is also limited by requiring many execution steps(> 1× 106 iterations), large structures to accommodate all relevant phononwavelengths[111, 122], and a thermal gradient disallowing equilibrium ther-mal conductivity calculations. Preliminary simulations are also required insetting up the model to determine an appropriate energy transfer rate toachieve the desired temperature gradient.Another method, homogeneous non-equilibrium molecular dynamics(HNEMD), provides a variation of NEMD that is significantly more com-putationally efficient by using linear response theory along with a me-chanical analog of the thermal transport process to calculate transportcoefficients[123]. HNEMD leverages information from the force field po-tentials used in the MD simulation and can provide results of comparableaccuracy to Green-Kubo with an order of magnitude fewer computations,but requires several simulations to determine an appropriate range of simula-tion constants[124]. HNEMD is very material-specific and must be properlyconfigured for both the material system and potential to yield meaning-ful results, but with recent support for multiple material systems, it is apromising methodology for the analysis of nanostructural features.A subclass of methods for determining κ that depend on EMD or NEMDresults involves a combination of lattice dynamics calculations and the Boltz-mann transport equation (BTE). For an isotropic, periodic solid with natoms per unit cell, the phononic BTE along a specific material directionis[125]κ =3n∑s∫qv2g(q,m)C(q,m)τ(q,m)dq, (2.2)where vg(q,m) is the phonon group velocity, C(q,m) is the mode heat ca-pacity, τ(q,m) is the phonon lifetime, q refers to the phonon wavevector,and m is the phonon mode[125]. The heat capacity can be calculated usingthe temperature derivative of the Bose-Einstein distribution directly fromthe mode information, meaning that group velocity and phonon lifetimemust be determined from the modelling results. A typical approach involvesfirst solving the dynamical matrix of the system after minimizing the systemenergy through a relaxation procedure under NPT conditions. The eigenvec-182.1. LVDOS-EMDtors can then be used to calculate group velocity as described by McGaugheyand Larkin[126]. Several methods exist for then determining phonon life-time, including normal mode decomposition (NMD)[126], first principlesmolecular dynamics[125], and spectral energy density calculations[127]. Allof these methods operate within reciprocal or phonon space, requiring thecomputationally intensive task of determining phonon modes from a dynam-ical matrix calculation and/or modelling results.LVDOS-EMD is applied to both EMD and NEMD (LVDOS-NEMD)simulation environments developed herein can be applied in both EMD andNEMD simulations and uses local vibrational density of states (LVDOS)combined with the Boltzmann Transport Equation (BTE) to calculate therelative thermal conductivity between multiple similar structures, such asstructures with varying densities of defects, or varied surface morphology.The methodology, herein called LVDOS-EMD, requires very few computingcycles at equilibrium and is targeted toward examining the effect of progres-sive, small nanostructural modifications on material thermal properties atidentical temperatures. It is primarily intended for qualitatively support-ing more rigorous EMD and NEMD methods by determining trends andpatterns, and is not intended to provide an absolute thermal conductivity.By operating within real space using simulated velocity data, insights intolocalized wave behaviour around nanostructural features can be realized. Itis demonstrated using notched, square silicon nanowires and is comparedto NEMD MP and finite element analysis (FEA) results. FEA results areincluded to highlight the importance of including wave effects over classicalcontinuum heat transfer models.Nanowire roughness is represented by notches of various depths (D), pe-riods (p), and widths (w) to create regions of differing VDOS and MFP asshown in Figure 2.1. Tests are performed on nanowires of various thick-nesses (k). Silicon nanowires are first used to aid in validating the theorydue to their ease of simulation and well established force fields for thermalconductivity calculations. Simulating the thermal conductivity of ZnO hasfew rigorously examined force fields available and little established literatureon simulating thermal properties[109, 128–130].2.1.1 Formulation of Theory2.1.1.1 Boltzmann Transport EquationFollowing the derivation of Grimvall, the quantum statistical BTE for vibra-tions in real space is used to provide an equation for thermal conductivity192.1. LVDOS-EMD5.43 nm (10 uc)as shownFigure 2.1: A visual representation of a Si lattice structure showing roughen-ing parameters is shown. This figure shows the structure prior to relaxationand is intended to highlight the parameters varied in the notching in ad-vance of executing the simulation. Nanowires are structured along the 〈001〉direction.[131],κvib =N3Vvg∫ ωmax0Cvib(ω)l(ω)D(ω)dω, (2.3)where N is the number of particles in the system, V is the total volume, ω isthe vibrational frequency, vg is the average wavelet group velocity, l(ω) is themean free path (MFP), D(ω) is the vibrational density of states (VDOS),and Cvib(ω) is the heat capacity, which, using the temperature derivative ofthe Bose-Einstein distribution, can be expressed as[131]Cvib(ω) = kBy2ey(ey − 1)2 , (2.4)wherey =h¯ωkBT. (2.5)Appropriate normalization for calculating thermal conductivity requires that∫ ∞0D(ω)dω = 3. (2.6)If the atomic density, overall volume, and group velocity is taken tobe the same between two structures, we can generate a ratio of thermal202.1. LVDOS-EMDconductivities between two similar nanostructured materials,κvib,1κvib,2=∫ ωmax0 Cvib(ω)l1(ω)D1(ω)dω∫ ωmax0 Cvib(ω)l2(ω)D2(ω)dω, (2.7)where li(ω) and Di(ω) represent the MFP and VDOS of each structure,i. An MD simulation using a more rigorous methodology, such as Green-Kubo or Mueller-Plathe, is run on a reference structure to determine itsMFP, VDOS, and κvib. The relative thermal conductivity of other, similarstructures, can then be calculated using the reference structure as a scalingfactor. After the rigorous simulation is complete, two variables per similarstructure must be solved: 1) The VDOS and 2) the frequency-dependentmean free path. Vibrational Density of StatesReal space VDOS can be calculated from MD simulations using the velocityautocorrelation function (VAF) on aggregates of atoms [132, 133]. If thevelocity vector of atom a is va(t) then the VAF, Za(t), can be written asZa(t) =〈va(0) · va(t)〉〈va(0) · va(0)〉 , (2.8)where va(0) represents the velocity at the beginning of the captured data(t = 0) after the system has reached equilibrium. The frequency spectrumcan be determined through the application of a Fourier transform,Fa(ω) =1√2pi∫ ∞−∞e−iωtZa(t)dt, (2.9)resulting in a discretized, VDOS ofD(ω) =∑aFa(ω)F∗a (ω). (2.10)Morphological changes in nanostructured materials along the path trav-elled by vibrational energy can significantly change the VDOS by anhar-monic collisions. These shifts can be significant, causing order of magnitudechanges in thermal conductivity [134]. When examining the VDOS of thestructure as an aggregate whole, the influence of small structural featurescan be lost, leading to large errors in the calculated thermal conductivity.It is for this reason that local vibrational density of states is used for bothVDOS and MFP calculations.212.1. LVDOS-EMDThe structure is separated into segments of equal volume such that eachsegment has a minimum of 50 atoms and the segments are stacked along thedirection of measurement. The segment length should be selected to avoidcorrelation with surface features and minimize the variation in number ofatoms between adjoining segments. Ideal segment length is typically relatedto material lattice parameters to ensure an even distribution of atoms. TheVDOS is calculated separately for each segment, providing localized densityof states throughout the structure. An example of the VDOS for a 4.9 nm di-ameter silicon nanowire is shown in Figure 2.2. Shown are spatially localizedvibrational components of optical and acoustic phonons along the length (z-axis) of both straight and notched nanowires with the band spreading effectsof the notching visible in Figure 2.2b.Calculating the LVDOS for each segment is based on (2.10) whereDs(ω) =∑aFa,s(ω)F∗a,s(ω) (2.11)is the aggregate LVDOS for a segment or slice, s, of the nanostructure(s)along the direction of measurement. A cross-sectional area that encompassesthe largest necessary cross-section for the structure must be selected for thesegments. The cross-sectional area and the width of each segment must beidentical. The LVDOS of each segment cannot be normalized by the numberof atoms in the segment, meaning that the segment size should be selectedto minimize the variation in total atoms between segments.Determining an approximate mean free path using only the LVDOS be-gins with a discretization and modification of the survival equation. Survival EquationIn the derivation of the survival equation for determining the mean freepath of a particle travelling through a random collection of identical par-ticles within a defined volume (a gas), the gas is first segmented into aseries of volumes and the particle is represented as a bullet as shown inFigure 2.3. The following derivation follows Sears[135]. The probability ofa bullet striking a particle while travelling through a segment is∆NN=Target areaTotal area, (2.12)where N is the total number of travelling bullets (or density of bullets) and∆N is the number of collisions[135]. If A represents the cross-sectional area222.1. LVDOS-EMDFigure 2.2: LVDOS along the z-axis of a 4.9× 4.9× 27nm3 (a) straight and(b) notched silicon nanowire. The roughened nanowire in (b) has 1.6 nmdeep, 0.54 nm diameter notches every 5.4 nm along its length. Slices weremade every 0.135 nm along the nanowire and are labeled along the x-axis.232.1. LVDOS-EMDof the targets and n is the number of targets per unit volume thendNN= −nAdx (2.13)From (2.13), if every slice is assumed to be identical then the survivalLΔxBulletParticleTargetsFigure 2.3: Illustration of a particle (bullet) travelling through a slice ofgas for the purpose of solving the survival equation. ∆x represents thethickness of the slice and L is the length of the slice in this two dimensionalrepresentation.equation,N = N0e−nAx, (2.14)is determined to be a decaying exponential function where N0 is the to-tal number of bullets at the origin. Mean free path is then a normalizedweighted average of the number of bullet collisions travelling through aninfinite distance,l =∑x∆NN0= nA∫ ∞0xe−nAxdx =1nA. (2.15)In the original kinetic theory of gasses derivation of the mean free path,the assumption is made that successive layers or segments of target atomsoccupy the same configuration, meaning that the probability of a collisionas a particle travels through a material is identical per unit distance [135].A variation on this derivation is proposed. Rather than treating the prob-ability of collision as a function of “microscopic collision cross-section” and242.1. LVDOS-EMD“target area”, the probability of a collision is approximated by the changein VDOS between neighbouring segments. When wavepackets travel froma region with many states to a region with fewer states, some collisions arestatistically required. For wavelets moving in a single direction, from seg-ment s − 1 to s, and for small δx, if the transition from a region of highoccupied DOS to a region of low occupied DOS is large, then an approximatesurvival probability, Zs, can be derived by considering the ratio in occupiedvibrational density of states, N , between the two regions,Zs ≈ NsNs−1for Ns < Ns−1. (2.16)If we then assume that the probability of a wavelet colliding is identicalfor all wavelets, the probability of collision from wavelets travelling from aregion of low density to high density can be approximated from waveletstravelling in the opposite direction using the same principles as (2.16),Zs ≈ Ns−1Nsfor Ns−1 < Ns. (2.17)Equations (2.16) and (2.17) represent the maximum probability of survival ofwavelets travelling through these spaces. A more rigorous model consideringwavelets travelling in both directions for a single mode can be constructedbeginning with the principal statement of the Boltzmann Transport Equa-tion (BTE),δNsδt=δNsδt∣∣∣∣force+δNsδt∣∣∣∣diff+δNsδt∣∣∣∣coll, (2.18)describing the time varying change in density of states as a summation offorce, diffusion, and collision influences for every segment, s. Assuming thatthe system is in equilibrium and that no force is applied, (2.18) becomes0 =δNsδt∣∣∣∣scatt−in− δNsδt∣∣∣∣scatt−out+ (2.19)δNsδt∣∣∣∣diff−in− δNsδt∣∣∣∣diff−out,where scattering terms represent interactions with wavelets in the same seg-ment but in different modes, and diffusion terms represent wavelets in thesame mode entering and leaving the segment from neighbouring segments.Wavelets can arrive by travelling into the segment from a neighbouring252.1. LVDOS-EMDsegment or by scattering in from a different mode in the same segment.Wavelets depart either by travelling out of the segment ballistically or byinteracting anharmonically and scattering to a different mode within thesame segment. This equation can also be understood as an expression ofconservation of energy. For a system where Ns−1 > Ns and Ns+1 > Ns,δNsδt∣∣∣∣scatt−in= ζNs, (2.20)δNsδt∣∣∣∣diff−in= βNs−1 + βNs+1, (2.21)δNsδt∣∣∣∣scatt−out= (1− Zs)[δNsδt∣∣∣∣diff−in+δNsδt∣∣∣∣scatt−in](2.22)= (1− Zs)ζNs + (1− Zs)βNs−1 +(1− Zs)βNs+1,δNsδt∣∣∣∣diff−out= 2βNs, (2.23)where β represents the proportional rate of wavelets in the same mode en-tering or leaving the segment due to diffusion, ζ is the proportional rateof wavelets scattering into the segment from other modes, and Ns−1 andNs+1 represent the LVDOS adjacent to each segment boundary, as shownin Figure 2.4. The scattering out term applies to all wavelets entering thesegment per unit time. Survivability, Zs, is not a time-dependent term andis applied only once to wavelets as they enter the segment. All waveletswithin segment s are assumed to have the same probability of collision, in-cluding wavelets that have scattered into the mode. All wavelets that collidescatter out to a neighbouring mode within the same segment. Combining(2.20)-(2.23) with (2.19) yieldsZs =2βNsβ( ζNsβ +Ns−1 +Ns+1)(2.24)for Ns−1 > Ns, Ns+1 > Ns.The β terms are analogous to the group velocity of the system, which istaken to be identical for wavelets entering and leaving each segment due262.1. LVDOS-EMDΔxZ ZN -1 N +1Ns sFigure 2.4: Illustration of the transport of wavelets within a multi-segmentedstructure, where red particles are travelling within the same mode along thestructure, and blue particles originate from intermode scattering in the diffusion. Similar to (2.16) and (2.17), (2.24) represents the maximumsurvivability of wavelets travelling through the segment. Provided that thematerial MFP is defined predominantly by structural features in the mate-rial, we assume that β >> ζ. The resulting equation is the approximateprobability of survival for each segment,Zs =2NsNs−1 +Ns+1(2.25)for Ns−1 > Ns, Ns+1 > Ns.The equations for the other neighbour configurations of Ns are determinedsimilarly to (2.16) and (2.17), yieldingZs =Ns +Ns+1Ns +Ns−1(2.26)for Ns−1 > Ns, Ns+1 < Ns,Zs =Ns +Ns−1Ns +Ns+1(2.27)for Ns−1 < Ns, Ns+1 > Ns,272.1. LVDOS-EMDZs =Ns−1 +Ns+12Ns(2.28)for Ns−1 < Ns, Ns+1 < Ns. Determination of Mean Free PathThe frequency dependent MFP can now be determined from MD resultsthrough a weighted average of collision probabilities across all segmentboundaries. Equations (2.25)-(2.28) can be described in terms of LVDOSand vibrational frequency asPs(ω) =2Ds(ω)D(ω)s−1 +D(ω)s+1(2.29)for D(ω)s−1 > D(ω)s, D(ω)s+1 > D(ω)s,Ps(ω) =D(ω)s +D(ω)s+1D(ω)s +D(ω)s−1(2.30)for D(ω)s−1 > D(ω)s, D(ω)s+1 < D(ω)s,Ps(ω) =D(ω)s +D(ω)s−1D(ω)s +D(ω)s+1(2.31)for D(ω)s−1 < D(ω)s, D(ω)s+1 > D(ω)s,Ps(ω) =D(ω)s−1 +D(ω)s+12D(ω)s(2.32)for D(ω)s−1 < D(ω)s, D(ω)s+1 < D(ω)s,where Ps(ω) is the wavelet probability of survival travelling through segments such that P0(ω) = 1, and Ds(ω) represents the cumulative, frequencydependent LVDOS of a segment and is determined using (2.11). With theprobability of survival calculated for every segment, the probability of alocalized wave surviving exactly s segments, Qs(ω), isQs(ω) = [1− Ps(ω)][P0(ω)P1(ω)P2(ω)...Ps−1(ω)] (2.33)[1− Ps(ω)]s−1∏y=0Py(ω).The distance traveled, ds, is simplyds = sa, (2.34)282.1. LVDOS-EMDwhere a is the length of each segment, which is taken to be identical for allsegments, and s is the segment index such that the product sa is the totaldistance travel from the origin (s = 0) to ds. Combining the probabilityof particle survival from (2.33) and distance traveled for all segments yieldsthe approximated frequency dependent MFP,l(ω) ≈ aS∑s=1[s(1− Ps(ω))s−1∏y=0Py(ω)], (2.35)where S is the total number of segments.2.1.2 Validation of TheoryThe validity of (2.35) is first examined using a Monte Carlo simulation thatuses particles to approximate wavelets. These particles traverse a one di-mensional medium that follows simple rules defined by (2.20)-(2.23). Thesimulation is used to determine whether the non-frequency dependent equiv-alent of (2.35) can be used to determine the MFP of particles in a simple sys-tem using only the measured number of particles in neighbouring segments.Following the Monte Carlo simulation, the dynamical matrix is solved forsome of the nanostructured unit cells used in the MD simulations. VAF-based VDOS using MD results is compared with the DOS calculated usingonly the normal modes from the dynamical matrix of the system. Thegroup velocities of various structures are calculated and compared to exam-ine the effect of small structural changes, and normal mode decomposition isused to calculate phonon lifetime and conceptual MFP for comparison withLVDOS-EMD results. Straight nanowires and phonon VDOS variation overthe entire sampling period are also considered.LVDOS-EMD molecular dynamics data was generated using plain androughened silicon nanowires ranging from 1.6 nm to 4.9 nm diameter andwere all 217.2 nm (400 unit cells) long. The selection of this length isdiscussed in Section 2.1.3. The software used was LAMMPS with theStillinger-Weber potential [136]. The Stillinger-Weber potential has beenpreviously demonstrated to accurately model the thermal properties of sili-con [136, 137]. All simulations began by applying a Gaussian velocity profileto all atoms representing an aggregate temperature of 300 K. This step wasfollowed by 50,000 iterations at 1.0 fs of simulation time per iteration of con-stant number of particles, pressure, and temperature (NPT) equilibration.A constant number of particles, volume, and energy (NVE) equilibrationfor 25,000 iterations was then used to allow any temperature transients in292.1. LVDOS-EMDthe system to settle. At this stage, either Mueller-Plathe was applied for areverse NEMD simulation or LVDOS-EMD was applied for a short durationsimulation. Stabilization of a thermal gradient for reverse NEMD calcula-tions then required 1,000,000 iterations, followed by 200,0000 iterations forcollecting temperature and flux data for calculating the thermal conduc-tivity. The final mean temperature of the entire nanowire was measured toconfirm 300± 5 K to ensure that each simulation properly equilibriated. Thestructures were also studied after simulation to ensure that no atoms werelost and that the nanowire remained straight throughout the simulation. Monte Carlo SimulationA stochastic Monte Carlo computational simulation was developed to de-termine the accuracy of (2.35) in an ideal system. Particles represent-ing wavelets in a single mode were initially generated and placed alonga segmented, one-dimensional axis representing a structure analogous to ananowire. The simulation used (2.20) - (2.23) to determine particle creationand destruction behaviour, where Z was predetermined for each segment inthe simulation. Each particle starting location, speed, and direction wererandomly determined using a uniform distribution function. Particle posi-tions were updated over several thousand simulated time steps and local-ized, instantaneous particle density was calculated for each segment withevery time step. Each segment along the “nanowire” was assigned a sur-vival probability from 10 - 100%, representing the probability of particlescolliding upon entering the segment, simulating scattering due to collisions.This probability is analogous to physical structural features such as holesor notches that increase phonon scattering along a nanostructured material.Scattered particles were replaced with a new particle at a random locationalong the nanowire with particle density in each segment proportional to therelative probability of the particle appearing in that segment. The numberof particles in motion was set to be constant for every time step. Particlemean free path was measured directly for each particle then averaged overseveral hundred thousand particles to determine the measured mean freepath. To improve the accuracy of the simulation, the number of particles ineach segment was summed with each time step to represent the large numberof samples required to perform a Fourier transform in a physical simulation.Analysis was only performed on the summed particle occupation data.A periodic structure was first modelled with segments of high collisionsand low collisions to represent an inhomogenous, nanostructured material.Particle survivability in high collision segments was varied from 10 - 80%302.1. LVDOS-EMDover eight simulations. The resulting cumulative particle density over 2,000simulation time steps for a configuration where every 10 segments was as-signed an 80% survival probability is shown in Figure 2.5 as an example. Thefigure shows that regions of 100% survivability have a similar, but randomnumber of accumulated particles in each, and regions of 80% survivabilityhave a correspondingly lower number of total particles due to collisions re-moving particles from those segments throughout the simulation. Similarsimulations were also conducted where 80% survivability was replaced withlower values.Figure 2.5: A plot of the cumulative particle density across 200 segmentsof a 1,000 segment structure where each segment has a 100% survival rateexcept for each 10th segment, which has an 80% survival rate. The sim-ulation assumes an instantaneous particle density expectation value of 10particles/segment and runs over 2,000 simulation time steps.Equation 2.35 provides an approximate MFP along one dimension ex-clusively using the calculated cumulative LVDOS of the structure over aspecified time interval. Analyzing VDOS at a moment in time is not pos-sible as the Fourier transform must take place over a range of time steps.Figure 2.6 demonstrates the resulting calculated MFPs as a function of sim-ulation time window duration. The rapid convergence indicates that in anidealized model, the MFP is independent of sampling time window provideda minimum window size is met. This minimum is necessary for the systemto reach equilibrium as required by (2.19). Deviations in Figure 2.6 from the312.1. LVDOS-EMDconverged MFP early in the simulation are the result of the model establish-ing an equilibrium where the regions of lower survivability converge to theappropriate density shown in Figure 2.5. Vibrations travelling through a realstructure must also demonstrate the same behaviour for LVDOS-EMD to beapplied successfully. Discussion of VDOS as a function of sampling windowsize can be found in Section and demonstrates a similar consistencyprovided a minimum sample window size and VDOS are met.Figure 2.6: Calculated MFP as a function of time window size using (2.35)applied to simulations with segments of 10% survivability (lowest curve)through 80% survivability (highest curve).Figure 2.7 shows the simulation results with a constant simulation timewindow size of 2000. In addition to comparing the correct MFP by trackingparticle travel distance and MFP calculated as described above, a variationon (2.16)-(2.17) was considered where the mean of all three DOS terms areused in the denominator. Using the mean represents the average survivalat boundaries N and Ns−1 rather than the minimum. Although using themean particle density of the two adjacent segments does provide a bettermatch to the measured density for regions of greater survivability, using themaximum DOS between neighbouring regions, represented by the equationsas presented, provides a more consistent approximation across the entirerange. Using equations (2.25) - (2.28) produced nearly identical results.322.1. LVDOS-EMDFigure 2.7: MFP results showing simulation MFP, calculated MFP usingparticle density mean approximation, and calculated MFP using particledensity max approximation results. Shown are curves for a mean free pathof 20 (top), 10 (middle), and 5 (bottom). Lattice Dynamics Density of StatesLattice dynamics involves determining the permissible phonon modes in k-space by forming and solving a discretized dynamical matrix that capturesthe force interactions between atoms in a structure. Studying the behaviourof phonons should provide an analogous reference to the vibrational waveletsthat are the focus of LVDOS-EMD. A full discussion of lattice dynamics andnormal mode decomposition can be found elsewhere[126]. The dynamicalmatrix can be used in the eigenvalue problem,ω(q,m)2e(q,m) = D(q)e(q,m), (2.36)where ω(q,m) is the phonon mode-dependent angular frequency, e(q,m)is the eigenvector matrix, and D(q) is the dynamical matrix. There arethree modes per atom, and the dynamical matrix scales with number ofmodes squared, requiring significant computational resources to solve verylarge systems of atoms. Calculations herein used the Stillinger-Weber po-tential and the GULP software package to generate the dynamical matrixbased on a provided structure and create the corresponding eigenvectorsand VDOS[136, 138]. GULP was configured to optimize the structure first,then generate the full dynamical matrix and perform phonon calculations.332.1. LVDOS-EMDMatrices were generated at 300 K using the smallest possible unit cell thatcould periodically replicate the desired nanostructure. Thirty k-points wereused along the 〈001〉 axis for each structure studied. A custom Matlab scriptthen loaded the output data from GULP to perform further calculations.Total phonon density of states was produced using GULP lattice dy-namics for 2.7 nm and 3.8 nm diameter straight and notched nanowires, andwas compared with the VDOS generated using MD and VAF for the iden-tical structures. The results are shown in Figure 2.8. There is excellentagreement between the straight nanowires calculated using both techniques,but the VDOS using VAF generated for the notched nanowire diverges fromthe theoretical ideal. Although acoustic phonons match well in all datasets, optical phonons are not as prominent in the MD data. The error islikely caused by dangling silicon bonds in the MD simulation warping thestructure of the nanowire around the notches, modifying the dispersion andcorresponding VDOS of the structure. It is also possible that some avail-able, high energy optical states were not filled by phonons due to very shortphonon lifetimes and the finite temperature of the chosen structure. TheLVDOS-EMD method assumes that all available states are filled, so struc-tures with significantly different VDOS may have higher error.0 5 10 1500. (THz)Normalized DOSDynamical MatrixVAF 5x5 NotchedVAF 7x7 StraightFigure 2.8: The vibrational density of states calculated using VAF for a2.7 nm (5 unit cells) diameter silicon nanowire notched every two unit cellsand a 3.8 nm straight nanowire, and the total phonon density of states calcu-lated using a dynamical matrix for a similar 〈001〉 periodic 2.7 nm diameterstraight nanowire.342.1. LVDOS-EMD2.1.2.3 Lattice Dynamics Group VelocityThe group velocity can be calculated using the dispersion relation directly[126],vg(q,m) =δω(q,m)δq, (2.37)or using the dynamical matrix,vg,i(q,m) =12ω(q,m)[e†(q,m)δD(q)δqie(q,m)], (2.38)where e†(q,m) is the transpose conjugate of e(q,m).Both methods were used and with the exception of near the gamma pointof the material where the second method yielded an erroneously high groupvelocity, the results were interchangeable. Group velocity was calculated forstraight and notched structures, as shown in Figure 2.9. The results for thevarious structures examined are very similar, which is necessary for LVDOS-EMD as group velocity cannot be easily calculated directly from MD results.The group velocity does vary significantly across the vibrational spectrum,which can cause error in the LVDOS-EMD calculation if vg is taken to aconstant independent of vibrational frequency as shown in (2.3), but pro-vided that the structural changes in material equally affect the MFP for allfrequencies, the error is less than 5%. Nanostructured systems designed toaffect the vibrational mean free path differently depending on the waveletfrequency should use a frequency-dependent vg(ω). It can be calculated fora similar, simpler unit cell to determine the spectral weighting of the veloc-ity, which can then be applied as part of the frequency integration in (2.3). Normal Mode DecompositionThis section follows the derivation of normal mode decomposition discussedby McGaughey and Larkin[126]. Normal mode decomposition combinesatom displacements and velocities from molecular dynamics results with theeigenvector normal modes determined through lattice dynamics. By over-laying normal modes onto MD results and studying energy dispersion overtime using an autocorrelation function, it is possible to approximate phononlifetimes for all modes. Although phonons are non-localized within a struc-ture, combining the lifetime with group velocity from lattice dynamics can352.1. LVDOS-EMD0 5 10 15 20−1500−1000−5000500100015002000Frequency (THz)Group Velocity (m/s)5x5 Notched7x7 Straight5x5 StraightFigure 2.9: The k-averaged group velocity calculated from lattice dispersionfor a 2.7 nm (5 unit cells) silicon nanowire notched every two unit cells, a2.7 nm (5 unit cells) straight nanowire, and a 3.8 nm (7 unit cells) straightnanowire periodic along the 〈001〉 plane.produce a hypothetical mean free path that can be compared with LVDOS-EMD results of the same MD simulation[126]. Atoms from lattice dynamicscalculations and MD calculations were matched using a least squares mini-mization and manual adjustment after simulation.The first step produces the normal mode coordinates and time deriva-tives, b(q,m; t) and b˙(q,m; t), respectively, using MD and lattice dynamicsresults usingb(q,m; t) =∑i,j(MiN)1/2eik·r0(j)e∗i (q,m) · u(j, i; t), (2.39)b˙(q,m; t) =∑i,j(MiN)1/2eik·r0(j)e∗i (q,m) · v(j, i; t), (2.40)where i is an iterator for all atoms, j is an iterator for all unit cells, M isatomic mass, r0(j) is the initial position of the unit cell, and u(j, i; t) is thedisplacement of the atom from its mean average position. With these valuescalculated, the potential energy, U(q,m; t), kinetic energy, T (q,m; t), and362.1. LVDOS-EMDtotal energy, E(q,m; t), can be calculated usingU(q,m; t) =12ω(q,m)2b∗(q,m; t)b(q,m; t), (2.41)T (q,m; t) = b˙∗(q,m; t)b˙(q,m; t), (2.42)E(q,m; t) = U(q,m; t) + T (q,m; t). (2.43)The normalized autocorrelation function of the energy term can then bedetermined for each mode to produce a decaying oscillation that can berelated directly to the phonon mode lifetime, τ(q,m), such that〈E(q,m; t) · E(q,m; 0)〉〈E(q,m; 0) · E(q,m; 0)〉 = e−t/τ(q,m). (2.44)A simplified means establishing a fit for calculating τ involves integratingthe autocorrelation through all time, or until the function decays to zero,τ(q,m) ≈∫ ∞0〈E(q,m; t) · E(q,m; 0)〉〈E(q,m; 0) · E(q,m; 0)〉dt, (2.45)and the mean free path can then be determined usingl(q,m) = |vg(q,m)|τ(q,m). (2.46)NMD was applied to a 2.7 nm (5 unit cells) nanowire notched every twounit cells and the resulting MFP was compared to results from LVDOS-EMD simulations, shown in Figure 2.10. The MFP produced using theNMD composition produces an output of similar magnitude as LVDOS-EMD, particularly in the low frequency, acoustic band region which signif-icantly contributes to material thermal conductivity. Where discrepancyexists, the LDOS of the vibrational frequency is low, increasing the errorof LVDOS-EMD calculations. There is also some discrepancy in the opti-cal phonon spectrum, but this is expected as vibrational occupation in thatband differs between the MD results and lattice dynamics results as dis-cussed in Section Other MFP calculations performed for straight,silicon nanowires using LVDOS-EMD, shown in Figure 2.11 produced shapesmore consistent with the NMD MFP shown in Figure 2.10.372.1. LVDOS-EMD0 5 10 1500.511.522.5Frequency (THz)Mean Free Path (nm)Normal ModeDecomposition LDOS-EMDFigure 2.10: The vibrational wavelet mean free path calculated usingLVDOS-EMD of a 2.7 nm (5 unit cells) silicon nanowire notched every twounit cells is shown and compared with the phonon mean free path of anidentical structure calculated using normal mode decomposition. LVDOS of Straight SegmentsLVDOS-EMD involves collecting velocity data over a long period in timewhere vibrations travel throughout the structure potentially impacting theLVDOS of each segment. In an idealized, large, periodic material lacking anynanostructuring, one would expect little or no variation between adjacentslices which would be interpreted by LVDOS-EMD as a system with nocollisions. In this section, the impact of sampling window size on the resultsare considered, as are the variations in LVDOS over time.In an ideal, conceptual, isotropic material lacking any nanostructuralfeatures, summing LVDOS segments over multiple time samples would re-duce the variability between segment totals to produce an LVDOS that isessentially identical for every segment. One might also expect this behaviourin a straight nanowire, however this is expected to lead LVDOS-EMD to pro-duce an MFP bounded only by the structure’s simulation length rather thanphonon collision behaviour. However, simulations of multiple nanowires indifferent configurations and widths have yielded reasonable MFPs consistentover multiple simulations with different starting conditions. The MFPs alsoscale with nanowire diameter, as shown in Figure 2.11.The behaviour observed in simulated, straight nanowires that explains382.1. LVDOS-EMD1.5 2 2.5 3 3.5 4 4.5 5012345Magnitude (nm)Nanowire Width (nm)  Mean MFPSpectral Standard DeviationFigure 2.11: MFP calculated using LVDOS-EMD for straight, siliconnanowires from 1.6 nm to 4.9 nm in width. The MFP displayed representsthe mean average and standard deviation of all calculated spectral compo-nents from 0 - 25 THz for each width.the success of the algorithm is the formation and temporary persistenceof localized regions of high and low vibrational activity. Throughout eachstructure tested, regardless of nanostructuring, LVDOS varied slowly in eachsegment, providing variations that could be used normally by the LVDOS-EMD algorithm to approximate a finite MFP. Examples of these regionalvariations can be seen in Figure 2.2 and Figure 2.14 as changes in colouralong the nanowire in each band. Careful analysis of the behaviour of theseregions have shown that they can persist for over 50 ps, which is sufficientlylong to apply the LVDOS-EMD algorithm and approximate an appropriateMFP. This was studied in more detail by examining the MFP sensitivity tovariations in acquisition window time and atomic velocity initial conditions. LVDOS Sampling Window SizeLVDOS-EMD requires that simulations of all structures demonstrate thatcalculated LVDOS magnitude varies linearly as a function of FFT windowsize. A linear correspondence indicates that the underlying wavelet density isnot changing over the measurement window. Any change in wavelet densityrelative to neighbouring segments over the measurement window will causeerror in the approximation as a constant underlying structure with static392.1. LVDOS-EMDwavelet densities over the period of measurement is a requirement of themethodology. The velocity autocorrelation method does not provide aninstantaneous measurement of phonon density. Longer time window periodsare desired to reduce FFT windowing effects and improve spatial resolution.A consequence of using longer periods is that wavelets travel throughout thenanostructure during the sampling period, potentially causing blurring anddouble counting between adjacent segments. To verify that the LVDOS isreasonably unchanged over the 25 ps FFT windows size, the coefficient ofdetermination was calculated for each frequency band[139],Rs(ω)2 = 1−∑w (Ds,w(ω)− fs,w(ω))2∑w (Ds,w(ω)−Ds(ω))2, (2.47)where w represents the time window width (varied from 1-25 ps) used for allcalculations, f is the regression linear fit, and Ds(ω) is the mean average ofthe LVDOS across all windows. Figure 2.12 shows high linearity of LVDOScalculations over a large time window size in regions of high occupation.This correlation indicates that despite high phonon velocity, regions of highand low density persist for the majority of the chosen time window. The co-efficient of determination is smaller in bordering frequency bands with loweroverall occupation as survivability and density are both small enough toprevent the formation of temporary, localized scattering regions. Similarly,thinner diameter nanowires exhibit poorer performance for this same rea-son. The high correlation in linearity of LVDOS of notched and unnotchednanowires, as evidenced in Figure 2.12, are consistent with the expectationof the Monte Carlo simulation shown in Figure 2.8, and its correspondingsurvivability equation, for both pristine and nanostructured simulations.The proposed methodology works well in equilibrium scenarios whereregions of collisions do not change in time, and the LVDOS does not varysignificantly throughout the window of observation. These conditions shouldapply in the majority of solid, nanostructured materials. Satisfactory datasets from MD modelling results can be identified by observing a linear in-crease in the standard deviation of the LVDOS as a function of time windowsize, and an MFP mean that converges with increasing time window size.A comparison of the calculated MFP of a straight and notched 4.9 nmdiameter silicon nanowire is shown in Figure 2.13. The greater variationbetween trials of the straight nanowire demonstrates the lower precisionin estimating the mean free path of a material with negligible structuralvariation. The mean free path of the straight nanowire is significantly longerthan that of the notched equivalent, and both have MFPs on the same402.1. LVDOS-EMDFigure 2.12: Studies using the MD results of simulations based on 3.8 nm(top), 2.7 nm straight and notched (middle), and 1.6 nm (bottom) siliconnanowires. a) Average frequency-dependent LVDOS, and b) coefficient ofdetermination showing how well the spatially-averaged LVDOS for each seg-ment increases linearly with FFT time window size.412.1. LVDOS-EMDorder as the thickness of the nanowire, which is expected due to boundaryscattering on the surface of the nanowire. Multiple simulations of the samenanowire with different atom starting velocities also yielded similar results,showing that the MFP is not dependent on phonon initial conditions foridentical simulation procedures.This method is most effective when the structure presents regions of sig-nificant scattering into otherwise unoccupied bands. Large structures thatpresent very little variation in scattering rates along the direction of mea-surement will typically have scattering underestimated as phonons move be-tween already occupied bands. It is also important to ensure that segmentsare small enough to capture shifts in VDOS caused by wavelet generationor scattering, and that the structure is symmetric around the axis of mea-surement. Standing waves and direct phonon exchanges between bands areneglected in this estimation as the former do not contribute significantly tothermal transport within the model and the latter would require the iden-tification and tracking of individual phonons which would greatly increasecomputational cost.Figure 2.13: Comparison of MFP calculation of a straight (top) and a rough-ened/notched (bottom) silicon nanowire 4.9 nm diameter. The roughenednanowire has 1.6 nm deep, 0.54 nm diameter notches every 5.4 nm along thelength of the nanowire. The straight nanowire is shown as a mean aver-age (black line) of four simulations with different starting conditions (greyoverlay).422.1. LVDOS-EMDThe computational simplicity of this method drastically reduces bothcomputation time and memory requirements. Only 104 simulation steps arenecessary to calculate the VAF to sufficient resolution for LVDOS-EMD,and it can be calculated for each slice independently, allowing very largestructures to be separated during simulation and formed into segments be-fore a mean free path calculation takes place. This removes the need to storeall atom velocities and positions in memory concurrently, further reducingcomputation requirements for analyzing large structures.2.1.3 Methodology and Performance on SiliconNanostructuresResults using LVDOS are compared with full MD results before (LVDOS-EMD) and after (LVDOS-NEMD) Mueller-Plathe simulation results for avariety of silicon nanostructured wires. LVDOS-EMD uses atom velocity(z-axis, or 〈001〉, only) and position data (z-axis, or 〈001〉, only) collectedafter completion of the aforementioned Mueller-Plathe simulation. LVDOS-EMD data is collected after relaxation over 25,000 iterations of velocity andposition data acquisition. The highest occupied vibrational states are below20 THz, allowing position and velocity data exports at 20 fs intervals withoutsignificant aliasing effects. A comparison of the LVDOS of each technique forboth thin and thick nanowires is shown in Figure 2.14. The greater phonondensity is visible in the thicker nanowire, resulting in a smoother LVDOSalong the length of the nanowire and corresponding increase in mean freepath. Results from EMD and NEMD data sets are shown to emphasize thatthey are similar, meaning that the LVDOS-EMD method can be expectedto yield similar results with and without a temperature gradient.The nanowires were simulated at a time step of 1 fs and a length of217 nm (400 unit cells) to ensure that all phonon frequencies and wavelengthsrelevant to thermal conductivity were included. The chosen time step issimilar to that used by others, although a slightly longer step size was chosento reduce computational requirements with the understanding that directcomparisons to experimental results cannot be made[101, 111, 122]. Tofurther save memory and reduce computation time, a full length, 4.9 nmdiameter nanowire was simulated, segmented, and analysed to determinethe minimum necessary export structure size and running time.A straight, 217 nm nanowire was simulated with the velocity data of allatoms exported. The simulation data was truncated in post-processing todetermine that a running time of 25 ps and an 81 nm segment of the structurewould be sufficient for the LVDOS analysis. The impact of nanowire length432.1. LVDOS-EMDFigure 2.14: LVDOS profile for k = 4.9 nm (a,b) and k = 1.6 nm (c,d) siliconnanowires generated from EMD (a,b) or NEMD (c,d) simulations.and simulation time on the LVDOS-EMD technique is shown in Figure 2.15.Export segment lengths of 80 nm and a running time of 25 ps were selectedfor these simulations. The variation in conductivity as a function of structurelength is due to the minimum structural length required to ensure that theMFP is fully computed. Simulations of shorter, periodic structures can alsobe used, but the LVDOS-EMD algorithm must continue to operate throughperiodic boundary conditions to ensure that longer duration phonons arerepresented within the calculation.Figure 2.16 shows the normalized thermal conductance of nanowires invarious configurations using four different computational methods. TheMueller-Plathe method involved first relaxing the structure for 75,000 it-erations, followed by 1,000,000 iterations of developing the thermal gradi-ent along the structure, and 200,000 iterations to collect spatial tempera-ture information under equilibrium conditions. The internal Mueller-Plathe442.1. LVDOS-EMDFigure 2.15: Thermal conductance using LVDOS-EMD as a function ofexported silicon nanowire a) length data and b) time data based on 4.9 nmnanowires. Time data is normalized by calculated thermal conductance at1 ps for each nanowire.452.1. LVDOS-EMDLAMMPS module was used with a swap configured every 500 simulationsteps and the nanowire sliced into 20 segments[121, 140]. An example scriptis shown in Appendix F.While developing the gradient, a weak Berendsen thermostat was used tomaintain an average temperature near 300 K [141]. Velocity data from atomsin a 80 nm long segment over a 25 ps span was collected after equilibriation(LVDOS-EMD) and at the end of the simulation (LVDOS-NEMD). A single,straight silicon structure was sliced equally into segments 0.1 nm to 10 nmthick to determine the optimum slicing thickness, 0.135 nm, that yielded theleast deviation in number of atoms per slice, assuming a minimum of 50atoms/slice, over the entire structure. The same slicing thickness was thenused for all structures. The VAF for each atom was calculated and summedfor all the atoms in each segment (slice) to determine the LVDOS along thenanostructure. Finally, the MFP and thermal conductivity were calculatedas described in Section 2.1.1. Of the four methods shown, the direct Mueller-Plathe method is considered to be the most accurate NEMD-based methodfor silicon[107].Computations were also performed using vg(ω) with results within 1% ofcomputations performed using a frequency-invariant group velocity. Resultsassuming that vibrations only travel in one direction were also computed,using (2.16)-(2.17) instead of (2.25)-(2.28) to calculate MFP, yielding valueswithin 1% of one another. The more comprehensive, bidirectional set ofequations acts as a rolling average of the survival calculation. For simplerstructures where the width of the segment is significantly smaller than anynanostructural features, equations (2.16)-(2.17) act as a reasonable approx-imation.Molecular dynamics methods are particularly useful when studyingstructures with nanoscale features. To illustrate the utility of LVDOS-EMDover a modified bulk heat transfer model, Comsol Multiphysics R©, a finiteelement analysis (FEA) solver, was used. Equivalent, ideal structures ofnotched silicon nanowires were constructed within Comsol where Mueller-Plathe MD simulation results for straight nanowires were used to providethe thermal conductivity of nanowire segments of various cross-sectional ar-eas. An example of one such model is shown in Figure 2.17. Boundaryconditions of 300 K and 400 K were set at opposite ends of the nanowire,and thermal flux was measured near the centre of the nanowire to calculatethermal conductivity.Normalized FEA thermal conductance shows large errors compared tothe MD-based techniques for thin, notched nanowires (Figure 2.16b/d). Theerror is likely due to enhanced phonon boundary scattering caused by the462.1. LVDOS-EMDFigure 2.16: Normalized thermal conductance of silicon nanowires by a)variable nanowire thickness of smooth nanowires, b) variable notch depthfor k = 4.89 nm, p = 5.43 nm, w = 0.543 nm, c) variable notch period fork = 2.72 nm, D = 0.543 nm, w = 0.543 nm, and d) variable notch width fork = 3.80 nm, D = 0.543 nm, p = 5.43 nm. Calculated thermal conductanceis normalized to a) a 3.26 nm thick straight nanowire, b-d) an unnotchednanowire of similar thickness. The error bars show the variation in Mueller-Plathe simulation results for thermal conductivity.morphology of the nanowire, which would not be considered within a bulkcontinuum simulation, even if it is provided information on thermal con-ductivity as a function of material cross-sectional area [92]. The enhancedscattering further reduces mean free path and the corresponding materialthermal conductivities, although this behaviour can only be observed inatomistic scale models that incorporate the wave properties of phonons.LVDOS-EMD does capture some of these behavioural features, providinga more accurate calculation for thermal conductance. Errors could also bethe result of variations in nanowire structure after molecular relaxation whencompared to the ideal shape programmed within Comsol.LVDOS-EMD and LVDOS-NEMD show similar normalized thermal con-472.1. LVDOS-EMDFigure 2.17: Comsol model of a notched nanowire where each segment isdesignated a thermal conductivity from Mueller-Plathe results of straightnanowires of identical thickness.ductance results, with small variations due to changes in mean free pathand density of states resulting from the NEMD temperature gradient. TheNEMD method also involves a much longer running time, allowing phononsadditional time to stabilize. Compared to the FEA method, the LVDOS-EMD and LVDOS-NEMD methods more closely capture changes in ther-mal conductance resulting from phonon boundary scattering and reducedMFP, however both methods still deviate from Mueller-Plathe results as thenanowires increase in diameter. This deviation is likely due to a change ingroup velocity as the nanowires begin to develop bulk conductance proper-ties.The mean absolute error between the LVDOS-EMD method and Mueller-Plathe results is 12%, with the error of the unnotched nanowires contributingmore significantly. To minimize this error, a reference nanowire with dimen-sions similar to the configurations under consideration should be selected.The time required to calculate all configurations using Mueller-Plathe, in-cluding the relaxation of the structure was 845 cpu days. The time requiredfor the LVDOS-EMD method was 50 cpu days, for a reduction in simulationtime of 17 fold. Eighty percent of the running time of the LVDOS-EMDsimulations was structural relaxation, meaning that further improvementsin algorithm performance are possible. Neglecting relaxation, LVDOS-EMDrequires 40× fewer simulation steps per structure.482.2. Zinc Oxide Nanostructures2.1.4 Discussion of ValidationThe LVDOS-EMD method proposed and demonstrated herein showspromise as a rapid computational methodology for exploring variations inthermal conductivity in similar structures, but there are significant limita-tions guiding the potential applications of the methodology. Only nanoscalematerials with surface/structure phonon scattering as the dominant scat-tering mechanism and with small variations in structure at identical tem-peratures can be rapidly investigated. The calculation of wavelet mean freepath is an approximation and thus more rigorous EMD and NEMD meth-ods must be used to confirm observed material behaviours. Structures withcomplex configurations internal to the nanowire, or features that reduce thenumber of atoms per segment to less than 50, may also reduce the accuracyof the methodology.Despite these shortcomings, LVDOS-EMD presents several opportuni-ties. By studying the thermal conductivity of a material through its meanfree path and LVDOS, phononic wave effects which might be ignored bycontinuum or FEA models can be included. LVDOS-EMD enables a pre-dominantly qualitative comparative study of thermal conductance effects ofsmall structural changes with MD simulations in less than 6% the durationof other NEMD and EMD methods when including molecular relaxation,and less than 0.1% if relaxation is not included. It can also function on verylarge structures by performing calculations on independent subsections priorto final post-processing, thereby reducing memory requirements. Althoughthe assumption of consistent group velocity between simulations does limitthe potential accuracy of the method, the dynamical matrix of the systemneed not be solved. If group velocity information is generated as part ofthe simulation then the information can be included in the calculations toproduce more accurate results for varied structures. Further work on morecomplex structures must be done to determine the accuracy of the method-ology over a wide range of temperatures, material systems, and structuralconfigurations.2.2 Zinc Oxide NanostructuresZnO as a material system has very different properties than silicon, andit is therefore necessary to run simulations using the ZnO material systemto explore Al:ZnO nanostructures with amenable thermoelectric properties.The basic structure of ZnO used for these molecular dynamics simulationswas nanowires as shown in Figure 2.18. For bulk simulations, a fully periodic492.2. Zinc Oxide Nanostructuressupercell either 5× 5 unit cells in size or 8× 8 unit cells in size was used.Figure 2.18: The 5 × 5 unit cell (5 unit cells along the long, outside edge)ZnO nanowire configuration used for MD simulations is shown. Red atomsare zinc and grey atoms are oxygen. The image is rendered using VMD[49].The overarching motivation of simulating ZnO nanostructures was toexamine the comparative thermal properties of various nanostructures andassess their relative thermoelectric performance. Computational limitationsnecessitated performing simulations on structures that could not be exper-imentally synthesized due to their small size or poor stability. This sectionpresents an analytical framework that can be applied to larger structures toderive more meaningful, quantifiable results to better guide thermoelectricresearch, but, as presented, certain limitations in the modelling approachmust be elucidated.• The heavily ionic composition of ZnO places additional computa-tional constraints on modelling the material as discussed in Sec-tion 2.2.1. The corresponding additional computational requirementsfurther limit the length and width modelled structures when comparedto silicon. Structures presented in this section typically required 7 daysto compute data sets suitable for Mueller-Plathe using 128 CPU cores.• The small size of the nanostructures herein examined can provide someinsight into larger, bulk materials. Extrapolating small structures intobulk materials using the Matthiessen Law is discussed in Section Zinc Oxide NanostructuresTable 2.1: MD NEMD results for simulations of 8× 8× 200 unit cell, fullyperiodic ZnO bulk simulations showing relaxation lattice constants and cal-culated thermal conductivity for three different force field models.Force Field a (A˚) c (A˚) κ (W m−1 K−1)Wolf 3.18 5.02 29.4Pedone 3.08 5.27 34.1ReaxFF 3.29 5.32 15.0Experimental[47] 3.25 5.21 37− 147Ab Initio[144] N/A N/A 62Extrapolation assumes that the structure is possible to synthesize asa bulk material without changing feature size, which is not a reason-able assumption for the proposed electrochemical method. Therefore,although MD results were used to inform experimental work, a directcomparison between modelled and experimentally grown structurescannot be drawn.• A proper examination of the improvement of the thermoelectric prop-erties of a material due to nanostructuring requires considering theimpact of structures on thermal and electronic material parameters.Electronic modelling of ZnO is also computationally intensive due tothe involvement of core electrons in Zn-O bonding behaviour. Classicalconsideration of electronic behaviour is discussed in Section 2.2.3, butneglecting quantum effects adds substantial error to structures withfeatures on the order of angstroms.2.2.1 Molecular Dynamics Simulation of ZnOMultiple force field models were considered and tested for their accuracyand speed in simulating the thermal and structural properties of ZnO. Thechoice of force field was constrained by the the strongly ionic and binarynature of the crystal. The force field had to provide accurate modellingof phonon propagation for thermal conductivity calculations, accommodateinteractions with other elements, and support molecular rearranging suchas those resulting from thermal annealing. Three ZnO force field models,Wolf[129], Pedone[128], and ReaxFF[109, 130, 142, 143] were examined. Thelattice constants and bulk thermal conductivity calculated by relaxing iden-tical ZnO nanowires until thermal equilibrium using the corresponding forcefield, followed by a NEMD measurement are summarized in Table 2.1.512.2. Zinc Oxide NanostructuresAlthough Wolf and Pedone force fields both operated up to 5× fasterthan ReaxFF, ReaxFF produced lattice constants closer to the experimentalvalues of ZnO and also afforded the ability to examine changes in chemicalbonding between systems of mixed material systems such as heterostruc-tures. For these reasons, and the demonstrated accuracy of ReaxFF in ther-mal conductivity calculations of ZnO, ReaxFF was selected[130]. ReaxFFis a model based on ab initio calculations of potentials and charges betweentwo atoms, and includes off-diagonal terms, torsions, angles, and forces be-tween all combinations of atom and bonds. The set of coefficients selectedincluded interactions between zinc, oxygen, and hydrogen. The hydrogencoefficients were not generally used for the simulations performed herein,but were used for special cases where the behaviours of zinc and ZnO inwater were explored.There is a significant error between bulk thermal conductivity of simu-lated ZnO and experimental ZnO in Table 2.1. Simulating the bulk usingMueller-Plathe can be constrained by the inability of the system to accom-modate the wavelengths and full mean free path of the phonons[101, 145].A method to derive the thermal conductivity despite this limitation is tosimulate the same structure under identical conditions at different lengthsand then plot the inverse thermal conductivity against the inverse structurelength. The resulting plot should be linear and the y-axis intercept can beused to extrapolate the thermal conductivity of a simulated structure of in-finite length[101]. Figure 2.19 shows the results of this test using ReaxFFon ZnO which provides a thermal conductivity of 55± 15 W m−1 K−1, com-paring favourably with other modelled thermal conductivity estimations of62 W m−1 K−1[144].The simulation was performed with a 8 × 8 × 300 unit cell parallelo-gram prism nanowire of ZnO oriented along 〈002〉 with triclinic, periodicboundary conditions using a 0.5 fs time step, 500,000 NPT relaxation steps,and 2,600,000 Mueller-Plathe steps using NVE conditions. The large degreeof scattering around the linear fit in the plot is likely due to inconsistentadditional contributions to thermal conductivity by new phonons of longerwavelength. The MFP of phonons in ZnO can also exceed the length of thesimulation cell. Based on the thermal conductivity calculations at shorterlengths, a simulation over 1 µm in length would be necessary to properlycalculate the thermal conductivity of bulk ZnO. Full simulation details canbe found in Appendix F.3.Although another method, such as Green-Kubo, could be used to cal-culate the thermal conductivity of the bulk material and nanostructures,Green-Kubo does not perform very well with structurally complex materials522.2. Zinc Oxide Nanostructuresy = 6.711x + 0.018300. 0.007 0.012 0.017 0.022Inverse Thermal Conductivity(Km/W)1/L (1/unit cells)Figure 2.19: A plot of inverse, simulated, bulk ZnO thermal conductivityusing Mueller-Plathe against inverse simulation cell length. The lengthssimulated range from 50 unit cells (26 nm) to 300 unit cells (156 nm). Twothermal conductivities were calculated per length with the results beingaveraged. Uncertainty at each length is within 0.5 W m−1 K.and may not converge[119, 120]. Green-Kubo is also typically performed onsmaller supercells and would require significant computational resources tomodel nanostructured materials with long sections of aperiodic features dueto the need to average multiple simulations[107, 119].Simulation time steps of 0.25 fs, 0.5 fs, and 1.0 fs were tested on 5×5×200unit cell nanowires using ReaxFF. There was not a significant difference inthermal conductivity results between simulations operating at 0.25 fs and0.5 fs, however simulations operating at 1.0 fs yielded a thermal conductivitysignificantly higher, demonstrating poor suitability. As simulations usingReaxFF are very computationally intensive, a time step of 0.5 fs was chosen.Using NEMD to determine the thermal conductivity of a single 5× 5× 200unit cell nanowire required 6 days and 50 GB of memory when using 128cores.532.2. Zinc Oxide Nanostructures2.2.2 Extrapolating from Nanostructures to BulkDue to the computational resources required to examine nanowires andnanostructures on size scales congruent with experimental work, a 5×5×200unit cell nanowire aligned along the z-axis was chosen for all nanostructuralsimulations. By using a nanowire with a highly constraining diameter, theMFP of phonons was necessarily less than the length of the simulated struc-ture, allowing thermal conductivities to be calculated without the need touse multiple length steps and extrapolation. A consequence of this effectis that any thermal reduction resulting from the examined nanostructuralfeatures will be influenced by the surface scattering effects of the nanowire.A method to compensate for this effect involves the Matthiessen rule,1τ=1τboundary+1τdefects+1τfeature+ ..., (2.48)where τ is the phonon lifetime, which is proportional to the mean free path.The Matthiessen rule indicates that the influence of each nanostructuralfeature on the overall MFP of the system can be expressed as an inversesummation of the individual mean free paths. While the surface effects of thenanowire will play a significant role in the reduction of thermal conductivity,assuming this effect is the same for each simulation, any further reductionin mean free path is attributable to the effects of additional nanostructuringimposed on the material. To leverage this consistency, identical startingnanowires are used in all simulations and no comparisons are made withbulk materials.2.2.3 Electronic ModellingConcurrently with phononic studies, electron transport studies were alsoperformed to determine if examined structures maintained a high electricalconductivity and Seebeck coefficient. The Seebeck coefficient is predom-inantly a function of material bandgap and Fermi energy, meaning thatstructural changes, provided their effects remain classical in the electronicdomain, should not have a significant effect[16]. In both classical and quan-tum models, electrical conductivity is strongly affected by changes in mate-rial structure.Rigorous quantum calculation of electron transport was explored in de-tail with results discussed briefly in Appendix A.1. For pragmatic reasonsowing to the simulation time required for quantum electronic simulation ofZnO, a classical approximation for modelling electronic behaviour in the542.2. Zinc Oxide Nanostructuresexamined nanostructures was selected. In this approach, the nanowire wassegmented along the z-axis into thin slices of atoms. These slices wereeach superimposed on a dense grid of squares to determine the effectivecross-sectional area defined by atoms within the slice. The slices were thenassigned effective resistance based on their area and were summed in seriesto produce an effective resistance for the entire wire. This method allowedthe accommodation of very large structures with high densities of localized,random defects dispersed throughout. Atoms were assigned point volumesand lines were drawn between originating atoms and 10 nearest neighboursto improve coverage on the area map. The number of nearest neighbourswas selected to maximize the discernment between occupied and unoccupiedregions in the structure. All area calculations were performed on structuresafter molecular dynamics simulations in order to incorporate any twisting,distortion, and other irregularities in the structures resulting from the struc-tural modifications. An example of a slice examined for atomic occupationis shown in Figure 2.20.−15 −10 −5 0 5 10 15 20−10−505101520x-axis Position (Å)y-axis Position (Å)Figure 2.20: Cross-sectional slice of a hexagonal nanowire consisting of ir-regular voids showing the grid of squares used to determine occupation forarea calculations. Points representing the atoms were first overlayed ontothe grid squares and then lines were drawn between nearest and next nearestneighbours to fill in the space between atoms.552.2. Zinc Oxide NanostructuresThe nature of the approximation neglects quantum effects such as con-finement, tunneling, and conduction limits imposed by the Pauli exclusionprinciple in very narrow segments of the nanowires. Given the scale of thestructures under consideration, the classical model overestimates the con-ductivity of the structures considered herein. Although quantum tunnelingmay offset some of the conductivity losses due to confinement and electronband availability, its effect is comparatively small. Other effects such asreduced electronic mean free path in some structures will also further limitelectron transport, where electronic MFP is 5 A˚ - 50 A˚[146]. The classicalmodel employed applies the same rules to all structures and uses normalizedresults based on a straight nanowire to better reflect the restricted predictivecapabilities of this model.2.2.4 Structural Thermoelectric Enhancement FactorA new term, the Structural Thermoelectric Enhancement Factor (STEF),ξ, of the nanostructure is defined asξ =AKlatticeξref. (2.49)STEF is a performance metric representing the ratio of effective cross-sectional area (see Section 2.2.3) to thermal conductance for structures ofidentical length. The normalization term, ξref , is determined using a ref-erence material with no nanostructural modifications, a straight nanowirein this work. It is conceptually similar to comparing the thermal resistivityfor structures of equal length, but differs in that it represents a materialwith a cross-sectional area that varies throughout its length rather than theperiodic, uniform structure used for conventional thermal resistivity. Whenused to compare similar structures, it indicates how effectively modifica-tions to the structure reduce thermal conductivity relative to the reductionin classical electronic conductivity.2.2.5 Intrastructural LVDOS-EMDOne limitation of the LVDOS-EMD method as presented in Section 2.1 isthat it assumes no structural variation along the x-y plane of the nanos-tructure. This assumption is safe if the nanostructural features are predom-inantly on the outer edges of the nanowire, but in some structures wherethe features appear randomly throughout the bulk in high densities, such asin nanowires with random voids, characteristics of the phonon interaction562.2. Zinc Oxide Nanostructuresimmediately around these structures may be lost. To accommodate for thiseffect, an intrastructural LVDOS-EMD method was developed that breaksapart each structure after simulation into extremely thin nanowires less than1 nm×1 nm in cross-sectional area that span the length of the original struc-ture. LVDOS-EMD was employed on each thin nanowire, yielding multipleparallel thermal conductance calculations for each nanostructure. In orderto maintain the minimum requisite number of atoms in each segment, thesegment length along the z-axis had to be increased. Another restriction isthat wavelets travelling in a diagonal direction are not as accurately repre-sented; the assumption is made that wavelets travel nearly parallel to thez-axis. A fully 3D Monte Carlo method with random pathing throughoutthe structure was considered to improve accuracy, but the computationalcost overcomes the benefit the LVDOS-EMD methodology.A further enhancement to the original theory is to render the full struc-ture periodic along the z-axis and vary the starting position for the MFPcalculation along its entire length. If the nanostructural effects are not con-sistently periodic along the z-axis over short distances, calculating the MFPonly once at the origin can trivialize structural features located further alongthe nanowire. By calculating a new MFP at several points along the wireand producing an MFP as a function of z-axis origin, structures with lessperiodicity were better represented.By combining the two above enhancements, the intrastructural LVDOS-EMD methodology produced a matrix of thermal conductances with originsthroughout the x, y, z volumetric space of the simulated nanowire. To yield afinal thermal conductance, individual thermal conductances calculated withthe same z-axis origin were summed. The resulting conductance, which isonly a function of starting position along the z-axis, was then reduced to afinal conductance using an inverse sum. The performance and limitationsof this methodology are explored in the following sections.2.2.6 Straight NanowiresA straight, hexagonal ZnO nanowire was simulated to act as a reference forother structures studied in this section. The longer edge of the nanowirein the x-y plane is 16.05 A˚ long, and the nanowire is 1060 A˚ long along thez-axis prior to relaxation. The cross-sectional area of the nanowire priorto simulation is 6.73× 10−18 m2. A segment of the nanowire can be seenin Figure 2.18. The simulations were performed using the LAMMPS MDsimulation engine over approximately three million iterations[147] at a timestep of 0.5 fs. NPT/NVE equilibriation took place over 200,000 iterations572.2. Zinc Oxide Nanostructureswith the Mueller-Plathe swapping process occurring over 2,600,000 itera-tions. Detailed scripts showing all simulation parameters can be found inAppendix F.Length-wise cutaways through the centres of the nanowires are shownin Figure 2.21. The relaxation of the straight nanowire involved small vari-ations in the total length of the simulation box, resulting in a slight defor-mation of the nanowire along the z-axis. A periodic boundary condition isassumed along the z-axis and no stress was applied to the wire. The Mueller-Plathe methodology was discussed in Section 2.1. The thermal conductiv-ity of the straight nanowire resulting from the reverse NEMD simulationswas 4.4± 0.4 W m−1 K−1, representing a 12.5× reduction in lattice thermalconductivity compared to the simulated bulk material. The LVDOS plot,shown in Figure 2.22, shows three major optical phonon bands and one ma-jor acoustic phonon band. The optical and acoustic phonon bands are wellseparated and contained few variations in phonon DOS along the length ofthe wire, which indicates that, with the exception of surface scattering ef-fects, there are no major nanostructural influences on phonon propagation.The effective cross-sectional area after relaxation calculated by summing themeasured area of all slices, as discussed in Section 2.2.3, is 501 A˚2.582.2.ZincOxideNanostructures0 100 200 300 400 500 600 700 800 900 1000-200200 100 200 300 400 500 600 700 800 900 1000-200200 100 200 300 400 500 600 700 800 900 1000-200200 100 200 300 400 500 600 700 800 900 1000-200200 100 200 300 400 500 600 700 800 900 1000-20020z-axis Position (Å)y-axis Position (Å)StraightHollowHeterostructuredVoidedHCP VoidedFigure 2.21: The cross-section of a variety of ZnO nanostructured materials post simulation. Red dots are zincatoms and blue dots are oxygen atoms.592.2. Zinc Oxide NanostructuresFrequency (THz)Slice (0.265 nm)  100 200 300010203040Occupation (arb)2468101214Figure 2.22: An image showing the LVDOS of a straight, 104 nm long, 5× 5unit cell, hexagonal ZnO nanowire oriented along the z-axis.2.2.7 Hollow NanowiresHollow nanowires or nanotubes are shaped as an extruded ring of ZnO. Byreducing the size of the material as with straight nanowires, a reductionin lattice thermal conductivity can be realized. This reduction is due toanharmonic scattering of phonons against the surfaces of the nanowire. Byremoving the core of the nanowire, the scattering mechanism can be en-hanced by offering another boundary against which to scatter. A cutawayof a hollow nanowire is shown in Figure 2.21. Removing the core of thenanowire reduces its structural strength and affects the lattice constantsthroughout the material by adding dangling bonds at the new surface. TheLVDOS of phonons within the hollow wire, shown in Figure 2.23, indicateslower band availability for phonon occupation due, in part, to the reducedcross-sectional area of the nanowire. The brighter bands that were partic-ularly visible in the LVDOS of the straight nanowire have also disappearedindicating that harmonic bands are less clearly defined. This reduced defi-nition is likely the result of greater variation in lattice spacing.602.2. Zinc Oxide NanostructuresFrequency (THz)Slice (0.265 nm)  100 200 30005101520Occupation (arb)2468101214Figure 2.23: An image showing the LVDOS of a hollow, 104 nm long, 5× 5unit cell, hexagonal ZnO nanowire oriented along the z-axis.The performance of the structure can be seen in Figure 2.24. As theradius of the etch through the centre of the nanowire increases, the effec-tive area for electron transport through the nanowire decreases. Etchingthe nanowire beyond a radius of 5 A˚ caused the nanowire to collapse duringsimulation. Despite this limitation, it is clear from the data collected thathollow nanowires do have a lower thermal conductivity than filled nanowires,however the reduction in cross-sectional area for electron transport withinthe bulk of the nanowire offsets any gains caused by reduced phonon trans-port.Large, hollow nanowires with walls nanometres in thickness are suc-cessfully fabricated at much larger diameters using a variety of single andmultistep processes, including electrodeposition[40]. The thermal proper-ties of hollow ZnO nanowires have not been experimentally measured andcompared to their bulk equivalents. Although it may be possible to fabri-cate hollow nanowires as modeled herein, such structures have not yet beenexperimentally synthesized.612.2. Zinc Oxide Nanostructures2 3 4 5 5010020030040050000.511.522.533.5Area Thermal ConductivityEtch Radius ( ) ThermalConductivity(W/mK)and(normalized)STEFSTEFÅArea (Å2 )Figure 2.24: A plot showing the effective area, simulated thermal conduc-tivity, and normalized STEF of hollow nanowires as a function of etchingradius.2.2.8 Heterostructured NanowiresHeterostructured materials are composite materials consisting of thin, alter-nating layers of different materials. The heterostructure considered in thisapplication is a superlattice consisting of alternating zinc and ZnO layers. Ifthe deposition process is starved of oxygen by increasing the applied voltageduring electrodeposition, then metallic zinc may be deposited, allowing forthe formation of a zinc/ZnO heterostructured material. Heterostructuressimulated consisted of 2-10 unit cells of each material stacked throughout.Heterostructures with such frequent oscillations between materials are pos-sible to fabricate using vacuum deposition techniques but have not beendemonstrated repeatably using electrochemistry. They are considered tobe excellent candidates for thermoelectric materials as each transition be-tween material systems forms a boundary layer which can interfere withphonon transport. Electronically, using materials of different bandgaps canalso allow for band tailoring, such as creating regular barriers within thestructure to assist with electron energy confinement or blocking the trans-port of lower energy electrons and improving entropic reversibility usingenergy-filtering[50]. Heterostructures are difficult to fabricate as the depo-sition process must cleanly and rapidly cycle between materials. They also622.2. Zinc Oxide Nanostructurestend to demonstrate poor mechanical properties due to lattice mismatchesat each boundary. In the case of zinc and ZnO, the former is a hexagonalclosely packed lattice and the latter is wurtzite, which are not well matchedin lattice shape. The resulting superlattice nanowire is shown in Figure 2.21.The LVDOS of a superlattice with 8 unit cells of ZnO and 8 unit cellsof Zn can be seen in Figure 2.25. The division between materials is veryapparent. The ZnO band contains both significant quantities of optical andacoustic phonons, whereas the zinc metal LVDOS is composed only of acous-tic phonons as zinc metal is monatomic[148]. On closer examination of theoptical bands at the interface, significant crossband scattering is apparentby the very low density of optical phonons in Zn segments of the heterostruc-ture. The asymmetry of the scattering is caused by ZnO presenting wurtzitezinc on the left and wurtzite oxygen on the right of the hexagonal zinc lat-tice. The acoustic band also shows significant differences in occupationbetween zinc and zinc oxide, creating boundaries in the material interfacesthat promote phonon collision. These regular, enhanced scattering regionsat material interfaces greatly reduce thermal conductivity.Frequency (THz)Slice (0.265 nm)  100 200 30005101520Occupation (arb)24681012141618Figure 2.25: An image showing the LVDOS of a superlattice, 104 nm long,5× 5 unit cell, hexagonal ZnO nanowire oriented along the z-axis.632.2. Zinc Oxide NanostructuresTable 2.2: Results of ZnO heterostructure simulations showing effective area,simulated thermal conductivity, and the normalized effect of changing theperiodicity of Zn-ZnO superlattice nanowires for superlattice configurationsinvolving different sizes of zinc and zinc oxide segments.StructureEffectiveArea (A˚2)ThermalConductivity(W m−1 K−1)STEFHeterostructuresZn (8 uc) / ZnO (8 uc) 500 1.87 2.35Zn (4 uc) / ZnO (6 uc) 499 1.1 3.98Zn (6 uc) / ZnO (4 uc) 500 1.13 3.89Zn (4 uc) / ZnO (4 uc) 501 1.04 4.23The results from thermal conductivity simulations are shown in Ta-ble 2.2. Favouring one material over the other in the overall compositionof the nanowire had little effect, however the number of boundaries cre-ated did play a prominent role in reducing the thermal conductivity of thenanowire. One major limitation of fabricating a superlattice nanowire usingzinc is that the low melting point of zinc metal would limit the operation ofthe thermoelectric module to under 400◦C, which is a prohibitive limitationfor a module that would otherwise achieve peak conversion efficiency near1000◦C. Other metals with higher melting temperatures or semiconductingoxides such as aluminum oxide should be considered to complement ZnOin a superlattice configuration. Electron transport across the boundarieswould also be impinged, which is not considered within the electronic trans-port method used herein. As a result, the thermoelectric performance of thematerial is likely to be poorer than what is shown in the table.2.2.9 Nanovoided NanostructuresNanovoids are small, vacant shapes such as spheres within either lower di-mension or bulk material. The voids serve as defects or scattering boundariesfor phonon travel. Voids in a straight, simulated nanowire were producedby first defining a rectangular prism around the nanowire then randomlyselecting (x,y,z) coordinates within the prism. The radius of each sphericalvoid was determined by multiplying a given mean radius by a randomlyselected scaling factor between 0.5 and 1.5. Voids were generated until thetotal volume of spherical voids exceeded the specified ratio of void space tonanowire space. The simulation were carefully studied, with randomization642.2. Zinc Oxide Nanostructuresseeds varied to generate structures capable of maintaining integrity untilthe desired void density was achieved. Void density was constrained by thestability of the nanowire structures. A cutaway of a nanovoided nanowire isshown in Figure 2.21.Using LVDOS to examine the phonon behaviour around voids is moredifficult as the nanowire is asymmetric on every axis. An LVDOS plot thatuses conventional LVDOS described in Section 2.1 is shown in Figure 2.26.The LVDOS is chaotic with many gaps and noisy bands indicative of sig-nificant phonon scattering and lattice interruptions. Regions of particularlyhigh void density cause small gaps in the LVDOS as phonon occupationdiminishes significantly. Additional scattering to the region between opticaland acoustic phonons is also visible, further illustrating the effect of latticedefects on the LVDOS.Frequency (THz)Slice (0.265 nm)  100 200 30005101520Occupation (arb)2468101214Figure 2.26: An image showing the LVDOS of a randomly voided nanos-tructure with spherical voids 3.0± 1.5 A˚ in size and representing 20% of thetotal volume of the 104 nm long, 5 × 5 unit cell, hexagonal ZnO nanowireoriented along the z-axis.Thermal conductivity was calculated using NEMD for a series of ZnOnanowires with a specific set of random voids at varying densities. The652.2. Zinc Oxide NanostructuresLVDOS-EMD plots were also prepared for the same set of nanowires byprogressively introducing voids to a nanowire within the LAMMPS environ-ment. Only one simulation was required to produce LVDOS-EMD resultsfor 14 different void configurations as additional voids could regularly beadded throughout the simulation followed by settling periods and data col-lection. The results were then passed through conventional LVDOS-EMDwhich calculated thermal conductivity at one position in the nanowire andsliced the nanowire along the x-y plane. Intrastructural LVDOS-EMD wasalso employed by expanding the length of the segments along the z-axis andconstraining x-y axis segment size to 1 nm×1 nm. The length along the z-axis had to be increased to ensure that a statistically significant number ofatoms (>50) remained within each segment. 20 sets of thin nanowires andtheir z-axis thermal conductances were generated prior to combining all theelements into a single thermal conductance as described in Section 2.2.5. Ifa void was encountered that completely severed the thin nanowire, the MFPwas necessarily truncated, leading to a much lower thermal conductivity. Incases where the nanowire randomly started within a void, a thermal con-ductivity of 0 was used. Since segments of all thin nanowires representingthe same position along the complete nanowire were first averaged, nanowirethermal conductivity could be calculated for a variety of void configurationsup to 50% volumetric void density. The results are shown in Figure 2.27.Increasing the number of voids in the material consistently improved thethermal conductivity and ξ until voids had consumed approximately 30% ofthe original volume of the material. Although LVDOS-EMD results showedthe same trend, the magnitude of the impact of the voids on the thermalconductivity of the material was less. In the case of simple LVDOS-EMD,the random dispersion of voids within the slices tended to average the LV-DOS of each slice, underestimating the impact of the voids on the meanfree path. Although the intrastructural LVDOS-EMD did compensate moresuccessfully for this effect, lengthening the slices along the z-axis yieldeda similar problem where multiple voids would fit into the same slice, in-accurately representing void configuration and their effect on the thermalconductance.To confirm this effect, a second set of simulations were run for largerradius voids, shown in Figure 2.28. In these results, both the simple and in-trastructural methods produced relative thermal conductivities much closerto the value expect from the NEMD calculation. Simulations with largerdiameter voids resulted in unstable structures at void volumetric densitiesabove 40%.The overall performance of voided nanostructures is high, with STEF662.2. Zinc Oxide Nanostructures00.511.522.533.544.550% 10% 20% 30% 40% 50% 60%Thermal Conductivity (W/mK)Voids by Total Nanowire VolumeLVDOS-EMD Advanced LVDOS-EMD MDFigure 2.27: A chart plotting the NEMD, simple LVDOS-EMD, and ad-vanced (intrastructural) LVDOS-EMD thermal conductivities as a functionof void density for ZnO nanowires. The voids are 3.0± 1.5 A˚ in radius and2600 voids represents 50% of the volume of the nanowire.scores above 5 as shown in Figure 2.29. Nanowires simulated with differentrandom seeds showed similar promise. It should be noted that the high den-sity and proximity of voids would likely interfere with electron propagationthrough the material, detrimentally impacting electrical conductivity in afabricated device. The benefits of a voided structure have also been demon-strated through simulations and in nanobulk and similar experimentally-realized materials[30, 31, 62, 69, 149–152]. Some have also built analyticalmodels in an attempt to describe the best void configuration for a givenmaterial, although these models are generally purely classical and neglectphonon wavelike behaviour[149].2.2.10 HCP-Voided NanostructuresA hexagonal close packed (HCP) structure is one that maximizes the numberof spheres within a given volume. An analogy to an HCP lattice is that theatoms are positioned as though they are stacked bowling balls or cannon672.2. Zinc Oxide Nanostructures00.511.522.533.544.550% 10% 20% 30% 40% 50%Thermal Conductivity (W/mK)Voids by Total Nanowire VolumeLVDOS-EMD Advanced LVDOS-EMD MDFigure 2.28: A chart plotting the NEMD, simple LVDOS-EMD, and ad-vanced (intrastructural) LVDOS-EMD thermal conductivities as a functionof void density for ZnO nanowires. The voids are 5.0± 2.5 A˚ in radius and525 voids represents 40% of the volume of the nanowire.balls. An HCP voided lattice is one that takes advantage of the benefits ofvoids within a structure, but rather than applying the voids randomly, thevoids are integrated into the material in an HCP configuration, maximizingvoid density while preventing any overlap. Structures tested with maximumvoid density such that the edges of voids touched one another within thelattice yielded a structure that collapsed or lost atoms during the simulation.To improve nanostructure stability, the space between voids was increasedby reducing their radius while holding their positions constant. A cut awayof an HCP lattice is shown in Figure 2.21 and the LVDOS plot can be seenin Figure 2.30.HCP voided structures were tested with void radii of 3± 1 A˚. Despiteconsuming more volume in the nanostructure, the reduction in thermal con-ductivity was not as significant as with random voids, with 1.0 W m−1 K−1being the lowest achieved thermal conductivity in any HCP configuration.The corresponding ξ = 3.8 at its best, indicating that although integratingthe voids still improved the performance of the material, fully random voids682.3. Comparison and Summary of ZnO Nanostructures0% 10% 20% 30% 40% 50% 60%01002003004005006000123456Area Thermal ConductivityVolumetric Density of Voids (%) ThermalConductivity(W/mK)and(normalized)STEFSTEFArea (Å2 )Figure 2.29: A plot showing the effective area, simulated thermal conductiv-ity, and normalized STEF of voided nanowires as a function of void densityfor R = 3.0± 1.5 A˚ voids.produced greater benefits for thermoelectric materials.2.3 Comparison and Summary of ZnONanostructures2.3.1 Comparison of Modelling ResultsA summary of many simulations performed can be found in Table 2.3. Re-ducing the dimensionality of ZnO from a bulk material to a small diameternanowire demonstrated a 12.5× drop in thermal conductivity relative tothe bulk material, predominantly due to enhanced surface scattering at thesurface of the nanowire. This behaviour is expected with the increase in sur-face area to volume ratio. Of the structures examined, heterostructures andrandomly voided structures demonstrated the greatest reduction in ther-mal conductivity to cross-sectional area. In simulation, the heterostructuresperformed best when layer transitions occurred very frequently, such as ev-ery four unit cells of material (approximately 2 nm), although transitionsthat rapid cannot be realized through electrochemical deposition. Voidednanostructures functioned best with very small diameter voids (<1 nm) atdensities of nearly 30% the volume of the material. Similarly, such a voided692.3. Comparison and Summary of ZnO NanostructuresFrequency (THz)Slice (0.265 nm)  100 200 30005101520Occupation (arb)246810Figure 2.30: An image showing the LVDOS of a 104 nm long, 5 × 5 unitcell, hexagonal ZnO nanowire with 3 A˚ radius spheres removed in hexagonalclosely packed configuration with sphere centers 10 A˚ apart.material cannot be fabricated using known electrochemical methods, butstructures with larger voids will be investigated.The thermal properties of Al:ZnO are assumed to behave similarly toZnO for the same structural modifications. Doping ZnO with aluminumconsistently reduces the thermal conductivity of the material by a 2-6×factor by adding defects into the material and thereby creating additionalscattering sites for phonons[32, 52, 53, 62, 153]. Some adjustments to theZnO models would be necessary for determining optimized nanostructuralfeatures such as nanovoid size for the Al:ZnO material system.By using (2.48), results for modelled structures based on nanowirescan be roughly extrapolated to a bulk material by removing the nanowireboundary contribution to reducing mean free path. At best, exclusively het-erostructured bulk Al:ZnO and exclusively nanovoided bulk Al:ZnO wouldprovide thermal conductivities of 1.32 W m−1 K−1 and 0.77 W m−1 K−1, re-spectively. The heterostructured configuration is anticipated to have ahigher electrical conductivity than a pure Al:ZnO bulk material due to the702.3. Comparison and Summary of ZnO NanostructuresTable 2.3: Summary of the area calculations used to estimate classical elec-tronic conductivity, thermal reverse NEMD conductivity calculations, andSTEF for each modelled nanostructure.StructureAdjustedArea (A˚2)ThermalConductivity(W m−1 K−1)STEFStraight 501 4.4 1Voided StructuresR = 3.0± 1.5 A˚, 30% density 397 0.66 5.3R = 3.0± 1.5 A˚, 50% density 355 0.76 4.1R = 5.0± 2.5 A˚, 40% density 352 1.3 2.4Hollow StructuresR = 2 A˚ 460 2.9 1.4R = 3 A˚ 423 3.2 1.2R = 4 A˚ 346 1.5 2.0R = 5 A˚ 283 1.9 1.3HeterostructuresZn (8 uc) / ZnO (8 uc) 500 1.9 2.4Zn (4 uc) / ZnO (6 uc) 499 1.1 4.0Zn (6 uc) / ZnO (4 uc) 500 1.1 3.9Zn (4 uc) / ZnO (4 uc) 501 1.0 4.2HCP VoidsR = 3 A˚, spaced 8 A˚ 361 1.1 3.0R = 3 A˚, spaced 10 A˚ 433 1.0 3.8integration of metal Zn layers, and the nanovoided material would lose 30%of its volume, with a corresponding 30% minimum drop in electrical conduc-tivity. Practically, if the modelled void densities and sizes could be achieved,the electrical conductivity would drop more than the proposed 30% due toa reduction in electron mean free path. Full, quantum scale electronic mod-elling would be necessary to accurately determine electronic conductivity forthe proposed nanovoided structures.LVDOS-EMD was useful for studying the behaviour of phonons at in-terfaces within the nanostructures and provided some insights into the opti-mization of the materials. Figure 2.31 shows a summary of many structuressimulated using simple LVDOS-EMD, advanced (intrastructural) LVDOS-EMD, and NEMD. There is good agreement in simpler, axisymmetric struc-tures such as heterostructures, but there remains greater discrepancy in712.3. Comparison and Summary of ZnO Nanostructuresstructures presenting a large degree of asymmetry and randomness. Allnanostructural effects were applied at exceptionally small scales, and onewould expect better performance from LVDOS-EMD at larger scales wherethe features under consideration are larger than the slices used for studyingthe material.0123456Thermal Conductivity (W/mK)LVDOS−EMDNEMDAdv. LVDOS−EMDStraightVoid 20%Void 30%Void 50%Hollow R=2Hollow R=3Hollow R=4Hollow R=5Hetero 4/6Hetero 6/4Hetero 8/8HCP 4/3HCP 5/3Hetero 4/4Figure 2.31: A plot showing simple and advanced (intrastructural) LVDOS-EMD and NEMD results for a variety of structures. The intrastructuralLVDOS-EMD results show the thermal conductivity determined for eachthin segment as well as the average and standard distribution.2.3.2 Summary of Modelling ResultsMolecular dynamics modelling work began with the development of a rapidthermal conductivity prediction tool for nanostructures, called LVDOS-EMD. This tool was used to study the local density of states of phononsaround nanostructural boundaries to determine the relative effect of these722.3. Comparison and Summary of ZnO Nanostructuresboundaries on phonon propagation. The model, which worked well forthe simple nanostructural features of a monatomic species like silicon, wasenhanced to study ZnO with more complex structural properties such asnanovoids. Good agreement was found when comparing the intrastructuralLVDOS-EMD method with NEMD results for ZnO, enabling the rapid pre-diction of changes in thermal conductivity of nanowires with varying voiddensities and radii. A voided structure, which is difficult to model, was alsoused to demonstrate the lower limitation of the statistical nature of LVDOS-EMD, where voids smaller than the slices used to study the material causedLVDOS-EMD to underestimate the effect of the feature. LVDOS-EMD isfurther constrained by the approximation method used for determining thewavelet mean free path and the requirement that the material structure bethe dominant scattering mechanism in the material.Reducing the thermal conductivity of a material by increasing its surfacearea to volume ratio is an established method, but one that has implicationson electron transport as well. Calculating the electronic properties of thematerials examined at the quantum scale was determined to be out of scopefor this work, and a rough, classical approximation was used instead. Thecross-sectional area of slices along the modelled nanostructures was calcu-lated to produce an effective cross-sectional area for the material. Thismethod would account for choke points along the material and other sub-stantial variation in material dimensions, but neglected quantum and somesize effects, limiting its accuracy at the nanometre scales considered. Thethermal conductivity and effective cross-sectional area were combined toproduce a performance metric, the STEF, to rate the relative benefit of thenanostructural modification.A combination of LVDOS-EMD and conventional NEMD was used toanalyze ZnO nanotubes, heterostructures, very low diameter nanowires,nanovoided nanowires, and HCP voided nanowires. By applying theMatthiessen rule, enhancements in performance due to nanowire boundaryscattering conditions and other nanostructural efforts could be consideredseparately. Final results show that heterostructures and nanovoided struc-tures offered the greatest improvements to electrical vs. thermal conductiv-ity within the constraints of the simulation environment, and should be thefocus of experimental research using the Al:ZnO material system providedthat the materials could be readily synthesized. These observations areconsistent with results published for other material systems[134]. Unfortu-nately, simulation limitations in structure size necessitated that the featuresizes in the modelled voided and heterostructured materials be less thanthose reproducible using established ZnO electrochemical growth methods.732.3. Comparison and Summary of ZnO NanostructuresDespite this acknowledgment, these structures were selected for experimen-tal investigation. If voids and heterostructures can be produced with largerfeature sizes, reducing the feature size using the electrochemical method tomore closely match the modelled results is a potential subject for futurework.74Chapter 3Experimental Growth andRelease of Al:ZnOBased on the work in Chapter 2 and the work of others[134], Al:ZnO mate-rials with nanovoids and heterostructural features were selected for electro-chemical growth toward realizing a higher efficiency Al:ZnO thermoelectricmaterial. Before considering the introduction of nanostructural features,suitable Al:ZnO films first had to be synthesized. Existing experimentalliterature on Al:ZnO focused exclusively on thin film growth of Al:ZnO fordurations under two hours. The resulting film thicknesses were typicallyunder 10 µm, which, though feasible as a thermoelectric material, adds sig-nificant complexity to the design of the module and interface due to theincreased relative effects of interface and other material layers in the mod-ule. To reduce the influence of interface layers, increase the accuracy of thethermoelectric film measurements, and simplify the measurement procedureby increasing mechanical strength of the films, thicker, higher quality, Al-doped ZnO films first had to be produced. The films would also have to beremoved from the substrate to allow access to both sides for the purpose ofthermoelectric characterization and integration into a thermoelectric mod-ule. Optimal growth conditions for long duration growth were experimen-tally explored, as were different methods for detaching the ZnO from thegrowth substrate.Testing yielded that a vertically oriented-slide, situated in the centre ofthe solution (at least 1 cm from the base of the beaker) without stirringyielded the best results. Further discussion on these and other ZnO growthconsiderations not discussed in this chapter can be found in Appendix A.2.Each section includes a literature review and separate equipment andmethodology to introduce information and procedures specifically appropri-ate to the problem.753.1. Equipment and Methodology3.1 Equipment and MethodologyA potentiostat was constructed using an Agilent 34401A digital multimeter,a Keithley 2601 SourceMeter, LabView, and a GPIB network. The poten-tiostat was capable of both potentiostatic and galvanostatic deposition whilealso supporting two and three electrode configurations. In a potentiostaticmode, the applied voltage was adjusted to maintain the desired referencepotential using a proportional-integral-derivative (PID) control loop. Theexperiments were conducted on a Fischer Scientific hotplate using a thermo-couple for temperature regulation. Experiments involving small quantitiesof liquid (<30 mL) were placed within a hot water bath on the hotplate toimprove temperature regulation. Charge transferred was monitored usinga LabView project and depositions were configured to terminate once thedesired electronic charge exchange had occurred. For more details on theLabView project, see Appendix E.The reference electrode (Sigma Aldrich Z113085-1EA) used was anAg/AgCl refillable, medium flow electrode containing saturated KCl. Work-ing electrodes of copper, aluminum, platinum, zinc, and gold were all usedthroughout the experimental work. Platinum wire (99.99% pure) and zincbars (99.9% pure) were acquired from Sigma Aldrich. The growth solutionwas composed of >99% pure Zn(NO3)2 · 6 H2O (Sigma Aldrich 96482-500G,with trace chloride and sulphate ions) and 99.997% pure Al(NO3)3 · 9 H2O(Sigma Aldrich 229415-10G) when doping was necessary. Distilled waterfrom the same source was used in all experiments. The substrates were ei-ther indium tin oxide (ITO) on glass or gold (1000 A˚) on chromium (50 A˚)on glass wafers from EMF Corporation (CA134). Adhesive copper tape wasused to connect the electrodes to wires leading to the potentiostat, and poly-imide tape (3M 1205-series) was used in solution for any required masking.At high temperatures, the experimental apparatus lost water due toevaporation. To compensate, a solenoid-actuated, DI water cistern was con-structed above the hotplate, controlled by the LabView potentiostat soft-ware, that released solution (either DI water or DI water with dopant chemi-cals) into the growth beaker every 2.5 minutes to maintain a consistent waterlevel.A simple diagram of an electrochemical apparatus is shown in Figure 1.4.Specific details regarding probe spacing, solution concentrations, and ana-lytes can be found in each subsection. The final apparatus for depositingAl:ZnO films used in thermoelectric characterization (Chapter 4) was a twoelectrode galvanostatic apparatus described in Section 3.4.1.X-ray Diffraction (XRD) measurements were conducted using a Rigaku763.2. Counter Electrode SelectionMultiFlex XRD equipped with a Cu long fine focus and Cu Kα1+2 bandpassgraphite monochrometer at 40 kV acceleration potential and 20 mA emissioncurrent. Scanning Electron Microscopy (SEM) was used to produce micro-scopic images of materials surfaces. The images were recorded using anHitachi S3000N VP-SEM at either 15 kV or 20 kV.Energy-dispersive x-ray spectroscopy (EDX) measurements were per-formed using an Hitachi S3000N VP-SEM at 15 kV. Unless otherwise indi-cated, EDX measurements were performed in beam scanning mode wherecounts were collected over a five minute period. Quantitative values werecalculated through automatic peak selection, manual trimming false peaks,and applying the Lorimer-Cliff method with ZAF correction using defaultk factor calibration coefficients[154, 155]. Reference ZnO powder (SigmaAldrich) was used to verify the calibration of the instrument, yielding a Zn-O molar ratio average of 49.03% to 50.97% with a standard deviation of4.1%. Uncertainty reflected in EDX measurements in this work representsvariation in multiple consecutive measurements, not overall measurementerror, which should be taken to be 5% in the worst case. An example en-ergy spectrum of a galvanostatically grown, Al-doped, chloride contaminatedAl:ZnO thin film is shown in Figure 3.1. There are no obvious peaks notalready attributed to the labeled elements. The count intensity and spacingbetween the aluminum and chloride peaks also facilitates higher resolutionand accuracy measurement of these elements as there is no overlap in energy.3.2 Counter Electrode SelectionThe first consideration involved the examination of the counter electrode.Earlier publications involving the growth of ZnO using Zn(NO3)2 used zincsheets as the counter electrode in the deposition to maintain availabilityof zinc ions during the process [72, 81, 88]. Although some modern re-search continues to use Zn sheets [85, 156, 157], many other researchershave switched to inert counter electrodes composed of platinum or graphite[77–80, 83, 84, 86, 89].The risk of using an inert electrode for thicker film ZnO deposition basedon Zn(NO3)2 is apparent from the electrochemical equations. Many papersdescribe the half cell reaction equation as similar to [40, 77, 80, 82, 84, 89]:Zn2+ + NO −3 + 2 e− −−→ ZnO ↓ + NO −2 (3.1)Equation (3.1) neglects the ratio of usage of zinc and nitrate ions during773.2. Counter Electrode SelectionFigure 3.1: Example EDX spectrum of a galvanostatically grown, Al-doped(5 µmol/L growth solution concentration), chloride contaminated Al:ZnOthin film.the growth process, discussed by Marotti et al. and shown here [87]:Zn(NO3)2 −−→ Zn2+ + 2 NO −3 (3.2)NO −3 + H2O + 2 e− −−→ NO −2 + 2 OH− (3.3)Zn2+ + 2 OH− −−→ Zn(OH)2 −−→ ZnO ↓ + H2O (3.4)The overall reaction can be described as:Zn(NO3)2 + 2 e− −−→ ZnO ↓ + NO −3 + NO −2 (3.5)The significant difference between (3.1) and (3.5) is in the inclusion of theremaining NO –3 ion for every Zn2+ consumed by the reaction, which causeszinc ions within the growth solution to be consumed more rapidly than ni-trate ions. Unusual effects such as extremely thin films during depositions783.2. Counter Electrode Selectionat high potentials using inert electrodes have been reported, with the for-mation of hydrogen bubbles coating the surface of the film being cited asthe cause [84]. The half cell reaction occurring at an inert counter electrodeis:2 H2O −−→ 4 H+ + O2 + 4 e− (3.6)which is significantly different from the reaction at a zinc counter electrode:Zn −−→ Zn2+ + 2 e− (3.7)Note that it is also possible in both cases for hydrogen ions to form intohydrogen gas at the working electrode, although this is much more probableunder acidic conditions.The effect of Zn2+ reduction on ZnO film quality using a NO –3 systemwas examined by comparing films grown using an inert platinum counterelectrode with those grown with a zinc metal counter electrode. Experimentswere performed at different temperatures, applied potentials, stirring rates,and beaker sizes.3.2.1 Experimental MethodsThe experiments were performed with either 20 mL or 100 mL of 0.1 MZn(NO3)2 · 6 H2O solution in 30 mL and 140 mL beakers, respectively. Astandard three electrode potentiostatic set up was used, with a gold-platedglass working electrode (1000 A˚ gold on 50 A˚ chromium from EMF Corpora-tion, 2.54 cm×7.62 cm total area, 2.54 cm×3 cm used), Ag/AgCl saturatedKCl reference electrode, and either platinum wire or zinc rod (99.9% pure)counter electrode. The working and counter electrodes were 2 cm apartwith the reference electrode within 1 cm of the working electrode. All volt-age are expressed vs. Ag/AgCl. The growth solution was kept at 75 ◦C,measured by both thermocouple and glass thermometer, although solutionsranging from 65 ◦C through 85 ◦C were tested and were found to present thesame trend. Reported results were based on experiments with a 250 RPMstir rod, although experiments without the stirring effect showed the samecharacteristics at lower current densities. Gold coated slides, used as zincoxide deposition substrates, were washed with distilled (DI) water, acetone,methanol, and DI water again prior to use. The active region for depositionwas masked using polyimide tape, which was experimentally determined notto significantly impact deposition results.pH measurements were made with BDH35309.606 (VWR International)full range pH test strips with values recorded 10 seconds after removal from793.2. Counter Electrode Selectionthe growth solution to maximize consistency. Substrates were left in thegrowth solution after the completion of the electrodeposition process to coolgradually and prevent fracturing. Cooled films were rinsed thoroughly withDI water and left to air dry.3.2.2 Single Potential DepositionTo confirm the persistence of evolved hydrogen ions in the growth solution,two identical film depositions of 13.3 C/cm2 were performed at a range ofpotentials (Vset = −1.0 V, −1.1 V, and −1.2 V) in 20 mL beakers. Using theplatinum counter electrode, available Zn2+ was reduced faster than NO 2–3 ,encouraging the persistence of H+ ions from the counter electrode and acorresponding drop in pH as shown in Figure 3.2. A drop in solution pHis seen for all three deposition potentials, with stronger potentials yieldinga lower overall pH at the conclusion of the experiment. The plateau islikely caused by the preferential formation of hydrogen gas at the workingelectrode. Bubbles were also seen forming rapidly at both electrodes laterin the experiment.A test using 100 mL showed a similar trend with a more gradual decreasein pH terminating at 4.1 after 75 minutes. The gradual increase in pH seenin the zinc counter electrode deposition is the consequence of hydroxyl ionformation within the solution. The presence of nitric acid was specificallytested by adding copper shavings into the growth media after the conclusionof the experiment and witnessing a slight blue shift in colour of the solu-tion. Resulting film thickness was negligible (1 µm) for the platinum-grownsamples and varied from 4 µm to 15 µm for the zinc-grown samples. Theplateauing effect limiting the further acidification of the solution to approx-imately pH = 4 was likely due to reaction kinetics favouring the productionof hydrogen gas over increased hydromium production in the solution.H+ and oxygen gas are formed by electrolysis at the counter electrode(anode). A test enclosing the platinum counter electrode within a glass en-closure with a 1 mm2 outlet was performed. The same reduction in solutionpH was observed, but the drop in pH occurred at a slower rate, adjusted forcurrent. The addition of the glass enclosure reduced the Faraday efficiencyof the reaction by limiting mass transport and increasing the concentrationof H+ immediately around the platinum electrode. Once the solution pHstabilized, it reached the same pH shown in Figure 3.2. Tests without theglass enclosure also do not run at perfect Faraday efficiency, with the voltageapplied to the anode being adjusted by the potentiostat controller to priori-tize a constant potential between the cathode and the surrounding solution803.2. Counter Electrode SelectionFigure 3.2: pH of 20 mL, 0.1 M Zn(NO3)2 solutions grown on 2.54 cm×3.1 cmof exposed gold-coated glass using different counter electrode materialswhere a) shows pH as a function of deposition time and b) shows pH asa function of total applied charge. Uncertainty in pH measurement is ±0.3.rather than minimize overpotential for the hydrolysis reaction.The current vs. time plot is shown in Figure 3.3. Whereas both deposi-tions begin with the same trend, as the pH dropped in the solution with theplatinum counter electrode, the current increased and stabilized, indicatinggradual damage to the existing very thin film and no additional deposition.Oscillation in the current when using the platinum electrode could be due813.2. Counter Electrode Selectionto bubble formation which was visible later in the experiment. The decreas-ing current of the deposition involving the zinc counter electrode is due toincreasing resistance of the ZnO film, and is consistent with the growth ofa good quality film.Time (s)0 200 400 600 800 1000Current Density (mA/cm2 )12345PtZnFigure 3.3: Deposition current density of 20 mL, 0.1 M Zn(NO3)2 solutionsgrown using different counter electrode materials at a Vset =−1.2 V. Growthconditions were otherwise identical to those in Figure 3.2.Samples grown at (Vset = −1.2 V) with different electrodes were alsotested for their structural properties. SEM images of the surfaces of twofilms grown with inert and zinc counter electrodes are shown in Figure 3.4. Aclear difference in surface morphology is visible, with the zinc-grown samplemuch more consistent with the results of others [72, 87, 88, 156]. It is alsoclear that the Pt-grown film is very thin and difficult to distinguish fromthe substrate (bottom of the image) when compared to the Zn-grown film.Tests were also performed with samples immediately removed from solutionafter the deposition was complete. These tests showed a slightly thickerfilm of similar surface morphology to Figure 3.4c, indicating that furtherdissolution of the ZnO film occurred in the 20 mL beaker after the 3 hourdeposition at −1 V vs. Ag/AgCl completed. Films removed immediatelywere still morphologically different in appearance than films grown with Zncounter electrodes, appearing darker and inconsistent. XRD data shownin Figure 3.5 similarly shows highly crystalline growth along 〈002〉 withthe zinc-grown film and greater variability in growth orientation, apparentby visible peaks along 〈100〉 and 〈101〉 with the platinum-grown film. Filmsgrown using inert electrodes for long durations were also visibly discoloured.823.2. Counter Electrode SelectionFigure 3.4: SEM images at identical scales of uncoated ZnO films grownusing a) Zn-grown film viewed overhead, b) Zn-grown film viewed at 45◦, c)Pt-grown film viewed overhead, and d) Pt-grown film viewed at 45◦.3.2.3 Multiple Potential DepositionThe effect of zinc exhaustion was also explored at different deposition poten-tials using zinc counter electrodes. Figure 3.6 shows the deposition currentsfor depositions at Vset =−1.10 V, −1.05 V, and −1.00 V where −1.00 V istypically used in high quality ZnO growth [77, 81, 83, 86]. Each curve rep-resents 1.3 C/cm2 of charge transferred. The dehydration of Zn(OH)2 intoZnO as shown by (3.5) is rate limited, allowing an increased rate of Zn(s)and Zn(OH)2 integration into the film [156].Figure 3.7 shows a single growth using a platinum electrode and 100 mLbeaker at gradually increasing potentials. At potentials weaker thanVset = −1.0 V, there is a small drop in pH as very little Zn2+ is consumed. Atpotentials stronger than Vset = −0.95 V, the drop in pH is quite sudden andcorresponds to a rapid increase in current density as zinc ions are stronglyinvolved in the reaction. 2.67 C/cm2 of charge was deposited without the833.2. Counter Electrode SelectionFigure 3.5: XRD measurements of films grown using either zinc or platinumcounter electrodes under otherwise similar conditions. Counts have beennormalized by intensity of (002) crystal orientation. The peak near scatter-ing angle 38◦ is due to the gold substrate beneath the film. No unexpectedout-of-band spikes were noted from 0-90◦.pH dropping below 5, which has been determined as a critical pH belowwhich film growth is significantly inhibited despite high deposition currentdensities. After exposure at pH below 5 for 1.5 hours, the appearance of thesurface of the film turned brown, although it still retained sufficient thick-ness and electrical resistance to indicate that exposure to the low pH didnot dissolve much of the good quality film deposited earlier in the process.3.2.4 Summary of Counter Electrode EffectsUnder all test conditions, the zinc counter electrode provided a pH neutralsolution that yielded high quality ZnO films with high transparency and〈002〉 crystallographic alignment. When an inert counter electrode was used,a reduction in the solution pH was measured during all growth conditions,with pH dropping more rapidly with increased applied growth potential.Hydrogen ions formed at the counter electrode remained in the solution dueto the ratiometric exhaustion of zinc ions, forming an acid that inhibited film843.3. Reference Electrode EffectsFigure 3.6: Deposition currents of 100 mL, 0.1 M Zn(NO3)2 solutions grownusing zinc counter electrodes at different reference potentials (Vset). Nor-malization currents (A0) used are 19.6 mA, 21.2 mA, and 22.0 mA for Vset =−1.10, −1.05, and −1.00 V, respectively.growth below pH = 5, disrupted aligned crystal growth, and discoloured thesurface of the film. Tests also showed that Vset = −1.0 V, which is commonlyused in ZnO growth, is at the inflection point where a small increase inpotential magnitude can very rapidly decrease the pH of the solution. Forlong term, high quality, or highly doped growth, or for growth that canpreserve the integrity of the growth solution for reuse, inert electrodes shouldnot be used.3.3 Reference Electrode EffectsThe effects of the reference electrode on the quality of the film must beconsidered for long depositions. In most cases, thin ZnO films are pro-duced potentiostatically over short durations of less than 2 hours using anAg/AgCl reference electrode to maintain the desired applied electrochem-ical potential[1, 40, 77, 89, 156]. ZnO growth under these conditions hasyielded thin films and nanostructures with desirable optical and crystallo-853.3. Reference Electrode EffectsFigure 3.7: Deposition pH and transferred charge of a 100 mL, 0.1 MZn(NO3)2 solution grown using a zinc counter electrode with potential (Vset)varying throughout the deposition. Uncertainty in pH measurement is ±0.3.graphic properties. As the film grows in a potentiostatic configuration, arapid decay of deposition current provides a natural limit to film thicknessas the electric resistance of the film increases with thickness[1]. Galvano-static growth of zinc oxide enables the growth of films exceeding 50 µm inthickness but requires long growth durations, rendering the films more sus-ceptible to impurities in the growth solution. Examined in this section isthe influence of chloride on ZnO thick film growth with deposition time upto and exceeding 11 hours.The effect of chloride in electrochemically deposited zinc oxide nanos-tructures has been examined[45, 46]. Xu et al. determined that the addi-tion of 0.06 mol/L chloride to a 0.05 mol/L Zn(NO3)2 solution forms inter-connected, stacked ZnO platelets rather than rods on an indium tin oxide(ITO) substrate[45]. Cui et al. concluded that adding ammonium chlorideto the growth solution reduces growth along the wire axis of ZnO nanowireswhile enhancing their radial growth and reducing optical transmission[46].In both cases the amount of chloride was carefully controlled at the begin-ning of the deposition. A study on the effect of chloride on ZnO thick films863.3. Reference Electrode Effectselectrochemically grown using Zn(NO3)2 has not been performed, nor havethe implications of chloride leakage from Ag/AgCl electrodes on ZnO filmsbeen reported in detail.3.3.1 Experimental MethodsAll experiments used 100 mL of solution within a 150 mL beaker. The solu-tion contained 0.1 M Zn(NO3)2 · 6 H2O with each experiment using distilledwater from the same source. A standard three electrode configuration wasused for all experiments consisting of a 99.9% pure Zn metal rod counter elec-trode, Ag/AgCl medium flow, saturated KCl reference electrode, and Au/Crglass slide working electrodes. The working electrode and counter electrodewere 6 cm apart with the reference electrode within 2 cm of the working elec-trode. Deposition occurred on gold and was masked using polyimide tapeto isolate a deposition area of 1.0 cm×1.0 cm. Deposition temperature wasmaintained by thermocouple control at 80◦C. Gold slides were rinsed withDI water prior to use, and all deposited films were left in the growth solutionas the solution cooled after deposition to minimize thermal stress. Unlessotherwise indicated, samples were grown galvanostatically at 1 mA/cm2 un-til 40 C/cm2 of charge was transferred, requiring approximately 11 hours ofgrowth time.Resistance measurements were taken using a two probe, IV curve methodwhere a 3 mm diameter drop of eutectic GaInSb was used as one electrodeand the gold substrate beneath the film was used as a second electrode. Thecontact angle between the bead and the ZnO film surface was similar withall samples. Resistance was measured through the film rather than along thesurface. All resistance data indicated herein results from a linear fit of theresulting IV curve when sweeping the applied potential from −2 V to 2 V.Since measured resistance values are two orders of magnitude greater thanshort circuit resistance, cable losses are neglected. At least three completemeasurement sets were made per film with a step resolution of 0.02 V and5 s between steps to allow time for settling. A Keithley 2601a Source Meterwas used for all measurements.3.3.2 Results and DiscussionRefillable, metal-ion reference electrodes, such as Ag/AgCl and saturatedcalomel electrodes (SCE), use a porous plug to allow ionic transfer betweenthe growth solution and the reference electrode. The solution within anAg/AgCl electrode is ideally saturated KCl that will very slowly drain into873.3. Reference Electrode Effectsthe growth solution depending on the flow rate of the electrode. Higherflow rates provide for better ion exchange which allows faster response tochanges in potential within the growth solution and greater measurementstability at the cost of more frequent electrode refills and contamination ofthe test solution. A saturated KCl, medium flow Ag/AgCl electrode witha measured flow rate of 127 µL/hour (445 µmol/hour Cl– ) was used for theexperiments reported herein. All experiments involved ZnO growth on agold substrate.Both galvanostatic and potentiostatic experiments were conducted toconfirm repeatability of the results. Potentiostatic films grown for short du-rations of under 2 hours demonstrated optical and morphological characteris-tics similar to other published films regardless of the presence of a Ag/AgClelectrode[85, 156, 157]. The potentiostatic deposition process begins at ahigh current density which diminishes rapidly within the first 15 minutes ofthe deposition[1]. The low estimated Cl– concentration of 9 mmol/L withinthe solution after 2 hours combined with the very low current density of thedeposition does not significantly impact the quality or character of the ZnOfilm.The impact of Cl– impurity within galvanostatically grown ZnO is muchmore significant than three electrode potentiostatically grown ZnO due to ahigher, sustained current density that does not decrease with increasing filmresistance. Galvanostatic growth maintains a constant current density thatallows the reference potential to increase in order to maintain a constantapplied current. Since the deposition current density is constant through-out the entire deposition and the deposition process can take a substantialamount of time, integration of Cl– into the film will occur throughout thedeposition process, including the later stages, when the concentration of Cl–in the solution is significantly higher. Chloride Concentration in ZnOAt the conclusion of an 11.1 hour deposition, 40 C/cm2 of charge was trans-ferred at 1 mA/cm2 over 1.0 cm2, and the reference electrode raised the Cl–concentration in the solution to 49 mmol/L, a concentration similar to thatused by others for intentionally integrating Cl– into ZnO[45]. Chloride con-centration within the grown films was characterized using energy-dispersivex-ray spectroscopy (EDX) where chloride content was compared to zinc andoxygen within the film. EDX measurements of the completed films showedthat films galvanostatically grown without a reference electrode had a chlo-ride molar concentration of under 0.5%, within measurement error. Films883.3. Reference Electrode Effectsgrown under identical conditions with a reference electrode had a Cl– molarconcentration of 4.5± 0.5 % measured at the surface of the film, and filmsgrown with a reference electrode at three times the speed (3 mA/cm2) had amolar concentration of 1.5± 0.5 %. Film thickness measurements provided afilm thickness independent of chloride concentration of 45± 5 µm. Based onfilm thickness and mass measurements, an estimated 270± 6 µmol of ZnOwas deposited with every 11.1 hour, 40 C/cm2 deposition. The amount ofchloride absorbed for films deposited at 1 mA/cm2 was 12± 4 µmol, indicat-ing that not all chloride was absorbed into the film.The integration of chloride into the film as a function of depth wasstudied for the first half of the film. Morphological changes approximately22 µm from the base of the film prevented an accurate analysis of the crosssection of the upper half of the film. The results are shown in Figure 3.8.The limitations of EDX, particularly when studying small concentrations00. 5 10 15 20 25 30Chloride Concentration (% mol) of Film (μm)ThicknessFigure 3.8: EDX measurements performed at 15 kV on the cross-section ofa ZnO film. EDX measurements were performed as discussed in Section 3.1except for the beam mode which was set to point to increase spatial resolu-tion. At least three samples were taken at different points throughout thefilm to determine the standard deviation as shown by the errors bars.of an element through the cross section of a film, restrict the quantitativeconclusions that can be drawn from this figure. Qualitatively, a clear trendis visible from the onset of the deposition to the conclusion of the plot,representing 5.6 hours of growth. A slight increase in chloride concentrationnear 18 µm also corresponds to a change in structural morphology where the893.3. Reference Electrode Effectsotherwise contiguous ZnO crystal begins to transition into larger platelets. Crystallinity of ZnOXRD measurements of representative galvanostatically grown films with andwithout a reference electrode are shown in Figure 3.9. The film grown withthe reference electrode presented many additional peaks not attributable toeither gold or ZnO. The additional peaks were not identical for every sample,but generally included a combination of 2θ = 11.7◦ and 28.6◦, with smallerpeaks at 23.3◦, 30.9◦, 31.9◦, 33.0◦, 35.0◦, 49.0◦, and 50.3◦. These peaks areconsistent with the presence of AgCl and other Cl-based crystals within thefilm. Samples grown without the reference electrode in otherwise identicalconditions only presented peaks corresponding with ZnO and Au, and alsoindicated favourable growth along 〈002〉 as only the (002) peak was visiblein the XRD spectrum.903.3.ReferenceElectrodeEffectsFigure 3.9: XRD results comparing peaks of a ZnO film grown with and without an Ag/AgCl reference electrodeover 11 hours. The inset shows higher resolution results from 2θ = 30◦ to 38◦ which is the region of greatestinterest for assessing the crystallinity of ZnO film. Crystal orientations apply to ZnO unless indicated otherwise.913.3. Reference Electrode Effects3.3.2.3 Morphology of ZnOSEM measurements were taken of galvanostatically grown films producedat 1 mA/cm2 and 3 mA/cm2 involving 40 C/cm2 of charge transfer withand without a reference electrode. The SEM measurements are shown inFigure 3.10. The surface morphology of the films grown with and without theelectrode are very different, with the films grown with the reference electrodeshowing increased surface roughness and less consistency across the surface.Figure 3.10h is an example of the surface structure most commonly foundin potentiostatically grown films using an Ag/AgCl reference electrode asreported by others[72, 89].Figure 3.10: SEM results taken at a 45◦ angle showing low (a,c,e,g) and highmagnification (b,d,f,h) comparisons of ZnO films galvanostatically grown at1 mA/cm2 (a,b,e,f) and 3 mA/cm2 (c,d,g,h) until 40 C/cm2 of charge hadexchanged. Films in the top row were grown without an Ag/AgCl referenceelectrode, whereas films in the bottom row were grown with an Ag/AgClreference electrode.The impact of the chloride on the film is also visible through opticalmicroscopy. Higher concentrations of chloride render the film visibily greyand translucent; the surface also grows rougher with large crystals visiblewithout microscopy. Optical microscopy photographs from two films gal-vanostatically grown with and without an Ag/AgCl electrode are shown in923.3. Reference Electrode EffectsFigure 3.11. The film grown without the reference electrode is opticallytransparent and very smooth, showing the gold substrate beneath the film.Figure 3.11: Optical microscope images using yellow light to facili-tate qualitative contrast between ZnO film crystallinity and yellow lighttransmission. Both ZnO films were galvanostatically grown a) using anAg/AgCl reference electrode and b) without using a reference electrode.The chloride-contaminated film (a) appeared optically grey, translucent,and non-homogenous when visually compared to the film grown withoutthe reference electrode. Resistance of ZnOResistance measurements of galvanostatically grown films were completed onseveral films grown both with and without a reference electrode. All filmswere otherwise grown under identical conditions with measured thicknessesof 45± 5 µm and cross-sectional areas 1.0 cm2. The resistance of films grownwith the reference electrode varied significantly from 20 kΩ to 2 MΩ. Filmsgrown without the reference electrode provided a consistent resistance of1000± 200 Ω. The same bead of InGaSn was used to test each sampleto maximize the consistency of the resistance measurements to maximizeconsistency in results. Annealing at 200◦C for 2 hours did not affect theresistance of the chloride contaminated films, although discolouration of thefilm did occur. The current-voltage (IV) curve of the chloride-contaminatedfilm was measured to be highly non-linear when compared with films grownwithout the reference electrode.933.4. Growing and Characterizing Al:ZnO Films3.3.3 Summary of Reference Electrode EffectsUsing a saturated KCl Ag/AgCl reference electrode when growing ZnO withZn(NO3)2 necessitates an exchange of chloride ions into the growth solution.Potentiostatic deposition, which is self limited by the decay of the deposi-tion current, is not significantly impacted, however some small amount ofCl– is incorporated into the film and this has a measurable effect on thecrystallinity and morphology of the ZnO. Galvanostatic growth of thickerfilms is more significantly impacted by Cl– leakage due to the extendeddurations of the deposition and the high, sustained current density. Chlo-ride is detectable in the films at thicknesses of only 5 µm although effectson morphology are not apparent until chloride molar concentration exceedsapproximately 1%. The variations in crystallinity, morphology, opacity, elec-trical resistance, and surface roughness are quite severe, with films grownusing an Ag/AgCl reference electrode showing generally less desirable char-acteristics. If potentiostatic growth of ZnO is required then Hg/HgO orHg/HgSO4 electrodes should be considered.3.4 Growing and Characterizing Al:ZnO FilmsAluminum can be integrated into the film in a variety of ways[64, 65, 67, 68].The preferred type of integration involves substitution doping whereby zincions are replaced by aluminum ions in a predominantly ZnO crystal lattice.The replacement results in localized distortions in the lattice structure andserves to n-type dope the material, in some cases yielding extremely highelectrical conductivity exceeding 2000 S/cm[54]. A type of integration whichis common in hydrothermal and electrochemically deposited films involvesthe absorption of a Zn-Al double layered hydroxide, or the absorption ofZn(OH)2 and Al(OH)3 nanoparticles directly into the film[67, 156]. Theabsorption of hydroxides reduces film electrical conductivity and cannot beconsidered a type of doping. In addition to aluminum doping, oxygen dopingof ZnO by varying the applied electrochemical potential can also have dra-matic effects on the electrical properties of the film[156]. Aluminum dopingof ZnO has been demonstrated at Al:Zn ratios of 0.1:1 (10% substitution),although 2% is nominal for Al:ZnO thermoelectric materials[44, 52, 53, 62–64].An important limitation in the available literature for producing Al:ZnOelectrochemically involves the study of Al-doping in thicker (>20 µm)Al:ZnO films based on the nitrate growth system. Existing experimentsgenerally limit growth times to under 2 hours[45, 46, 59] and focus primarily943.4. Growing and Characterizing Al:ZnO Filmson potentiostatically grown films, which are practically restricted in theirgrowth thickness due to long growth times resulting from decaying deposi-tion current and contamination as the film thickens[1, 158]. Thicker filmsare desirable for some applications, such as thermoelectrics, where thickermaterials can more easily be integrated into modules, and thickness can beused to regulate thermal power absorption of the device. These thicker filmsare best grown galvanostatically, with applied current affecting both ZnOfilm characteristics[156] and Al/Zn ion selectivity during growth[58]. In thissection, the feasibility of growing low resistance, Al:ZnO thick films using agalvanostatic, nitrate-based electrochemical method is discussed.3.4.1 Experimental MethodsAll films were grown using an electrochemical galvanostatic growth method.150 mL beakers containing 100 mL solutions of 0.1 M Zn(NO3)2 · 6 H2O wereplaced on a standard hotplate with thermocouple control and set to 80◦C.99.9% pure zinc metal counter electrodes were used along with gold-platedglass slides. The working electrode and counter electrode were 6 cm apartwith the reference electrode within 2 cm of the working electrode. The slideswere masked with polyimide tape (3M 1205-series) to provide a depositionarea of 1.0 cm×1.0 cm and were washed using distilled water prior to be-ginning each experiment. An Ag/AgCl reference electrode (Sigma AldrichZ113085-1EA) was used for voltammogram experiments but was not usedfor thick film growth in order to minimize chloride contamination within thegrown films.Al(NO3)3 was introduced into the growth solution at 2.5 minute inter-vals by solenoid-switched gravity feed from a 500 mL chemical cistern locatedabove the galvanostat. The doping solution concentration within the cisternwas selected to achieve the desired dopant concentration within the growthsolution while concurrently replacing water lost due to evaporation. The cis-tern release period was chosen to allow absorption of available Al(NO3)3 andminimize the amount of distilled water added with each release to preventsudden cooling of the growth solution. The valve was opened for 400-500 msper cycle, representing approximately 1.8 mL of solution, depending on thedopant concentration used to adjust for variations in solution evaporationrate.The growth solution was allowed to stabilize in temperature with thecounter electrode in place. The working electrode was only added to thebeaker after the latter had reached the desired temperature and the deposi-tion could begin. The cistern was activated concurrently with the beginning953.4. Growing and Characterizing Al:ZnO Filmsof the deposition. The deposition process for each film required slightlyover 11 hours to grow a nominally 45 µm thick film with a total charge den-sity transfer of 40 C/cm2. Unless otherwise indicated, a constant depositioncurrent density of 1 mA/cm2 was used.Film thickness was measured using both SEM cross-section measure-ments and a high resolution Nikon MM-400 optical microscope with goodagreement. Photographs were taken with a standard optical microscope at10× optical zoom. Resistance measurements were performed using the twoprobe method described in Section Results and Discussion3.4.2.1 ZnO Film Base CompositionAs discussed in Section 3.2, the process of depositing ZnO from a Zn(NO3)2solution involves two predominant steps: 1. Nitrate ions electrochemicallybreak down into hydroxide ions. 2. The hydroxide formed at the workingelectrode then reacts with the Zn2+ in solution and thermally decomposeinto ZnO. The rate of the first reaction is largely governed by the appliedelectrochemical potential between the working and counter electrodes. Therate of the second reaction is largely governed by the temperature of thesolution. A solution temperature of 80◦C was selected due to its ubiquitoususe by others performing a similar deposition[1, 77, 156, 159]. Depositioncurrent densities ranging from 1.0 mA/cm2 to 3.0 mA/cm2 are equivalentto initial reference potentials of −0.90 V - −1.0 V vs. Ag/AgCl, with thelatter potential being commonly used in nitrate-based deposition[72, 77,156]. Films grown using various currents in this range were examined fortheir influence on the composition of an undoped ZnO film.Films were grown at 1 mA/cm2 and 3 mA/cm2 under identical conditionsuntil 40 C/cm2 of charge had been transferred. As shown by Figure 3.12 thechange in zinc to oxygen ratio within the film is quite small for the two dif-ferent current densities. In both cases, the amount of oxygen within the filmis greater than the 50% expected and shown by the ZnO reference samples(Sigma Aldrich 255750-100G). The additional oxygen in the film is likely dueto excess Zn(OH)2 stored in the film during deposition[156]. The introduc-tion of aluminum dopant into the film by maintaining 5 µmol/L Al(NO3)3in the growth solution displaces zinc atoms as desired, but otherwise doesnot significantly impact the ratio of zinc and oxygen in the film.The film cross-section shown in Figure 3.13 is consistent with SEM im-ages produced by others and presents a polycrystalline film consisting of963.4. Growing and Characterizing Al:ZnO Films010203040506070O Al ZnMolar Concentration (%)ElementReference1 mA/cmZnO 3 mA/cmZnO 1 mA/cmAl:ZnO Figure 3.12: Quantitative EDX results showing a molar concentrationcomparison between a commercially purchased ZnO reference powder andgalvanostatically grown ZnO films prepared at different current densities andaluminum concentrations. EDX measurements were performed as describedin Section!3.1. Error bars represent the maximum and minimum of at leastthree measurements across the surface of the material. Accuracy should beconsidered within 5%.large segments of ZnO closely packed and oriented along the c-axis. Thecrystallinity of the ZnO is determined by XRD measurements where agrowth preference along 〈002〉 is shown by Figure 3.14. Although somecounts are detected at 2θ = 31.7◦ and 36.2◦, representing growth along〈100〉 and 〈101〉 axes, respectively, they are nearly within the noise floor ofthe measurement. There are no unidentified peaks on the XRD plot, whichindicates that despite a long deposition time of 11 hours, the film is of highcrystal purity. EDX measurements also did not indicate the presence ofother unexpected, heavier elements within the film.The average film thickness measured using both the SEM and microscopeof samples grown at 1, 2, and 3 mA/cm2 were all 45± 5 µm, with one side(closer to the bottom of the beaker during growth) up to 10 µm thicker973.4. Growing and Characterizing Al:ZnO FilmsFigure 3.13: 45◦ SEM cross-section of an undoped ZnO sample galvanostat-ically grown on gold at Iset = 2.0 mA/cm2 for 5.5 h at T = 80 ◦C.than the top of the film (edge of the masked region near the surface of thegrowth solution). The measured thickness is also approximately 50% largerthan the theoretical thickness of 31.2 µm determined using Faraday’s Law.This sizable discrepancy further indicates the inclusion of zinc and oxygenin different, non-crystalline configurations within the bulk of the film. Theextra volume is most likely water and Zn(OH)2, supported by the oxygenconcentration of the film being higher than the zinc concentration as shownin Figure Aluminum AbsorptionThe aluminum dopant was introduced at regular intervals into the growthsolution. Aluminum ions electrochemically react with greater favorability tozinc ions in the range of interest as shown in Figure 3.15. The voltammogramanalysis indicates that the aluminum ion reaction begins at potentials as lowas Vref = −0.3 V vs. Ag/AgCl and remains dominant until Vref = −1.0 V vs.Ag/AgCl. As the dopant concentration in the growth solution will be smallrelative to the zinc ion concentration, favourable Al3+ reaction is desired.Although it is common in literature to introduce the desired dopant onceat the onset of deposition, thicker film growth must accommodate for the983.4. Growing and Characterizing Al:ZnO Films2θ (°)20 30 40 50 60 70 80Normalized Counts10-210-1100ZnO(002)Au(111)ZnO(003)ZnO(004)ZnO(104)Figure 3.14: XRD spectrum of ZnO and gold substrate showing high (002)(c-axis) orientation of the film.effect of rapid Al3+ absorption. Figure 3.16 shows the measured referencepotential of an Ag/AgCl electrode when drops of Al(NO3)3 are introducedto a Zn(NO3)2 growth solution during a galvanostatic ZnO deposition. Therapid drop in potential and its subsequent return to normal is a consequenceof the appearance and rapid consumption of Al3+. Some of the aluminumis absorbed into the film, but the Al3+ ions also react favourably with OH–produced by the decomposition of nitrate ions, yielding a white particulate,Al(OH)3, that precipitates out of the solution. The rate of reaction is depen-dent on the concentration of aluminum with the majority of Al3+ consumedwithin 2 - 10 minutes of introduction (10 - 1000 µmol/L).A final deposition current density of 1.0 mA/cm2 was selected to main-tain high electrical conductivity in the grown film and maximize electronmobility[156], while also encouraging aluminum absorption into the film[58].Using Figure 3.16, an assumption is made that nearly all Al3+ is consumed2.5 minutes after the previous drop of Al(NO3)3 is introduced into thegrowth solution for peak growth solution concentrations of approximately10 µmol/L Al(NO3)3. The cistern solution Al(NO3)3 concentration is pre-pared to raise the concentration of Al3+ in the growth solution from zero tothe indicated concentration with every refill. Approximately 450 mL of refill993.4. Growing and Characterizing Al:ZnO Films-1 -0.8 -0.6 -0.4 -0.2 0-2.5-2-1.5-1-0.50Reference vs. Ag/AgCl (V)Measured Current (mA/cm2 )Al(NO3)3 1Al(NO3)3 2Al(NO3)3 3Zn(NO3)2 1Zn(NO3)2 2Zn(NO3)2 3Zn(NO3)2Al(NO3)3Measured Current Density (mA/cm2 )Reference vs. Ag/AgCl (V)Figure 3.15: A plot showing voltammograms of 0.1 M Zn(NO3)2 and 0.1 MAl(NO3)3 taken on identical gold substrates and at identical temperatures of80◦C. Each test was performed three times consecutively with all six curvesshown in the plot.solution is required to complete an 11 hour deposition. Chemically stablepolymer components were used in the cistern construction to maximize po-tency and stability of the dopant solution throughout the deposition. Noprecipitates were noted in the cistern during or after deposition experiments.Figure 3.17 shows quantitative EDX measurements of the molar ratio of alu-minum atoms in grown films compared to oxygen and zinc atoms. The bestfit line represents a logarithmic trend, suggesting that, under the conditionslisted, the quantity of aluminum in the ZnO film is a logarithmic functionof the concentration of Al(NO3)3 available in the growth solution.Al(NO3)3 in the growth solution interferes with the formation of ZnOby reacting with hydroxide ions and precipitating them out of the solution.The resulting reduction in measured film thickness for a constant 40 C/cm2charge transfer is shown in Figure 3.18. The reduction in film thicknessis due to the parasitic removal of electrochemically generated hydroxideby aluminum ions. A further constraint to applying Al(NO3)3 concentra-1003.4. Growing and Characterizing Al:ZnO Films0 100 200 300 400 500 6000.470.480.490.50.510.520.53Time (s)Reference Voltage vs. Ag/AgCl (V) 1 mol/L10 mol/L100 mol/L1 μmol10 μmol100 μmolReference Voltage vs. Ag/AgCl(V)Time (s)-------Figure 3.16: A plot showing the Ag/AgCl reference voltage response to theintroduction of varying concentrations of Al(NO3)3. 100 µL to 1 mL vol-umes of Al(NO3)3 were introduced to a 100 mL solution of 0.1 M Zn(NO3)2undergoing galvanostatic deposition at 1.0 mA/cm2 to raise the solutionconcentration of Al3+.tions above 10 µmol/L throughout the growth process is the formation of anAl(OH)3 barrier layer over the ZnO growth surface as shown in Figure 3.19.A critical concentration of Al(OH)3 is reached in the growth solution thatresults in the formation of an aluminum hydroxide film that completely cov-ers the ZnO growth surface, preventing further deposition. The combinationof these effects limit the growth of a ZnO film to an approximate growthsolution dopant concentration of 10 µmol/L.The composition of the Al(OH)3 layer was confirmed through quantita-tive EDX measurements, which consistently indicated a molar ratio of onealuminum atom to three oxygen atoms. The layer forms later in the depo-sition as the amount of floating precipitate increases, and eventually beginsto coat the surface of the ZnO, interfering with further growth by decreasingavailable surface area and blocking ion migration. The hydroxide layer doesnot bind to the surface of the ZnO and was removed through light physicalabrasion and compressed gas. The hydroxide layer is very brittle and thin,1013.4. Growing and Characterizing Al:ZnO Films00.511.522.50 5 10 15 20 25 30 35Molar Ratio of Aluminum in Film (%)Dopant Concentration (μmol/L)Figure 3.17: A plot showing quantitative EDX measurements of Al3+ molarconcentration within the film as a function of sustained dopant concentrationwithin the electrochemical growth solution. The molar quantity of aluminumis compared to that of zinc, oxygen, and chloride also found in the film. Thesolid line represents a logarithmic fit.readily fracturing into an insoluble powder.Approximately 20% of the aluminum ions provided throughout the de-position are integrated into the film, with the remainder precipitating fromthe solution, forming a protective layer over the film, or remaining dissolvedwithin the growth solution. Dopant IntegrationIn an ideally doped material, the Al3+ ions replace Zn2+ ions in the ZnOcrystal lattice, contributing electrons to the crystal and improving elec-trical conductivity. More commonly in hydrothermally or thermochemi-cally deposited ZnO formed in the presence of hydroxide and aluminumions, a hydroxide double layer is formed that replaces the preferred ZnOlattice[64, 65, 67, 68]. It is clear that aluminum ions are interacting withhydroxide in the solution by the formation of a white precipitate that isonly apparent when Al(NO3)3 is added to the solution. Higher integrationof aluminum into the film also affects the visible properties of the film by1023.4. Growing and Characterizing Al:ZnO Films01020304050600 5 10 15 20 25 30 35Film Thickness (μm)Dopant Concentration (μmol/L)Figure 3.18: A plot showing film thickness measurements as a function ofsustained aluminum dopant concentration within the electrochemical growthsolution. All films were grown at identical current densities of 1 mA/cm2 foridentical durations of 11.1 hours. The solid line represents a logarithmic fit.increasing its opacity and rendering the film optically grey as the total mo-lar concentration of Al3+ in the film exceeds 1%. Further effects to themorphology and crystallography of the film are also measurable.Figure 3.20 shows SEM images of ZnO film surfaces at increasing concen-trations of Al3+. At low molar concentration of aluminum (<0.5%), the filmforms large, highly oriented slabs. As the aluminum concentration increases,the slabs decrease in size and consistency, the film develops a nearly porousstructure (1% molar concentration, 5 µmol/L used during growth), and, atconcentrations approaching 2% Al3+, the film appears nearly amorphous atthe surface. Despite the apparent change in morphology, the materials areoptically similar and transparent at all tested concentrations. The contactangle and adhesion of a GaInSb drop does not change significantly with thesurface morphology of the material. The roughness of the surface preventsadhesion and wetting by liquids with high surface tension.The effect of doping on crystallinity was also examined using XRD analy-sis as shown in Figure 3.21. The impact of higher concentrations of Al(NO3)3in the growth solution on the crystallinity of the resulting film is very small.Despite the significant morphological changes and the possible formation of1033.4. Growing and Characterizing Al:ZnO FilmsFigure 3.19: 45◦ SEM images of an Al:ZnO sample grown with 30 µmolAl(NO3)3 solution where a) shows both the ZnO film surface (below) andthe layer of caked Al(OH)3 (above), and b/c) shows closer images of theAl(OH)3 layer.a hydroxide double layer within the film, the overall bulk of the film remainshighly oriented along (002) (c-axis). If the angular offset of each XRD mea-surement is carefully adjusted to align with the substrate gold peak (111)to compensate for subtle changes in film measurement parameters, a veryclose examination of the peaks of the ZnO (002) peak do show a changein crystal lattice c parameter with the introduction of aluminum into thefilm. A change of 0.05◦(average change in diffraction angle along 〈002〉) rep-resents a contraction in c of 0.1%. This contraction could be the result ofsubstitution doping where the additional positive charge of the aluminumion would attract the surrounding oxygen ions, or it could be the result of1043.4. Growing and Characterizing Al:ZnO FilmsFigure 3.20: 45◦ SEM images of ZnO samples galvanostatically grown atIset = 1.0 mA/cm2 with approximately a) no dopant, b) 1 µmol/L Al(NO3)3,c) 3 µmol/L Al(NO3)3, d) 5 µmol/L Al(NO3)3, e) 10 µmol/L Al(NO3)3, andf) 30 µmol/L Al(NO3)3.a difference in internal stress within the film due to smaller crystal sizeswith increasing aluminum integration. There were no detected variations inother peaks within the 2θ = 1◦ - 90◦ band. No peaks representing ZnAl2O4,aluminum metal, or Al2O3 were found.Resistance measurements along the (002) plane through the thickness ofthe film were performed on a probe stand using a bead of GaInSb as the topelectrode and gold substrate as the bottom electrode. Apparatus resistancewas measured and removed from film resistance measurements. Resistivity,shown in Figure 3.22, was approximated by estimating droplet size andaccommodating for film thickness. Both resistance and resistivity show verysimilar trends. As more aluminum is integrated into the film, the resistivityof the film drops, but not as quickly as would be expected for full substitutiondoping. Once the dopant concentration is sufficient to interfere with filmgrowth (10 µmol/L), a new behaviour is observed where the resistivity isnearly constant. This latter behaviour is consistent with a reduced rateof aluminum uptake by the ZnO during growth at high concentrations ofAl(NO3)3. In all cases, measured current vs. voltage (IV) curves werelinear and intercepted 0 A. At least three samples were taken per film atdifferent locations.Although the drop in resistivity of the film with increasing aluminumindicates substitution doping, the gradual rate of change suggests that thealuminum/zinc substitution is imperfect. The integration of Al(OH)3 di-1053.4. Growing and Characterizing Al:ZnO Films30 31 32 33 34 35 36 3700.511.522θ(°)Normalized CountsPure ZnO1 μmol/L3 μmol/L5 μmol/L10 μmol/L30 μmol/L(100) (101)(002)34.32 34.34 34.36 34.380.99511.0051.011.0152θ (°)Normalized CountsPure ZnO 30 μmol/L10 μmol/L5 μmol/L3 μmol/L1 μmol/LFigure 3.21: An XRD spectrum comparing 2θ angle of ZnO galvanostati-cally grown at Iset = 1.0 mA/cm2 with different concentrations of Al(NO3)3with a) showing the primary range of interest for ZnO structures and b)emphasizing the slight difference in peak position between the doped films.1063.4. Growing and Characterizing Al:ZnO Films1101001000100001000000 5 10 15 20 25 30 35Measured Resistivity (Ωcm)Dopant Concentration (μmol/L)Figure 3.22: ZnO film resistivity as a function of estimated Al(NO3)3 dopantconcentration in the growth solution. Measurements represent c-axis resis-tivity.rectly into the film is more probable. AnnealingLow temperature annealing of the films was performed in air to explorethe presence of hydroxide within the films and determine whether anneal-ing could improve substitution doping in the films containing aluminum.Annealing was performed for 2 hours at 200◦C in a forced air temperaturechamber and 400◦C on a covered hotplate. Within the first 30 minutes ofannealing all tested films turned fully opaque and white, dissociating fromthe gold substrate, cracking and deforming (curving). All resulting filmsappeared identical, regardless of doping concentration, and fractured intopieces up to 0.5 cm2 in size. Annealing began visibly affecting the film attemperatures as low as 60◦C.Additional resistivity calculations were performed on larger pieces of thefilms along 〈100〉. GaInSb was formed into two contacts on a glass slideand the pieces of fractured film were measured and then placed on the glassslide bridging the two GaInSb electrodes where additional eutectic liquidwas added to form full contact with the edges of the film. Measurements1073.4. Growing and Characterizing Al:ZnO Filmsindicated a significant drop in electrical resistivity of all films, with the un-doped film at 20± 10 Ωcm and other films annealed at 200◦C also providinga similar resistivity. Films annealing at the higher temperature, 400◦C,demonstrated a higher resistivity of 200± 50 Ωcm.XRD analysis of the annealed films produced identical, but broader,peaks as those show in Figure 3.21. The increased peak width can be at-tributed to the samples under study being curved by the annealing process.The significant change in optical and electronic properties of the films af-ter a low temperature anneal indicate that a significant amount of unreactedZn(OH)2 or Al(OH)3 is still present in the film. The application of furtherheat prompts a thermal decomposition process but at such low temperaturesthe resulting products cannot effectively integrate into the existing ZnO lat-tice, causing deformation and fracturing of the film. Sintering at very hightemperature would likely return the ZnO film to a more resistive, opticallytransparent state.3.4.3 Summary of Al:ZnO GrowthThe formation of thick film Al:ZnO was explored using an electrochemicalnitrate system. A new growth methodology is presented where Al(NO3)3 isused as a dopant agent and is introduced into the growth solution gradu-ally throughout the deposition to maximize doping consistency in the film.Films up to 45± 5 µm are grown over 11 hour depositions with Al3+ molarconcentrations of up to 1.72% (Al.034Zn.966O) being realized. The influ-ence of Al(NO3)3 concentration in the growth solution on film thickness wasexplored, where approximate concentrations above 30 µmol/L precipitatedsufficient Al(OH)3 to significantly interfere with ZnO film growth.ZnO crystal size and overall crystallinity for variably doped ZnO filmswas examined. The crystal size began dropping with dopant concentrationsabove 3 µmol/L, demonstrating two contrasting dopant integration effects.Some substitution doping occurs, causing a shift in XRD (002) peak anda drop in film resistivity, but increasingly higher concentrations of Al3+ inthe growth solution interfere with monocrystalline ZnO growth, reducingthe substitution doping effect, and integrating more Al(OH)3 directly intoand onto the film. Evidence supporting the integration of hydroxide intothe films include 50% greater film thickness than electrochemically predictedbased on charge transfer, chemical reactions at 80◦C after deposition comple-tion and film drying, a higher measured percentage of oxygen to zinc withinthe grown films, and work by others on electrochemical and hydrothermalgrowth of ZnO drawing the same conclusion[67, 156].1083.5. Release of Films from the SubstrateUnder no conditions was it possible to achieve the theoretical 2000 S/cmelectrical conductivity reportedly possible for the Al:ZnO material sys-tem. The highest electrical conductivity was achieved at a growth solutionAl(NO3)3 concentration of 30 µmol/L yielding 2.5 mS/cm prior to anneal-ing. Low temperature annealing significantly improved the film electricalconductivity of all samples tested while concurrently rendering the filmswhite, opaque, and structurally uneven.3.5 Release of Films from the SubstrateIn order to access both sides of the ZnO film for thermoelectric testing, theZnO film must first be removed from the glass slide on which it was grown. Avariety of methods were explored for gaining access to both sides of the film,with some discussed in Appendix A.3. Considering the utility of releasing agrown structure from a glass slide after undergoing a deposition procedurein solution, a versatile technique was developed to accommodate ZnO filmsand potentially some biological and MEMS devices as well by etching awaythe chromium layer that binds the gold layer of the substrate to the glass.This room temperature process consisting of non-toxic and optionally pH-neutral solvents presents a useful contrast to many other sacrificial layeringtechniques that require strong acids and bases, vacuum environments, ortoxic chemicals to perform the etching process. Compatibility with solution-based material deposition further increases the utility of this method overusing materials such as NaCl as a sacrificial layer.Gold is commonly used in the fabrication of many microelectromechani-cal systems (MEMS) and other microscale and nanoscale devices. Its manyuses derive from its high electrical conductivity, ductility, resistance to oxida-tion, comparative chemical inertness, biocompatibility, and special catalyticproperties[160–164]. Gold is used as a substrate for the sputtering or electro-chemical deposition of thin films[1, 165], MEMS structural components[163],and nanostructured materials[82]. Its special surface properties also makeit an ideal material for biological cell adhesion[161, 166] and as a substratefor the deposition of evaporated nanoscale oxide structures[167].Devices that use gold as the substrate are often based on gold-coatedglass slides. These slides consist of a thin layer of gold, typically 100 nm -1 µm thick, deposited on a 5 nm thick chromium adhesion layer initiallyevaporated on to the glass slide. These glass slides are used in applicationssuch as microfluidics[168] and thin film thermoelectrics[1]. These and po-tentially other applications can benefit from lifting the gold and associated1093.5. Release of Films from the Substratestructures from the glass slide using a process that does not physically orchemically damage the structure. When working with oxides or biologi-cal structures, it is particularly necessary to avoid strongly acidic and hightemperature process steps.A practical method for releasing the gold film and accompanying surfacestructure is the etching of the chromium (Cr) adhesion layer between thegold film and the glass substrate to release the gold, which has a low adhesionto glass.3.5.1 Chemical Etching of ChromiumChromium etching is typically performed using a mixture of nitric (HNO3)or perchloric (HClO4) acid and a strong oxidizer such as ceric ammoniumnitrate (H8N8CeO18)[169–171]. This method of chromium etching has sev-eral disadvantages, including the immersion of the device into an acidic andoxidizing bath, slow etching times, and high reagent cost. Tests using thisprescribed formula were performed on ZnO samples grown on gold substratesas described in Section 3.2. Despite attempts to cover the ZnO layer, whichis highly reactive to acid, using kapton tape and acrylic conformal coat,the etching dissolved the ZnO layer in every test. During the etching pro-cess, the gold became brittle and curled, creating small cracks that allowedthe etching to contact the ZnO film, destroying the sample. After severalattempts, chemical etching under extremely acidic conditions was halted.3.5.2 Electrochemical Etching of ChromiumConventional electrochemical chromium etching is generally performed ina low pH solution of sulphuric acid and is believed to follow one of manypotential dissolution paths. Commonly described possibilities are[172]:Cr(s) −−→ Cr2+ + 2 e− (3.8)orCr(s) + H2O←−→ CrOH(ad) + H+ + e− (3.9)CrOH(ad) ←−→ CrOH+ + e− (3.10)CrOH+ + H+ −−→ Cr2+ + H2O (3.11)Both sets of equations describe a constant pH reaction where the acid-ity of the etching solution does not change. Similarly, no precipitates are1103.5. Release of Films from the Substrateformed, and the free Cr2+ is deposited on the cathode throughout the ex-periment. Problematically, strong acids are still necessary for the reaction,limiting the potential applications of the technique.A new approach was examined for releasing the gold thin film that ad-dresses these issues by using a pH-neutral or basic electrochemical etchingprocess to selectively dissolve the chromium.3.5.3 Procedure and EquipmentThe standard reduction potentials to dissolve chromium, ZnO, and gold ina pH neutral, room temperature solution are 0.91 V, −1.26 V, and −1.43 V,respectively[173]. These potentials allow for a preferential etch of chromiumover ZnO and gold, which require a larger potential. Non-conductive ma-terials such as insulators and many biological molecules do not participatesignificantly in the electrochemical etching process and must only toleratephosphate or hydroxide ions in neutral or basic conditions. Strongly elec-trically insulating materials such as glass and polyimide tapes do not allowelectrons from the working electrode to penetrate the surface and oxidizethe material. Similarly, although many biological materials allow for ion ex-change through a membrane, they do not act as high conductivity electronconduits that undergo oxidation when within an electrochemical bath. Slide Preparation2.0 cm×1.5 cm gold-coated slides consisting of 1 mm glass, 5 nm of Cr as anadhesion layer[174], and 100 nm of Au as the substrate layer were acquiredfrom EMF Corp (P/N CA134). Process characterization was performed us-ing these blank gold slides with copper tape adhered at one end, protectedwith polyimide tape (3M 1205-series), acting as the wire to the potentio-stat. Etching distance was measured by marking the glass on the rear ofthe slide with permanent marker and observing the regression of chromiumthroughout the etch.Slides were separately coated and tested with 1.0 cm×1.0 cm segments ofpolyimide tape placed directly over the gold in the center of the slide and thinfilms of deposited ZnO. A diagram of the slide after ZnO deposition can beseen in Figure 3.23. Slides were prepared for 1.0 cm×1.0 cm (2.0 cm×1.5 cmslide) and 0.5 cm×0.5 cm (1.0 cm×1.0 cm slide) depositions of ZnO film. Thefilms were grown using the methods described in Section 3.4.All slides were rinsed briefly with distilled water using a spray bottle toremove any debris prior to performing the etching procedure.1113.5. Release of Films from the SubstrateFigure 3.23: A sample configuration, not shown to scale. 2.0 cm x 1.5 cmgold coated slides were procured and then partially electrochemically coatedwith a 1.0 cm×1.0 cm×20 µm thick layer of ZnO or a 1.0 cm×1.0 cm×76 µmthick layer of polyimide tape. Copper adhesive tape, protected by polyimide,was used to electrically connect the slides to a potentiostat. Solution SelectionSeveral solution ions were tested for their suitability. Preliminary testingshowed that 0.1 M KCl etched both the gold and chromium layers equally,resulting in the destruction of the test film and surrounding material. Sim-ilar effects were also seen with 0.1 M Zn(NO3)2, although some selectivityfor etching chromium preferentially to gold was apparent in that the goldfilm did not dissolve as rapidly. Other common ions, including sulphate,acetate, and cyanide were ruled out due to poor selectivity or undesirableenvironmental effects[172, 175–178]. Both sodium hydroxide (NaOH) andphosphate solutions (Na2HPO4 and NaH2PO4) showed excellent selectivityfor etching chromium without damaging the gold film. ApparatusA diagram of the electrochemical apparatus is shown in Figure 3.24. The ap-paratus required a standard potentiostat capable of providing a DC voltage,measuring current, and optionally displaying the solution potential relativeto the cathode using a reference electrode. The same apparatus used for de-positing the ZnO thin film was also used to release the gold and ZnO filmsfrom their substrates. The cathode was a conventional, reusable, 4 cm2copper strip for collecting the ionized chromium from the solution. Cop-per adhesive tape was used to attach both electrodes to the glass dish andconnect them electrically to the potentiostat. A medium flow, Ag/AgCl ref-erence electrode was also used, although precision potential control within1123.5. Release of Films from the SubstratePO43- orOH-Anode (+) Cathode (-)Cu(s) stripCr2+AdditionalSolutionSolutionLevel100 mLPolyimideLoop30°40 mL10 mLFigure 3.24: Schematics of the setup for etching the chromium from the slideand releasing the gold film. The optional reference electrode is not shownbut would be located in close proximity to the glass slide.the solution was not strictly necessary. A loop of polyimide tape securedthe sample in the pyrex dish when required. For ZnO-coated samples inexcess of 0.25 cm2 in area exposed to the etching solution, submerging thesample gradually by periodically adding additional solution, as discussed inthe following section, improves the yield of the etching process. A simplerprocedure acceptable for bare or small (<0.25 cm2), coated substrates al-lowed for mounting the device vertically on the wall of the dish and coveringthe entire substrate with etching solution at the onset of the experiment. ProcedureThe slide and solution was first prepared. Sufficient solution was necessaryto cover the slide as mounted within the apparatus by the end of the etchingprocess. When using a 300 mL, 90 mm diameter dish, 100 mL of solution isrequired.Two separate procedures were employed depending on the coating of1133.5. Release of Films from the Substratethe slide. For all slides except those coated with 1.0 cm×1.0 cm of ZnO, theslide was aligned vertically along the side wall of the dish and the entiretyof the etching solution was added at the beginning of the etch. For etchingbeneath ZnO films greater than 0.5 cm×0.5 cm in size, the slide was tiltedat 30◦ as shown in Figure 3.24 and the solution was added gradually. Thisapproach allowed chromium outside of the initial etching solution to holdthe gold in place and regularly provide new channels to allow the etchingsolution to access trapped regions of chromium when the ZnO or similarcoating material forced the gold layer against the substrate to block existingpathways as shown in Figure 3.25. In this configuration, 40 mL of initial so-lution was used with 10 mL of additional solution added every 10 minutes togradually expose the entire slide to the etching solution. If the gold film wasnot placed under tensile stress from the coating during the etching, drawingthe gold film against the substrate to interrupt the channel, then the slidecan be oriented vertically, fully immersed in the etching solution. It wasalso determined that increasing solution to temperature to 45◦C would sig-nificantly increasing etching rate and tolerance for larger films as discussedbelow.The total etching time was determined as the total time from when thepotential was applied to when the chromium was visibly absent from theetching area. A completely etched slide produced using a tilted substrateand gradual addition of etching solution can be seen in Figure 3.26.Handling of the slide and etching solution during the etching processalso required significant care. Disturbances to the solution during and afteretching could cause the gold to delaminate from the glass and float in thesolution. Under extreme disturbances the gold would tear away completely.Once the etch was complete, as determined through a visible inspectionof the backside of the substrate, the handling of the slide depended on thedesired effect on the gold film and device. Drawing the glass slide throughthe etching solution may lift the gold film away from the surface of the glass.If the device on the gold film is stiff, removing the slide from the etchingsolution and shaking the gold film or substrate while the slide is still wetpermits lifting or sliding the gold film and device from the glass slide. If theslide dries, the gold film lightly adheres to the glass surface, making removaldifficult.The effects of applied potential, temperature, ionic concentration, andstirring were all examined. Unless otherwise indicated, experiments wereconducted at a reference potential of 0.8 V vs. Ag/AgCl, a solution temper-ature of 20◦C, no stirring, and with an ionic concentration of 0.1 M, pH = 7for sodium phosphate or pH = 10 for sodium hydroxide. These are referred1143.5. Release of Films from the SubstrateGoldGlassZnOCrFilm Stress PinchedChannelEtchingStarting SolutionLevelEtched RegionUnexposed RegionGlassTrappedChromiumPinchLineSolution Level IncreasesNew Access to Trapped Region at Higher Solution Level ZnOa)b)zxz xFigure 3.25: Illustrations of a) how latent stress in the deposited film cancause the gold layer to deform against the glass, preventing etching solutionaccess to the remaining chromium, and b) how increasing solution heightcreates new paths to etched trapped regions of chromium. Illustrations arenot to as normal conditions.3.5.4 Results and Conclusions3.5.4.1 Characterization of Blank SlidesEtching time as a function of etching distance for both phosphate and hy-droxide solutions was measured and is shown in Figure 3.27. Polyimide tape1153.5. Release of Films from the SubstrateFigure 3.26: Photo through the glass of a 1.0 cm×1.0 cm slide showing afully chromium etched gold surface. The outline of the ZnO layer on thefront of the slide can also be seen as reducing wrinkling in the gold layer.was used to cover the long edges of the slides, only permitting etching alongthe 1.5 cm long base of the slide. Etching proceeded at the same rate alongthe full width of the slide, without favouring the centre of the slide over theedges. There is good agreement in etching rates between similarly preparedsamples with hydroxide consistently taking longer than phosphate to etch.The slower etching rate may be the result of the lower molar concentrationof hydroxide in the solution providing fewer ions to facilitate the chargetransfer between the electrodes.For uncovered slides (no ZnO or polyimide layer) the etching did notoccur exclusively from the outside edge inward; regions of chromium etchedconcurrently throughout the entire slide. No holes or abrasions were foundthrough SEM inspection of the gold surface. A slide was prepared with alledges covered to prevent etching from the edges of the slide inward. Etchingperformed using pH = 10 hydroxide under normal conditions indicated thatetching still took place beginning at dozens of sites on the surface of thegold slide, indicating the presence of holes in the gold layer through whichthe etchant could reach the chromium. The access of the etchant to thechromium layer through such pinholes was obstructed through the deposi-tion of an impermeable coating on top of the gold layer. A thicker goldlayer might reduce the number of pinholes or prevent them entirely. Foruncoated slides, the simultaneous etching of regions throughout the slidecontributed to the error in measuring rate, particularly near the conclusionof the etching process.1163.5. Release of Films from the Substrate01234560 5 10 15 20 25Etch Distance (mm)Time (min)HydroxidePhosphateFigure 3.27: A plot showing mean etching distance as a function of time forsolutions containing hydroxide or phosphate. The etching was performed onblank gold slides under normal conditions. Etching time was measured alongone axis when the etching process crossed marked distance threshold on theslides. The horizontal error bars represent one standard deviation from theaverage, and vertical bars represent uncertainty in distance measurementsdue to the line widths of the markings on the slides.The etching rate for a 5 nm thick layer of chromium and uncovered goldfilm is estimated at 2.4 µm/s for hydroxide and 5.5 µm/s for phosphate un-der normal conditions. These numbers represent the linear region near thebeginning of the etching process as shown in Figure 3.27. Acceleration ofthe etching rate later in the process occurred consistently with every test asthe area of chromium exposed to the etching solution rapidly decreased.Voltammetry measurements were performed using a blank gold slide andare shown in Figure 3.28a. Current saturation was achieved between 0.5 Vand 0.8 V with applied voltage vs. reference voltage, shown in Figure 3.28b,being linear in that range. Due to the wide operating range of the etchingprocess, the experiment was also be conducted without a reference electrodeby examining etching current and increasing it until the current is stablewithin 15% over a 0.2 V range.The effect of applied potential was also examined by changing the po-tential to select a reference potential between 0.6 V and 1.0 V as shown in1173.5. Release of Films from the SubstrateFigure 3.28: Electrochemical voltammogram showing a) current vs.Ag/AgCl reference electrode for hydroxide and phosphate-based solutions,and b) Ag/AgCl reference electrode potential vs. total applied potentialwhen sweeping the applied potential to produce a reference potential from 0- 1 V at a rate of 1 mV/s. The samples under test were smaller Au/Cr/glassslides approximately 1.0 cm×1.5 cm in dimension. The chromium was notcompletely removed from the sample by the end of this experiment.1183.5. Release of Films from the Substrate05101520253035400.4 0.6 0.8 1 1.2Time (min)Reference Voltage vs. Ag/AgCl (V)HydroxidePhosphateFigure 3.29: A plot showing total etching time as a function of electrochemi-cal reference potential for solutions containing hydroxide or phosphate. Theetching was performed on blank gold slides under otherwise normal con-ditions. Error bars indicate uncertainty in determining completion of theetch.Figure 3.29. The total etching time using hydroxide as the anion decreaseslinearly with increasing reference potential. From Figure 3.28, a non-linearresponse is expected between 0.6 V and 0.8 V although lower pH solutionsreduce the magnitude of this non-linear effect, as shown. The phosphateetching time does not vary significantly despite the change in potential asexpected from the relatively flat current response shown in Figure 3.28.The anion concentration was varied to determine the influence of ion con-centration on the total etching time with the results shown in Figure 3.30.Phosphate ion concentrations above 0.01 M yielded a slight increase in etch-ing rate with increasing concentration, whereas below that threshold theetching rate decreased significantly. A similar behaviour was seen for hy-droxide, where ionic concentrations above 0.1 mM increased the etching rategradually and concentrations below caused a rapid drop in etching rate. Al-though hydroxide is a slower etchant, it remains consistently effective atlower solution concentrations than phosphate.The pH of the phosphate and hydroxide solutions were measured beforeand after the etching was complete using pH strips and were found to be the1193.5. Release of Films from the Substrate0102030405060Time (min)Anion Molar Concentration (mol/L)HydroxidePhosphate10010-110-210-310-410-5Figure 3.30: A plot showing total etching time as a function of etching so-lution concentration for solutions containing hydroxide or phosphate. Theetching was performed on blank gold slides under otherwise normal con-ditions. Error bars indicate uncertainty in determining completion of theetch.same within measurement error, although a drop of 0.5 in hydroxide pH wasobserved at pH > 10, indicating that some hydroxide is chemically consumedin either the etching process or by reacting with the copper counter electrode.The effect of solution temperature is shown in Figure 3.31. Etching rateis similar within error for both solutions from 65◦C to 85◦C with 45◦C pro-viding the fastest etching time for both ionic solutions. Operating at 85◦Crequired refilling the solution with distilled water periodically to compen-sate for evaporation and ensure a consistent etchant concentration. It is notclear why 45 ◦C presented a local maximum in etching rate.The effect of stirring was also examined by adding a 1 cm long, 2 mmwide magnetic stir rod to the center of the dish and rotating the stir rodat 300 RPM throughout the etching process. Etching times of experimentsusing hydroxide conducted under normal conditions reduced from 25 minuteson average to 10 minutes. Similar experiments involving phosphate resultedin etching times of 6 minutes rather than the 9 minutes required to completethe etch without stirring. Stirring did have a negative consequence in thatthe freed gold film was torn away from the substrate in approximately half1203.5. Release of Films from the Substrate051015202530350 20 40 60 80 100Time (min)Temperature (°C)HydroxidePhosphateFigure 3.31: Total etching time as a function of solution temperature forsolutions containing hydroxide or phosphate. The etching was performedon blank gold slides under otherwise normal conditions. Error bars indicateuncertainty in determining completion of the etch.of the tests. Etching and Characterization of Coated SlidesEtching experiments were performed using both polyimide and ZnO coatedslides. Dimensions of coating materials were varied, but the coating mate-rials were always situated in the center of the test slide. The ZnO layer waselectrochemically deposited and varied between 40 µm and 50 µm in thick-ness. The 76 µm thick polyimide had an adhesive backing and was physicallyapplied to the gold surface. The surface coatings prevented the etching so-lution from reaching the chromium layers except by travelling between theglass and gold layers. They also applied stress to the gold layer, potentiallyimpeding the etching process by pinching the gold against the glass and pre-venting etching solution from reaching chromium beneath the coating layer.The etching times are summarized in Table 3.1. In all cases, coated slidesdid etch more slowly than uncoated slides. The etching rate for the poly-imide coated slides was consistent between experiments and did not changesignificantly with coating size. Etching ZnO samples was less predictable,1213.5. Release of Films from the SubstrateTable 3.1: Etching Times for Coated SlidesMaterial Size (cm2) Etchant Total Time (min)Polyimide 0.36 Phosphate 50± 15Polyimide 1.0 Phosphate 58± 20ZnO 0.25 Phosphate 154± 50ZnO 1.0 Hydroxide 420± 140with some samples failing to completely etch free from the glass substrate.Tilting the substrate and gradually applying the solution as described in theAppendix A.2 helped significantly and was necessary for etching slides withZnO coatings greater than 0.5 cm×0.5 cm in size.The etching distance profile of a partially covered slide is shown in Fig-ure 3.32. A 1 cm wide strip of polyimide tape was adhered to the slide2.5 mm from the edge in the direction of etching. Etching rates are similarfor both the covered and uncovered films prior to encountering the obstruc-tion. Once under the tape, etching slows significantly and proceeds with asimilar profile as the hydroxide etch shown in Figure 3.27. The etching ratecalculated early in the etching of the covered area is 2.2 µm/s compared tothe etching rate of 9.1 µm/s of the uncovered section.For slides coated with 1.0 cm×1.0 cm of ZnO, it was not possible tocomplete an etch at room temperature without tilting the slide and addingetching solution gradually. The etching process would proceed only to ter-minate prematurely, presumably due to latent stress in the film forcing theunderetched portion of the gold film against the glass and preventing theionic solution from reaching the remaining chromium. Smaller dimensionZnO films of 0.5 cm×0.5 cm were successfully etched to completion with ev-ery test.No particulates were formed in any etching experiment. The impact ofthe hydroxide etching procedure on the surface morphology of the ZnO filmis shown in Figure 3.33. There is no discernible difference in the morphologyof the surface of the bare ZnO film after the etching process, suggesting thathydroxide is a good etching anion for removing the underlying chromiumwithout impacting the structural and morphological properties of oxideslike ZnO.Unlike using hydroxide as the anion, a distinct effect on the surfacemorphology of the ZnO film is apparent when etching with phosphate asshown in Figure 3.34. Figure 3.34a compares the bulk of the etched film to1223.5. Release of Films from the Substrate0246810120 50 100 150Etch Distance (mm)Time (min)UncoveredPartially Covered (Polyimide)Partially Covered (ZnO)Transition to Covered (Polyimide)Transition to Covered (ZnO)Figure 3.32: Shown are etching times as a function of distance of 1) asample with only glass/Au/Cr etched in phosphate under normal conditions,2) a sample covered with a 1 cm wide strip of polyimide tape beginning2.5 mm from the edge etched in phosphate under normal conditions, and3) a sample covered with a 1 cm2 ZnO layer beginning 4 mm from the edgeetched vertically in hydroxide (did not complete) under normal conditions.Time was measured as the etching process crossed marked distances on theslides.that of the pristine, unetched ZnO film shown in Figure 3.34b. The bulkmorphology remains very similar, indicating that the damage imposed bythe phosphate etching is limited to the surface of the film. The etched filmis also visibly discoloured, further indicating a change in its composition. Summary of Slide ReleaseThe electrochemical etching of nanoscale-thickness chromium adhesion lay-ers to lift off gold layers and a deposited structure using an electrochemicalmethod was demonstrated. Total etching time as a function of appliedpotential, anion concentration, temperature, and solution agitation was ex-plored. The effect of coating the gold surface was also examined for varyingsizes of polyimide and ZnO coating layers. Using hydroxide as the reac-tion anion resulted in a basic solution but facilitated a fast etch and release1233.5. Release of Films from the SubstrateFigure 3.33: SEM images taken at 20 kV showing a ZnO film grown at3 mA/cm2 current density a) before and b) after etching the chromium layerin pH = 11 sodium hydroxide.of gold and ZnO film without damaging the ZnO structure. A similar etchusing phosphate as the anion was also examined due to its potential applica-tions in biological and pH-sensitive MEMS devices. The phosphate etchingprocess was faster than using hydroxide but it did modify the surface of theZnO film, indicating poor chemical compatibility with oxides. Other an-ions such as nitrates and chlorides were tested and showed poor selectivity,etching the gold as well as the chromium.1243.6. ZnO Nanostructural GrowthFigure 3.34: SEM images taken at 20 kV showing the effect of a 90 minutesodium phosphate etch on the surface morphology of ZnO where a) is theedge of the film exposed after etching and taken at 45◦to the horizontal andb) is a similar image of a pristine, unetched ZnO film. The effect appearsconfined to the surface and does not change the morphology of the bulk.3.6 ZnO Nanostructural GrowthZnO-based nanostructures are defined here as materials based on ZnO thatpossess features, such as dimensional constraints (ie. nanowires), interfaces(ie. sintered nanoparticles), or structural variations (ie. nanovoids, het-erostructures) with dimensions under 1 µm in size. ZnO can be formed intonanowires, stacked platelets, thin films, nanotrees, nanotubes, and othercomplex structures[40]. In Section 2.2 various nanostructures were theoret-ically considered for their relative thermoelectric potential. Although these1253.6. ZnO Nanostructural Growthstructures cannot be electrochemically synthesized using the methods pro-posed herein, attempts were made to demonstrate proof of concept formationof nanostructures at a larger scale. Of the structures considered, templateassisted nanowires, nanovoided bulk films, and heterostructures were ex-plored experimentally. Of these structures, only the nanovoided bulk filmswere fully synthesized and characterized. Experimental details and the re-sults on the growth of the other structures can be found in Appendix A. Nanovoided Bulk GrowthNanovoided bulk materials are bulk materials that have a high density oflocalized lattice defects (voids) that scatter phonons, thereby reducing ther-mal conductivity. The modelling study described in Chapter 2 suggestedthat a nanovoided bulk ZnO configuration may be the best performing ther-moelectric configuration possible of the nanostructured variations studied.Nanovoided materials have been successfully fabricated through a varietyof processes with some of the best examples coming from ball mill and sin-tered Al:ZnO[62, 69, 85, 179–182]. Methods such as ball mill and sinteringare limited in their ability to generate anisotropic features such as gradientdoping patterns, so the focus in this section is the formation of nanovoidedstructures grown using an electrochemical method and sacrificial material. Zinc Hydroxide MethodAs observed in Section 3.4, the electrochemical formation of Al:ZnO doesnot generate a pure crystal. Some particles of Zn(OH)2 persist within thefilm, interfering with crystal growth and film conductivity. This effect wasalso witnessed by others, who demonstrated that a subsequent low tempera-ture (<400◦C) annealing step thermally decomposed the remaining hydrox-ide, leaving multiple submicron-sized pockets within the film[156]. Usinga similar procedure, a reaction was noted in this work when Al:ZnO filmswere annealed at low temperatures, with films turning from transparent toopaquely white while concurrently deforming along all axes. The low tem-perature anneal was also accompanied with a improvement in film electricalconductivity when measured independently.To better understand the behaviour of the intermediate Zn(OH)2 step,separate solutions of 0.1 M Zn(NO3)2 and 1 M NaOH were prepared. Atroom temperature, 100 µL drops of NaOH were added to the solution ofzinc nitrate. Every drop generated a sudden burst of nearly transparent,fine, white precipitate that appeared in solution and sunk to the bottom1263.6. ZnO Nanostructural Growthof the beaker without aggregating. The material retained structure andtranslucency such that subsequent drops of sodium hydroxide quickly filledthe beaker with a hazy, white suspension giving the beaker a cloudy lookwithout forming a solid structure. Straining the solution through a filterand then analyzing the resulting white power with an SEM produced imagesshown in Figure 3.35.a)b)Figure 3.35: SEM images taken at 20 kV showing Zn(OH)2 particles gener-ated in solution by adding small quantities of NaOH analogous to hydroxideformation during electrochemical deposition.The white powder consisted of nanoparticles of Zn(OH)2 measurablyranging from 10 nm to 300 nm in size. Although the conditions in an elec-trochemical bath are not identical to those in this experiment, the tendencyfor Zn(NO3)2 to form nanoparticles when exposed to small quantities of ba-1273.6. ZnO Nanostructural Growthsic hydroxide may inform the formation of pockets of zinc hydroxide withinthe film. To confirm the presence of these particles, conventional 1 mA/cm2films were galvanostatically grown under the conditions described in Sec-tion 3.2 and Section 3.3.1. The films were annealed at 200◦C and the re-sulting white film was mechanically broken in half. The cross-section of thefilm was examined using an SEM as shown in Figure 3.36, indicating thepresence of varying densities of voids throughout the film. The void sizesare also consistent with the Zn(OH)2 particles shown in Figure 3.35.a) b)c) d)20 μm 2 μm3 μm 1 μmFigure 3.36: SEM images taken at 15 kV showing 200◦C annealed, undopedZnO where a) shows the cross-section of the film, b) shows a higher zoomsection of the cross-section covered in small voids, c) shows another sectionof the film also covered in holes, and d) magnifies the voids themselves whichrange from 50 nm to 400 nm in diameter.The integration of voids into the film by performing a low temperatureanneal of the film was successfully demonstrated, although more work tobetter control the size and distribution of the voids is recommended.1283.7. Growth and Release Summary3.6.1.2 Eosin Y Dye MethodEosin Y is a common red/yellow organic dye. When used during electro-chemical deposition of ZnO, the dye integrates into the film and can thenbe dissolved after the deposition is complete, leaving pores within the ZnOfilm[85]. Experiments have been successfully completed using both nitrateand chloride ZnO growth systems[179, 180, 183, 184]. Once film growth iscomplete, applying a diluted base solution dissolves the dye, leaving voidsand a highly porous ZnO film[85].Undoped films were grown using the conditions described in Section 3.2and Section 3.3.1 with the addition of 50 µmol/L Eosin Y to the grownsolution at the beginning of the deposition. The dye adsorbed very effec-tively into the film, producing a bright red colouring once the depositionwas complete. The red film was then immersed in 100 mL of pH = 12 KOHsolution for 12 hours to remove the dye. Despite the long duration, therewas no detectable change in the colour in the film. Desorption experimentsperformed by others used very thin films of ZnO, with some authors notingthat even with thin films the dye did not completely desorb[184]. The redfilm after desorption was placed in the SEM to examine its morphology,but although small voids were seen on the surface of the film, they did notpermeate throughout the film.Although the use of the dye as a sacrificial material is well established inliterature, the ability to remove the dye from thicker ZnO films is very lim-ited due to the inability of deeply integrated dye to desorb through exposureto potassium hydroxide.3.7 Growth and Release SummaryZnO was successfully synthesized using an electrochemical method. A signif-icant challenge was improving the existing ZnO electrodeposition methodol-ogy to enable the growth of thicker, high quality films. Existing methodolo-gies involved counter electrodes that resulted in a drop in solution pH duringthe growth period, causing damage to the grown films. Potentiostatic growthwith an Ag/AgCl reference electrode also proved inappropriate for thickerfilm growth due to the buildup of contaminant chemicals within the film asthe growth proceeded. The contaminants caused morphological, crystalline,and electrical effects all detrimental for a ZnO-based thermoelectric mate-rial. Al:ZnO was successfully synthesized with aluminum integration above2% demonstrated, a ratio that others have determined provides the bestthermoelectric performance in the material system[44, 53]. One significant1293.7. Growth and Release Summarychallenge to overcome is in improving the conductivity of the film. Althoughthe films show extremely good growth selectivity along 〈002〉, the electricalconductance of the film is much lower than expected, likely attributableto Zn(OH)2 nanoparticles that are integrated into film during depositioninterfering with the monocrystallinity of the film. The activation of thealuminum within the film is also poor, but can be improved through lowtemperature annealing.Al:ZnO films up to 45± 5 µm in thickness were successfully synthesizedusing a low cost, scalable fabrication technology. Conventional methods forgaining access to both sides of the ZnO film were explored but were foundnot suitable. A methodology was developed for separating the films from theglass growth substrate by using electrochemical chromium etching, enablingaccess to both sides of the films without the risk of mechanically freeing thefilm or affecting the chemical and morphological integrity of the samples.Nanostructured films were also successfully grown, although feature sizeswithin the films were 1-2 orders of magnitude larger than those examinedthrough modelling work in Chapter 2. Template-assisted nanowire arraysand ZnO/Zn heterostructure films were synthesized, but were not pursuedfurther due to fabrication challenges involving their consistency, quality, andfragility (see Appendix A.4). Voided nanostructures were fabricated usingtwo methods: Dye integration and low temperature annealing. The formerwas able to produce small voids across the surface of the ZnO film but thedye removal process was unable to penetrate the full thickness of the film.The latter worked well, producing voids throughout the bulk of the film withdiameters ranging from tens of nanometres to hundreds of nanometres. Theannealing of the films caused the films to warp and change shape, whichmust be considered when characterizing the films in a thermoelectric testapparatus.The voids in the ZnO films were larger than those modelled in Sec-tion 2.2.9 and their consistency within the bulk material was qualitativelyless than the 30% volumetric voiding proposed in that section. Voids inthe experimentally grown films should reduce film thermal conductivity toa lesser extent than those examined in the modelling work, but may stillhave a favourable STEF due to the reduced effect on electrical conductiv-ity. Phonons with long MFP will still be disrupted where electrons, whichgenerally have much shorter MFP, will propagate unhindered by the voids.The integration of hydroxide and poor crystallinity will be the dominantfactors affecting both electrical and thermal conductivity. For greater mod-elling accuracy, future work could increase simulation cell size to optimizethe void size and density at larger scales to allow comparison with experi-1303.7. Growth and Release Summarymental results. Growth parameters affecting the void size and density, suchas solution pH and nanoparticle preloading, could also be explored. Moreimmediate challenges to overcome are the poor dopant activation of thealuminum and overall low electrical conductivity of the doped films.131Chapter 4ThermoelectricCharacterization of ZnOFilmsFull characterization of a thermoelectric material involves determining crit-ical material parameters over a range of temperatures such as the Seebeckcoefficient, electrical and thermal conductivities, thermal expansion coef-ficients, and melting temperature. The former three parameters are themost critical for determining the thermoelectric performance of a mate-rial as described by (1.11) and (1.19). Characterization of thermoelectricmaterials is commonly performed using either direct measurement or Har-man measurement[185–187]. Direct measurement involves placing a materialsample between two electrodes and applying a known thermal flux throughthe material. The temperature on either side of the material is measured,along with its electrical conductivity and Seebeck-induced voltage. Thematerial is tested at multiple temperatures to determine the temperature-dependent Seebeck coefficient and conductivity trends.The Harman method involves situating a material in an adiabatic envi-ronment and applying a current through the material. The applied currentgenerates a Peltier cooling response across the material which produces atemperature gradient. The current is then stopped and the potential acrossthe material is immediately measured, which, when combined with an alter-nating current (AC) potential measurement to yield film electrical resistance,can be used to calculate ZT directly[186],ZT =VdcVac− 1. (4.1)Enhanced versions of the Harman method also exist, incorporating tem-perature measurements to yield specific material properties[187], or tran-sient excitation for greater accuracy in measurements[188]. Like the directmethod, the Harman method is best applied to thick thermoelectric mate-rials where thermal conductance is lower and interface uncertainties can be132Chapter 4. Thermoelectric Characterization of ZnO Filmsminimized. The Harman method also requires that the material have suffi-cient thermoelectric performance to produce a useful temperature differenceacross the material that won’t immediately dissipate back through the film.Despite its growing popularity, the Harman method may provide largeerrors when characterizing thin film materials due to the non-negligible ef-fects of contact resistance and heat leakage[189]. Direct measurement is thepreferred method for characterizing anisotropic, low dimensional, thermo-electric materials, although its use also presents challenges[190–193]. Ther-mal losses and ambiguity in interface effects between the test apparatus anddevice under test (DUT) often limit accurate thermoelectric characterizationto only the material Seebeck coefficient[191–193].To minimize interface errors, direct and Harman methods for character-izing thin film thermoelectric materials are typically performed by applyingheating and characterization electrodes directly on to a material throughcleanroom techniques such as metal evaporation[188, 194, 195]. New mod-elling and characterization methods are also continuously under developmentto allow more accurate characterization of microscale material samples andmodules[124, 130, 196–199]. A significant limitation in these methods whendeployed experimentally is that integrating the thermoelectric test appara-tus onto the film or module requires that the apparatus be reconstructedwith every film tested. Calibration and independent verification of perfor-mance are also difficult as each apparatus can only test a single sample.Characterizing the effect of the interface between the thermoelectric ma-terial and the test apparatus is another challenge in thin film thermoelectriccharacterization. Due to the small volume of material under consideration,the interface between that material and the surrounding apparatus can playan important role in electrical and thermal characterization of the device.Malleable interface materials with exceptionally high thermal and electricalconductivities are desired which can mount flush against the surface of thetest material while also permitting the direct application of a known thermalflux and temperature gradient to the material.Many material properties, including electrical resistance, crystallinity,and surface morphology, have already been investigated in Chapter 3. Avariety of thermal interface materials are tested for their potential use inthermoelectric direct measurement, and a custom, reusable thermoelectrictest apparatus is constructured, calibrated, validated, and used for the char-acterization of thin films.1334.1. Interface Materials4.1 Interface MaterialsAn interface material forms the interconnect between the thermoelectricmaterial, Al:ZnO, and the surrounding module or test apparatus. The ma-terial must provide an ohmic contact with very high thermal and electricalconductivities, deform to fill vacancies between the apparatus electrode andtest material surface, and be deployable in extremely thin layers to min-imize its influence on the characterization of the thermoelectric material.Five materials were examined for their viability, including GaInSn liquidmetal eutectic from GalliumSource, LLC, Carbon Conductive Grease fromMG Chemicals, CW7100 Silver Conductive Grease from Chemtronics, HighConductivity Silver Paint from SPI Supplies, and Wire Glue from AndersProducts. GaInSn and other gallium-based liquid metals have been usedin thermoelectric characterization for over 50 years[200], whereas the othermaterials selected are newer and are designed for heat sinking or high con-ductivity adhesion applications.4.1.1 Material Electrical CharacterizationTable 4.1 details the results of electrical resistance measurements. First,a template was used to shape the potential interface material into a 3 mmlong by 1 mm wide strip on glass. Stainless steel needle probes were placedon opposite ends of each strip to act as electrodes. Current-Voltage (IV)curves were taken using a Keithley 2635A Source Meter by sweeping thevoltage from −2 V to 2 V at 0.02 V steps taken every 5 seconds. At leastthree data sets were collected for each experiment and median values areshown. The Drop on Gold experiments involved placing a 3.0± 0.5 mmdroplet of the material directly onto a gold coated, glass slide and measuringthe conductance from a steel needle probe through the material to the goldsubstrate. The Drop on ZnO experiments were identical to the Drop onGold experiments except that the droplet of interface material was placedon identical, 45 µm thick films of ZnO grown on gold using the proceduresdescribed in Section 3.4. The ZnO was still located on the original goldgrowth substrate for the drop test.Materials demonstrating an ohmic contact presented a constant slopebetween the indicated voltages. Materials demonstrating a Schottky con-tact were non-linear, showing exponential growth in current with increasingvoltage, decreasing voltage, or both. Of all the materials characterized, onlyGaInSn was deemed electrically suitable for interfacing directly to ZnO.1344.1. Interface MaterialsTable 4.1: Summary of IV test results for characterizing the measured re-sistance, R, and IV curve shape of different interface pastes, glues, liquids,and greases. Values should only be considered accurate within an order ofmagnitude and are intended for the comparison of different possible interfacematerials rather than providing data on the absolute electrical performanceof the tested materials. Contact area between the material and substratewas regulated to 5± 2 mm2.CompoundDroplet Drop on Gold Drop on ZnOR(Ω) Shape R(Ω) Shape R(Ω) ShapeGaInSn 0 Ohmic 0 Ohmic 1000 OhmicCarbonGrease100000 Ohmic 300NearlyOhmic3000NearlyOhmicSilverGrease100 Ohmic 0 Ohmic 3000 SchottkySilverPaint10 Schottky 2NearlyOhmic200 SchottkyCarbonWire Glue3000000 Ohmic 300 Ohmic 20000 Schottky4.1.2 Interfacing to ZnO FilmsSEM images of grown ZnO films, shown in Figure 4.1, were taken to de-termine the roughness of the interface on both sides of the film. UndopedZnO films were grown using the parameters discussed in Section 3.4. Thefilms were grown to a thickness of approximately 95± 5 µm as measured bySEM, and chromium etching was used to remove the films from the glasssubstrate as described in Section 3.5. The gold film on the underside of theZnO was also gently removed using tweezers, exposing both sides of the film.As shown in Figure 4.1a and 4.1b, the underside of the ZnO has excellentcoverage on the gold substrate and is acceptably flat with average roughnessunder 200 nm. The side exposed to the solution where growth occurs is sig-nificantly rougher, with roughened blades of ZnO extending up to 5 µm fromthe surface of the ZnO. GaInSn, a yield stress fluid, demonstrated high vis-cosity and malleability when tested with probe tips, suitable for contactinga rough surface.A method for applying a thin layer of GaInSn over contact materialswas developed. Placing a drop of the material onto any substrate, includingglass, polyimide, and metals such as copper and steel, then using the syringeto recover the majority of the GaInSn, left a microscale layer of the liquid1354.1. Interface Materialsa) b)c) d)50 μm50 μm2 μm50 μmFigure 4.1: SEM images taken 20 kV at 45◦ angles showing a) gold side ZnOfilm surface and cross-section, b) gold side ZnO film surface (close up), c)solution side ZnO film surface and cross-section, and d) solution side ZnOfilm surface (close up).metal lightly adhered to the substrate. The thin layer could then be spreadacross the surface of the substrate using a conventional Kimberly Clark KimWipe. Once the surface of the substrate was coated with a thin layer ofliquid metal, more GaInSn could be added using a syringe. The additionalmaterial would wet extremely well across the entire substrate, forming avisibly flat and reflective layer of liquid metal that could serve as an interfacebetween two stiff, porous surfaces. Although this method was not attemptedon ZnO due to the fragility of the film, it was successfully deployed onboth steel and graphite surfaces, which were then used as physical electrodematerials for the thermoelectric test apparatus. The transparency of theZnO films enabled verification of a good contact by observing the spreadingof GaInSn on the underside of films as they were pressed against GaInSn-coated apparatus electrodes.Although it is possible that gallium diffused into the ZnO films during1364.2. Themoelectric Testertesting, there was no evidence of changes in film electrical or thermal prop-erties over multiple days of testing. The expectation is that gallium wouldeither replace zinc or aluminum within the film lattice, effectively dopingthe films. This behaviour would correspond to an increase in thermal andelectrical conductivity, which was not apparent throughout testing.4.2 Themoelectric TesterAs the general thermal properties of the electrochemically grown ZnO filmswere unknown, and given the high electrical resistivity of the films testedin Section 3.4, the Harman method could not be chosen as an initial testmethodology. Testing materials with high thermal conductivity and elec-trical resistivity cause measurement errors due to resistive heating, andrapidly dissipate the Peltier-induced temperature gradient, requiring ex-tremely high resolution instruments to measure the Seebeck coefficient. Thedirect method was therefore chosen to measure the thermoelectric proper-ties of the films. The direct measurement of the thermoelectric properties ofthin films occurs almost exclusively using heater and sensor elements applieddirectly to the thin films using clean room techniques, as large, reusable ap-paratuses often have difficulty in distinguishing between interface materialsand the DUT[194, 195, 201]. Despite this challenge, with ZnO films in excessof 40 µm in thickness realized through electrochemical growth, and given thehigh electrical resistivity of the film, a low cost, two electrode, reusable directmethod apparatus was constructed to perform thermoelectric measurementsof the grown films.4.2.1 DesignThe design of the apparatus was separated into two components: The en-closure and the heater probe. Each component was designed to be fabri-cated using low cost processes and materials while concurrently facilitatingmeasurements of thin films down to 50 µm in thickness and 1 cm2 in cross-sectional area. Support for temperature gradients from room temperatureto 450◦C at the heater probe was also considered essential. Early FEA sim-ulations and experiments using a simple resistive heater and doped siliconpieces of various dimensions confirmed that open air thermoelectric mea-surements were too inaccurate and impractical regardless of the complexityof the calibration process, and a design capable of performing measurementsin a vacuum was deemed essential. A maximum applied thermal power of1374.2. Themoelectric Tester20 W was chosen for the design, allowing for the use of forced air cooling ofthe apparatus heat sink.Electrical resistivity and the Seebeck coefficient were measured usingan Agilent 2635A System Sourcemeter. Power for the electrical heater ele-ment was provided by an Agilent N5751A DC power supply. Temperaturemeasurement was performed using Maxim MAX31855 K-type cold junc-tion temperature compensated thermocouple interface ICs connected to aNetburner kit for SPI to Ethernet conversion. The vacuum was providedby a Vacuubrand RZ-6 rotary vane pump and was measured to be below0.01 mBar for all experiments. LabView was selected as the software packageto interface with measurement equipment and perform automated temper-ature steps and measurements. Both Netburner and Labview code can befound in Appendix B and Appendix C, respectively. Test Apparatus EnclosureThe test apparatus enclosure consisted of a polished, 1/4” thick aluminumplate drilled with holes for wire feedthroughs. A drawing for the plate canbe found in Appendix B. A groove was cut in the plate to allow the enclosurelid to sink into the rubber gasket and form a seal. Bolts in each corner ofthe enclosure outside of the vacuum area provided mounting for supportposts which raised the apparatus high enough to allow the adhesion of aheat sink and fan to the underside of the base plate directly beneath thelocation of the device under test. Figure 4.2 illustrates the configuration ofthe test apparatus enclosure. Wire feedthroughs were populated with brasspins soldered to wire and then potted in place using two part resin epoxy.Thermocouple interface electronics were located within the vacuum areaof the enclosure to minimize potential sources for noise and interference onthermocouple leads. The thermocouples used were Omega CHAL-005 K-type base wire thermocouples with 12” lengths and 0.005” diameters. Thesmall diameter was selected to minimize conductive heat losses through thethermocouple leads. The entire apparatus was covered during operationusing a hemispherical aluminum bowl resting on a 1/8” neoprene rubbergasket. Both metal and glass covers were considered, but metal produceda more reliable seal at low cost, and its opaqueness and high thermal con-ductivity facilitated a more consistent radiative power transfer calculation asdiscussed in Section 4.3.1. An opaque cover also prevented optical excitationof oxygen dopants in the ZnO films[202].To apply a consistent force on the heater probe and DUT, a pivot arma-ture was constructed. A T-shaped steel and glass rod assembly connected1384.2. Themoelectric TesterThermal Epoxy, Fan and HeatsinkAluminumBaseplateNeopreneGasketWireFeedthrusVacuumPortVacuumSteel pivotGlass rodAluminum LidMassThermocoupleElectronics HeaterFilmFigure 4.2: Overview diagram of thermoelectric test apparatus.loosely to an inverted steel bolt rested on the heater probe during testing asshown in Fig. 4.2. Weights placed on the opposite end of the horizontal steelrod allowed for the configuration of the applied force to the heater probelocated at the base of the vertical glass rod component of the assembly. The1 mm thin, 7.5 cm glass piece provided good thermal resistance while alsosupplying sufficient mechanical stiffness to hold the heater probe in place. Adesign involving a strain gauge and two bolts on either side of the rod assem-bly was also constructed and tested, but even slight flexure in the aluminumbase plate while transitioning to and from the vacuum state caused radicalshifts in the force applied to the DUT. A free weight system compensatesfor slight mechanical deformations of the base plate, permitting the use of athinner material and correspondingly improved heat dissipation. The entirerod assembly weighed 48 g and 36 g of additional weight was added at thefar end of the 9.2 cm long pivot, yielding a downward force of 1.2 N ontothe probe. Attempts at providing a greater force typically resulted in thefracture of the ZnO films. Test Apparatus Heater ProbeThe heater probe provided several functions. It converted applied electricalcurrent to thermal power, measured temperature as close to the top of theDUT as possible, conveyed a uniform force across the surface of the film,provided a uniform and low resistance electrical contact across the surfaceof the DUT, and withstood high temperatures in a vacuum environment1394.2. Themoelectric Testerwithout significantly changing its electrical, thermal, or optical characteris-tics. On the underside of the DUT, the base plate performed complementaryfunctions, including sinking thermal energy, measuring temperature as closeas possible to the bottom of the DUT, providing a low electrical resistancecontact, and evenly contacting the entire bottom surface of the DUT. Oneof the greatest challenges in measuring thin films using this direct methodwas in avoiding a short circuit between the heater probe and base plate.An illustration of the heater probe and base plate assembly is shownin Figure 4.3. The heater probe was designed using a conventional bottlecap as a substrate. The thin steel, once sanded and polished, provided anacceptably flat and conductive surface. The ridges around the cap also pro-vided crimping sites for connecting a 26 AWG electrical wire to the heaterprobe without the need for solder, thereby simplifying interconnectivity athigh temperature and allowing easy and low cost replacement of the heat-ing element. The 26 mm outer diameter, 5.5 mm high cap was filled witha 3 mm thick layer of Omega OB-400 thermally conductive cement. Ap-proximately 30 cm of Manelco NW60-36 AWG nichrome (nickel chromiumalloy) wire was coiled and then placed in a circular formation into the cap.Earlier experiments with pre-wound tungsten coils failed to reach tempera-tures of 350◦C without failure, as the tungsten oxidized due to contact withthe cement and fractured from thermal stress. The nichrome wire survivedabove 450◦C and demonstrated negligible drift in resistance over the fulltemperature range. A thermocouple was then placed in the centre of thecap while the cement cured. The cement acted as a good electrical insu-lator, and despite the proximity between the nichrome, thermocouple, andsteel of the cap, negligible electrical leakage current was detected. Boththe nichrome coil and thermocouple were placed as low as possible into thecement to minimize the amount of material between the steel cap, thermalpower source, and thermocouples.Once cured over 24 hours, the cap was heated to 350◦C for 12 hoursto further cure the cement, at which point it turned a beige/rose colour.High current leads were connected to the nichrome element by twisting thewire ends together and thermocouple leads were directly soldered to theirrespective instrumentation ICs, leaving at minimum 15 cm of open wire tomaximize thermal resistance. Similarly, a minimum of 15 cm in all otherwire leads connecting to the heater probe was used to minimize conductivelosses through the wiring assembly. Once in place, a thin GaInSn layer wasapplied to the underside of the heater probe in the approximate shape ofthe DUT. Experimentally, the DUTs tested strongly adhered to the heaterprobe through a vacuum suction effect resulting from a combination of the1404.2. Themoelectric TesterBase plateThermocoupleAg Conductive GreaseGraphite SheetFilmNichromeWindingThermalCementSteelHolderGaInSnFigure 4.3: Close up diagram of the thermoelectric test apparatus heatingelement, interface, and DUT.liquid metal interface material and smooth surfaces of the DUT and probe.Excess GaInSn could then be removed from around the DUT to minimizethe likelihood of a short circuit between the heater probe and the base plate.Due to the strong chemical interaction between gallium and aluminum,a secondary material to cover the base plate and form the thermal andelectrical contact with the DUT was selected. A thin graphite sheet (Pana-sonic EYGS091203), 3 cm long and 2 cm wide was selected for this purpose.The graphite sheet datasheet reported a thickness of 25 µm with an in-plane thermal conductivity of 1600 W m−1 K−1 and electrical conductivityof 20 000 S/cm. The graphite was adhered to the aluminum plate using ITWChemtronics CW7100 silver conductive grease. Adjacent to the 2 cm×2 cmtarget area, a thermocouple was covered with polyimide tape and was placedon the graphite film. Measuring temperature directly beneath the DUTwould have been challenging as the surface of the substrate must be ex-tremely flat. The high thermal conductivity of the graphite was leveragedto minimize the temperature difference between the underside of the DUTand the thermocouple. The graphite was then covered with a thin layerof GaInSn using the same method and parameters for covering the heaterprobe.Electrical measurements were performed using a 2-wire or 4-wire method.For large starting resistance above 25 Ω a 2-wire method was used withresistance measured at 0.1 V applied across the film. For initial resistancebelow that threshold, both resistance and Seebeck voltage was measuredusing a 4-wire method with the signal wires connecting directly to the capand graphite to minimize the effects of other losses in the system. Measuredresistance of the 4-wire method under short circuit conditions was less than15 mΩ with 100 µΩ resolution.1414.3. Thermoelectric Tester Calibration and Validation4.3 Thermoelectric Tester Calibration andValidation4.3.1 Calibration MethodologyTo maximize the accuracy of the measurements, a three step calibrationprocess was devised. A simplified model of the heat transfer using electricalanalogs is shown in Figure 4.4. QH is the thermal power produced by thenichrome heating coil in the temperature probe. TH is the high tempera-ture measured from the heater probe in close proximity to the surface ofthe DUT. RO represents the non-linear losses due to radiation, convection,and conduction from the heater probe to the surrounding environment. RHrepresents the linear thermal resistance between the high temperature ther-mocouple and the bottom of the heater probe as well as any resistive lossesfrom the graphite on the base plate to its low temperature measurementthermocouple (represented by the ground in the figure). RI represents thetotal cross-sectional area dependent thermal resistance between the surfaceof the DUT and both the heater probe and graphite. RD is the thermalresistance of the DUT, which is what must be accurately measured.TRORHRIRDQH THFigure 4.4: Circuit analog for heat flow through the heater probe, interface,and device.1424.3. Thermoelectric Tester Calibration and ValidationThe first step in the calibration process is the open circuit measurement.For this measurement, no DUT is used and the heater probe assembly issuspended in the vacuum. Schematically, this represents the removal of RDand the direct measurement of RO by considering the difference betweenTH and ground (TL) as a function of applied power. Ideally, the vacuumminimizes convective losses and proper cable management and thin wiresminimize conductive losses. Both convective and conductive losses wouldpresent a linear relationship between power and temperature. Radiativelosses follow the Stefan-Boltzmann law for power transfer,Qloss(T ) = eσA(T4 − T 4C), (4.2)where e is the emissivity and σ is the Stefan-Boltzmann constant. Theequation represents a strictly fourth order relationship between power andtemperature. Although an ideal instrument would only use the fourth orderterm, a full polynomial fit is performed over a wide range of temperaturesand power settings to derive the open circuit relationship between heaterprobe temperature vs. enclosure temperature (TC) and thermal power lossthrough methods other than the DUT.The second step in the calibration process is the closed circuit measure-ment. This measurement involves coating a matching surface area of theheater probe and graphite base plate with GaInSn and then connecting thetwo together. This measurement sets RD to 0 and allows the determinationof RH+RI . Electrical resistance and Seebeck coefficient are also measured asa function of temperature to provide a linear compensation factor for futureDUT measurements. Ideally, this measurement would yield no temperaturechange as a function of heater power.The third step requires the placement of a characterized, high conduc-tivity material with a large Seebeck coefficient between the heater and thegraphite. The purpose of this test is to determine the ratio between RHand RI . This discrimination is important as the former is not dependent onthe cross-sectional area of the DUT whereas the latter is. A proper ratio,with open and closed calibration data also considered, will yield concurrentlycorrect thermal conductivity and Seebeck coefficients for the material underexamination.An additional correction involves measuring the resistance between thecontacts on the heater probe to the source of the current for the heater.Knowing this resistance enables compensation for losses along the wiring tothe heater. A continuous 4-wire measurement would be a better solution,but it was desirable to minimize the amount of wiring both within the domeand to the heater probe.1434.3. Thermoelectric Tester Calibration and ValidationThe calibration as a whole is only strictly necessary when performingtests on materials with very high thermal conductivity or at high temper-atures. Measuring the former is very sensitive to RH and RI whereas thelatter is sensitive to e and the accuracy of temperature measurements. Ear-lier experiments using a cooling coil located in the same vacuum chamberas the DUT and heater probe failed due to variations in temperature alongthe coil making predicting radiative transfer prohibitively complex.The calibration coefficients are determined using the following steps:• Load data sets from open and closed calibration runs.• Subtract wiring resistive losses from the thermal power measurementsof both losses, providing a corrected thermal power generated at theheater probe.• Calculate a fourth order polynomial fit of open circuit differential tem-perature, TH−TC , vs. thermal power for RO, normalized by full heaterprobe surface area.• Calculate a first order fit of closed circuit differential temperature vs.thermal power for RH + RI , normalized by contact area between theprobe and plate.• Calculate first order fits for electrical resistance and Seebeck coeffi-cients as a function of differential temperature.• Load data from the high thermal conductivity sample.• Apply open and closed circuit calibration coefficients (see below) iter-atively while adjusting RHIratio until measured thermal conductivityand Seebeck agree with material values.These coefficients are then applied to data using the follow steps:• Load calibration coefficients and sample data set.• Subtract wiring resistive losses from the thermal power measurementsusing measured cable resistance and current.• Subtract thermal power due to radiative and conductive losses usingRO, after first adjusting the coefficients for the cross-sectional area ofthe DUT.1444.3. Thermoelectric Tester Calibration and Validation• Recalculate TH usingTHnew = TH −QH(RadjRHIratio +Radj(1−RHIratio)AclosedADUT)(4.3)where Radj = RH,closed +RI,closed, (4.4)QH is the thermal power traveling from the heater element into thefilm, RHIratio is the ratio of thermal resistance of the heater elementto the interface thermal resistance, Aclosed is the cross-sectional area ofcontact between the heater element and the base plate during closedcalibration, and ADUT is the cross-sectional area of the device undertest.• Subtract closed circuit calibration resistance from the DUT electricalresistance measurement.• Subtract closed circuit calibration Seebeck from the DUT Seebeck co-efficient measurement then subtract a further 3 µV/K to adjust thevalue to reference platinum metal.The following sections consistently use the above procedures for deter-mining calibration coefficients and adjusting raw data collected from filmsamples.4.3.2 Repeatability and CalibrationOnce constructed, the apparatus was characterized using open and closedcalibration methods and heavily doped n-type silicon as the high thermalconductivity material for the final calibration step. The calibrated systemwas used to characterize the thermoelectric performance of a variety of dopedand undoped electrochemically grown ZnO samples to ascertain their valueas thermoelectric materials. Seebeck coefficients listed in this section arereferenced to platinum.Experiments are performed by first positioning the heater probe, DUT,and armature assembly on the base plate. Electrical resistance measure-ments are checked throughout the procedure to ensure that no unexpectedelectrical short circuits are formed between the heater and the base plate. Ifthe specified force of 1.3 N is successfully applied without an apparent short,the dome is placed onto the apparatus and the enclosed space is vacuumedto at least a moderate vacuum of 0.01 mBar. After thermal stabilization1454.3. Thermoelectric Tester Calibration and Validationmonitored using LabView, a small adjustment at room temperature is ap-plied to compensate for any error in the thermocouples (typically 0.25◦C to0.5◦C). A preprogrammed series of voltages are then applied to the temper-ature probe at 30 minute intervals first stepping up to a maximum thermalpower output and then stepping back down. The process may be repeatedwithin the same log to verify repeatability. An example of this sequence isshown in Figure 4.5.0 5 10 15050100150200250300350Time (h)Temperature (degC)Figure 4.5: Probe and plate temperature as a function of time for twomeasurements of a ZnO film (see Section 4.4).Data points for detailed analysis are selected by hand by examining theplateaus at each power (or voltage) setting. Once a point on a plateau isselected, a mean average of 20 samples around that point is used in thefollowing calculations, including calibration. Calibration MeasurementsNumerous open and closed calibrations were performed regularly to ensureconsistency in device operation. Open calibrations may drift in time dueto oxidation or discolouration of the heater probe changing its emissivity.Closed calibrations may vary due to changes in material properties, forma-tion of oxide layers, and changes in surface roughness.1464.3. Thermoelectric Tester Calibration and ValidationThe temperature vs. thermal power curves for a series of open calibra-tions are shown in Figure 4.6. Measurements were taken 5 weeks apart yetstill showed excellent consistency despite heavy usage of the test appara-tus. The non-linear fit shown in the figure represents a strictly fourth orderfit using (4.2). The close fit indicates that the predominant mechanism ofheat loss during open calibration is radiation, with conduction through wiresplaying only a very small role. Using the measured surface area of the heaterprobe, the calculated emissivity of the probe is 0.47. A fourth order polyno-mial fit including including lower order terms is indistinguishable from theexperimental data on the plot and was used for compensating other data inthis section.0 2 4 6 8 10 12−50050100150200250300350Thermal Power (W)Temperature Difference (K)  Open Cal 1: ExperimentalOpen Cal 1: Non−linear FitOpen Cal 2: ExperimentalOpen Cal 2: Non−linear FitOpen Cal 3: ExperimentalOpen Cal 3: Non−linear FitFigure 4.6: Induced temperature gradient between heater probe and baseplate as a function of applied thermal power. The fit shown is a purely 4thorder fit using (4.2). Three separate calibrations are shown.A similar plot for a closed calibration is shown in Figure 4.7. Unlike theopen calibration, the resulting plots are linear and represent a much smallerchange in temperature. If no thermal resistance was present between thethermocouples, the curves would be flat lines independent of power. Thepresence of the curves allowed the calculation of the total thermal resistancebetween the high temperature and low temperature thermocouples, approx-imately 0.36 K/W. Methods of reducing this thermal resistance, such as the1474.3. Thermoelectric Tester Calibration and Validationremoval of the steel cap, were explored, but failed to yield an improvementin performance that offset the resulting detrimental effects such as increasedfragility and the poor electrical isolation of components in the heater probe.0 2 4 6 8 10 12 14 16 18−10123456Thermal Power (W)Temperature Difference (K)  Closed Cal 1Closed Cal 2Closed Cal 3Closed Cal 4Closed Cal 5Closed Cal 6Figure 4.7: Temperature difference as a function of thermal power for aseries of closed calibrations.Figures 4.8 and 4.9 show the measured electrical conductance and in-duced voltage (related to the Seebeck coefficient) resulting from the closedcalibration. Electrical conductance did not vary significantly as a function oftemperature and remained within 10% between tests. Electrical conductiv-ity compensation was only used for 2-point measurements. Induced voltagedid change properties as the apparatus aged, possibly due to the formationof oxide or other material metallurgical changes affecting the Seebeck coeffi-cient of the heater probe. The change indicates the development of an n-typeSeebeck coefficient under closed calibration conditions. The initial Seebeckcoefficient is −1.5 µV/K and grows to −10µV/K. A value of −2.5 µV/Kwas chosen for compensating silicon and ZnO Seebeck measurements in thefollowing sections.1484.3. Thermoelectric Tester Calibration and Validation24 26 28 30 32 34 36 38 40 42 4411. Temperature (degC)Electrical Conductance (S)  Closed Cal 1Closed Cal 2Closed Cal 3Closed Cal 4Closed Cal 5Closed Cal 6Figure 4.8: Electrical conductance as a function of average temperature fora series of closed calibrations.0 1 2 3 4 5 6−8−7−6−5−4−3−2x 10−5Temperature Difference (K)Induced Voltage (V)  Closed Cal 1Closed Cal 2Closed Cal 3Closed Cal 4Closed Cal 5Closed Cal 6Figure 4.9: Induced voltage as a function for temperature difference a seriesof closed calibrations.1494.3. Thermoelectric Tester Calibration and Validation4.3.2.2 Silicon MeasurementsTo determine RHIratio, a 500 µm thick piece of n-type silicon was used.The piece had a rated electrical resistivity of 0.001-0.005 Ωcm, indicatinga doping concentration of between 1 × 1019 and 1 × 1020 cm−3. A samplewith a cross-sectional area of 0.75 cm2 was cleaned with acetone and distilledwater using ultrasonication for 5 mins. Figure 4.10 shows the temperaturedifference across the wafer as a function of thermal power before and afterthe calibration, including RHIratio, was applied. The effect of calibration onthe induced voltage can also be seen in Figure 4.11. RHIratio was selectedto provide an optimally linear thermal conductivity and Seebeck coefficientclose to the experimentally published values for doped silicon.0 2 4 6 8 10 12012345678910Thermal Power (W)Temperature Difference (K)  Silicon RawSilicon CalibratedFigure 4.10: Temperature as a function of applied thermal power before andafter calibration of a 500 µm thick silicon wafer n-type doped to a resistivityof 0.002 Ωcm.For a RHIratio value of 0.63, the performance of the calibration canbe seen in Table 4.2. The good agreement between thermal conductiv-ity and Seebeck coefficient of the sample after calibration indicates thatthe calibration parameters and measurement methodology are suitablefor measurements of films with thermal conductivity below approximately10 W m−1 K−1.1504.4. ZnO Thermoelectric Measurements0 1 2 3 4 5 6 7 8 9 10−3−2.5−2−1.5−1−0.5x 10−4Temperature Difference (K)Induced Voltage (V)  Silicon RawSilicon CalibratedFigure 4.11: Induced voltage as a function of the temperature differencebetween the probe and the plate before and after calibration of a 500 µmthick silicon wafer n-type doped to a resistivity of 0.002 Ωcm.Table 4.2: Pre-calibration and post-calibration silicon wafer measurements.Measurand Pre-Calibration Calibrated Reference[203]ThermalConductivity(W m−1 K−1)7.44± 1 142± 10 140± 10SeebeckCoefficient(µV K−1)−16.9± 5 −430± 20 −420± 204.4 ZnO Thermoelectric MeasurementsZnO films were grown in accordance with the procedures developed in Chap-ter 3. 1 cm×1 cm ZnO films 45 µm thick were grown and removed from theirgrowth substrates using the chromium etching process described in Sec-tion 3.5 with hydroxide solution at pH = 11. When placed in the thermoelec-tric test apparatus, the films universally cracked or shorted. Thicker, largerfilms were grown to reduce the probability of the films fracturing, althoughsome cracks were still detected in the films after testing. ZnO films 95± 5 µm1514.4. ZnO Thermoelectric Measurementsthick were then grown without difficulty or visible change in film propertieswith thickness as verified by SEM measurements of the cross-section of thefilms. Films without doping were grown larger with cross-sectional areasvarying from 1.2 cm2 to 1.7 cm2, measured using calipers. With the excep-tion of longer depositions leading to thicker films, the growth methodologyof doped films was identical to that developed in Section 3.4. A chemical tar-get doping concentration of 4 µmol/L was used in all doped films to achievean Al to Zn ratio close to 2%. The doped films were thinner than the pureZnO films and were measured at 79± 5 µm in thickness using a SEM withthe film tilted at 45◦. The additional mechanical strength resulting fromusing thicker films enabled a significantly higher test yield.4.4.1 Experimental PreparationSamples were rinsed with distilled water and were dried in open air for 12hours. After drying, they were inspected with a microscope where a fineneedle was used to remove any remaining gold and break away sections offilm with visible anomalies such as obstructions or discolouration. Sam-ple dimensions were measured using calipers and area was calculated. Theheater probe and graphite base plate were cleaned, polished, and coatedwith GaInSn before each sample was placed into the apparatus. The samplewas placed onto the base plate, and the distribution of the GaInSn beneaththe sample was visibly studied through the film to ensure good coverage.GaInSn was added or removed as required, with special care being neces-sary that no GaInSn beads escaped the circumference of the film. The heaterelement was placed onto the sample and weights were added to the assemblyto achieve the desired force on the film. Electrical resistance measurementswere then performed with voltages ranging from 0.1 V to 1.0 V to detectshort circuits and ensure a linear response. The force on the heater probewas also perturbed by hand to determine the magnitude of response in theresistance and thus assess the reliability of the contact. Resistance was per-mitted to vary within 30% of its initial value. If any of these initial testsfailed, the heater probe was removed, the apparatus was inspected, and theheater probe was returned for another attempt. Initial testing was repeateduntil the resistance was sufficiently stable to begin thermoelectric testing.4.4.2 Annealing ProcessEarly experimentation revealed that testing newly grown films in the ther-moelectric test apparatus would cause the films to anneal during the test in1524.4. ZnO Thermoelectric Measurementsa fashion consistent with observed results discussed in Section Attemperatures as low as 60◦C, films would fail to maintain a temperatureplateau during a continuous application of a non-varying thermal power.This behaviour would persist for several temperature steps in the test pro-cess until the film stabilized in a new configuration, which typically occurredafter a prolonged (2 hour) anneal at the peak temperature of the test. Aclear example of this behaviour is shown in Figure 4.12. Temperature isincreased in regular increments until the 3.5 hour mark. Annealing is ap-parent beginning at the 1.5 hour mark and manifests as a sharp increase inthermal conductivity, although not all films were observed to behave in thesame manner during annealing. The apparent dips in the plot correspond tothe gradual increase in film thermal conductivity throughout the annealingprocess.0 1 2 3 4 5 6 7050100150200250Time (h)Temperature Difference (K)  Figure 4.12: Temperature differential across the film of a 3 mA/cm2 currentdensity ZnO sample showing ramp up and annealing as well as ramp down.Both ramp up and ramp down are programmed with the same thermal powerstep configuration and, without changes in film properties, should convergeto identical temperature plateaus.The annealing process occurs in both oxygenated and vacuum environ-ments and affected all tested films. The annealing is likely the thermaldecomposition of embedded hydroxide ions in the film, yielding ZnO and1534.4. ZnO Thermoelectric MeasurementsAlO products and leaving vacancies such as nanoholes and microholes inthe film as discussed in Section 3.6.1. Films deposited with higher currentdensities are more likely to integrate hydroxide ions into the film as less timeis available during growth for the electrochemically evolved hydroxide ionsto decompose into ZnO in the film.All of the figures in this section represent nine sets of data collected fromthree samples of each indicated type of material. The power, rather thanthe applied temperature, was controlled throughout the measurement pro-cess, meaning that each sample converged to slightly different temperatureplateaus depending on their material properties and dimensions. Samplescould only be tested once prior to annealing. Data from films of the sametype (ie. 3 mA/cm2) are indicated with the same colour and symbol. Threefilms of each material type are shown. Linear regression fits on the avail-able data are used to show trending for each sample (dashed lines) and theoverall average of all samples of a given type (thick, solid lines). Althoughsample behaviour is not expected to be purely linear over the temperaturerange considered, linear behaviour is a reasonable approximation.Figure 4.13 shows the measured thermal conductivity as a function ofaverage temperature of films sample grown at 1 mA/cm2, 3 mA/cm2, and1 mA/cm2 with aluminum doping. A noteworthy observation is that thethermal conductivity of all films is orders of magnitude below bulk ZnO andAl:ZnO doped films fabricated using other methods[32, 52, 53, 62, 153]. Anumerical comparison can be found at the end of this chapter. A flat ordecreasing trend of thermal conductivity with temperature is expected andobserved. The thermal conductivity of all samples measured was initiallyquite similar, with the exception of one Al:ZnO trial which produced anotably higher thermal conductivity prior to annealing.The electrical conductivity and Seebeck coefficients of the films can beseen in Figures 4.14 and 4.16, respectively. The poor electrical conductivityof all grown films is consistent with observations made in Section is a significant hindrance in the thermoelectric performance of the films.The addition of the aluminum dopant does not have a significant effect onthe electrical conductivity of the films, which is consistent with poor dopantactivation. The high variability in the electrical conductivity results betweendifferent films is expected, as small variations in growth parameters can leadto significant variations in oxygen doping and electrical conductivity[61, 204–208].The Seebeck coefficient is negative, indicating an n-type doped mate-rial as expected, but the Seebeck coefficient is a lower magnitude (−30to −150 µV/K) than commonly reported for the indicated level of doping1544.4. ZnO Thermoelectric MeasurementsAverage Temperature (K)300 310 320 330 340Thermal Conductivity (W/mK) mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.13: Pre-annealed thermal conductivity as a function of averagetemperature for a variety of ZnO-based samples.Average Temperature (K)300 310 320 330 340Electrical Conductivity (S/cm)×10-300.511.523 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.14: Pre-annealed electrical conductivity as a function of averagetemperature for a variety of ZnO-based samples.1554.4. ZnO Thermoelectric MeasurementsAverage Temperature (K)300 310 320 330 340Seebeck Coefficient (µV/K)-160-140-120-100-80-60-40-203 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.15: Pre-annealed Seebeck coefficient vs. Pt as a function of averagetemperature for a variety of ZnO-based samples.(−150 to −350 µV/K), although others have also reported lower magni-tudes in doped samples[32, 52, 53, 62, 153]. As expected, the doped sam-ple provides the lowest Seebeck coefficient. Unexpectedly, the 3 mA/cm2film demonstrates the highest Seebeck coefficient, suggesting that furtherresearch may benefit from focusing on higher current density deposition de-spite the rougher film surface and other limitations discussed in Section 3.4.A flat or slight increase in Seebeck coefficient magnitude with temperature isalso expected and is generally seen with ZnO and Al:ZnO up to 500◦C[153].The dimensionless figure of merit of pre-annealed films is shown in Fig-ure 4.16. The gradual upward slope with temperature is expected as Al:ZnOand ZnO typically demonstrate their peak ZT at approximately 1000◦C. The3 mA/cm2 current density films outperform the other samples, primarily dueto having a superior Seebeck coefficient. The overall ZT of all the testedsamples is too low for economic viability as a thermoelectric material in apre-annealed state.4.4.3 Performance of Annealed FilmsFilms were ramped up to a temperature exceeding 200◦C and kept abovethat threshold for a period of 2 hours to allow any low temperature anneal-1564.4. ZnO Thermoelectric MeasurementsAverage Temperature (K)300 310 320 330 340Figure of Merit×10-501233 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.16: Pre-annealed figure of merit as a function of average tempera-ture for a variety of ZnO-based processes, such as hydroxide thermal decomposition, to complete. Thestabilized films were then characterized using multiple temperature steps ina similar manner as in the previous section.All of the figures in this section represent at least 25 sets of data collectedfrom three samples of each indicated type of material. Data are representedidentically to the previous section with the exception of the inclusion oferror bars. Error bars represent the variation in a single sample’s measuredproperties over multiple tests, with a test representing either a ramp up orramp down in temperature (room temperature to peak test temperature)with multiple plateaus.The thermal conductivities of the annealed samples are shown in Fig-ure 4.17. After annealing, the thermal conductivity of the undoped samplesincreased on average, with the thermal conductivity decreasing on averagefor the doped samples, suggesting that the improved activation of aluminumduring the annealing process acts as a mechanism for improved phonon scat-tering. All films continue to present exceptionally low thermal conductivi-ties.Annealing did not significantly affect the electrical conductivity of the3 mA/cm2 sample. However, consistent with measurements taken in Sec-1574.4. ZnO Thermoelectric MeasurementsAverage Temperature (K)350 400 450Thermal Conductivity (W/mK) 3 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.17: Annealed thermal conductivity as a function of average tem-perature for a variety of ZnO-based samples.tion, the electrical conductivity of both the doped and undoped1 mA/cm2 samples increased significantly after annealing, exceeding theelectrical conductivity of the annealed 3 mA/cm2 sample. Electrical con-ductivity results are shown in Figure 4.18.The Seebeck coefficients, shown in Figure 4.19 show an improvement forall samples, indicating either less internal electrical dissipation, lower dopantactivation, or the additional formation of crystalline ZnO within the film.The concurrent improvements in Seebeck and electrical conductivity for thedoped and undoped 1 mA/cm2 samples indicate that a low temperatureanneal, even under vacuum conditions, is beneficial to the thermoelectricperformance of the material. Considering that the material is intended tooperate at very high temperatures, this behaviour is a useful characteristic.The samples grown at 3 mA/cm2 demonstrated a particularly favourableSeebeck coefficient, which is greater after annealing.The final ZT of the samples can be seen in Figure 4.20. After anneal-ing, the performance of the 1 mA/cm2 film shows the greatest performance,although some samples of the Al:ZnO samples outperformed the 1 mA/cm2samples. Better activation of the aluminum within the samples with a corre-sponding improvement in electrical conductivity would lead to a much more1584.4. ZnO Thermoelectric MeasurementsAverage Temperature (K)300 350 400 450Electrical Conductivity (S/cm)×10-301234563 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.18: Annealed electrical conductivity as a function of average tem-perature for a variety of ZnO-based samples.Average Temperature (K)300 350 400 450Seebeck Coefficient (µV/K)-300-250-200-150-100-5003 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.19: Annealed Seebeck coefficient vs. Pt as a function of averagetemperature for a variety of ZnO-based samples.1594.5. Characterization Summarypronounced improvement of the doped samples over the undoped samples.All samples benefited from the low temperature annealing process, withZT being an order of magnitude greater for the 1 mA/cm2 samples afterannealing.Average Temperature (K)300 350 400 450Figure of Merit×10-5123453 mA/cm2 ZnO1 mA/cm2 ZnO4 µM Al:ZnOFigure 4.20: Annealed figure of merit as a function of average temperaturefor a variety of ZnO-based samples.4.5 Characterization SummaryVarious thermally conductive interface materials were examined for theirpotential to enable the testing of thin films using a contact-based directmethod of thermoelectric measurement. GaInSn was the only interface ma-terial tested with the properties necessary for use in thin film thermoelectricmeasurements. A method for coating a surface with a thin layer of GaInSnwas developed and then deployed as part of the design and construction of alow cost thermoelectric apparatus suitable for measurements of ZnO-basedthin films. The thermoelectric test apparatus was designed and constructedfor under $1,000 CAD in materials, excluding the vacuum system and instru-mentation, and was successfully calibrated using open, closed, and siliconsample configurations.Samples representing high current density (3 mA/cm2) ZnO deposition,1604.5. Characterization Summarystandard current density (1 mA/cm2) ZnO deposition, and Al-doped stan-dard current density (1 mA/cm2) deposition were tested using the thermo-electric test apparatus to determine their properties prior to and after lowtemperature annealing. Film properties of these electrochemically grownfilms were compared to the room temperature performance of ZnO filmsproduced by others using different methodologies in Table 4.3. Though thetable represents some of the best known methods for developing thermo-electric Al:ZnO, the listed ZT is lower than expected as room temperatureperformance is shown to ensure consistent comparison between materials.As illustrated in the table, there is great variability in the electrical andthermal properties of ZnO and Al:ZnO fabricated using different technolo-gies, although no variations have produced thermal conductivities as lowas those provided by the electrochemical method used herein. The electri-cal conductivities of the electrochemically grown ZnO films agree within anorder of magnitude with thinner samples tested using the drop method de-scribed in Section and are comparable to ZnO results published byothers[156, 204, 207–209].The low electrical conductivity is a significant limitation in the mate-rial. It leads to a low ZT when compared to measurements of films grownusing alternative methods. If the electrical conductivity could be improvedwithout proportionately increasing thermal conductivity, the resulting filmwould present significant promise as a thermoelectric material.1614.5. Characterization SummaryTable 4.3: A room temperature comparison of the thermoelectric propertiesof ZnO and Al:ZnO grown electrochemically (this work) and using othermethods (other publications).Technologyκ(W m−1 K−1)σ(S cm−1)α(µV K−1) ZTElectrochemical ZnO1 mA/cmˆ2 Pre-Anneal0.020 0.00023 -79 8.2e-7Electrochemical ZnO1 mA/cmˆ2 Post-Anneal0.028 0.0022 -69 1.2e-5Electrochemical ZnO3 mA/cmˆ2 Pre-Anneal0.023 0.00031 -96 4.2e-6Electrochemical ZnO3 mA/cmˆ2 Post-Anneal0.037 0.00041 -140 6.6e-6Electrochemical Al:ZnO1 mA/cmˆ2 Pre-Anneal0.066 0.00015 -42 2.3e-7Electrochemical Al:ZnO1 mA/cmˆ2 Post-Anneal0.011 0.00075 -88 1.3e-5Chemical CodepositionZnO[153]35 10 -245 <0.01Chemical CodepositionZn0.97Al0.03O[153]20 125 -225 0.02Ball Sintering ZnO[53] 24 0.4 -300 <0.01Ball SinteringZn0.98Al0.02O[53]18 2.4 -180 0.018RF Plasma + SinteringZnO[62]37 10 -350 <0.01RF Plasma + SinteringZn0.98Al0.02O[62]27 750 -40 <0.01Microwave-ActivatedThermal DecompositionZnO[32]7 <10 -490 N/AMicrowave-ActivatedThermal DecompositionZn0.98Al0.02O[32]2 <20 -280 N/A162Chapter 5Conclusions and FutureWorkThe thermoelectric potential of electrochemically grown, aluminum dopedZnO was studied. The lattice thermal conductivity was modelled usingmolecular dynamics to determine which nanostructural features would pro-vide reductions in thermal conductivity while minimizing their effects onelectrical conductivity. These modelling results combined with classicalelectrical conductivity estimation indicated that the greatest improvementsin thermoelectric performance could be realized with nanovoided and het-erostructured ZnO-based materials. Although nanoscale features with thedimensions used in the MD simulations could not be realized experimen-tally, these structures were still chosen for experimental synthesis as theyhave been otherwise independently confirmed as effective for improving ther-moelectric performance in other material systems.Growing ZnO and Al:ZnO films with sufficient thickness for directmethod characterization required a rigorous examination of established elec-trochemical growth methods for preparing ZnO thin films, leading to contri-butions that enabled the development of thicker, higher quality films. Thesechanges included using zinc metal counter electrodes, removing the referenceelectrode and focusing on galvanostatic deposition, and vertically orientingthe substrates a centimetre above the bottom of the beaker during growth.The chemical doping of the films using aluminum was also characterizedin detail to produce films with controlled amounts of aluminum integratedthroughout the film. Poor aluminum dopant activation and strong evidencefor the integration of hydroxide into the films were two new challenges un-covered during the experimental work that seriously impacted the thermo-electric performance of the material.Tools were developed to assist with the modelling, preparation, and char-acterization of the films. To help facilitate rapid exploration of the parame-ter space associated with small nanostructural modifications to a material,LVDOS-EMD was developed, validated with modelled silicon nanostruc-tures, and used to study nanovoided and cored structures for their optimal1635.1. Contributionsstructural configurations. ZnO films of varying current densities and dopantconcentrations up to 95 µm thick with and without nanoscale features weregrown using a custom designed galvanostat. The films showed good purity,strong (002) crystal alignment, and consistent surface morphology. A pro-cess of releasing the gold film from a gold/chromium coated glass slide underpH neutral or basic conditions was developed and realized using chromiumetching. The etching process was characterized at different temperatures,applied potentials, and anion concentrations for the purpose of generalizingthe methodology for MEMS and other microscale device fabrication. Over100 ZnO films were grown with 20 films etched free from their substratesfor thermoelectric characterization.A reusable, direct measurement apparatus was designed, constructed,calibrated, and used to characterize the thermoelectric performance of thefilms. The apparatus was designed and constructed specifically to accom-modate the measurement of thin films by using a new technique of coatingelectrodes with very thin layers of highly conductive liquid metal. Ther-moelectric measurements revealed that all grown, annealed, films presentedextremely low thermal conductivity (<0.1 W m−1 K) and reasonable See-beck coefficients (−50 µV K−1 - −300 µV K−1). The doped films’ electricalconductivity (∼0.7 mS/cm at room temperature) represents the greatest lim-itation in thermoelectric performance, restricting the ZT of the materials to1.3× 10−5 at room temperature, significantly below Al:ZnO films producedusing other methods.5.1 Contributions5.1.1 Modelling• Developed a method, LVDOS-EMD, for rapidly studying the impactof nanostructural changes on thermal properties of nanoscale materialsusing molecular dynamics, the velocity autocorrelation function, and anew method for estimating vibrational mean free path using localizedvibrational density of states.• Performed Mueller-Plate and LVDOS-EMD studies on a variety ofZnO structures to determine the potential gain in thermoelectric mate-rial performance those structures would provide. Based on these sim-ulations, nanovoided and heterostructured bulk materials are worthgreater consideration as thermoelectric materials than straight andhollow nanowires provided that they can be synthesized due to a 3-5×1645.1. Contributionsreduction in relative thermal conductivity when adjusted for effectivecross-sectional area.5.1.2 Experimental Growth and Etching• Determined that using an inert counter electrode, such as platinum,rather than a Zn-based electrode causes acidification of the ZnOgrowth solution when using Zn(NO3)2, preventing thick film (>10 µm)deposition of ZnO onto a gold substrate.• Characterized the effect of using a reference electrode for ZnO thickfilm electrochemical deposition, determining that using a Ag/AgClelectrode leaks chloride into the growth solution which is absorbedby the growing film, impacting its crystallinity, morphology, opacity,electrical resistance, and surface roughness.• Successfully grew the thickest known ZnO films (>95 µm) using anitrate-based, electrochemical method.• Explored the process of chemical aluminum doping of ZnO films duringgrowth and developed a new experimental method for the regular,controlled introduction of aluminum into the film.• Developed a new electrochemical etching technique to allow for thefreeing of nanoscale gold film from glass slides under pH neutral orbasic conditions. Successfully used this method to free ZnO thickfilms from glass slides to enable thermoelectric characterization.5.1.3 Thermoelectric Characterization• Directly compared common thermal/electrical interface materials andconcluded that GaInSn or a close analog was suitable for thin filmthermoelectric material characterization using a contact-based directmethod.• Designed, constructed, and calibrated a low cost, direct measurementthermoelectric test apparatus for thin thermoelectric films (tested to79 µm film thickness).• Thermoelectrically characterized electrochemically grown, nanovoidedZnO and Al:ZnO films, demonstrating their exceptionally low thermalconductivity. A reasonable Seebeck coefficient was also shown. The1655.2. Future Worklimiting factor, electrical conductivity, was demonstrated and high-lighted as the next challenge to overcome in producing viable electro-chemically grown Al:ZnO thermoelectric materials.5.2 Future WorkThe most critical limitation that must be overcome is the poor electrical con-ductivity of the material. Numerous potential solutions exist for enhancingthe electrical conductivity, such as high temperature annealing, testing acti-vation of other dopants such as gallium, and exploring the growth parameterspace to improve crystallinity.A high temperature anneal of films after growth would encourage thealuminum ions in the film to engage in substitution doping and completethe thermal decomposition of any remaining hydroxides in the film, ideallyleaving voids that yield the beneficial reduction in thermal conductivity.Creating a viable film through high temperature annealing is a non-trivialtask. Al:ZnO must be annealed at 950◦C for 2 hours to preserve the stoi-chiometric ratio of Zn and O while activating the aluminum dopant[32, 62].Concurrently improving dopant activation and enhancing crystallinity inthe electrodeposited films would require exploring annealing between 950◦Cand 1800◦C (the melting temperature of pure ZnO is 1975◦C). Annealingat such high temperatures for extended durations is energy intensive, andmany of the benefits of electrochemically depositing the Al:ZnO, such as lowenergy and equipment cost, dopant concentration control, and nanostruc-turing could be lost if a high temperature anneal is required. An apparatusto prevent warping of the films during the annealing process would need tobe constructed using materials that would not engage in chemical exchangeswith the film sample.The parameter space for ZnO and Al:ZnO films should be further ex-plored for different growth conditions in an attempt to improve electricalconductivity without significantly increasing the thermal conductivity ofthe films. Depositing films at higher current density, as shown with the3 mA/cm2 films, warrants further investigation as these films demonstratea superior Seebeck coefficient relative to those grown at lower current den-sities. Small variations in the growth parameters of the films have a largeimpact on their thermoelectric properties. A study on controlling oxygendoping of the films during growth would also be valuable.The modelling of synthesizable nanostructures was not exhaustive. Ad-ditional nanostructured shapes could be considered using the described mod-1665.2. Future Workelling methodologies. LVDOS-EMD and NEMD can be used to examine thepotential of roughened ZnO nanowires, as well as stacked ZnO platelets andtree formations[40]. These alternative nanostructures may yield interestingimprovements in thermoelectric performance. A variety of heterostructuresshould be considered as well, including other material systems such as alu-minum oxide or gallium nitride within the superlattice, as they would pro-vide interesting opportunities for bandstructure engineering. GaN also haslattice parameters that closely match ZnO as well as a tolerance for hightemperatures making it an excellent mechanical pairing for the oxide.The thermoelectric test apparatus demonstrated remarkable utility con-sidering the low cost of components. For longer term, reliable use, severalmodifications to the design are recommended. The base plate should bereplaced by stainless steel or another stiff material that is impervious to gal-lium. Reducing the flexure of the plate would allow probe support designsthat provide better control of the force applied to the DUT. The heater probecould be improved using clean room techniques and higher conductivity ma-terials, with a concept design shown in Appendix B.4. Better mechanicalinterconnects that place less stress on wires throughout the vacuum regionof the apparatus would also improve system longevity. Although the vac-uum proved sufficient for preventing convective thermal losses, long periodsof operation at high temperature did permit residual oxygen in the air tooxidize some of the materials in the heater probe, such as the nichrome wire.Operating at a higher vacuum would improve the longevity of the system.The test apparatus could also be improved by verifying its performance us-ing other known thermoelectric materials with varying degrees of surfaceroughness and thermoelectric properties.Provided that the challenges discussed herein can be overcome with littleadditional cost, electrochemically grown Al:ZnO has the potential to yieldan inexpensive, environmentally friendly, and high ZT material. Modellingindicates that the thermal conductivity of monocrystalline bulk Al:ZnO canbe kept low (reduced by over 50× vs. bulk) while maintaining approximately70% of the electrical conductivity of the material, with experimental resultsillustrating that significant reductions in thermal conductivity are indeedachievable. The flexibility of electrochemical growth could also enable thefabrication of large thermoelectric modules where the materials are growndirectly on the module substrate, and interfaces are electrochemically de-posited with the application of some masking between growth stages. Thehigh Seebeck coefficient and temperature performance of oxides gives themthe potential to be some of the highest efficiency thermoelectric materialsavailable, and their chemical stability increases their suitability and relia-1675.2. Future Workbility for future thermoelectric generators. 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ISSN 1530-6984. doi: 10.1021/nl3044986.195Appendix ASupplemental ResultsA.1 Electronic Quantum ModellingA consistent modelling method that directly incorporates quantum effectswould be ideal for modelling electronic behaviour. Quantum modelling ofelectronic behaviour in nanostructures generally involves combining an abinitio solver using Hartree Fock (HF) or density functional theory (DFT)with various approximations such as the local-density approximation (LDA)to determine material bandstructure with a transport solver such as non-equilibrium Green’s Function (NEGF) formalism, boundary wave func-tion (WF) formalism, quantum transmission boundary method formalism(QTBM), or the boltzmann transport equation[210, 211]. Solving systemsof atoms involving thousands of atoms for all electronic states is extremelycomputationally intensive, meaning that large nanostructured systems re-quire approximations to simplify the computations. Tools such as Abinit andthe Spanish Initiative for Electronic Simulation with Thousands of Atoms(SIESTA)[212] are capable of solving DFT problems using pseudopotentials,which reduce the number of bonding electrons involved in quantum calcu-lations.Significant exploration with tools such as SIESTA, NEMO5 from Pur-sue University, BoltzTraP for BTE transport calculations[213], Opium forgenerating pseudopotentials, and Smeagol did not yield a model suitable forefficiently modelling the electronic quantum behaviour of ZnO nanostruc-tures. ZnO presents a unique challenge when working with pseudopoten-tials as core electrons in the 3s2 and 3p6 orbitals still influence the bondingenergies between zinc and oxygen atoms within the lattice. Attempts to in-clude these orbitals in the valence shell of the pseudopotentials did not yieldmodels that, once relaxed, produced both lattice spacing and bandstruc-ture consistent with ZnO experimental results. Others have succeeded ingenerating models involving bulk ZnO but at a much higher computationalcost[214, 215]. An alternative solution, LDA+SIC (local-density approx-imation with self interaction correction) as implemented by Smeagol wasable to efficiently produce ZnO models with either correct bandstructure196A.2. Other ZnO Growth Considerationsor correct lattice constants, but both could not be concurrently producedwith the available pseudopotentials[216, 217]. Figure A.1 shows the resultsof ZnO bulk and nanowire bandstructure calculated using Smeagol and itscomparison to bulk ZnO simulated by others. Quantum Modelling of ZnOwas therefore not further pursued in this work.A.2 Other ZnO Growth ConsiderationsIn addition to studying the effects of the electrodes used during growth,many other considerations were also examined to improve consistency be-tween samples and overall film quality. The factors considered in this sectionwere examined under a variety of experimental configurations following theequipment and methodology described in Section 3.2.A.2.1 Solution Stirring During GrowthStirring involves either agitating the growth solution surrounding the sub-strate using a magnetic stirrer, or agitating the substrate itself through amechanical armature. Stirring the solution using a small stir rod and hot-plate magnetic stirring mechanism at 300 RPM increased film growth rateby 1.5× by improving the replenishment rate of nitrate at the substratesurface. The improvement in film growth rate was measured during poten-tiostatic depositions as a sharp increase in deposition current for a givenreference potential. The increase persisted only as long as the solution wasagitated. A similar increase in current was also noted when the substratewas rotated 180◦ back and forth along the length of the substrate using aservo mechanism at a three second period.To test the impact of agitation on the quality of the film, a stir rod wasplaced in close proximity to one section of a large growth substrate where3 cm of substrate was located beneath the surface of the solution. A 2 hourdeposition under these conditions yielded a typical ZnO film near the sur-face of the growth solution and very little film on the substrate near thestir rod. A similar effect was noted when regularly agitating the substrate.Although deposition current does increase, the hydroxide produced by theelectrochemical reaction was moved from the surface of the substrate dueto the strong fluid currents at the surface, preventing the thermal decom-position of ZnO onto the substrate, as shown by (3.4). As a result of thisobservation, regular stirring during electrodeposition was not used. A stirrod was used to mix the Zn(NO3)2 solution during solution warm up, butit was then disabled.197A.2. Other ZnO Growth ConsiderationsFigure A.1: Bandstructures from LDA+SIC simulations of a) bulk ZnO, andb) a hexagonal nanowire composed of ZnO segments of 4 unit cell length.The inset in a) shows bulk ZnO bandstructure calculated using LDA+SICas a reference[47].198A.2. Other ZnO Growth ConsiderationsA.2.2 Bubble Formation on Film IntegrityHeating water to 80◦ C for long durations causes the formation of bubbleswithin the solution. The bubbles formed on all surfaces during deposition,including the bottom and walls of the beaker and the surface of the sub-strate. The bubbles on the substrate could also have resulted from theformation of hydrogen gas due to electrolysis near the substrate surface.Once in place, the bubbles prevented the deposition of ZnO by preventingthe growth solution from accessing the surface of the substrate. For thisreason, bubbles had to be regularly removed from the substrate by eitherbriefly agitating the substrate or by using a syringe to fire a jet of growthsolution at the substrate. The latter method proved to more consistentlydisburse collected bubbles and did not place as much stress on the electricalinterconnects leading to the substrate surface. Correspondingly, electrode-positions involved spraying the substrate once every 1-4 hours depending onneed. The effect of bubbles left on the surface can be seen in Figure A.2.1 mmFigure A.2: Microscope image showing a chloride-contaminated (for bettercontrast) ZnO film where bubbles were no longer removed once the deposi-tion reached 50% completion.199A.2. Other ZnO Growth ConsiderationsA.2.3 Substrate Orientation and LocationThe effect of substrate orientation was studied as hydrothermal ZnO depo-sitions have indicated the importance of the substrate orientation for highquality films[66]. ZnO growth was attempted with substrates aligned verti-cally, horizontally facing up, and horizontally facing down. Samples alignedvertically, which is typical, presented minimal bubbles formation and highquality ZnO films. The majority of the samples grown in this work weregrown vertically. Measurements indicated that vertically grown films werenot deposited evenly along the substrate. The bottom of the substrate in-variably produced film thicknesses up to twice that of films grown on thesubstrate 2 cm higher. The gradient in thickness was much less when thesolution was stirred, suggesting that a natural ion gradient forms in the so-lution, with nitrates and zinc ions presenting at higher concentrations closerto the bottom of the beaker. In support of this hypothesis, films grown atthe very bottom of the beaker were much darker in colour and more er-ratic in shape than films grown even 5 mm above the bottom of the beaker.For this reason, high quality films were all grown at least 5 mm above thebottom of the beaker, demonstrating even colouration and thickness acrosstheir entire surface.Films oriented horizontally facing up were generally low quality. Someprecipitation occurs during long depositions, typically in the form of sloughfrom the zinc electrode. When facing up, the substrate can catch particlesprecipitated from the solution, causing irregularities in the shape and colourof the film. When facing down, very high quality films were produced, par-ticularly when the counter electrode was located above the film allowing theions to sink and encounter the substrate. In this configuration, bubble for-mation is a significant challenge. Whereas bubbles will slide off a verticallyaligned or top facing substrate, when facing down bubbles would rapidlycollect, requiring frequent dislodgement and interfering with the consistentgrowth of the film. For this reason, horizontal, downward facing growthwas not typically used. Vertical alignment of the substrate also allowed forplacing the reference electrode very near to the surface of the substrate,providing more accurate reference potential measurements.A.2.4 ZnO Growth Denouement and CoolingAfter the completion of growth, the hotplate was immediately turned off andthe beaker containing the sample was removed to cool. Removing the sampleimmediately after the deposition completed caused cracks to form in the ZnO200A.3. Alternative ZnO Substrate Release Methodsfilm as the film cooled significantly faster than the underlying substrate. Tominimize damage to the film, the beaker containing the growth solution andthe sample was left until it returned to room temperature before removingthe sample. The sample was then cleaned using a hand-pressurized jet ofdistilled water from a squeeze bottle. No ultrasonication or other chemicalcleaning was necessary. The film was either left to air dry or compressednitrogen gas was used to expedite drying the film with no apparent effectson the quality or surface properties of the film.A.3 Alternative ZnO Substrate Release MethodsIn order to form a low impedance electrical and thermal pathway to bothsides of the ZnO film, the growth substrate must either have a high ther-mal and electrical conductivity or the film must be removable. Mechanicalmethods were explored for removing the films from rigid substrates aftergrowth using tape or shearing action. Graphite as a flexible substrate wasalso examined. Chemical and electrochemical methods for releasing the filmwere also examined in detail to determine their feasibility and are discussedin Section 3.5.A.3.1 Mechanical RemovalMechanical removal of the film involved separating the film from the growthsubstrate through the application of mechanical force. The most directmethod for removing the ZnO involved applying conventional Scotch tapeto the surface of the film and drawing the tape away. This method was verysuccessful at removing film from the substrates, particularly if the film hadpoor adhesion. Films presented lower adhesion when they were removedimmediately after growth as discussed in Section A.2.4 or were grown withhigh concentrations of contaminants such as chloride. The bond betweenthe gold and ZnO could also be weakened at the beginning of depositionif heightened current densities of 3 mA/cm2 were applied for 10 minutes.Although removing film using tape was practical for some experimental in-vestigations, such as a ultraviolet spectrography, the strong adhesion andflexibility of the tape would invariably lead to the destruction of the film,leaving only powdered remnants.201A.3. Alternative ZnO Substrate Release MethodsA.3.2 Growth on GraphiteAn alternative to removing the film from the substrate is selecting a flexiblesubstrate that can be incorporated into the thermoelectric module alongwith the ZnO film. Graphite thin films have very high thermal and electri-cal conductivities. The Panasonic PGS series of pyrolytic sheets were alsoavailable in 10 µm thick varieties at reasonably low cost. The films were flex-ible and had a slightly rough or thatched surface. Several experiments wereconducted growing ZnO on graphite substrates. The graphite was taped toa glass slide to provide a flat surface and the experimental conditions wereotherwise similar to those presented in Section 3.2. Some precedents existsin literature for successfully electrodepositing ZnO on graphite[218].Many films were grown and characterized. XRD results of a ZnO-on-graphite film are shown in Figure A.3. Additional peaks inconsistent with ei-ther graphite or ZnO were found in all grown samples. The additional peaksvaried between samples and did not correspond to any materials within theavailable NIST database. When the ZnO film was removed from the graphitesubstrate after growth and the components were tested separately, unidenti-fied peaks were found in both the graphite and the ZnO, suggesting that thecontaminants are formed on or near the graphite surface during deposition.It was also noted that mechanically removing the ZnO from the graphitetypically resulted in some carbon remaining adhered to the underside of theZnO film.SEM images were also taken of the graphite surface and resulting ZnO asshown in Figure A.4. These images show the roughness of the graphite sur-face and the corresponding sloped hills and valleys on the surface of the ZnOfilm. Due to the rough nature of the surface and impurities during growth,the ZnO crystals did not properly align leading to anomalous structuresthroughout the ZnO lattice, an example of which is shown in Figure A.4c.The films also had poor adhesion to the substrate and would readily breakfree, indicating low electrical and thermal contact. Despite varying experi-mental parameters such as growth temperature and substrate pretreatment,high quality ZnO films with good substrate adhesion and negligible contam-ination were not successfully produced.202A.4. Experimental Synthesis of Additional ZnO Structures10 20 30 40 50 60 70 80 9000.θphaseNormalized CountsZnOSampleFigure A.3: XRD measurements of a ZnO-on-graphite film along with goldand ZnO reference patterns are shown.A.4 Experimental Synthesis of Additional ZnOStructuresIn addition to nanovoided bulk structures, attempts were made to growother structures that demonstrated good theoretical performance as ther-moelectric candidates.A.4.1 Template Assisted GrowthAlthough ZnO nanowires can be synthesized in a wet environment eitherthrough hydrothermal or electrochemical deposition, their aspect ratiosand lengths are very limited and typically yield 10 µm long, 700 nm thicknanowires[40, 46, 66, 75, 218–220]. Templated assisted growth involves grow-ing ZnO through the pores of a stiffer template material such as polycar-bonate or alumina[86, 221]. The former are fabricated from 5 to 15 µmpolycarbonate films that are bombarded by radiation of a known velocityand energy that tunnels holes through the polycarbonate with a consistentdiameter and known density. These holey polycarbonate membranes areoften used as filters in biological applications. To use them for electrochem-ical growth, a thin layer of gold is deposited on one side of the template,which then serves as the cathode in an electrochemical deposition. ZnO is203A.4. Experimental Synthesis of Additional ZnO Structuresa)b)c)Figure A.4: SEM measurements of a) the graphite surface, b) ZnO grownon graphite, and c) anomalous structures embedded into the film.204A.4. Experimental Synthesis of Additional ZnO Structuresformed in the cavities in the template, forming nanowires bounded by thedimensions of the holes. Once the holes have been filled with electrochemi-cally deposited ZnO, a separate deposition procedure can be used to depositthe top electrode on the structure, securing the nanowires at both ends.The template can then be dissolved, leaving a forest of vertically alignednanowires interconnected at both ends.Figure A.5 shows the result of copper-coated ZnO nanowires extendingfrom the top of a 100 nm hole diameter polycarbonate template. One sideof the template was sputter coated with 50 nm of gold with the templates atan angle to prevent filling the holes with gold. Potentiostatic deposition at−1.0 V was then performed in a standard 80◦C solution of 0.1 M Zn(NO3)2for 6 hours. The substrate was then immersed in a copper sulphate solu-tion with copper electrode for an additional hour of electrodeposition in anattempt to form a continuous, interconnected film on the surface of the tem-plate. The copper did not fully interconnect the nanowires, indicating thata different deposition method would be necessary. The polycarbonate filmwas etched in a 1 M NaOH solution after the SEM images were taken, butrather than entirely dissolve the template, the polycarbonate formed a gelthat warped and destroyed the nanowires.Thicker substrates on either ends of the nanowires would be necessaryto achieve the mechanical strength necessary to remove the template with-out damaging the nanowires. Smaller diameter nanowires with larger aspectratios would also be required to achieve a significant reduction in thermalconductivity, further increasing the risk and reducing the yield of thermo-electric material fabrication. Due to the slow growth rate, low nanowiredensity, clean room fabrication steps, and mechanically fragile growth prod-uct, this methodology was not further pursued.A.4.2 Heterostructural GrowthGrowing heterostructure films involves depositing ultra thin layers of twoor more materials in sequence. Superlattice nanowire heterostructures havebeen theoretically and experimentally demonstrated using Si/Ge[21, 22, 25],Si/SiGe[222], Kr/Ar[223], AlN/GaN[224], BiTe/BiSbTe[113], and others.Forming a heterostructure using the electrochemical process has been suc-cessfully demonstrated by varying the applied deposition potential to pref-erentially select the elements for deposition[113]. With the Al:ZnO mate-rial system, possible candidates include heterostructures of ZnO/AlO andZnO/Zn. As discussed in Section, aluminum preferentially depositsto zinc where Vref is between −0.4 V and −1.0 V vs. Ag/AgCl. Due to this205A.4. Experimental Synthesis of Additional ZnO Structuresa)b)Figure A.5: SEM images taken at 20 kV showing ZnO nanowires potentio-statically grown at Vref = −1.0 V emerging from the top of a polycarbonatetemplate. The nanowires were then electrochemically coated with copper ina Cu(SO4) solution in an attempt to develop a film.selectivity, and provided that a consistent level of a aluminum dopant canbe maintained within the solution, the potential-driven selection betweenZnO/AlO is plausible by varying the applied potential between −0.5 V forAlO deposition and −1.0 V for doped Zn deposition. AlO is a strong in-sulator with a large bandgap, meaning that either very thin layers or highdopant concentrations would be necessary to maintain the desired electricalconductivity of the material. Due to this constraint, AlO was not selectedas the preferred heterostructure for investigation.The ZnO/Zn heterostructure can also be selected by varying the applied206A.4. Experimental Synthesis of Additional ZnO Structurespotential during electrodeposition. Applying a high potential (Vref>>1.0 V)begins to deposit zinc metal directly onto the cathode as the thermal decom-position step in the formation of ZnO is rate limiting. Figure A.6 comparesXRD measurements of a conventionally grown ZnO film with a heterostruc-ture grown galvanostatically by swapping applied current density between1 mA/cm2 and 10 mA/cm2 every 10 C of charge transferred. The XRD datashows that the highly directional growth of the ZnO crystal is disrupted withgrowth occurring along many more crystal axes. Zinc metal is also visiblewithin the XRD data, confirming that some pure Zn metal was depositedin the process.20 40 60 80−θ phaseNormalized Counts(1ZnOAu/ZnZnZnOZnO/ZnWithout Ag/AgClFigure A.6: XRD plot comparing conventionally electrochemically grownZnO with a ZnO heterostructure grown by swapping applied current densityfrom 1 mA/cm2 to 10 mA/cm2 every 10 C of charge transferred.Visually, the ZnO/Zn heterostructured film was translucent and veryinconsistent. rather than laying down contiguous sheets of Zn and ZnO,high current Zn deposition favoured growing outwards from several pointson the ZnO film, creating large, plated structures of Zn that were subse-quently covered by ZnO and additional layers of Zn. There structures were207A.4. Experimental Synthesis of Additional ZnO Structuresnot continuous across the surface of the film, resulting in a very poor super-lattice structure. The SEM images are shown in Figure A.7. In the figure,segments of ZnO can be seen capped with zinc metal, creating either mush-room (Figure A.7a) or pine cone (Figure A.7b) like structures. Althoughthese examples do illustrate the intention behind a heterostructure, the pooruniformity across the entire surface of the substrate reduces the practicalutility of the methodology for thermoelectric applications. Forming and us-ing ZnO/Zn superlattice nanowires may be more functional as uniformityover a large surface area is not as critical.a) b)50 μm 20 μmFigure A.7: SEM images taken at 15 kV showing the cross-section of aheterostructured ZnO/Zn film. The object seen in the figure is a protrusionfrom the film and is representative of many other protrusions along thesurface.208Appendix BThermoelectric TesterDesignB.1 Front Panel209B.1.FrontPanelFigure B.1: Labview Front Panel of Thermoelectric Tester Application.210B.2. Labview ProgrammingB.2 Labview Programming211Keithley ResourceCurrent01E-9201E-91500KeithVoltageKeithVoltageVoltage True  "Voltage" Function20001000Heater VoltageHeater Output VoltageHeater Output CurrentHeater Power (W)Heater Address%.5e,1000Log TimeHeater Output VoltageHeater Power (W)Probe Temp (C)Temp 3Plate Temp (C)KeithPowerKeithResistanceKeithVoltageTemp 2Temp 1 True Log On/Off1000Probe Temp (C)Temperature Gradient (DegC)KeithVoltageSeebeck Coefficient (V/K) False CalibrateCalibration (DegC)1Electrical Conductance (S)Heater Power (W)Thermal Conductance (W/K) 2Z2273.15ZT 2LockKeithResistance False Temperatures (degC)Plate Temp (C)Temperature Gradient (K)Tab ControlThermal Conductance (W/K)ZTHeater Power (W)Conductance RatioElec Cond (S)Seebeck Voltage (V) False On/Off1000Tab Control 2Device Addresstelnet connection0FunctionVoltage True FunctionPower True 1000Cycle Rate (s)01000Doubleall rows%fPath True Load FileTime60 True 0Active Step1Applied VHeater Voltage0 True Start00000212 True  True  False  False 00 False  False line line lineline\n \nRequest #121211.1111 True  True 213lineProbe Temp (C)Temp 3Plate Temp (C)\n121211.111111.111111.1111\nTemp 11211.1111lineTemp 2 False  "Current", Default  False Voltage1KeithResistanceKeithResistanceResistance True 1500 "Resistance"  False Current-0.0010.01-0.011500 False  "Power" KeithPowerKeithPowerPower True  False 1 False 214B.3. Plate DesignB.3 Plate Design215B.3.PlateDesign 20  120  130  140  150  160  170  180  280  300  70  150  50  280  20  300  2 X 3.50  7 X 1.50  252  248 4 x  6.76 THRU ALL 12.88 X 100°AACCAn o-ring will be seated here - intention is to provide a vacuum in the chamber. 5  300 Material thickness can vary +/- 1mm 280  180  170  160  150  140  130  120  20  300  280  20  50  70  300  9 X 3.50  7 X 1.50 4 x  6.76 THRU ALL 12.88 X 100° 2 X 8 These will be epoxied pin feed-thrus 3  3 SECTION A-AThese holes do not need to meet at right angles - some tapering is fine. 3 SECTION C-CThese holes do not need to meet at right angles - some tapering is fine.Any common, tapered screw hole is fine.Aluminum BaseplateRev0WEIGHT: A1SHEET 1 OF 1SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWNFigure B.2: Drawing of Thermoelectric Test Apparatus enclosure base plate. 1/4a¨luminum was used.216B.4. Microheater DesignB.4 Microheater DesignAlthough this design was considered for microfabrication, it was never im-plemented. It is included here as a reference should others wish to replicatethe work with a higher quality, better performing heater element.217B.4.MicroheaterDesignChannel forthermocoupleEtch along <111>Heating element(~20nm metal)Pads for wirebonding (10 ummetal)2 cm1 cm0.25 mmFigure B.3: Concept mock-up of a thin film heating element based on a microfabricated silicon wafer. A thermo-couple is inserted into the back grove of the substrate.218 R50  10  10  15  10  10  10 <100> waferHached areais maskedFigure 1a:  KOH Etch of Si Top SideKOH etch depth of 0.25 mm (for 500 um wafer) or 0.7 mm (for 1 mm wafer) at deepest point:Given 30% solution of KOH at 80 degrees C•Etch rate of ~80 um/hour•The mask should be tolerant to within +/- 1 mm.Primary EdgePolished sideis on topTop heating elementwith temperature sensorBottom plate withtemperature sensorHeater2WEIGHT: A4SHEET 1 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN219 R50  8  12  3  21  2  2  21  2  8  2  3  12  5  5 <100> waferHached areais maskedFigure 1b:  KOH Etch of Si Bottom SideKOH etch depth of 0.25 mm at deepest point:Given 30% solution of KOH at 80 degrees C•Etching requires 3 hours (etch rate of ~80 um/hour)•The mask should be tolerant to within +/-1 mm.  Alignment with the top should be tolerant within +/-2 mm.Primary EdgeNote that imageis flipped verticallyas though youhave flipped thewafer and arelooking at itsunderside.Heater2WEIGHT: A4SHEET 2 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN220 R50  10  30  20  10 <100> waferFigure 2:  SiO2 GrowthSiO2 deposition or growth of 100 - 300 nm of SiO2 over total area.  The area for SiO2 deposition must be at least the dimension of the box indicated.Heater2WEIGHT: A4SHEET 3 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN221 R50  10  10  10  10  0.90  0.10  10 <100> waferHached areais maskedFigure 3: Chromium DepositionEvaporation or sputtering of chromium onto the substrateTarget thickness of chromium layer is 100 +/- 20 nm•Mask tolerance of 10 um in all directions permitted•100 um wide strips ofchromium should bedeposited betweentwo larger chromiumplates, all on SiO2.Heater2WEIGHT: A4SHEET 4 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN222 R50  10  10  10  10  10  5 <100> waferHached areais maskedFigure 4:  Gold DepositionGold should be applied until between 300 - 500 nm thick using evaporation or sputtering.  Mask tolerance of +/- 1 mm is acceptable.Heater2WEIGHT: A4SHEET 5 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN223 R50  10  20  10  5 <100> waferHached areais maskedFigure 4:  SiO2 DepositionPECVD deposition of 200 - 400 nm of SiO2 over unmasked area.  +/-2 mm mask tolerance is acceptable for SiO2 deposition.Heater2WEIGHT: A4SHEET 6 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN224 R50  10  30  20  10  20  30 <100> waferFigure 6:  Wafer CutThe area not cut out may be discarded.  It is better if excess material is included (cut is larger than indicated) than cutting into the device.Cut out this areaCut out this areaWaste siliconHeater2WEIGHT: A4SHEET 7 OF 7SCALE:1:1DWG NO.TITLE:REVISIONDO NOT SCALE DRAWINGMATERIAL:DATESIGNATURENAMEDEBUR AND BREAK SHARP EDGESFINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:Q.AMFGAPPV'DCHK'DDRAWN225Appendix CThermoelectric Tester SourceC.1 FirmwareA standard Netburner MOD5282 development kit was used to form a bridgebetween Ethernet and SPI/I2C temperature sensors. The following code wasdeveloped using the NBEclipse IDE and SDK.#include "predef.h"#include <stdio.h>#include <string.h>#include <ctype.h>#include <startnet.h>#include <serial.h>#include <iosys.h>#include <utils.h>#include <ip.h>#include <tcp.h>#include <autoupdate.h>#include <command.h>#include <taskmon.h>#include <stdlib.h>#include <i2cmaster.h>#include <networkdebug.h>#include <pins.h>#include <qspi.h>#define SERIALPORT_TO_USE (0) //0 for the main port ,1 for the 10pin aux serial port#define BAUDRATE_TO_USE (115200)#define STOP_BITS (1)#define DATA_BITS (8)#define TCP_PORT_TO_USE (23) //The Telnet port226C.1. Firmwarefloat sensorData [16];int dataread [4];extern "C"{void UserMain( void *pd );}/* The User Authentication Callback */int ProcessAuth( const char *name , const char *pass){return CMD_OK;}void ProcessPrompt( FILE *fp , void *pData ){/* For fun give each session its nmumber in theprompt */fprintf( fp , "Channel #1: %.4f (%04x)\n",sensorData [0], dataread [0] );fprintf( fp , "Channel #2: %.4f (%04x)\n",sensorData [1], dataread [1] );fprintf( fp , "Channel #3: %.4f (%04x)\n",sensorData [2], dataread [2] );fprintf( fp , "Channel #4: %.4f (%04x)\n",sensorData [3], dataread [3] );}/* The command processing Callback */int ProcessCommand( const char *command , FILE *fp ,void *pData ){if ( command [0] ){fiprintf( fp, "  # %s Sent Cmd[%s]", pData ,command );}227C.1. Firmware/* Close the connection if we receive Logout */if ( stricmp( command , "logout" ) == 0 ){return CMD_CLOSE;}return CMD_OK;}void * ProcessConnect( FILE *fp ){const char *prompt;fiprintf( fp, "Connected:  TE Tester Rev3\n" );if ( ( int ) ( fp ->_file ) == (SERIAL_SOCKET_OFFSET ) ){prompt = "Serial0";}else if ( ( int ) ( fp ->_file ) == (SERIAL_SOCKET_OFFSET + 1 ) ){prompt = "Serial1";}else{prompt = "Telnet";}/* To test arbitray data tracking return thesession number */return ( void * ) prompt;}void ProcessDisconnect( FILE *fp , int cause , void *pData ){switch ( cause )228C.1. Firmware{case CMD_DIS_CAUSE_TIMEOUT:fputs( "\nTimed out\n", fp );break;case CMD_DIS_CAUSE_CLOSED :fputs( "\nGoodBye\n", fp );break;case CMD_DIS_SOCKET_CLOSED:fputs( "Socket closed\n", fp );break;case CMD_DIS_AUTH_FAILED:fputs( "Authentication failed\n", fp );break;}}const char *AppName = "TETester";const char sensAddr [4] = {0x48 , 0x49 , 0x4a , 0x4b};float getSensor( int i ){BYTE ret [2];signed short int data;ret[0] = 0x00;ret[1] = 0x00;I2CSendBuf( sensAddr[i], ret , 1, 0);I2CRestart( sensAddr[i], I2C_START_READ );I2CReadBuf( sensAddr[i], ret , 2, 1);dataread[i] = (int)(ret [0]) * 256 + (int)(ret [1]);data = (signed short int)(ret [0]) * 256 + (int)(ret [1]);return (float)(data) / 128.0; // Returns indegC}float getSensorSPI( int i )229C.1. Firmware{signed long int ret;float Text , Tint;// Acquire dataif( i < 2 )J2[40] = 0;elseJ2[30] = 0;QSPIStart( NULL , (BYTE*)(&ret), 4, NULL);//Wait until completewhile(! QSPIdone ());J2[30] = 1;J2[40] = 1;// CalculationText = (float)(ret >> 18) / 4;Tint = (float)((ret & 0x0000ffff) >> 4) /16;if( !(i & 0x1) )// External temperature channelreturn Text;elsereturn Tint;}void initSPI (){J2[25]. function(PINJ2_25_SPI_CLK);J2[27]. function(PINJ2_27_SPI_DIN);J2[28]. function(PINJ2_28_SPI_DOUT);J2[30]. function(PINJ2_35_GPIO);J2[40]. function(PINJ2_40_GPIO);J2[30] = 1;J2[40] = 1;QSPIInit (2000000 , 32, 0, 1, 1, 1, TRUE , 5, 5);230C.1. Firmware}void initI2C (){I2CInit( 0x15 ); // Should be 100 kHzOSTimeDly( 10 );// Initialize each of the temperature devices// Config reg (addr 0x3) = 0x80for( int i = 0; i < 4; i++ ){//Reset the partI2CStart( sensAddr[i],I2C_START_WRITE );I2CSend( 0x2f ); //AddressI2CStop ();OSTimeDly( 10 );// Setup configI2CStart( sensAddr[i],I2C_START_WRITE );I2CSend( 0x03 ); //AddressI2CSend( 0x80 ); //Control register valueI2CStop ();}}void UserMain( void *pd ){InitializeStack ();OSChangePrio( MAIN_PRIO + 1 );EnableAutoUpdate ();EnableTaskMonitor ();OSTimeDly( 10 );#ifdef _DEBUG231C.1. FirmwareInitializeNetworkGDB ();// InitializeNetworkGDB_and_Wait ();#endif// Close the serial port incase it is already open.SerialClose( SERIALPORT_TO_USE );//Open the serial portint fdserial = OpenSerial( SERIALPORT_TO_USE ,BAUDRATE_TO_USE ,STOP_BITS ,DATA_BITS ,eParityNone );ReplaceStdio( 0, fdserial );ReplaceStdio( 1, fdserial );ReplaceStdio( 2, fdserial );writestring( fdserial , "Starting\n" );CmdAuthenticateFunc = ProcessAuth; /* Noauthentication to start */CmdCmd_func = ProcessCommand;CmdConnect_func = ProcessConnect;CmdPrompt_func = ProcessPrompt;CmdDisConnect_func = ProcessDisconnect;CmdIdleTimeout = TICKS_PER_SECOND * 3600;Cmdlogin_prompt = "Logged in. Rev 0.\n";CmdStartCommandProcessor( MAIN_PRIO );CmdAddCommandFd( fdserial , TRUE , TRUE );CmdListenQuietOnTcpPort( 23, 1, 5 );// initI2C ();initSPI ();while ( 1 ){232C.1. Firmwareint i;for( i = 0; i < 4; i++ ){OSTimeDly( 2 );// sensorData[i] = getSensor(i);sensorData[i] = getSensorSPI(i);}}}// UserMain233C.2.FrontPanelC.2 Front PanelFigure C.1: Labview Front Panel of Thermoelectric Tester Application.234C.3. Labview ProgrammingC.3 Labview Programming235Keithley ResourceCurrent01E-9201E-91500KeithVoltageKeithVoltageVoltage True  "Voltage" Function20001000Heater VoltageHeater Output VoltageHeater Output CurrentHeater Power (W)Heater Address%.5e,1000Log TimeHeater Output VoltageHeater Power (W)Probe Temp (C)Temp 3Plate Temp (C)KeithPowerKeithResistanceKeithVoltageTemp 2Temp 1 True Log On/Off1000Probe Temp (C)Temperature Gradient (DegC)KeithVoltageSeebeck Coefficient (V/K) False CalibrateCalibration (DegC)1Electrical Conductance (S)Heater Power (W)Thermal Conductance (W/K) 2Z2273.15ZT 2LockKeithResistance False Temperatures (degC)Plate Temp (C)Temperature Gradient (K)Tab ControlThermal Conductance (W/K)ZTHeater Power (W)Conductance RatioElec Cond (S)Seebeck Voltage (V) False On/Off1000Tab Control 2Device Addresstelnet connection0FunctionVoltage True FunctionPower True 1000Cycle Rate (s)01000Doubleall rows%fPath True Load FileTime60 True 0Active Step1Applied VHeater Voltage0 True Start00000236 True  True  False  False 00 False  False line line lineline\n \nRequest #121211.1111 True  True 237lineProbe Temp (C)Temp 3Plate Temp (C)\n121211.111111.111111.1111\nTemp 11211.1111lineTemp 2 False  "Current", Default  False Voltage1KeithResistanceKeithResistanceResistance True 1500 "Resistance"  False Current-0.0010.01-0.011500 False  "Power" KeithPowerKeithPowerPower True  False 1 False 238Appendix DMatlab Source FilesD.1 Nanowire Area Calculation1 %area.m - Approximates the cross -sectional area ofan arbitrary structure23 clear all;4 close all;56 %Load data7 fname = ’/data/phonon/ZnOvoidR3V50D17rng1 -5 x5x200/dumpforce40pre.ZnO’;8 extractFrame;910 index = 1;11 levels = 40; %Granularity of squares12 numDots = 20; %Number of interconnecting dotsbetween nearest neighbours13 numAtoms = 10; %Draw dots between this manyneighbours14 maxLength = 4; %Maximum distance (in A) betweennearest neighbours15 sliceThickness = 4; %In Angstroms16 sliceIncrement = 1; %In Angstroms1718 %Clear existing video files19 system(’rm video /*. png’);2021 %Generate slice regions22 dx = full(squeeze(datax(:,index)));23 dy = full(squeeze(datay(:,index)));24 dz = full(squeeze(dataz(:,index)));239D.1. Nanowire Area Calculation25 top = max(dz);26 bottom = min(dz);2728 %More setup29 figure(’Color’, [1 1 1]);30 set(gca , ’fontsize ’, 15);31 xlabel( ’x-axis position (A)’ );32 ylabel( ’y-axis position (A)’ );33 hold on;3435 if matlabpool(’size’) == 036 matlabpool37 end3839 %Iterate through regions40 zIndex = bottom;41 k = 1;42 while zIndex < top - sliceThickness43 %Prepare/Flatten data44 dx = full(squeeze(datax(:,index)));45 dy = full(squeeze(datay(:,index)));46 dz = full(squeeze(dataz(:,index)));4748 zMin = zIndex;49 zMax = zMin + sliceThickness;50 disp(sprintf(’Doing %.2f to %.2f...’, zMin , zMax));51 zIndex = zIndex + sliceIncrement;52 dx((dz<zMin)|(dz >zMax)) = [];53 dy((dz<zMin)|(dz >zMax)) = [];54 dz((dz<zMin)|(dz >zMax)) = [];5556 %Delete bad points57 li = find(dx >100|dx <-100|dy >100|dy <-100);58 dx(li) = [];59 dy(li) = [];60 dz(li) = [];6162 %Start by finding extreme edges of data63 topleft = [min(dx) max(dy)];240D.1. Nanowire Area Calculation64 botright = [max(dx) min(dy)];65 axis([ topleft (1) botright (1) botright (2) topleft(2)]);6667 %Add points between nearest neighbours to helpfill in the gaps68 dotsx = [];69 dotsy = [];70 parfor i = 1: length(dx)71 [dist ,tmp] = sort(sqrt((dx(i) - dx) .^ 2 + (dy(i) - dy) .^ 2 + (dz(i) - dz) .^ 4));72 for j = 1: numAtoms %Nearest 10 atoms73 if dist(j+1) < maxLength74 %Generate new dots75 dotsx = [dotsx;linspace(dx(i), dx(tmp(j+1)), numDots) ’];76 dotsy = [dotsy;linspace(dy(i), dy(tmp(j+1)), numDots) ’];77 end78 end79 end8081 dx = [dx;dotsx ];82 dy = [dy;dotsy ];8384 %Start digging in to determine area85 xblocks = 1:( levels);86 yblocks = 1:( levels);87 xsize = (botright (1) - topleft (1)) / (levels);88 ysize = -(botright (2) - topleft (2)) / (levels);89 tot = 0;90 clf;91 for x = xblocks92 for y = yblocks93 itopleft = [(x-1)*xsize -(y-1)*ysize] +topleft;94 ibotright = [x*xsize -y*ysize] + topleft;95 if( find(dx>itopleft (1)&dx <ibotright (1)&dy <itopleft (2)&dy>ibotright (2)) )241D.1. Nanowire Area Calculation96 tot = tot + 1;97 hold on;98 r = rectangle(’FaceColor ’ ,[1 0.80.8], ’Position ’,[itopleft (1)ibotright (2) xsize ysize ]);99 end100 end101 end102103 totarea(k) = tot * xsize * ysize;104 areaMsg = sprintf(’Area of %d atom slice is %.2f’, length(dx) - length(dotsx), totarea(k));105 disp(areaMsg);106107 %%{108 %Plot all atoms109 hold on;110 plot(dx , dy , ’.’);111 title(areaMsg);112 set(gcf ,’PaperUnits ’,’inches ’,’PaperPosition ’ ,[00 5 5])113 drawnow;114 %}115116 %Save frame to array117 print(sprintf(’video/area %04d.png’, k), ’-dpng’,’-r100’);118119 k = k + 1;120 end121122 %Calculate series area adjustment (1/A1 + 1/A2 +...) ^(-1)123124 areaAdj = 0;125 for i = 1: length(totarea)126 areaAdj = areaAdj + 1 / totarea(i);127 end128 areaAdj = 1 / areaAdj * length(totarea);129242D.2. Extract Single Time Frame from LAMMPS Data130 disp(sprintf(’Final adjusted area is %.2f’, areaAdj));131132 matlabpool close;D.2 Extract Single Time Frame from LAMMPSData1 %fname must be predefined23 timeperstep = 40e-15; %in seconds45 %Extra data from file6 fp = fopen(fname , ’r’);78 basetimestep = 0;9 numatoms = 0;10 bounds = [];11 datax = sparse ([]);12 datay = sparse ([]);13 dataz = sparse ([]);14 datamass = sparse ([]);15 datatype = sparse ([]);16 datavx = sparse ([]);17 datavy = sparse ([]);18 datavz = sparse ([]);19 datafx = sparse ([]);20 datafy = sparse ([]);21 datafz = sparse ([]);22 dataactive = false;2324 while(~feof(fp))25 s = fgetl(fp);26 if strcmp(s, ’ITEM: TIMESTEP ’)27 if dataactive == true28 %Write intermediate values to matrices29 tstep = timestep - basetimestep + 1;30 datatype(:,tstep) = inttype;31 datamass(:,tstep) = intmass;243D.2. Extract Single Time Frame from LAMMPS Data32 datax(:,tstep) = intx; %x33 datay(:,tstep) = inty; %y34 dataz(:,tstep) = intz; %z35 datavx(:,tstep) = intvx;36 datavy(:,tstep) = intvy;37 datavz(:,tstep) = intvz;38 % datafx(:,tstep) = intfx;39 % datafy(:,tstep) = intfy;40 % datafz(:,tstep) = intfz;41 break;42 end4344 dataactive = false;45 s = fgetl(fp);46 if basetimestep == 047 basetimestep = str2double(s);48 end49 timestep = str2double(s);50 disp(sprintf(’Loading timestep: %d’,timestep));51 continue;52 end53 if strcmp(s, ’ITEM: NUMBER OF ATOMS’)54 dataactive = false;55 s = fgetl(fp);56 numatoms = str2double(s);57 continue;58 end59 if strcmp(s, ’ITEM: BOX BOUNDS xy xz yz pp pp pp’)60 dataactive = false;61 s = fgetl(fp);62 s = regexp(s,’ ’,’split ’);63 bounds (1) = str2double(s(2));64 s = fgetl(fp);65 s = regexp(s,’ ’,’split ’);66 bounds (2) = str2double(s(2));67 s = fgetl(fp);68 s = regexp(s,’ ’,’split ’);69 bounds (3) = str2double(s(2));244D.3. Thermal Conductivity Using Muller-Plathe70 continue;71 end72 if findstr(s, ’ITEM: ATOMS’)73 dataactive = true;74 continue;75 end7677 if dataactive78 s = regexp(s,’ ’,’split ’);79 atom = str2double(s(1));80 %Intermediate vectors81 inttype(atom) = str2double(s(2));82 intmass(atom) = str2double(s(3));83 intx(atom) = str2double(s(4)); %x84 inty(atom) = str2double(s(5)); %y85 intz(atom) = str2double(s(6)); %z86 intvx(atom) = str2double(s(7));87 intvy(atom) = str2double(s(8));88 intvz(atom) = str2double(s(9));89 % intfx(atom) = str2double(s(9));90 % intfy(atom) = str2double(s(10));91 % intfz(atom) = str2double(s(11));92 end93 end9495 fclose(fp);D.3 Thermal Conductivity Using Muller-Plathe1 % Determine thermal conductivity from stored LAMMPSdata23 clear all;4 close all;56 type = ’Zn’;78 dir = ’ZnO5x5x200ts050thermo500 ’;910 cd ’/data/phonon ’;245D.3. Thermal Conductivity Using Muller-Plathe1112 fnameProfile = [dir ’/tmp.profile ’];13 fnameLog = [dir ’/log.si_flux ’];14 %fnameProfile = [dir ’/tmp.initprofile ’];15 %fnameLog = [dir ’/log.warm_up ’];1617 if type == ’Si’18 %%%Si19 timeperstep = 1e-15; %Time per step inseconds20 len = 400 * 5.43e-10; %Length in metres21 area = (5 * 5.43e-10) ^ 2; %Cross -sectionalarea in m^222 q = 1.60217646e-19;23 else24 %%%ZnO25 a = 3.219e-10;26 c = 5.366e-10;27 timeperstep = 0.5e-15;28 len = 200 * c;29 uc = 5; area = sqrt (3) * (a * uc / 2) ^ 2 * 6; %%Hex nanowire30 % uc = 8; area = sqrt (3) / 2 * (uc * a) ^ 2; %%Bulk31 q = 1.60217646e-19 * 0.04336;32 % q = 1.60217646e-19;33 end3435 %Load data from file36 disp(’Loading data from file ...’);3738 fp = fopen(fnameProfile , ’r’);39 step = [];40 stepnum = 0;41 data = [];42 datanum = 1;43 while(~feof(fp))44 s = fgetl(fp);45 if s(1) == ’#’46 continue;246D.3. Thermal Conductivity Using Muller-Plathe47 end4849 r = regexp(s,’ ’,’split ’);50 if length(r) == 251 stepnum = stepnum + 1;52 % if(stepnum == 4001 )53 % break;54 % end55 step(stepnum) = str2double(r(1));56 datanum = 1;57 end58 if length(r) == 659 data(1,datanum ,stepnum) = str2double(r(4));60 data(2,datanum ,stepnum) = str2double(r(5));61 data(3,datanum ,stepnum) = str2double(r(6));62 datanum = datanum + 1;63 end64 end65 s = size(data);66 datanum = s(2);67 stepnum = s(3);68 step = step - step (1) + (step (2) - step (1)); %Removing starting offset6970 fclose(fp);7172 %Now to the flux file to acquire kinetic energytransfer73 fp = fopen(fnameLog , ’r’);74 logdata = [];75 logdatanum = 1;76 while(~feof(fp))77 s = fgetl(fp);78 r = regexp(s,’ ’,’split ’);7980 if (length(r) > 5) && strcmp(r{1}, ’’)81 %Strip whitespace82 r(find(strcmp(r,’’))) = [];83 logdata(1, logdatanum) = str2double(r(2));84 logdata(2, logdatanum) = str2double(r(3));247D.3. Thermal Conductivity Using Muller-Plathe85 logdata(3, logdatanum) = str2double(r(4));86 logdata(4, logdatanum) = str2double(r(5));87 logdata(5, logdatanum) = str2double(r(6));88 logdatanum = logdatanum + 1;89 end90 end91 logdatanum = logdatanum - 1;9293 fclose(fp);9495 %Restructure data (ugly!)96 disp(’Preparing data ...’);97 for i = 1: stepnum98 for j = 1: datanum99 Ncount(i,j) = data(2,j,i);100 temp(i,j) = data(3,j,i);101 end102 end103104 %Plotting results105 disp(’Plotting results ...’);106 x = linspace(0, len , datanum) * 1e9;107 y = step * timeperstep * 1e12;108109 figure(’Color’, [1 1 1]);110 set(gca , ’fontsize ’, 15);111 contourf(x, y, temp , 50, ’edgecolor ’, ’none’);112 xlabel(’Position [nm]’);113 ylabel(’Timestep [ps]’);114 colorbar;115116 %figure(’Color ’, [1 1 1])117 %contourf(x, y, Ncount , 50, ’edgecolor ’, ’none ’);118 %set(gca , ’fontsize ’, 15);119 %xlabel(’Position [nm]’);120 %ylabel(’Timestep [ps]’);121 %colorbar;122123 %Temp124 %figure248D.3. Thermal Conductivity Using Muller-Plathe125 %for i = 2: length(y)126 % plot(x,temp(i-1,:), ’b’,’linewidth ’,2);127 % hold on128 % plot(x,temp(i,:), ’b--’);129 % axis ([0 400 240 360]);130 % hold off131 % i132 % pause (1);133 %end134135 %Computations136 disp(’Performing computations ...’);137138 %Average over time to get temperature gradient plot139 ttemp = sum(temp) / size(temp , 1);140 figure(’Color’, [1 1 1]);141 set(gca , ’fontsize ’, 15);142 plot(x, ttemp , ’linewidth ’, [2.0]);143 xlabel(’Position [nm]’);144 ylabel(’Average Temperature (K)’);145146 start = floor (0/8 * datanum + 1);147 stop = floor (4/8 * datanum + 1);148149 %Method 1150 coeffs = polyfit(x(start:stop) * 1e-9, ttemp(start:stop), 1);151 ctemp = polyval(coeffs , x * 1e-9);152 hold on;153 plot(x, ctemp , ’r--’, ’linewidth ’, [2.0]);154 thermgrad = coeffs (1);155156 %Now the calculation of thermal conductivity157 ketotal = (logdata(5, logdatanum) - logdata (5,1)) * q;158 timetotal = max(logdata (4,:)) * timeperstep;159 heatflow = ketotal / timetotal; %Factor of 2 forperiodicity160 kappa = heatflow / 2 / area / thermgrad; %in W/m/K249D.4. Si Nanowire/Bulk Creation161 avgtemp = mean(ttemp);162163 %Second slope164 start = floor (4/8 * datanum + 1);165 stop = floor (8/8 * datanum);166 coeffs = polyfit(x(start:stop) * 1e-9, ttemp(start:stop), 1);167 ctemp = polyval(coeffs , x * 1e-9);168 thermgrad = -coeffs (1);169 %ketotal = (logdata(5, logdatanum) - logdata (5,1)) *q;170 %timetotal = max(logdata (4,:)) * timeperstep;171 heatflow = ketotal / timetotal; %Factor of 2 forperiodicity172 kappa2 = heatflow / 2 / area / thermgrad;173174 disp(sprintf(’Thermal gradient: %.2e K/m’, thermgrad));175 disp(sprintf(’Heat flow: %.2e W’, heatflow));176 disp(sprintf(’Area: %.2e m^2’, area));177 disp(sprintf(’Total duration: %.2e s’, step(stepnum)* timeperstep));178 disp(sprintf(’Thermal conductivity 1: %.2f W/K/m’,kappa));179 disp(sprintf(’Thermal conductivity 2: %.2f W/K/m’,kappa2));180 disp(sprintf(’Average temperature: %.2f K’, avgtemp));D.4 Si Nanowire/Bulk Creation1 %Generate Si crystal lattice23 clear all4 close all56 %Parameters7 a = 5.43; %Lattice spacing in A8 numx = 3; %Number of unit cells alongx axis250D.4. Si Nanowire/Bulk Creation9 numy = 3; %Number of unit cells alongy axis10 numz = 20; %Number of unit cells alongz axis11 roughen = false;12 roughperiod = 10*a; %Period of breaks in A13 roughdepth = 1*a; %14 roughwidth = 1*a;15 roughspecial = 0;16 ucellx = 5.43; %Unit cell along x in A17 ucelly = 5.43; %Unit cell along y in A18 ucellz = 5.43; %Unit cell along z in A19 celltype = ’FCC’;20 passivate = false; %Add hydrogen to passivategenerated structure21 passlength = 1.46; %Passivation length (A)22 outp = ’’; %Output file name23 elem = ’Si’;24 lattice = [0.0 0.0 0.0;0.0 0.5 0.5;0.5 0.0 0.5;0.50.5 0.0;.25 .25 .25;.25 .75 .75;.75 .25 .75;.75.75 .25];2526 %Generate27 unitcell = (lattice * a) ’;2829 %Build supercell structure , defining where unitcells will go30 supercell = [];31 m = 1;32 for i = 1:numx33 for j = 1:numy34 for k = 1:numz35 x = (i - 1) * ucellx;36 y = (j - 1) * ucelly;37 z = (k - 1) * ucellz;38 supercell (:,m) = [x y z];39 m = m + 1;40 end41 end42 end251D.4. Si Nanowire/Bulk Creation4344 %Special conditions45 if roughspecial == 1 %Add one additionalledge46 for k = 1:( numz * a / roughperiod + 1)47 for i = 1:( numx + 2)48 x = (i - 2) * ucellx;49 y = numy * ucelly;50 z = (k - 1) * roughperiod + roughwidth;51 supercell (:,m) = [x y z];52 m = m + 1;53 y = -1 * ucelly;54 supercell (:,m) = [x y z];55 m = m + 1;56 end57 for i = 1:numy58 y = (i - 1) * ucelly;59 z = (k - 1) * roughperiod + roughwidth;60 x = numx * ucellx;61 supercell (:,m) = [x y z];62 m = m + 1;63 x = -1 * ucellx;64 supercell (:,m) = [x y z];65 m = m + 1;66 end67 end68 end6970 %Assemble list of atoms71 atoms = [];72 n = 1;73 for i = 1:(m - 1)74 for j = 1: length(unitcell)75 x = supercell(1,i) + unitcell(1,j);76 y = supercell(2,i) + unitcell(2,j);77 z = supercell(3,i) + unitcell(3,j);78 atoms(:,n) = [x y z];79 n = n + 1;80 end81 end252D.4. Si Nanowire/Bulk Creation82 n = n - 1;8384 %Roughen if required85 if roughen == true86 rx = 0;87 ry = 0;88 rz = -roughperiod;89 while rz < a * numz90 rz = rz + roughperiod;91 x1 = roughdepth; %Less than92 x2 = a * numx - roughdepth; %Greaterthan93 y1 = roughdepth;94 y2 = a * numy - roughdepth;95 atoms(:,( atoms (3,:) >=rz)&( atoms (3,:) <(rz+roughwidth))&(( atoms (1,:)<x1|atoms (1,:)>x2)|( atoms (2,:)<y1|atoms (2,:)>y2))) = [];96 end97 end9899 %Passivate if required100 bondlist = sparse ([]);101 hydlist = [];102 others = [];103 o = 1;104 if passivate == true105 %Test all atoms for number of close atoms/bonds106 bondedlength = a / 2;107 for i = 1:n108 x = atoms(1,i);109 y = atoms(2,i);110 z = atoms(3,i);111 tmparray = [(x-atoms (1,:)).^2+(y-atoms (2,:)).^2+(z-atoms (3,:)).^2];112 bondlist(:,i) = sparse(tmparray <bondedlength ^ 2);113 end114115 %Fix up bondlist116 for i = 1: length(bondlist)253D.4. Si Nanowire/Bulk Creation117 bondlist(i,i) = 0;118 end119120 %Add hydrogens based on number of bonds121 for i = 1:n122 bonds = sum(bondlist(:,i));123 others = full([ bondlist(:,i).* atoms (1,:)’bondlist(:,i).*atoms (2,:)’ bondlist(:,i).* atoms (3,:) ’]);124 others(all(others ==0 ,2) ,:) = [];125 others = others ’;126 if(bonds == 3)127 %Add one hydrogen128 vect1 = atoms(:,i) - others (:,1);129 vect2 = atoms(:,i) - others (:,2);130 vect3 = atoms(:,i) - others (:,3);131 newvect = vect1 + vect2 + vect3;132 newvect = newvect * passlength / sqrt((newvect (1,1) ^ 2) + (newvect (2,1) ^2) + (newvect (3,1) ^ 2));133 hydlist(:,o) = newvect + atoms(:,i);134 o = o + 1;135 end136 if(bonds == 2)137 %Add one hydrogen138 vect1 = atoms(:,i) - others (:,1);139 vect2 = atoms(:,i) - others (:,2);140 vect1 = vect1 * passlength / sqrt((vect1(1,1) ^ 2) + (vect1 (2,1) ^ 2) + (vect1 (3,1) ^ 2));141 vect2 = vect2 * passlength / sqrt((vect2(1,1) ^ 2) + (vect2 (2,1) ^ 2) + (vect2 (3,1) ^ 2));142 hydlist(:,o) = atoms(:,i) + vect1;143 o = o + 1;144 hydlist(:,o) = atoms(:,i) + vect2;145 o = o + 1;146 end147 end148 end254D.5. ZnO Nanowire/Bulk Creation149 o = o - 1;150 n = length(atoms);151152 disp(sprintf(’Total number of atoms: %d’, n + o ));153154 if roughspecial == 0155 disp(sprintf(’Boundaries: [0 0 0] - [%f %f %f]’,a * numx , a * numy , a * numz));156 else157 %Realign atoms prior to writing158 atoms (1,:) = atoms (1,:) + ucellx;159 atoms (2,:) = atoms (2,:) + ucelly;160 disp(sprintf(’Boundaries: [%f %f %f] - [%f %f %f]’, 0, 0, 0, a * (numx + 2), a * (numy + 2),a * numz));161 end162163 %Write to file164 fid = fopen(outp , ’w’);165 fprintf(fid , ’%d\r\n\r\n’, n + o);166 for i = 1:n167 fprintf(fid , ’%s %f %f %f\r\n’, elem , atoms(1,i), atoms(2,i), atoms(3,i));168 end169 for i = 1:o170 fprintf(fid , ’%s %f %f %f\r\n’, ’H’, hydlist(1,i), hydlist(2,i), hydlist(3,i));171 end172173 fclose(fid);D.5 ZnO Nanowire/Bulk Creation1 %Generate ZnO crystal lattice23 clear all4 close all56 %Structmod 1 = Core7 %Structmod 2 = Roughness255D.5. ZnO Nanowire/Bulk Creation8 %Structmod 3 = Wurtzite/Zincblende (sphalerite) Mix(Polymorphic blend)9 %Structmod 4 = Needles10 %Structmod 5 = Nanovoid11 %Structmod 6 = Track etched (synchotron)12 %Structmod 7 = ZnO/Zn superlattice1314 %Parameters15 a = 3.21; %Phonon16 c = 5.30; %Phonon17 charge = 0.0; %Ionic charge in eV18 %a = 3.29; %Phonon - new after minimzation19 %c = 5.33; %Phonon - new after minimization20 %charge = 2.0; %Ionic charge in eV21 zb = 4.62; %Phonon22 zi = 2.66; %Phonon23 zic = 4.947; %Phonon24 %a = 3.21; %Electron25 %c = 5.1; %Electron2627 numx = 5; %Number of unit cells radius28 numy = 5; %Number of unit cells radius29 numz = 200; %Number of unit cells alongz axis30 makehex = true;3132 %Lattice vectors33 a1 = [a 0 0];34 a2 = [0.5*a sqrt (3) /2*a 0];35 a3 = [0 0 c];3637 %outp = ’ ’; fout = 0; %Output file name38 outp = ’ZnOvoidR5V50D40rng2 -5 x5x200.lammps ’; fout =2; %File output format3940 %Structural modification41 structmod = 5;4243 %Structmod = 1: Core44 corenumx = 7;256D.5. ZnO Nanowire/Bulk Creation45 corenumy = 7;4647 %Structmod = 2: Roughness48 roughperiod = 4*c; %Period of breaks in A49 roughdepth = 1*a; %depth of ring50 roughdia = 1*c; %Diameter/Length/Height ofring5152 %Structmod = 3: Polymorphic53 polythickW = 2; %Wurtzite number of uc thick54 polythickZB = 2; %Zincblende number of ucthick5556 %Structmod = 4: Needles57 needleperiod = 4*c;58 needleradius = 2;5960 %Structmod = 5: Nanovoids61 voidradius = 5;62 voidvariability = 50; %Percent randomness ofradius63 voiddensity = 40; %Percent coverage in thebody64 voidrng = 2;6566 %Structmod = 6: Track etched67 holeradius = 5;68 holevariability = 20; %Percent randomness ofradius69 holedensity = 20; %Percent coverage in thebody70 holeaxis = ’x’; %’x’ is just x-axis , ’y’ isjust ’y’ axis , ’xy ’ is a random angle along xyplane7172 %Structmod = 7: Superlattice73 polythickZnO = 2; %Wurtzite number of ucthick74 polythickZn = 2; %Zincblende number of ucthick257D.5. ZnO Nanowire/Bulk Creation7576 celltype = ’Wurtzite ’;77 elem1 = ’Zn’;78 elem2 = ’O’;7980 if structmod == 3 || structmod == 781 polyVec = [];82 if structmod == 383 for i = 1:numz84 if mod(i - 1, polythickW + polythickZB)< polythickW85 polyVec(i) = 0;86 else87 polyVec(i) = 1;88 end89 end90 else91 for i = 1:numz92 if mod(i - 1, polythickZnO + polythickZn) < polythickZnO93 polyVec(i) = 0;94 else95 polyVec(i) = 2;96 end97 end98 end99100 crystalgenPoly;101 else102 u = 1/3 * (a/c)^2 + 1/4;103 unitcellZn = [0 0 0;0.5*a sqrt (3)/6*a c/2]’;104 unitcellO = [0 0 u*c; 0.5*a sqrt (3)/6*a (u+0.5)*c]’;105106 %Build supercell structure , defining where unitcells will go107 supercell = [];108 m = 1;109 if makehex == true110 numx = numx * 2 - 1;258D.5. ZnO Nanowire/Bulk Creation111 numy = numy * 2 - 1;112 end113 for k = 1:numz114 for i = 1:numx115 for j = 1:numy116 x = (i - 1) * a1(1) + (j - 1) * a2(1);117 y = (i - 1) * a1(2) + (j - 1) * a2(2);118 z = (k - 1) * a3(3);119 supercell(:,m) = [x y z];120 m = m + 1;121 end122 end123 end124 if makehex == true125 numx = (numx + 1) / 2;126 numy = (numy + 1) / 2;127 end128129 %Assemble list of atoms130 atomsZn = [];131 atomsO = [];132 nZn = 1;133 nO = 1;134 for i = 1:(m - 1)135 for j = 1:size(unitcellZn ,2)136 uc = unitcellZn (:,j);137 x = supercell(1,i) + uc(1);138 y = supercell(2,i) + uc(2);139 z = supercell(3,i) + uc(3);140 atomsZn(:,nZn) = [x y z];141 nZn = nZn + 1;142 end143 for j = 1:size(unitcellO ,2)144 uc = unitcellO(:,j);145 x = supercell(1,i) + uc(1);146 y = supercell(2,i) + uc(2);147 z = supercell(3,i) + uc(3);148 atomsO(:,nO) = [x y z];259D.5. ZnO Nanowire/Bulk Creation149 nO = nO + 1;150 end151 end152153 if makehex == true154 %And trim155 m = (a1(2) * numy - a2(2) * numy) / (a1(1) *numx - a2(1) * numx);156 b = a2(2) * (numy - 1) - m * a2(1) * (numx -1);157 atomsZn(:,atomsZn (2,:) <(atomsZn (1,:)*m+b-a))= [];158 atomsO(:,atomsO (2,:) <(atomsO (1,:)*m+b-a)) =[];159160 b = (a2(2) + a1(2)) * (numy - 1) - m * (a2(1) + a1(1) * 2) * (numx - 1);161 atomsZn(:,atomsZn (2,:) >(atomsZn (1,:)*m+b+1*a)) = [];162 atomsO(:,atomsO (2,:) >(atomsO (1,:)*m+b+1*a))= [];163 end164 end165166 %Round and delete duplicate atoms167 %atomsZn = round(atomsZn *100) /100;168 %atomsO = round(atomsO *100) /100;169 %atomsZn = unique(atomsZn ’, ’rows ’) ’;170 %atomsO = unique(atomsO ’, ’rows ’) ’;171172 %Center173 shiftx = mean(atomsZn (1,:) ,2);174 shifty = mean(atomsZn (2,:) ,2);175 atomsZn = atomsZn - [ones(1,length(atomsZn))*shiftx;ones(1,length(atomsZn))*shifty;zeros(1,length(atomsZn))];176 atomsO = atomsO - [ones(1,length(atomsO))*shiftx;ones(1,length(atomsO))*shifty;zeros(1,length(atomsO))];177260D.5. ZnO Nanowire/Bulk Creation178 %Structural modification 1 - hex core the structure179 if structmod == 1180 rlim = a * corenumx;181 llim = -a * corenumx;182 tlim = 0.5 * a * corenumy;183 blim = -0.5 * a * corenumy;184185 atomstmp = atomsZn;186 atomstmp(:,atomstmp (1,:) .^2+ atomstmp (2,:).^2 <(0.5*a*corenumx).^2) = [];187 atomsZn = atomstmp;188189 atomstmp = atomsO;190 atomstmp(:,atomstmp (1,:) .^2+ atomstmp (2,:).^2 <(0.5*a*corenumx).^2) = [];191 atomsO = atomstmp;192193 end194195 %Roughen if required196 if structmod == 2197 %Get diameter198 dia = max(atomsZn (1,:)) - min(atomsZn (1,:));199 rz = -roughperiod; %Include offset200 while rz < c * numz201 rz = rz + roughperiod;202 atomsZn (:,( atomsZn (1,:) .^2+ atomsZn (2,:).^2 >=((dia -roughdepth)/2)^2)&( atomsZn(3,:) >=rz)&( atomsZn (3,:) <=(rz+roughdia)))= [];203 atomsO (:,( atomsO (1,:) .^2+ atomsO (2,:).^2 >=((dia -roughdepth)/2) ^2)&( atomsO (3,:) >=rz)&(atomsO (3,:) <=(rz+roughdia))) = [];204 end205 end206207 %Structural modification 5 - Nanovoids208 if structmod == 5209 %rng(’default ’);210 rng(voidrng);261D.5. ZnO Nanowire/Bulk Creation211212 %Determine apprx volume of structure and voids213 dia = max(atomsZn (1,:)) - min(atomsZn (1,:));214 len = max(atomsZn (3,:)) - min(atomsZn (3,:));215 volStruct = pi * (dia / 2) ^ 2 * len;216 volVoid = 4 / 3 * pi * (voidradius) ^ 3;217218 numVoids = volStruct * voiddensity / 100 /volVoid;219 disp(sprintf(’Number of voids: %d’, numVoids));220221 %Generate and implement voids222 for i = 1: numVoids223 voidX = rand() * dia + min(atomsZn (1,:));224 voidY = rand() * dia + min(atomsZn (2,:));225 voidZ = rand() * len + min(atomsZn (3,:));226 voidR = (rand() * voidvariability / 100 -voidvariability / 200 + 1) * voidradius;227 atomsZn (:,(( atomsZn (1,:)-voidX).^2+( atomsZn(2,:)-voidY).^2+( atomsZn (3,:)-voidZ).^2<=voidR ^2)) = [];228 atomsO (:,(( atomsO (1,:)-voidX).^2+( atomsO(2,:)-voidY).^2+( atomsO (3,:)-voidZ).^2<=voidR ^2)) = [];229 end230 end231232 %Structural modification 6 - Track etched233 if structmod == 6234 rng(’default ’);235236 %Determine apprx volume of structure and voids237 dia = max(atomsZn (1,:)) - min(atomsZn (1,:));238 len = max(atomsZn (3,:)) - min(atomsZn (3,:));239 volStruct = pi * (dia / 2) ^ 2 * len;240 volHole = dia * pi * (holeradius) ^ 2;241242 numHoles = volStruct * holedensity / 100 /volHole;243262D.5. ZnO Nanowire/Bulk Creation244 %Generate and implement voids245 for i = 1: numHoles246 if holeaxis == ’x’247 holeY = rand() * dia + min(atomsZn (2,:));248 holeZ = rand() * len + min(atomsZn (3,:));249 holeR = (rand() * holevariability / 100- holevariability / 200 + 1) *holeradius;250 atomsZn (:,( atomsZn (2,:)-holeY).^2+(atomsZn (3,:)-holeZ).^2<= holeR ^2) =[];251 atomsO (:,( atomsO (2,:)-holeY).^2+( atomsO(3,:)-holeZ).^2<= holeR ^2) = [];252 end253254 if holeaxis == ’y’255 holeX = rand() * dia + min(atomsZn (1,:));256 holeZ = rand() * len + min(atomsZn (3,:));257 holeR = (rand() * holevariability / 100- holevariability / 200 + 1) *holeradius;258 atomsZn (:,( atomsZn (1,:)-holeX).^2+(atomsZn (3,:)-holeZ).^2<= holeR ^2) =[];259 atomsO (:,( atomsO (1,:)-holeX).^2+( atomsO(3,:)-holeZ).^2<= holeR ^2) = [];260 end261262 %TODO263 if holeaxis == ’xy’264 holeX = rand() * dia + min(atomsZn (1,:));265 holeZ = rand() * len + min(atomsZn (3,:));266 holeR = (rand() * holevariability / 100- holevariability / 200 + 1) *263D.5. ZnO Nanowire/Bulk Creationholeradius;267 atomsZn (:,( atomsZn (1,:)-holeX).^2+(atomsZn (3,:)-holeZ).^2<= holeR ^2) =[];268 atomsO (:,( atomsO (1,:)-holeX).^2+( atomsO(3,:)-holeZ).^2<= holeR ^2) = [];269 end270 end271 end272273 nZn = size(atomsZn , 2);274 disp(sprintf(’Total number of Zn atoms: %d’, nZn ));275 nO = size(atomsO , 2);276 disp(sprintf(’Total number of O atoms: %d’, nO ));277278 if ~exist(’zTotal ’)279 zTotal = numz * c;280 end281282 %Shift for bulk283 if makehex == false284 shiftx = min(atomsZn (1,:));285 shifty = min(atomsZn (2,:));286 atomsZn = atomsZn - [ones(1,length(atomsZn))*shiftx;ones(1,length(atomsZn))*shifty;zeros(1,length(atomsZn))];287 atomsO = atomsO - [ones(1,length(atomsO))*shiftx;ones(1,length(atomsO))*shifty;zeros(1,length(atomsO))];288 end289290 %Write to file291 fid = fopen(outp , ’w’);292 if fout == 0 %xyz format293 fprintf(fid , ’%d\r\n\r\n’, nZn + nO);294 for i = 1:nZn295 fprintf(fid , ’%s %f %f %f\r\n’, elem1 ,atomsZn(1,i), atomsZn(2,i), atomsZn(3,i));296 end264D.5. ZnO Nanowire/Bulk Creation297 for i = 1:nO298 fprintf(fid , ’%s %f %f %f\r\n’, elem2 ,atomsO(1,i), atomsO(2,i), atomsO(3,i));299 end300 else301 if fout == 1 %SIESTA compatible format302 tcount = 1;303 for i = 1:nZn304 fprintf(fid , ’\t%f\t%f\t%f\t1\tZn\t%d\r\n’, atomsZn(1,i), atomsZn(2,i),atomsZn(3,i), tcount);305 tcount = tcount + 1;306 end307 for i = 1:nO308 fprintf(fid , ’\t%f\t%f\t%f\t2\tO\t%d\r\n’, atomsO(1,i), atomsO(2,i), atomsO(3,i), tcount);309 tcount = tcount + 1;310 end311 else312 if fout == 2 %LAMMPS compatible format313 fprintf(fid , ’LAMMPS data file\r\n’);314 fprintf(fid , ’ %d atoms\r\n’, nZn + nO);315 fprintf(fid , ’ 0 bonds\r\n’);316 fprintf(fid , ’ 0 angles\r\n’);317 fprintf(fid , ’ 0 dihedrals\r\n’);318 fprintf(fid , ’ 0 impropers\r\n’);319 fprintf(fid , ’ 2 atom types\r\n’);320 fprintf(fid , ’ 0 bond types\r\n’);321 fprintf(fid , ’ 0 angle types\r\n’);322 fprintf(fid , ’ 0 dihedral types\r\n’);323 fprintf(fid , ’ 0 improper types\r\n’);324 if makehex == true325 fprintf(fid , ’ -50.0 50.0 xlo xhi\r\n’);326 fprintf(fid , ’ -50.0 50.0 ylo yhi\r\n’);327 fprintf(fid , ’ 0.000 %.2f zlo zhi\r\n\r\n’, zTotal);328 else265D.6. Generate LDOS-EMD LA