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Optical multilayers with diamond-like thin films Clarke, Glenn Andrew 1995

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OPTICAL MULTILAYERSWITHDIAMOND-LIKE THIN FILMSbyGLENN ANDREW CLARKEB.Sc., Queen’s University, 1988M.A.Sc., University of British Columbia, 1990A THESIS SUBMITTED TN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDepartment of PhysicsWe accept this thesis as conformingto the required standardTHE UNWERS1TY OF BRITISH COLUMBIAOctober 1995© Glenn Andrew ClarkeIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_________________________Department of 1i-/ S L c cThe University of British ColumbiaVancouver, CanadaDate Oc i(7qDE-6 (2188)AbstractA series of studies were performed to aid in the development of a magnetron sputtersystem which would have the ability to deposit protective optical multilayers for operation inthe infrared. Diamond-like carbon was to be used as the top protective layer, while germaniumcarbide was chosen for the underlying layers due to its tunable refractive index.The microstructural, optical, mechanical and electrical properties of the diamond-likecarbon films were investigated as a function of argon sputter gas pressure, substrate bias andreactive gas partial pressure (H2, 02, and N2). The films were characterized by spectroscopicellipsometry, scanning and transmission microscopy, electron diffraction, resistivity andhardness measurements, along with infrared spectroscopy.It was found that the pseudo-bandgap and JR transparency increased with an increasein the sputter gas pressure, along with a decrease in the hardness. This appeared to be, in part,due to an increase in the amount of hydrogen incorporation and the development of a polymerphase in the film matrix. It was felt that the primary source of hydrogen was outgassing fromsurfaces inside the vacuum deposition chamber. Increasing the substrate bias resulted in anincrease in the film density only.The optimum diamond-like films were deposited at low sputter gas pressures (1 Pa). Awidening of the pseudo-bandgap was observed for an increase in the H2 partial pressure up to avalue of 0.1 Pa. The films deposited in a nitrogen/argon mix exhibited up to an order ofmagnitude increase in the deposition rate over the films deposited in pure argon. The opticalIIproperties of these materials were intermediate to those for the hydrogenated andunhydrogenated films.Germanium and carbon multilayers were deposited to determine if interdiffusionbetween the individual layers would result in germanium carbide. The purpose of thisinvestigation was to attempt to overcome the limitations on the carbon alloy fraction inconventional sputter techniques due to a poisoning of the germanium target from thehydrocarbon gas. The optical and microstructural properties of the multilayers were studied asa function of pressure and substrate bias through in-situ ellipsometry. It was found that agood deal of interdiffusion occurs at higher pressures (2 Pa) but at the cost of an increase inthe film porosity.A novel control system was developed by monitoring the film growth through in-situellipsometry. This routine has the capability to determine both the thickness and the opticalconstants of the individual layers in a multilayer stack. A Fabry-Perot filter consisting of 21quarter-wave layers was deposited with a peak transmission of 65 %. It is shown how thisroutine can be extended to optically absorbing materials such as carbon.ifiTABLE OF CONTENTSAbstractTable of Contents ivList of Tables viiList of Figures viiiAcknowledgements xvi1. Introduction 11.1 General 11.2 History and State of the Art of Diamond-like Films 31.3 Deposition Technique 61.4 Goals of this Thesis 61.5 Characterization Methods 71.6 Chapter Organization 82. Optical Theory 102.1 Introduction 102.2 Optical Polarization 102.3 Reflection and Transmission 142.4 Optical Multilayers 193. Instrumentation and Analytical Techniques 233.1 Introduction 233.2 Magnetron Sputtering 233.2.1 Deposition Mechanisms 233.2.2 Energetic Particle Bombardment 293.3 Ellipsometry 313.3.1 Introduction 313.3.2 Ex-situ Ellipsometer 323.3.3 In-situ Ellipsometer 343.3.4 Euipsometric Analysis 383.3.5 Effective Medium Theory 393.3.6 Parametric Modeling 423.3.7 Nonlinear Optimization 473.4 Infrared Spectroscopy 503.4.1 Introduction 503.4.2 Infrared Spectrometer 51iv3.4.3 Infrared Optical Analysis 543.4.4 Newton-Raphson Method 543.4.5 Optical Models in the Mid-Infrared 564. Diamondlike films 584.1 Introduction 584.2 Amorphous Carbon Films 594.2.1 Introduction 594.2.2 Experimental 614.2.3 Results 654.2.4 Discussion 764.3 Infrared Studies of Amorphous Carbon Films 874.3.1 Introduction 874.3.2 Experimental 874.3.3 Results 914.3.4 Discussion 994.4 Amorphous Carbon Films with Oxygen, Nitrogen and Hydrogen. 1064.4.1 Introduction 1064.4.2 Amorphous Carbon Films with Oxygen 1074.4.3 Amorphous carbon with Hydrogen 1094.4.4 Carbon Nitride Films 1164.5 Technical Feasibility 1205. Germanium Carbide 1245.1 Introduction 1205.2 Analytical Methods 1295.3Expenmental 1325.4 Films Deposited as a Function of Pressure 1345.4.1 Results 1355.4.2 Discussion 1375.5 Films Deposited as a Function of Substrate Bias 1445.5.1 Results 1445.5.2 Discussion 1515.6 Conclusions 1546. Optical Multilayers 1556.1 Introduction 1556.2 Single Layer Films 1596.2.1 Reactive Sputtering 1596.2.2 In-Situ Monitoring 1616.2.3 Silicon Oxide 1636.2.4 Tantalum Oxide 167V6.3 Optical Multilayers 1696.3.1 Multilayer Control Development 1696.3.2 Matrix Method 1716.3.3 Projection Method. 1776.3.4 Transform method 1836.4 Optical Monitoring of Absorbing Coatings 2046.5 Conclusions 2097. Conclusion 210References 212Appendix A 223LIST OF TABLESTable 4.1 Deposition parameters of films deposited as a function of pressure ontoelectrically isolated substrates. 66Table 4.2 Jhterband model parameters and unbiased estimators for films deposited as afunction of pressure onto electrically isolated substrates. 69Table 4.3 Measured properties of films deposited as a function of pressure onto -electrically isolated substrates. 70Table 4.4 Fitting Parameters and Possible Bonding Configurations for Films Depositedat 1, 2, 4 and 8 Pa in Argon. 98Table 4.5 Fitting Parameters and Possible Bonding Configurations for Films Depositedin Argon and in an Argon I Hydrogen Mix. 112Table 5.1 Parameters for inhomogeneous model in Fig. 5.4. The bu]lc optical constantsare that of the germanium film deposited at 0.5 136Table 5.2 Optical constants vs. pressure for single layers and multilayers. More than 1set of optical constants indicates inhomogeneities in the films. 137Table 5.3 Optical constants vs. substrate bias for single layers and multilayers. Morethan 1 set of optical constants indicate inhomogeneities in the films. 146Table 6.1 Initial and final optical thicknesses, refractive indices and substrate parametersfor a quarter-wave stack deposited at the HeNe wavelength. Theellipsometric transform is shown in Fig. 6.16. 190viiLIST OF FIGURESFigure 2.1 Polarization ellipse for light propagating in the z direction. The field vectoris right-handed polarized. 11Figure 2.2 Reflection and transmission at an interface between two mediums a and b.Both the p and s polarizations are shown. 14Figure 2.3 Thin film system on a thick transparent substrate. The film system is theshaded area. The reflection and transmission components are for lightincident on the ambient side of the film system, light incident on the substrateside of the film system and light incident on the back face of the substrate. 18Figure 2.4 Quarterwave stack of low and high index of refraction materials on asubstrate. The low index of refraction layers are physically thicker in order toachieve the same optical thickness as the high index of refraction material.If the substrate is also of a low refractive index, often an additional highindex of refraction layer is sandwiched between the substrate and thedisplayed stack. 21Figure 3.1 Schematic of a magnetron sputtering system. The cathode assembly is shownin greater detail in Fig. 3.2. 24Figure 3.2 Schematic of the cathode assembly of the magnetron system, which alsoshows the magnetic field lines. Also included is the electric biasing. 25Figure 3.3 Schematic of a cathode assembly with an unbalanced magnetron. Note thatthe first surface that intersects the field lines is the substrate. 27Figure 3.4 Main species at the target and substrate. The lines show the origins of thespecies. The species shown are the reflected neutrals (Ar), negative targetions (T), target atoms (T), electrons (e) and positive ions (Arj. 28Figure 3.5 Schematic of the spectroscopic ex-situ effipsometer used in this thesis. 32Figure 3.6 Schematic of the in-situ ellipsometer used in the course of this thesis. 35Figure 3.7 In-situ ellipsometer and its attachment to the sputtering chamber.77 37Figure 3.8 Schematic of a Michelson Interferometer.10°S: source, B: chopper, BS:beamsplitter, Ml: moveable mirror, M2: fixed mirror, G:sample, D: detector,x: mirror displacement. 51VII’Figure 4.1 Schematic representation of the bandstructure of amorphous carbon. 67Figure 4.2 Experimentally determined and theoretically calculated values of the real (a)and imaginary (b) parts of the complex reflectance ratio for films depositedatl,4and8Pa. 68Figure 4.3 Real (n) and imaginary (k) refractive indices for films deposited at 1, 2, 4and8Pa. 71Figure 4.4 Tauc plots as a function of pressure for the amorphous carbon films. Thelinear fits have been extrapolated back to the origin in order to determine thepseudo-bandgap. 71Figure 4.5 Scratch depth vs. load for films deposited at 1,2, 4 and 8 Pa. Thecorresponding linear least squares fit is also shown. 72Figure 4.6 SEM fracture cross-section photographs of films deposited at (a) 1 Pa,and (b) 8 Pa. The scale is indicated on the figures. 73Figure 4.7 TEM photos of films deposited at (a) 1 Pa, and (b) 8 Pa. The films wereapproximately 600 angstroms thick. The scale is approximately 50 nmlinch. 74Figure 4.8 Real and imaginary refractive indices for films deposited at 8 Pa withsubstrate biases of (a) —12 V and (b) — 30 V. 76Figure 4.9 Wiener bounds when the two phases are the ambient and the amorphouscarbon film deposited at 1 Pa (Ar) at the photon energies 1.5, 3.5 and 6 eV.The data points are spaced at intervals corresponding to a 20 % change inthe constituents. Also shown are the dielectric functions for the EMA andSSC models. In addition, the dielectric values for the film deposited at 8 Paat the above photon energies are presented. 79Figure 4.10 The energy loss function Im (-1IE(o)) vs. photon energy for the filmsdeposited at 1 and 8 Pa. Also included is the loss function for diamond andgraphite (E±c). 84Figure 4.11 Real and imaginary values of the experimentally determined complexreflectance ratio of a film deposited at 8 Pa on an electrically isolatedsubstrate and two theoretically modeled fits. The first model assumes novoids while the second contains 10% voids. 85Figure 4.12 Mid-infrared reflection (R) and transmission (T) spectra for a semi-insulating GaAs substrate. Also shown is the residue: 1-R -T. 88ixFigure 4.13 Theoretical reflection spectra of a 1.25 .tm thick film with a refractive indexof 2 on GaAs along with the reflection spectra of the substrate. Also shownis the reflection spectra of a film with dispersion and one that in addition hasa value of k = .025. The value of Av represents the distance between thereflectance maxima. 89Figure 4.14 The mid-infrared reflection and transmission spectra for a film deposited at1 Pa in argon. Also included is the calculated value of the absorbance (1-R-T). 92Figure 4.15 The near-infrared reflection measurements and the modeled fits are shownfor the films deposited at 1 and 8 Pa. 93Figure 4.16 Log of k vs. wavenumber for films deposited at 1,2,4 and 8 Pa in the nearinfrared. The values of k were determined through fitting the reflectionspectra to the Farouhi-Bloomer model. 93Figure 4.17 Experimentally determined and theoretically calculated absorption coefficientof the film deposited at 1 Pa in argon. The theoretical fit was determinedthrough equations 3.51 and 3.52 96Figure 4.18 Experimentally determined and theoretically calculated absorption coefficientof the film deposited at 2 Pa in argon. The theoretical fit was determinedthrough equations 3.51 and 3.52. 96Figure 4.19 Experimentally determined and theoretically calculated absorption coefficientof the film deposited at 4 Pa in argon. The theoretical fit was determinedthrough equations 3.51 and 3.52. 97Figure 4.20 Experimentally determined and theoretically calculated absorption coefficientof the film deposited at 8 Pa in argon. The theoretical was determinedthrough equations 3.51 and 3.52. 97Figure 4.21 Deposition rate vs. 02 partial pressure for amorphous carbon filmsdeposited in a 02 / Ar mix. The total deposition pressure was 1 Pa. 107Figure 4.22 Real (n) and imaginary (k) refractive indices vs. photon energy for carbonfilms deposited in an Ar/H2 mix for a number of different partial pressures ofhydrogen. The total deposition pressure was 1 Pa. 110Figure 4.23 Absorption coefficient of the film deposited in 0.1 Pa H2 and 0.9 Pa Ar. Thetheoretical fit was determined through equations 3.51 and 3.52. 111xFigure 4.24 Log of k vs. wavenumber for films deposited at 1 and 8 Pa in pure argonand for a film deposited in 0.1 Pa H2 and 0.9 Pa in argon. The values of kwere determined through the Farouhi-Bloomer model. 111Figure 4.25 C—H stretch vibrations for films deposited in pure argon at a) 2 Pa, b) 4 Pac) Pa and d) 0.1 Pa H2 and 0.9 Pa argon. The spectra has been shifted forcomparison purposes. 114Figure 4.26 Refractive index measurements for films deposited in argon and N2. Therefractive indices were determined through the Farouhi-Bloomer model. 119Figure 4.27 Deposition rates vs. N2 partial pressure for films deposited in a nitrogen Iargon mix. The deposition power was 100 W and the total pressure was 1Pa. 119Figure 4.28 Theoretical absorption as a function of wavelength for quarter-wave carbonfilms on germanium. Note that the thickness is not constant as a function ofwavelength but that of Eq. 4.11. 122Figure 5.1 Theoretical trajectory for a germanium/carbon multilayer deposited ontosilicon: The individual layer thickness are 2.0 nm. The inset shows thedifference between a sharp and diffuse layer. 127Figure 5.2 Wiener bounds for the germanium and carbon phases in Fig. 1. The datapoints correspond to a 5% change in the constituents. Also shown is theexpected dielectric values assuming the Bruggman effective medium theory.The inset shows the ellipsometric trajectory of Fig 5.1 along with that for afilm with the same pseudo-dielectric function. The value of the pseudo-dielectric function , GeC, is also shown on the main figure. 128Figure 5.3 Experimental data and theoretical fit to a germanium/carbon bilayer on asilicon substrate deposited at 0.5 Pa. The optical constants were determinedto be (4.78,1.78) for the germanium layer and (2.52, 0.56) for the carbon. 135Figure 5.4 Experimental data and three theoretical models for a germanium layerdeposited on silicon at 2.0 Pa. The parameters for the inhomogenous layerare given in Table 5.1 135Figure 5.5 Ellipsometric trajectory of a germanium/carbon multilayer deposited onto afloating substrate at 0.5 Pa. Also shown is the theoretical ellipsometrictrajectory for a material with the pseudo-dielectric function as the stack. 138Figure 5.6 EUipsometric trajectory of a germanium/carbon multilayer deposited onto afloating substrate at 1.0 Pa. Also shown is the theoretical ellipsometricxitrajectory for a material with the pseudo-dielectric function as the stack. Inthis case a two layer model is required. 139Figure 5.7 EUipsometric trajectory of a germanium/carbon multilayer deposited onto afloating substrate at 2.0 Pa. Also shown is the theoretical ellipsometrictrajectory for a material with the pseudo-dielectric function as the stack. 140Figure 5.8 Experimental data for the first few layers of the multilayer deposited at 1 Pa.Also shown is a theoretical simulation of layers 3, 4 and 5 with diffusionbetween the layers. Both sets of data have been displaced for comparisonpurposes. 142Figure 5.9 Experimental data and theoretical fits for carbon films deposited as a functionof substrate bias. The optical constants of the 1 layer theoretical models aregiven. The inset shows two of the experimental trajectories and twotheoretical models which assume the bulk material is that of the filmdeposited at —100 V. 145Figure 5.10 Effipsometric trajectory of a germanium/carbon multilayer deposited onto afloating substrate (—22 V). Also shown is the theoretical ellipsometrictrajectory for a material with the pseudo-dielectric function as the stack. 147Figure 5.11 Ellipsometric trajectory of a germanium/carbon multilayer deposited onto asubstrate biased at —50 V. Also shown is the theoretical ellipsometrictrajectory for a material with the pseudo-dielectric function as the stack. 148Figure 5.12 Ellipsometric trajectory of a germanium/carbon multilayer deposited onto asubstrate biased at —100 V. Also shown is the theoretical ellipsometrictrajectory for a material with the pseudo-dielectric function as the stack. 149Figure 5.13 Wiener bounds for the multilayer stacks deposited as a function of substratebias. The optical constants are determined from the single layer films. 150Figure 6.1 Theoretical reflection and transmission characteristics for two antireflectioncoatings on a transparent substrate with a refractive index of 4. The firstfilm has an n and k value of (2,0) while the second has a value of (2,.0l) 156Figure 6.2 Typical target voltage vs. 02 flow rate for reactive sputtering of silicon. Themetallic mode corresponds to the region where the target is partially coveredwith an oxide. 159xi’Figure 6.3 Theoretical ellipsometric trajectories for a number of dielectric films in thecomplex p plane. For a given refractive index the trajectory wifi follow thesame spiral each time a multiple of the half-wave thickness is reached. 162Figure 6.4 Theoretical ellipsometric trajectory for a film with a refractive index of(2.0,0.1) on silicon. Also shown are values of p for a silicon substrate andan infmitely thick film. 162Figure 6.5 Experimental data and theoretical fit for silicon oxide on a silicon substrate asa function of film thickness. The value of k was determined to be less thanlx . The film was deposited in the middle of the metal mode. 165Figure 6.6 Experimental data and theoretical fit for silicon oxide on a silicon substrate asa function of film thickness. The value of k was determined to be less thanlx . The film was deposited in the middle of the metal mode. 165Figure 6.7 Comparison between the ex-situ and in-situ ellipsometer. Presented are thein-situ readings during the growth of a silicon layer on silicon, the ex-situmeasurement of the film and the theoretical trajectories at each of theinstruments angle of incidence. 167Figure 6.8 Effipsometric trajectory for a tantalum oxide film. The results indicate verylittle absorption in the film. 168Figure 6.9 Effipsometric trajectory of a 300 nm quarter-wave stack on a silicon substrateat the He Ne (632.8 nm) wavelength. 170Figure 6.10 Ellipsometric trajectory of a HeNe (632.8 nm) quarter-wave stack on asilicon substrate with a wavelength of 632.8 nm. The trajectory has amaximum magnitude of approximately 20 beyond the asterisks 170Figure 6.11 Flow diagram for the matrix method of controlling the deposition of opticalmultilayers 175Figure 6.12 Flow diagram for the projection method for the control of the depositionmethod. 178Figure 6.13 Experimentally measured and theoretically predicted ellipsometrictrajectories for the eighth layer of the quarter-wave stack controlled by theprojection method. 182Figure 6.14 Projection of the theoretical data of Fig. 6.10 onto the z plane. The dataalways progress counter clockwise. The radius of the curves increase with aXli’greater number of deposited layers. The value of the Si substrate is alsoshown. 186Figure 6.15 Flow diagram for the first iteration of the z-transform method for thecontrol of the deposition of optical multilayers. 188Figure 6.16 Ellipsometric data in the z-plane for the layers in the quarter-wave stackdeposited through the z-transform method. 189Figure 6.17 Ellipsometric data in the z-plane for the first three layers in the quarter-wavestack deposited through the z-transform method. 191Figure 6.18 Experimentally measured and theoretically determined reflection spectra fora 5 period (HeNe) quarter-wave stack deposited through the transformmethod. The theoretical curve is calculated using the fmal thickness forlayer in table 6.1. Also shown is the theoretical spectra for an ideal stack. 192Figure 6.19 Flow diagram for the second iteration of the z-transform method for thecontrol of the deposition of optical multilayers. 194Figure 6.20 Experimentally measured and theoretically determined reflection spectra fora 5 period (HeNe) quarter-wave stack deposited through the revised ztransform method. The theoretical curve is calculated assuming a perfectstack. 195Figure 6.21 Experimentally measured and theoretically determined transmission spectrafor a 5 period (HeNe) Fabry-Perot filter deposited through the revised ztransform method. The theoretical curve is calculated assuming a perfectstack. 197Figure 6.22 Effipsometric data in the z-plane for a number of the layers of the FabryPerot filter deposited through the revised z-transform method. Thetheoretical curve is calculated assuming a perfect stack. 199Figure 6.23 The theoretical trajectory in the p plane of the last two layers of the FabryPerot filter. The data points are spaced 4 nm apart. The optical thicknessof the tantalum oxide layer is presented at a number of points along thecurve. 200Figure 6.24 The optimized fits to two generated sets of data in the z-plane for thenineteenth layer of the Fabry-Perot filter. The first assumes 10 %inhomogeneities and the second has a surface roughness layer equal to 10 %of the total thickness. The optimization model assumes an ideal film. Alsoxivshown is the experimental data. The curves have been offset for presentationpurposes. 202Figure 6.25 Experimental data and theoretical fit with a refractive index of (2.19, .377)for a carbon film deposited in Argon. Also shown are the theoreticaltrajectories for three dielectric films. 207Figure 6.26 The initial values of the data and models presented in Fig. 6.26. 207Figure 6.27 Experimental data and two theoretical fits to a carbon film deposited in 33%CH4167%Ar. 208xvACKNOWLEDGEMENTSFirst I would like to thank my research supervisor, R.R. Parsons for all of his help,friendship and support over the years of my thesis. In addition I would like to thank all of themembers of the lab for the help and the support they have given me, Norman Osborne for histechnical expertise, Al Kleinschmidt for his excellent work on the in-situ ellipsometer andSamir Aouadi for his discussions on x-ray multilayers. In addition I would like to thank JohnEldrige and Yidan Xie for the work performed on the infrared spectroscopy measurements.I would also like to acknowledge the excellent technical services in the department. Iwould not have been able to able to complete this thesis otherwise.In addition I would like to thank Brian Sullivan of the National Research Council ofCanada for his helpful discussions on ellipsometry.Finally I would like to acknowledge the financial assistance of R.R. Parsons, theUniversity of Columbia, Microtel Pacific Research and the Science Council of BritishColumbiaxviChapter] 1INTRODUCTION1.1 GeneralThe objective of this thesis is to develop the ability to deposit protective infraredoptical multilayers which employ diamond-like tilms for use over the wavelength range of 1 to12 urn. Diamond-like films have a number of properties which make them suitable for thisapplication. These properties include good JR transparency,1 high hardness,2 chemicalinertness3and impermeability to moisture penetration.4Diamond-like films in general are amorphous with a mixture of sp2 (graphitic) and sp3(diamond) bonds and, in the majority of cases, are fabricated containing between 20% and60% hydrogen.5 There is, however, a growing interest in diamond-like films that have beendeposited without hydrogen, since these materials are typically harder6 and, ideally, do notposses C-H resonance absorptions in the infrared.7 The main disadvantage of these materials isthat they generally have a lower optical bandgap than the hydrogenated films, though this isnot necessarily a problem for JR coatings. In addition, there is a small but growing body ofliterature concerning diamond-like films with nitrogen incorporation,8’9due to the potentialvery high hardness of the material.There are a good number of current and potential applications for protective opticalcoatings using diamond-like films. These include protective coatings for germanium,’° zincsulfide,” and salt optics12 in the mid infrared range, coatings for front surface aluminummirrors,’3 and photothermal conversion of solar energy.14 In addition, there is a wide rangeIntroduction I 2of non-optical applications for diamond-like films. These include wear resistant overcoats inmagnetic recording,’5 passivation layers,’6 dielectric p-n junctions,’7 and hard coatings forsteel and carbide tools.’8In many cases, for protective optics, one also desires that the coating be anti-reflectingin order to maximize the transmission through the optical element of interest. With a singlelayer coating, this property can only be achieved at discrete wavelengths and when therefractive index of the film is the square root of that of the substrate.’9 As a result, multilayerfilms are required for general broad-band anti-reflection coatings.2° For coatings of this naturediamond-like films can be employed as the top protective layer and other materials withdifferent refractive indices are required for the intermediate layers.2’An ideal material for the intermediate layers in the infrared region is germaniumcarbide.22 Germanium carbide is an alloy with a tunable refractive index from approximately4.1 to 1.8, making it very desirable for the above application. In addition, the material isquite hard if a significant fraction of the material is carbon. As a result, GeC can also be usedas thick, protective, refractive index-matched initial layer in the overall multilayer design.Germanium carbide develops an appreciable absorption in the near-infrared whichlimits its range of applications if thick layers are required. However, the useful optical range ofGeC overlaps with many materials which are also transparent in the visible, such as Si02 andTa205, which are also fairly hard. As a result, it should be possible to find suitableintermediate materials over the entire infrared range specified.One important requirement during the deposition process is thickness control, as theIntroduction I 3resulting properties of the optical coating are dependent upon the thickness of the individuallayers.2° In addition, for materials such as carbon and germanium carbide, one may also berequired to monitor the refractive index, as this factor is dependent upon the depositionconditions.23There are a number of different methods currently in practice which are used to depositdiamond-like films. These methods are outlined in the next section along with a brief historyof the development of diamond-like films.1.2 History and State of the Art of Diamond-like FilmsThe current interest in diamond-like films has evolved out of efforts to depositdiamond films at low pressures.24’5 In a typical deposition procedure for diamond, ahydrocarbon gas is dissociated either through a hot filament26 or through a high frequencyplasma discharge.27 The carbon atoms then condense onto the substrate, which is usually keptat a temperature on the order of 8000 C. The presence of hydrogen is thought to etch awaythe graphitic phases causing the resulting material to be predominately diamond.28Though thin films of diamond would appear to be ideal for optical applications thereare a number of drawbacks to the material in its present form. One problem is that diamondcan only be deposited at relatively high substrate temperatures, effectively eliminating a widerange of potential applications. Another problem is that, currently, the material ispolycrystalline with surfaces too rough for optical applications. As a result there has been agood deal of interest in the ability to grow diamond-like films as these can be deposited atIntroduction / 4relatively low substrate temperatures and with very smooth surfaces.The first case of diamond-like films in the literature was reported by Aisenberg andChabot.29 In their technique, diamond-like films were deposited from a beam of carbon ions.Work of this nature was continued by Spencer et al. 30 throughout the seventies. An importantadvancement in the field was the development of the r.f. self-bias method by Holland,31 whichat present is the most widely used deposition technique for diamond-like carbon. This methodand a number of others currently in practice are outlined below.R.F. self bias/Chemical vapour deposition method21’32In this method, an r.f. glow discharge is sustained in a mixed argon / hydrocarbon gas.Typical hydrocarbons used in this technique are methane, ethane, butane, propane andbenzene. In the r.f. discharge, the hydrocarbons are partially ionized and cracked, whichresults in the positively charged particles being accelerated towards the r.f. biasedsubstrate. The resultant film properties depend upon the deposition pressure and thesubstrate bias. A number of variations of this method exist including a dc process which ismore applicable for scale-up.3Ion Beam plating33’4In this technique, electrons which are emitted from a hot tungsten cathode are acceleratedthrough an anode grid with energies up to 200 eV. The electrons then enter thedeposition chamber where they ionize hydrocarbon gas molecules through coffisions;creating a plasma. The positively charged ions within the ion sheath region are thenaccelerated towards the negatively biased substrate, and form a carbon film.Introduction I 5Arc Deposition35’6In this method, the carbon film is deposited by the condensation of a highly ionizedcarbon plasma (70%) onto a substrate. The energy of the depositing ions are typically onthe order of several tens of electron volts. The plasma is created through an arc dischargebetween a cathode and an anode, both of which are made of carbon. A current problemwith this technique is the inclusion of graphitic macroparticles in the film. One potentialsolution to this problem is a magnetic filter which separates the ions from the feedstockmaterial.Laser Ablation37’8A typical laser ablation system39 operates as following. A Nd-YAG laser delivers 250-1400 mJ to a graphitic feedstock in a ultrahigh vacuum system at 10 Hz. The beam isfocused to ensure a high intensity at the target surface. As a result an intense, highlyionized, plasma is formed. The substrate is placed so it is exposed to the plasma to allowfor the deposition of a film. This procedure has the problem of unwanted graphiticparticles in the film.Magnetron Sputtering 12,40In the sputter process, a negatively biased carbon target in a plasma discharge isbombarded by positive ions. This results in the ejection of both carbon atoms and plasmasustaining secondary electrons. The sputtered carbon atoms then condense onto asubstrate, creating a film. Though the deposition rate is low in this technique, largeindustrial scale-ups are relatively straightforward. In addition, a wide range of materialsIntroduction I 6are readily sputtered, making the method suitable for multilayer deposition. For example,magnetron sputtering is the only technique which is used to deposit hard carbon overcoatsfor magnetic recording applications.411.3 Deposition TechniqueThe method chosen to deposit the optical multilayers in this thesis was magnetronsputtering.42 As described above, this technique is highly versatile allowing for the depositionof a wide range of materials. Therefore, for optical multilayers, one can deposit all of therequired materials through the one method. In addition, films deposited through magnetronsputtering exhibit excellent film uniformity, smooth surfaces, good adhesion and near bulk-like properties; all which are of importance for optical coatings. Also, development workperformed on a small research-size system can be readily extended to large scale productionprocesses.1.4 Goals of the ThesisThere are essentially three goals in this thesis. The first is the determination of theoptimum conditions for the deposition of magnetron sputtered diamond-like carbon forinfrared optical coatings. At present, these conditions cannot be determined from theliterature.The processes investigated in this thesis are intended to be directly applicable toindustry and allow for the deposition on as wide a range of substrates as possible. Therefore,Introduction I 7only dc sputtering is examined to allow for a large degree of scale-up. In addition, no heatingor cooling of the substrate is to be applied. The deposition parameters to be varied are thesubstrate bias, sputter gas pressure and the partial pressures of the reactive gases.The second goal of the thesis is to develop a method of depositing germanium carbidethrough magnetron sputtering over the entire refractive index range of 4.1 to 1.8, which iscurrently limited from 4.1 to 3 due to poisoning of the target.43The fmal goal of the thesis is to develop a control system for optical multilayers whichcan determine both the thickness of the individual layers and their corresponding opticalconstants. This control routine is intended to be applicable for both absorbing and non-absorbing materials.1.5 Characterization Methods.There are three main characterization methods used in the course of this thesis. Thesetechniques are spectroscopic ex-situ ellipsometry, single wavelength in-situ ellipsometry andinfrared spectroscopy.Spectroscopic ellipsometry’ is an ambient, non destructive optical technique whichallows for the analysis of such thin film microstructural properties as surface roughness,45voids,46 phase fractions,47 and intennediate layers.48 In addition, for high quality films, thetechnique can also determine such intrinsic properties as optical constants49 and band-gaps.5°The optical range of the effipsometer used in this thesis is 1.5 to 6 eV.Introduction I 8In single wavelength in-situ ellipsometry, the film properties are measured as a functionof layer thickness, rather than photon energy. Measurements of this nature can determine suchfactors as layer interdiffusion,51 fun inhomogeneities and roughness evolution,52 as well as theoptical constants at the monitoring wavelength.53 In addition, the thickness of the film can bedetermined for control purposes.54Infrared spectroscopy can be used to provide a chemical analysis of the thin film ofinterest through an examination of the molecular bond vibrations.55 This factor is useful indetermining the presence and nature of the hydrogen and nitrogen incorporation. In addition,this technique can solve for the optical constants in the infrared, allowing for a determinationof the technical feasibility of the material.Additional characterization methods used during the course of this thesis were scanningand transmission electron microscopy, electron diffraction, hardness and resistivity methods, aswell as reflection/transmission measurements in the visible/UV. These techniques arediscussed in greater detail in the later chapters.1.6 Chapter OrganizationThe thesis is divided into seven chapters. Chapter 1 is an introduction to the thesistopic. Chapter 2 outlines the necessary optical theory required for the subsequent analysis inlater chapters. The purpose of the third chapter is two-fold. The first purpose is to describethe main instrumentation used during the course of the thesis. The second is to discuss theaccompanying analytical techniques.Introduction / 9The experimental results along with the accompanying analysis and discussion are givenin the fourth, fifth and sixth chapters. Chapter 4 deals with the diamond-like films.Amorphous carbon films (a-C) and amorphous carbon films containing hydrogen (a-C:H)and/or nitrogen (a-C:N) are all examined and compared in terms of their feasibility for opticalcoatings. Chapter 5 looks at a novel approach in depositing germanium carbide and comparesthis technique with more conventional methods. A control routine for the deposition of opticalmultilayers is developed in chapter 6 using rn-situ ellipsometry. The routines are initiallydeveloped for dielectric films and are then extended to allow for those which exhibitabsorption.Chapter 7 concludes the thesis.Chapter 2OPTICAL THEORY2.1 IntroductionThe purpose of this chapter is to provide the basic optical theory required in theremainder of the thesis. When necessary, the theory presented here is developed in greaterdetail in the later chapters. Three main topics are discussed. The first is the concept of opticalpolarization. A number of representations are given including the Jones calculus. The secondtopic deals with the calculation of the reflection and transmission properties of single andmultilayer films. It is shown how the process can be simplified through the use of a matrixmethod. Finally, some practical configurations for optical coatings are presented.2.2 Optical PolarizationFor a monochromatic plane wave traveling in free space the electric field can be writtenasE(r,t) = Re(Eei0t)), (2.1)where k is the wavevector, o the angular frequency and E the complex field vector. For theremainder of the thesis the complex notation is used and it is implicitly assumed that the realpart is to be taken. As the electric field vector under the above condition is transverse, canbe represented by two components along the x and y axis= E e’, (2.2a)Optical Theory IllFigure 2.1 Polarization ellipse for light propagating in the z direction. The field vector isright-handed polarized.= E (2.2b)where E , E are the amplitudes and Ø, Ø are the phases of the field vectors. Therelationship between the amplitudes and the phases of the two field vectors is referred to as thepolarization of the light (defined below).The solution of Eq. 2.1 for a fixed value of z shows that the tip of the electric fieldvector sweeps out an ellipse in the x-y plane at a radial frequency o. This effect is illustratedin Fig. 2.1. The rotational direction of the field vector is referred to as the handedness of thelight. The light is defined to be right-hand polarized if the electric field vector rotates in theyy’x’xRFIP tane = EJEOptical Theory /12clockwise direction looking into the source, and left-hand polarized if it rotates in the oppositedirection.A convenient form for defining the polarization, X’ of the electric field vector isthrough the ratio between the complex amplitudesx = (E / E) (2.3)Hence the polarization is represented by a single complex number. One can then determine theform of the ellipse in Fig. 2.1 through the relation— tanO+itaneX— 1—itanetane’ (2.4)where 0 is the angle between the major axis (x’) of the polarization ellipse and the referencex- axis; and ellipticity, tane, is the ratio of the minor/major axis. The term, e, is referred to asthe ellipticity angle.There are two important forms of the polarization. For the case where the fieldvectors are in phase, x is real and the light is linearly polarized. For the case where x = ± ithe light is circularly polarized. A positive or negative sign before the i determines whether thepolarization is left-handed or right-handed respectively. This condition also holds forelliptically polarized light.Another representation for the polarization is through a Jones vector,56 J, where= [:1 (2.5)In this notation the vectors are normalized so thatOptical Theory I 13J*.J.. (2.6)As the vector space is two dimensional, it can be represented through a choice of twoorthogonal vectors. All forms of the polarization can then be written as a combination of thesetwo vectors. The two most common representations are light linearly polarized along the xand y-axis wherenil rol1x= [oj’ “ = [ j’ (2.7)and left-handed and right-handed circularly polarized light where1 nil 1 ru== [—if (2.8)One other advantage of the Jones representation is that the individual optical elementsof a system can be represented through a 2 x 2 matrix.57 If the effects of reflection off theindividual components is ignored, then the sum effect of N optical elements in series on theoutput polarization can be determined through the relationnj, T12JJaw = (CN...C21)J, = (T)Jm = I 7’ 7’ II I (2.9)L’21 122JL2Jjwhere C is the Jones matrix of an individual component and T the product matrix. The outputpolarization can be written in complex number form through the bilinear transformation58—T22X+T1x0 ( .0)Optical Theoiy I 14Erpx = (E I E)ab IFigure 2.2 Reflection and transmission at an interface between two media a and b. Both thep and s polarizations are shown. The dashed line represents the normal to the interface.2.3 Reflection and transmissionFig 2.2 shows the reflection and transmission of light at an interface between twomedia, a and b. In this system, the orthonormal vectors for the electric field are chosen to belinearly polarized along the p (parallel to plane of incidence) axis and along the s(perpendicular to the plane of incidence) axis. The polarization of the individual rays can thenbe represented through the notation(2.11)or alternatively through the vectors in Eq. 2.7, if the subscripts s and p are substituted for xandy.Optical Theory I 15The reflectance and transmittance at an interface for an electromagnetic wave isdetermined through the consideration of the boundary conditions for the tangentialcomponents of the electric and magnetic field vectors.59 In a non-magnetic medium themagnetic field vector H is related to the electric field vector through the relationx=z/4 <ft, (2.12)where . denotes a unit vector in the direction of propagation, eo and .to are the permittivityand the permeability of free space respectively, and E is the dielectric function where theconductivity of the medium has been included. Equation 2.12 also includes a term, N, thecomplex refractive index whereN=-J. =n+ik (2.13)where n is the refractive index and k is the attenuation constant. In the remainder of the thesisthe term “complex refractive index” will be denoted by N, and n will be referred to as therefractive index.Consideration of the boundary conditions for the electric and magnetic fields gives thevalues for the reflectance coefficients, r and r3 for p and s polarized light respectivelythrough the relationsr =cosØ,, (2.14a)Na C050a + Nb COSØ br =Na COSØ b b cosøa (2.14b)Na °Ø b +Nb COSaOptical Theory I 16where 0 is the angle of incidence of the propagation vector from the normal. The value of Ø,where i is the film index, is determined through the consideration of the phase relationships atthe boundary or equivalently through Snell’s lawN0 sinØ0 = 1, sin, (2.15)where the subscript o represents the ambient medium. As the two reflection coefficients arefor orthogonal components, the above relations can be used for any polarization.An important factor in optics is the ratio between r and r. To demonstrate this,consider the calculation of the polarization of the reflected beam through the Jones matrixFE1 Fr,, o1rE1[ESJ[O rj[Ej’ (2.16)or alternatively though Eq. 2.10x0 =(r/rj. 2.17This ratio is referred to as the complex reflectance ratio, p. and is given byp = rp /r,, = p r + ip = tani e , (2.18)where tan’qf is the relative amplitude attenuation and A the phase difference of the polarizationupon reflection from an interface. Hence, the value of p acts as a transfer function between theinput and output polarizations.The derivation of the reflection and transmission coefficients for a thin film system iscomplicated by interference effects between the individual layers. However, consideration ofthe boundary conditions at each film interface allows for the system to be analyzed as a seriesof matrices. In this method, each interface is represented through a reflection matrix , U, whereOptical Theory /17,j=__F r (2.19)tLr 1]where t = 1 - r is the transmission coefficient. In addition, a phase matrix, P, is used todescribe the propagation through a film , f, byr —1fd 10 (2.20).‘ [ 0 e’’]’where13 =(2t/ ).g(n. —n sin2 0) (2.21)where is the wavelength of interest. For a N-layer system, the electric field components atthe input and output of the system are then related through the relation[Eu]= uo1Iu12I...PNuN N+u[ ] = [‘‘ 2].[EN+l.i], (2.22)E1 N+1,r m21 m22 N+1,rwhere the subscript, N+1, denotes the substrate; which, in this case, is assumed to be infinitelythick. As the value of EN÷I, = 0 under these conditions the coefficients for reflection andtransmission arer = -, (2.23a)1t =—. (2.23b)m11Optical Theory I 18TbFigure 2.3 Thin film system on a thick transparent substrate. The film system is the shadedarea. The reflection and transmission components are for light incident on the ambient side ofthe film system, light incident on the substrate side of the film system and light incident on theback face of the substrate.The intensity of the reflected and transmitted electromagnetic radiation can then be determinedthrough the relationsR=r.r*, (2.24a)T=!t.t*. (2.24b)noThe inclusion of the refractive indices in Eq. 2.24b is to compensate for the difference in theratio between the electric and magnetic fields in the two media. It should also be noted thatEq. 2.23b is only applicable when the substrate is transparent. Hence the matrix methodTOptical Theory / 19outlined above can be used to determine the reflection, transmission, and the complexreflectance ratio of a thin film system.The above derivations make the assumption of coherent interference which is usuallyvalid for films with a thickness on the order of the wavelength of light. This assumptioncannot necessarily be made when the effects of a thick transparent substrate are included in thecalculation of the reflection and transmission values. In this situation it becomes necessary toaverage the phase change across the substrate.6° The intensities are then given by therelations- Tf•Tf’RbR — R+ 1— R’ . R ‘ (2.25a)f bT= (2.25b)l-R Rbwhere the terms are as shown in Fig. 2.3.2.4 Optical MultilayersInterference effects in thin film multilayers allow for the deposition of a wide range ofpassive optical devices. Three of these devices, which are of importance in this thesis, aredescribed below. These are antireflection coatings, dielectric mirrors and Fabry-Perotbandpass filters.One of the simplest thin film coatings is the single antireflection layer on a substrate.If we consider the substrate to be infinite, then the reflection and transmission of the system isgiven by the product of the matricesOptical Theory /20M = Uai Pf (2.26)where a, f, and s denote the ambient, film, and substrate respectively. For a dielectric film ona transparent substrate, where the ambient is taken to be free space, the conditions for 100 %transmission are= ..,J (2.27a)flfd = (2m+ 1) 2 o/4 m = 0,1,2...(2.27b)where is the wavelength of interest, d is the film thickness, and flf and n., are the filmand substrate refractive indices respectively.The single layer antireflection coating has a number of drawbacks. One problem is thatthe range of useful wavelengths is quite narrow. Also, it is often not possible to fmd a coatingmaterial with the required refractive index.The above problems can be solved through the application of a broadband multilayerantireflection coating. Coatings of this nature usually consist of 3 to 6 layers and are made upof 2 to 3 materials with different refractive indices. These systems are too numerous todescribe here and the reader is referred to an excellent summary by G. F. Dobrowolski.61However, one of the most popular designs is given by the relationsn1d = nd3 =A0/4, n2d = (2.28a)n3 =q, (2.28b)nl >nS, n2 >n3, (2.28c)Optical Theory / 21Figure 2.4 Quarter-wave stack of low and high index of refraction materials on a substrate.The low index of refraction layers are physically thicker in order to achieve the same opticalthickness as the high index of refraction material. If the substrate is also of a low refractiveindex, often an additional high index of refraction layer is sandwiched between the substrateand the displayed stack.where n1, fl2, fl3, denote the refractive indices of the topmost, second and third layersrespectively and n is the refractive index of the substrate. The above equations illustrate theneed for films with different refractive indices when depositing antireflecting coatings.At the other extreme, to achieve high reflectance values a dielectric mirror, or “quarterwave stack” is typically used. This multilayer system consists of alternating layers of twomaterials with high and low refractive indices (Fig 2.4), each a quarter-wave thick (nd = A/4).Under these conditions, the reflected waves off each interface interfere constructively leadingto very high reflectivities, typically higher than those which can be achieved with metal films.Optical Theory I 22For a multilayer of x high and x low layers the reflectance at the wavelength of interest is givenbyR = , (2.29)where flL and H are the refractive indices of the low and high medium respectively. Theeffective wavelength range may be derived from2 . _lrflH—flLlLn+nf (2.30)Hence, theoretically one can achieve as high a reflectance as desired, though the useful rangeis limited by the contrast between the refractive indices. Outside of this region the intensitydrops off rapidly and there is a series of small maxima, called side bands.The half-wave thickness, A/2, is also important in the design of optical filters. Froman examination of Eq. 2.22, the phase matrix becomes equal to —l under this condition.Hence the deposition of a half-wave layer has the effect of reversing the sign of the reflectioncoefficient of the underlying multilayer. This effect allows for the deposition of a Fabry-Perotfilter. In this device, a half-wave layer is sandwiched between two identical quarter-wavestacks. Hence the reflection from one stack wifi be 1800 out of phase with the other and thetwo mirrors will interfere destructively. This leads to a high transmission at the wavelength ofinterest. Away from the primary wavelength, the two dielectric mirrors are no longer 180° outof phase and the transmission drops off rapidly.Chapter 33. INSTRUMENTATION AND ANALYTICAL TECHNIQUES3.1 IntroductionThe purpose of this chapter is two-fold. The first is to provide a description ofmagnetron sputtering. Both the instrumentation and the mechanics of sputtering are discussed.This technique is described in some detail as a thorough understanding is required for thesubsequent analysis in later chapters.The second part of the chapter describes the main instrumentation used to characterizethe films and the accompanying analytical techniques. The most important technique discussedis that of ellipsometry. Two types of ellipsometers are described. The first is a high precisionspectroscopic ex-situ ellipsometer. The second is a single wavelength in-situ ellipsometercapable of real time measurements. The corresponding methods for data analysis are theninvestigated. The chapter ends with a discussion of infrared spectroscopy.3.2 Magnetron Sputtering3.2.1 Deposition MechanismsMagnetron sputtering is the sole deposition technique used in this thesis. The sputterprocess is essentially one of momentum transfer whereby the material of interest fordeposition, or target, is bombarded by energetic ions. This bombardment causes the ejectionof target atoms, a portion of which condense onto a substrate, resulting in a film.Instrumentation and Analytical Techniques / 24INERT REACTIVEGAS GASCATHODEASSEMBL’VACUUMCHAMBERSUBSTRATEHOLDERSUBSTRATEHIGH VACUUM PUMPFigure 3.1 Schematic of a magnetron sputtering system. The cathode assembly is shown ingreater detail in Fig. 3.2.A schematic of the deposition chamber is shown in Fig. 3.1 and a more detaileddrawing of the cathode assembly in Fig. 3.2. During the deposition process the vacuumchamber is initially pumped with a roughing pump from atmospheric pressure to approximately3 Pa, then taken down to a pressure of approximately 1 x i04 Pa through diffusion pumping.The diffusion pump is aided by a liquid nitrogen cold trap which freezes out the water vapour.An inert gas, usually argon, is then introduced to raise the pressure to 0.5 to 8 Pa. Reactivegases such as nitrogen, oxygen or hydrogen can also be supplied, allowing for the deposition ofInstrumentation and Analytical Techniques I 25// // //SHIELDTARGET/\__I1L////////MAGNETSFigure 3.2 Schematic of the cathode assembly of the magnetron system, which also shows themagnetic field lines. Also included is the electhcal biasing.a film of a different chemical composition than the target.62 After the gas is at the desiredpressure, a negative potential is applied to the target while the chamber and part of the targetassembly are grounded, creating a plasma discharge. Positive ions in the plasma bombard thetarget surface, resulting in the ejection of both neutral atoms and secondary electrons, as wellas other species such as negative ions and reflected neutrals. A portion of the ejected targetatoms condense onto the substrate, typically located at a distance of 4 to 10 cm from thetarget, producing a film.An important factor in the sputtering process is sustaining the plasma discharge. Inorder to achieve this, the loss of ion-electron pairs needs to be overcome. This loss resultsInstrumentation and Analytical Techniques / 26from ion-electron recombination on the chamber walls, ion neutralization on the target, andelectron loss through the grounded surfaces.The loss of ion-electron pairs can be overcome through the emission of secondaryelectrons during the process of ion bombardment of the target. The secondary electrons areinitially accelerated away from the target surface and gain kinetic energy through the appliedelectric field. The electrons undergo collisions with the gas atoms, which often involveexcitation and/or ionization. The newly created ions, in turn, bombard the target surfaceproducing more secondary electrons, making the process self-sustaining.The efficiency of the above process is aided by the application of a magnetic fieldparallel to the target surface. Under these conditions the electrons are initially acceleratedaway from the surface, but are forced back towards the target by the Lorentz force. Inaddition, the electrons undergo cycloidal motion with a drift velocity in a directionperpendicular to both the electric and the magnetic field (E xFor the magnetron assembly shown in Fig. 3.2, the field source consists of an annularand centre magnet mounted on a high permeability pole piece. As the outer magnet completelysurrounds the inner magnet, the E x . drift has a closed path. This traps the electrons closeto the target surface and increases their effective path length. This mechanism leads to asufficient ionization to sustain the discharge and also contains the plasma to within the vicinityof the target.Ideally all of the magnet field lines originating on the annular magnet should return tothe centre magnet in order to maximize the electron trap (Fig. 3.2). This configuration isInstrumentation and Analytical Techniques / 27/_/\_/\/\%%\\\ / / \/ .\./ \ 7 \sr )/\_____ __SUBSTRATE/Figure 3.3 Schematic of a cathode assembly with an unbalanced magnetron. Note that thefirst surface that intersects the field lines is the substrate.referred to as a balanced magnetron. Balanced magnetics are not possible in practice for aplanar magnetron due to fringing effects, though this effect can be approximated by equalizingthe strength of the centre and annular magnets.A different type of plasma discharge results if the annular magnet is made muchstronger and/or with a larger area than the centre magnet (Fig. 3.3). The magnetronconfiguration described above is referred to as an unbalanced magnetron. Under theseconditions, a large portion of the field lines intercept the substrate. As a result, the substratecan undergo a significant electron and ion bombardment.63 The electron flux is usually of aInstrumentation and Analytical Techniques I 28,Ar Ti TI e Ar351Figure 3.4 Main species at the target and substrate. The lines show the origins of the species.The species shown are the reflected neutrals (Ar), negative target ions (T), target atoms (T),electrons (e) and positive ions (Arj.low energy and, therefore, can be repelled by applying a small negative bias (—10 to —35 V) tothe substrate. Therefore one can control the density of the plasma in the vicinity of thesubstrate through a proper design of the magnetic assembly.Fig. 3.4 shows the main species at the target and at the substrate. The two mainbombarding species at the substrate are the reflected neutrals and the plasma ions. Theprospect of negative ions is ignored as these are unlikely in the case for carbon. The reflectedneutrals originate at the target and can bombard the growing film with energies up to the targetvoltage ( 300 to 600 eV). The positive ions originate in the plasma in the vicinity of thea:ret Y////instrumentation and Analytical Techniques I 29substrate and travel on average a distance equal to the Debye length,TM typically on the orderof a few millimeters. These ions bombard the substrate with an energy equal to difference involtage between the plasma and the substrate. As previously mentioned, the ion current can becontrolled through proper magnetron design.Energetic particle bombardment can be desirable under the proper conditions as it canenhance the quality of the deposited films. To understand this, it necessary to understand thevarious growth mechanisms of thin films, which are explained in the next section.3.2.2 Energetic Particle BombardmentFilms that are deposited under conditions where the growth temperature is less than about30% of the melting point of the bulk material have what is referred to as a zone-i microstructure.65At these temperatures the film initially grows around preferred nucleation sites located at areas ofsubstrate inhomogeneities and roughness. Atoms reaching these sites are initially loosely bound tothe film lattice and are referred to as adatoms. The mobility of the adatoms is low under the aboveconditions and they will not be able to travel between the nucleation sites. As the nucleation sitesgrow in size they will prevent further depositing atoms from reaching the substrate throughshadowing effects. Hence the microstructure is characterised by long columns separated bysignificant voids. The resulting film has a large surface roughness and properties that are quiteunlike that of the bulk material and is often unsuitable for many applications. A zone-imicrostructure results in poor quality optical coatings as the refractive index can change underdifferent atmospheric conditions due to moisture penetration. 66Instrumentation and Analytical Techniques I 30Different microstructures result at higher deposition temperatures. For temperaturesbetween 30 and 50% of the melting point, the mobility of the adatoms increases to the point wherethey can undergo significant diffusion on the grain boundaries. The film microstructure thenconsists of columnar grains separated by intercrystalline boundaries and is referred to as zone-2.For substrate temperatures above 50% of melting point of the deposited material the result is azone-3 microstructure where diffusion within the grains leads to a film characterized by equiaxedgrains.Though films with a zone-2 or zone-3 microstructure have desirable properties for anumber of applications, the deposition conditions required often makes this method of film growthimpractical, especially if the substrate has a melting point lower than that of the film or can bedamaged at high temperatures. Also polycrystalline films often make poor optical films due to lightscattering at the grain boundaries. Fortunately, high quality optical films can be grown at ambienttemperatures if the substrate is subjected to particle bombardment during the deposition process.The bombarding particles, either the ions or energetic neutrals, will both impart energy into thegrowing film, increasing the adatom mobility, and forward sputter the film material. The aboveprocesses result in a microstructure consisting of densely packed fibrous grains. Thismicrostructure, referred to as zone-T, results in films with smooth surfaces, high densities andproperties close to that of the bulk values.Energetic particle bombardment can also affect the film properties through changing thechemical composition of the film,67 either through preferential sputtering of the different types ofatoms, or by altering the bonding configuration of the individual atoms. Both of these effects areInstrumentation and Analytical Techniques I 31important in the deposition of diamond-like films. The first effect alters the film properties when adopant gas is added during the film deposition. The second effect is of importance as ionbombardment is thought to alter the sp3/s2 bond ratio.68In conclusion magnetron sputtering is a versatile technique capable of depositing a widerange of materials. However, the nature and resulting quality of the films is highly dependant uponthe deposition conditions.3.3 Ellipsometry3.3.1 IntroductionEffipsometry is a technique whereby the change in polarization is measured uponreflection from a sample. This allows for a determination of the complex reflectance ratio p(section 2.3). As p is dependent upon both the individual layer thicknesses and the opticalconstants, measurements of this kind can be used to determine such parameters as filmthickness, porosity, and surface roughness; i.e. discriminate between zone-i and zone-T films(section 3.2.2). Effipsometric measurements can also solve for the dielectric function ofindividual films. Hence ellipsometry can provide both microstructural analysis and informationabout the optical bandstructure.Two ellipsometers were used in the course of this thesis. The first was a spectroscopicex-situ ellipsometer used to analyze the samples upon removal from the deposition chamber.Instrumentation and Analytical Techniques I 32Figure 3.5 Schematic of the spectroscopic ex situ ellipsometer used in this thesis.The second was a single wavelength in-situ ellipsometer which collected measurements as thefilms were being deposited.The remainder of the section describes the two ellipsometers in some detail thendiscusses the methods used to analyze the data. The analytical methods discussed are limitedto those used for the ex-situ measurements as these are by far the most general. Thetechniques used to analyze the in-situ data are quite specific and are discussed in the relevantsections in chapters 5 and 6.Ml M2PolarizerArc LampAnalyzerTubeMonochrometerInstrumentation and Analytical Techniques I 333.3.2 Ex-situ EllipsometerA rotating analyzer ellipsometer with a spectroscopic range from 1.5 to 6 eV was usedduring the course of this thesis. This instrument was designed and built by Brian Suffivan aspart of his Ph.D. thesis.69A block diagram of the ex-situ ellipsometer is presented in Fig. 3.5. A 75 Watt xenonarc lamp is used for the light source. A concave mirror is used to focus the image of the arclamp onto the entrance slit of the double prism monochrometer which, in turn, selects thedesired wavelength. The bandwidth of the monochrometer is proportional to the slit width andis usually on the order of 3 nm. Upon exit from the monochrometer the mirror system, M2,focuses the image of the exit slit onto the sample. A rochon polarizer, capable of .005 ° steps,linearly polarizes the light at a selected angle from the p-axis of the sample. A vacuum chuck,capable of .02 rotational steps, is used to hold the sample. The analyzing stage consists ofa rotating rochon polarizer ( or analyzer) followed by a photomultiplier tube. Once the dataare collected, a discrete Fourier transform is performed at twice the frequency of revolution.The ellipticity of the light incident on the face of the analyzer can then be evaluated from thesecond harmonics. As the incident polarization, P. on the sample is known, the value of p canthen be determined through the relations7°tarnJ cot(P = [(1 +a2)/(1 —a2)1V2, (3.la)cosA = b2 (i —a)2, (3.lb)Instrumentation and Analytical Techniques I 34where a2 and b2 are second cosine and sine harmonics respectively. The error in the secondharmonics can be reduced through signal averaging over a number of cycles of the rotatinganalyzer. It should be noted that the handedness of the light can not be determined throughthis configuration as one solves for cosA rather than A.Though ellipsometry is a very powerful analytical technique, it is quite sensitive torelatively small amounts of misalignment and miscalibration.71 To compensate for this factor,the ex-situ ellipsometer can be aligned and calibrated to a high degree of accuracy through anumber of automatic routines. After each calibration, measurements are made on a Sisubstrate which has also been measured at AT &T labs by D.E. Aspnes. The disagreement incomplex reflectance ratio is typically on the order of i(13. This amount corresponds toapproximately a 1 Angstrom difference in the oxide thickness on a silicon substrate.3.3.3 In-situ EllipsometerIn-situ ellipsometry measures the complex reflectance ratio as a function of thicknessduring the growth of a film. This technique has been used for the control of x-raymultilayers,72 the determination of chemical composition in quantum well devices,73 interfaceanalysis74,process control,75 and the spectroscopic investigation of diamond films.76 An in-situ ellipsometer was designed and built during the course of this thesis through a collaborationwith A. Kleindschmidt as part of his Masters Thesis.77 This author’s role was to aid in theinitial basic design and help develop the alignment and calibration routines.Instrumentation and Analytical Techniques I 35Figure 3.6 Schematic of the in-situ ellipsometer used in the course of this thesis.The ellipsometric configuration decided upon was a single wavelength rotatingcompensator ellipsometer (RCE). An outline of the instrumentation is given in Fig. 3.6. AHeNe laser is used for the light source. A laser has the dual advantage over an arc lampthrough eliminating the need for a monochrometer and being relatively easy to align. The maindisadvantage of this configuration is the loss of spectroscopic information. However, it nowpossible to analyze the film properties as a function of thickness.The laser light is linearly polarized through a Glan Taylor polarizer capable of 0.10steps. The sample stage is mounted onto three adjustable feed-throughs on the back of thedeposition chamber. The analyzer optics consist of a rotating compensator (quarter-wave at632.8 nm) and an analyzer module identical to that of the polarizer. The resultant beamSi DiodeDetectorRotatingCompensatorLaserAnalyzer(Fixed)Substrate HolderPolarizer (Fixed)Instrumentation and Analytical Techniques I 36intensity is measured by a silicon photodetector. An optical filter is placed in front of thedetector in order to eliminate the background radiation from the plasma discharge. Themeasured signal is then Fourier transformed to give both the second and fourth harmonics.The rotating compensator ellipsometer possesses a number of advantages over therotating analyzer configuration. The first is the ability of the RCE to determine the handednessof the polarization upon reflection from a sample. This ability is crucial when analyzing opticalmultilayers as the complex reflectance ratio can lie in all four quadrants of the complex plane.The second advantage is that the RCE can make precise measurements when the effipticity ofthe reflected light is small. This ability allows for accurate measurements during the initialgrowth of materials on silicon and glass. The final advantage is that the instrument is free ofany polarization effects from the source and detector due to the fixed analyzer and polarizer.The main disadvantage of the RCE configuration over that of the RA and RP is thatthe compensator characteristics are wavelength dependant. As a result, the instrument has auseful range of approximately ± 2I4 where is the compensator quarter wavelength, whichfor the above instrument is 632.8 nm. However, as this particular instrument is operated at asingle wavelength, in this case, this is not a drawback.During the development of the in-situ ellipsometer one other disadvantage was, thatunlike the rotating analyzer configuration, there did not exist a good calibration routine in theliterature for this type of instrument. To address this problem, a calibration routine wasdeveloped and is given in A. Kleinschmidt’s thesis. However the routine has been expandedInstrumentation and Analytical Techniques / 37SAMPLE HOLDERDETECTOR ARMSOURCE ARMFigure 3.7 In-situ ellipsometer and its attachment to the sputtering chamber.77upon since to include the effects of the vacuum port windows.78 The complete routine isgiven in appendix A.Fig. 3.7 shows the ellipsometer mounted onto the deposition chamber designed for thisspecific application. The deposition chamber has an adjustable substrate holder for alignmentpurposes and rotatable targets. This configuration eliminates one problem associated within-situ ellipsometry, that of substrate wobble. In conventional systems, in order to ensure goodfIlm uniformity, the substrates are toggled during the deposition. However; this methodintroduces an error in the ellipsometric measurements due to small variations in the angle ofSPTER NG CHAMBERInstrumentation and Analytical Techniques I 38incidence. In the system used in this thesis, the targets are toggled while the substrate staysfixed, eliminating the above source of error.One further advantage of this system is that it lends itself well to the optical monitoringof multilayers. As the substrate stays fixed, only one ellipsometer is needed, greatly simplifyingthe process over systems where two or more ellipsometers are required.723.3.4 Ellipsometric AnalysisSpectroscopic measurements of the complex reflectance ratio allow for an analysis ofthin film properties through the use of an N-layer model.79 As shown in Chapter 2, thetheoretical value of p for a multilayer film can be calculated through a matrix method. For athin film on a substrate, such factors as diffusion and surface roughness can be modeled asindividual layers. Information on the film structure can then be deduced by fitting thetheoretical value of p to the experimental data.It is important, then, to be able to derive the optical constants of the individual layers.if the bulk optical properties are known, an effective medium theory8°can be used to predictthe individual layer optical constants. if the bulk optical constants are not known, then theoptical properties can be determined through the choice of an appropriate parametric model.The next two sections discuss the concepts of effective medium theories and the modeling ofoptical constants.Instrumentation and Analytical Techniques I 393.3.5 Effective Medium TheoryThe macroscopic equation for an applied electric field, E, in matter is given byD=E=4irP+E, (3.2)where D is the resultant displacement field, P is the polarization field and £ is the dielectricfunction. The dielectric function is related to the complex refractive index through the relationn + ik = + ia,, (3.3)where a and £2 are the real and the imaginary parts of the dielectric function respectively. Thedielectric function, then, is dependent upon the polarizability of the medium. In order to derivethe macroscopic dielectric constant from the film constituents, it is necessary to consider theeffects of the field at the microscopic level. For a cubic dielectric lattice with a polarizabilty,o, at each lattice site, the macroscopic dielectric function is related to the microscopic throughthe Clausius and Mosotti relationa—i 4it= —fl’X, (3.4)a+2 3where n is the volume density of the lattice points. The above relation is well known and isusually derived from the cavity method.8’ For a random distribution of two differentpolarizabilities a similar derivation82 leads toa—i 4ita+2=(flaa+flbC1b) (3.5)Instrumentation and Analytical Techniques I 40Equation 3.5 can be extended to three or more constituents but this is rare in practice for thinfilm systems. As the individual polarizabilities are not directly measurable, the above equationis often written in the more convenient form(3.6)a+2 Eb+2where fa and fb are the volume fractions of the individual phases. Eq. 3.6 is the LorentzLorenz effective medium expression.83’4The Lorentz-Lorenz expression becomes unsatisfactory when the two phases consist ofregions large enough to have their own characteristic dielectric response. Under theseconditions the assumption that the background dielectric is the ambient is no longer valid andone typically substitutes a host dielectric, Eh. One other factor which must also be consideredis the screening effect of the individual grains. In general, for a two phase system, the effectivemedium expression is given by85=faaEh+fb . (3.7)E +l(E8 Ea +1CZ8h Eb +KZEhwhere ic is the screening factor.86 For a three dimensional isotropy iç = 2. For magnetronsputtered films, when a columnar growth pattern is present, a two dimensional isotropy where= 1 is often more appropriate.For a random dispersion of the two constituents a suitable choice for the host dielectricis the effective dielectric function itself. This leads to the Bruggman effective mediumapproximation87(EMA):Instrumentation and Analytical Techniques / 41E E EbEa______=0, (3.8)£a +KE Lb +KEThough the effective medium approximation is applicable in a large number of cases, it isimportant to consider its limitations. One potential problem is the assumption of a randomdispersion of the constituent phases. For example if phase b is encapsulated in phase a then thechoice of Eh = La in Eq. 3.7 is a more suitable one. This choice results in the Maxwell-Garneteffective medium theory. 88 A more serious problem arises when the grain size can effect thedielectric functions of the individual phases, as is the case for semiconductors and metals.Also, the EMA can underestimate the amount of screening between a metal and dielectric ifthe individual dielectric phases are sufficiently connected. In this particular case it is moreappropriate to use a model by Sen, Scala and Cohen89’9°(SSC):Ev(LmE)=fd’ (3.9)E•(EmEd) (1÷iç)where Em and Ed represent the dielectric function of the metal and the dielectric phasesrespectively.Given the large number of effective medium models, and the problems associated witheach of them, it is desirable to have a method whereby one can determine if the measureddielectric function can result from a chosen set of phases. This ability is especially importantwhen changes in the dielectric function of one or more of the constituents are possible underdifferent deposition conditions. The above requirement can be achieved through theexamination of the theoretical bounds to the resultant dielectric function. These bounds can beInstrumentation and Analytical Techniques I 42determined through the consideration of the effects of screening. For the case of noscreening, which would correspond to long needle-like grains aligned with the electric field, theresultant dielectric function is given byE faa + fbb. (3.10)In the case of plate-like grains aligned against the field, we have the maximum possiblescreening and the resulting dielectric function is given by-1= fa’ + fb’. (3.11)As the above conditions represent the limits to the possible amount of screening, equations3.10 and 3.11 form the boundaries in the complex E plane for the resultant dielecthcfunction from two distinct phases. These limits are commonly referred to as the Wienerbounds.9’3.3.6 Parametric Modeling.if one desires to solve directly for the optical constants of the deposited material thenthere can be only two unknowns at each wavelength of interest. For the case of a transparentfilm, the two unknowns are the refractive index and the film thickness. However, in practice,it is often difficult to solve for n directly over the entire range of interest as even smallimperfections due to surface roughness, film inhomegeneity and film-substrate interdiffusioncan lead to relatively large errors in the solution of the refractive index at certain wavelengths.This situation becomes even more complicated for absorbing films, when one desires to solveInstrumentation and Analytical Techniques I 43for both n and k, as the film thickness typically has to be measured to a degree of accuracybeyond that of mechanical devices.92The situation described above can be simplified if a parametric model is used todetermine the optical constants. In this case the thickness of the fthn can also entered into themodel and the resulting value compared with other methods of measurement such asprofiometry. The model chosen depends on the material in question. Some of the morepopular models are described below.For a simple metal, the primary optical absorption mechanism is intraband excitationsof the conduction electrons. In this circumstance the Drude approximation93 is often used:EDn4de =—[c/o(o+i/t)j, (3.12)where hü is the photon energy, 2, the plasma frequency of the electrons, t the intrabandrelaxation time and the free space dielectric constant. The Drude approximation cannot beused in regions when the interband transitions of the core electrons become significant.For dielectric films, dispersion in the refractive index is often modeled through theSellmeier approximation:94n2 =A+2’ (3.13)where A and B are constants and 2 represents an electronic transition wavelength. As oneapproaches a value of ?, the absorption becomes appreciable, and an expression for k mustalso be included in the model.Instrumentation and Analytical Techniques I 44Semiconductors are often the most difficult to model as the dielectric function in thenear-infrared to UV region depends upon both the short and long range order of the material.A suitable model for this region has been developed by Farouhi and Bloomer.95 This modelderives the value of k through a method based on the quantum mechanical theory ofabsorption, then determines n through a Kramers-Kronig transformation. This method isapplicable for both crystalline and amorphous solids, however only the amorphous case isrequired for this thesis.The absorption coefficient at a given frequency 0 is defined asc (w) = 2cok/c = OcI/I, (3.14)where 1 is the probability that an electron will undergo a transition to an excited state and 9 isthe number of possible transitions. The value of c1 is derived through time dependentperturbation theory through the consideration of an electronic transition between a bonding ()and an afflibonding (a*) state :964h2I(*H)212 (3.15)3c {E_E_ho} +hy/4)where E is the energy of the state, x is the electron position vector, y is the reciprocal of thefinite lifetime of the state and * Ia) is the dipole matrix element between the initial andfinal states. The maximum probability of transition occurs when ho = Ea* — EG.The value of 0 depends upon the product of the number of occupied states in thevalence band times the number of unoccupied states in the conduction band separated by anInstrumentation and Analytical Techniques I 45energy ho). Let (E) and i (Es) stand for the density of states as a function of energy inthe valence band and the conduction band respectively. The value of 9 can be then bedetermined through the relation9oc +ho))[1—f(E +hO))]dE. (3.16)If a low temperature approximation to the fermi functions f and f is made then the aboveequation can be written as9cc jT1(E)n(E +ho))dE. (3.17)To solve for Eq. 3.17 a further assumption is made that the density of states in the conductionand valence bands can be approximated by parabolic functions where(E) = const(E°” — (3.18a)= const(E — E01t0m)V2. (3.18b)The solution to Eq. 3.16 is then9 = const(ho — E)2, (3.19)whereE8 = EOUO7?? — (3.20)is the difference between the lowest energy in the conduction band and the highest energy inthe valence band.The value for k can then be written asA(E — E )2 (3.21)k(E)=E2 -BE+CInstrumentation and Analytical Techniques / 46where the coefficients A, B and C represent the terms in Eq. 3.15 through the relationsA constl(a * y, (3.22a)B = 2(E— Es), (3.22b)Czz(E. Ea)2+h2”f/4. (3.22c)The refractive index n(E) is related to k(E) through the Kramers-Kronig dispersionrelationn(E)—n =-‘-f k(E)—lc, dE, (3.23)where P denotes the principle part of the integral. One obvious problem with the aboveequation is it requires a knowledge of k over all frequencies rather than the limited rangedescribed above. This is not a problem if the other absorption mechanisms are far in terms ofenergy as they will enter into the solution of Eq. 3.23 essentially as a constant.Substituting Eq. 3.21 into Eq. 3.23 results in a solutionn(E) = n(oo)+ BE+C(3.24)E2 -BE+CThe coefficients B and C are represented asB =(_4_+EgB_E + CJ. (3.25a)Instrumentation and Analytical Techniques / 47ç =.((E +C)_2EgC), (3.25b)whereQ=1/2(g4C_B2).(3.26)3.3.7 Nonlinear OptimizationOnce the appropriate effective medium theories and/or parametric methods have beenchosen for the N-layer model, the individual parameters must be adjusted to optimize the fit tothe experimental data. Typically, this type of procedure is performed through a Chi-squareminimization of the function2N y—y(,ç;a)X (a)= , (3.27)where x, are the independent variables, a the model parameters and Yi and y(x,, a) are theexperimentally measured and theoretical determined values respectively. Equation 3.27 alsocontains a term for the random experimental errors a. In ellipsometry, the term a1 in Eq. 3.27is usually ignored as errors due to the imperfections in the model and systematic errors due tosuch factors as misalignment are almost always larger than the statistical errors. The functionto be minimized is thenF(â) = — y(x;a)I. (3.28)The minimization technique is outlined below.Instrumentation and Analytical Techniques / 48An initial assumption is made that Eq. 3.28 can be expanded out to the second orderthrough the relationF(d + 6â) F(â) + dT â +âT.D.8 (3.29)where d is the vector of first derivatives with respect to the individual parameters of a and Dthe Hessian matrix of second derivatives. Around the minimum of Eq. 3.29, the firstderivatives are expected to be zero; hence the function should be minimized through the step= a + D’ [—VF(â)]. (3.30)In practice several steps of the type in Eq. 3.30 are required for convergence.The gradient and Hessian of Eq. 3.28 are derived as follows. The first partialderivatives of the function F with respect to the individual parameters areN.. y(x1;â)aa1= —2 [y — y(x1;a)]‘ (3.31)and the second derivatives are determined through2F 2Eay(x1;â) y(x1;â) —y(x1;â)]2y(x;&) 1. (3.32)aafaak i=i[ aak aaJaak jIn practice the second term in Eq. 3.32 is usually ignored as the term in brackets close to theminimum is expected to be small and average out to zero over the summation. If one then usesthe representationlaFf3 =———, (3.33a)2aaandInstrumentation and Analytical Techniques / 491 2Fa. =— ,(3.33b)‘then the steps to minimize F can be found through solving the linear equationsa .(3.34)Once the parameters which minimize Eq. 3.28 are found, it is necessary to assign errors to theparameters and examine the goodness offit. For ellipsometric models optimized through Eq.3.28 an independentgoodness of fit is not possible and a relative term, the unbiased estimatora, is used:a)Ffl(x).(3.35)where N is the number of data points and p the number of wavelengthindependentparameters. The unbiased estimator allows for a comparison between different models and isapproximately equalto the4ñ times theaverage absolute difference between the experimentaland the theoretical values. The calculation of the Hessianalso allows for a determination ofthe covariance matrix,97 V, wherev =a ‘.(3.36)The 90 % confidence limits, öa, for eachindividual parameter can then be foundthrough therelation98=1.67.,J7c(3.37)Instrumentationand AnalyticalTechniques / 50Also a correlation matrix,79 C, between theindividual parameters can be determined throughthe covariancematrix by the relationC.. =___.(3.38______—The elements of the correlation matrix can beexamined in order to determine the degree cindependenceof the individual parameters.Perfectly independent parameters have a crosterm value of zero while strongly correlated values have an absolute value close to 1.Eqs. 3.35 to 3.38 allow for the establishment of a set of criterion which can be used.1—---determine the validity of a particular model. If two different models have an equalparameters, then the generalrule is to choose the one withthe smallest unbiased estim--The introduction of an additional parameter into the model should only be accepted if the.—a significant reduction in the unbiased estimator, typically onthe order of 2.Tn addition _error bounds on the individual parameters should be reasonable and notincrease wisaddition of new parameters.Finally, the individual parameters should notbe too stD—I--—correlated, though this requiressome discretionon the part of the user.3.4 Infrared Spectroscopy3.4.1 IntroductionA Fourier-transform infraredspectrometer was used to examine the infrar—properties of the films. This allowed for botha determination of the opticalconstz—--_Instrumentation and Analytical Techniques / 51Mlx___________/]M2Figure 3.8 Schematic of a Michelson Interferometer.10°S: source, B: chopper, BS:beamsplitter, Ml: moveable mirror, M2: fixed mirror, G:sample, D: detector, x: mirrordisplacement.infrared and a chemical analysis through an examination of the molecular bond vibrations.99The infrared measurements and analysis in this thesis were performed in collaboration withYidan Xie as part of her Masters thesis.’°°The next sections describe the experimental apparatus and the techniques used toanalyze the resulting data.3.4.2 Infrared SpectrometerThe main component of the infrared spectrometer is a Michelson interferometer. Aschematic of the interferometer is shown in Fig. 3.8. The operation of the instrument isInstrumentation and Analytical Techniques I 52described below.Light from the source, S. is chopped, collimated, then focused onto a beamsplitter, B.The divided beam is then reflected from the mirrors Ml and M2 and recombined at the beamsplitter. The resultant intensity is then measured at the detector, D. For the sake of simplicityit is convenient to initially consider the light source to be monochromatic. The intensitymeasured by the detector is then1(x) = 10(1 + cos 2t V x), (3.39)where x is the total optical path difference between the two beams, 1 is the individual beamintensity and v is the wavenumber of the infrared radiation.In practice, the source is polychromatic and the measured intensity as a function of x is1(x) = $i(v )(1 + cos2itv x)dv, (3.40a)=-1(O)+Ji(v)cos27rvziv. (3.40b)Equation 3.40 can be converted to a Fourier transform through the following observations. Asthe intensity , 1(v), is real we have the relationJ°1(v )e’2dv = Ji * (v )e2’dv. (3.41)As a result, Eq. 3.40 can be written as1(x) — -1(O) 4j1(v)e12dv. (3.42)Hence the wavelength spectrum can be determined through the reverse transformInstrumentation and Analytical Techniques I 531(v) = 2fIt(x)e_12dx, (3.43)where 1’(x) = 1(x) - 1(0). The value of 1(v) can only be determined from Eq. 3.43 if theintensity is measured over all values of x. In practice the intensity is discretely sampled and anapproximation to Eq. 3.43 must be made:1(nAv) I(nAx) exp(i2it nAx / N), (344)whereAv=l/(NEix). (3.45)In order to obtain an accurate determination of the infrared spectrum, the intensity must besampled at the required intervals with a high degree of precision. This requirement isaccomplished through HeNe laser tracking. By sampling at the intensity minimums of thelaser one can achieve a highly accurate position measurement.Equation 3.44 does not give the true Fourier transform as the sampling is discrete andover a finite distance x. The problems associated with this, such as aliasing and apodization,and how they are compensated for are discussed in detail in Bell.’0’The Fourier-transform spectrometer is operated in two distinct ranges. The first,between 800 to 4000 cm’, is referred to in the remainder of the thesis as the mid-infrared. Thesecond range, between 4000 to 9000 cm’ is referred to as the near-infrared.For the mid-infrared range, a globar source was used and a tungsten-filament wasemployed in the near-infrared region. The beam splitters consisted of thin fthns on substrates.For the optical range of 800 to 4,000 cni’ a Ge film on KBr substrate was used while aInstrumentation and Analytical Techniques I 54CaF2 substrate was used in the 4,000 to 9,000 cm1 region. For the intensity measurements aMercury-cadmium-telluride (MCT) detector and a InSb detector were employed in the mid-infrared and the near infrared respectively.3.4.3 Infrared Optical AnalysisOnce a spectral measurement of the reflectance and transmittance of a thin film systemis made, it is necessary to solve for the optical constants in order to perform a chemicalanalysis. However, unlike the visible-UV region, no simple model exists for the dielectricfunction of carbon films in the mid-infrared due to the large number of molecular resonanceoscillations. Given the large degree of parameters necessary to describe the optical constantsover the wavenumbers of interest, it is simpler to solve for N directly. Once the values of nand k are determined, one can then analyze the chemical structure of the film by fitting theindividual resonances to an appropriate model. The next two sections discuss the methodsused to solve for the optical constants and to perform the subsequent chemical analysis.3.4.4 Newton-Raphson MethodIn order to determine the optical constants (n, k) of the system at each wavelength ofinterest, it is necessary to simultaneously solve the equationsRTh (n, k, d) — RE =0, (3.46a)TTh(n,k,d)TE =0, (3.46b)Instrumentation and Analytical Techniques I 55where R and T are the values of the reflection and transmission and the subscripts Th and Erepresent the theoretically determined and the experimentally measured values respectively. Asthere can be only two unknowns at each wavelength, the thickness, d, must be determinedthrough an alternate method.Eqs. 3.46a and 3.46b are not invertable in terms of n and k and must be solved througha numerical technique such as the Newton-Raphson method. The general case of this methodfor N unknowns is described below.Let X represent a vector of N variables, x, which result in the zeros of the Nequations, y,•. In the region around the zeros, the functions y can be expanded out to the firstorder through the relation:(347)By setting the term on the right hand side to zero, the value of X can then be found throughiterative solutions to the set of equationscLJ6XJ—13, (3.48)whereii — ax’ (3.49a)= —yz. (3.49b)Though the form of Eqs. 3.49a and 3.49b is quite similar to that of Eqs. 3.31 and Eqs.3.32, the Newton-Raphson method is inherently much more problematic than nonlinearInstrumentation and Analytical Techniques / 56optimization. This is the direct result of having to solve for n and k at each individualwavenumber, rather than over the entire spectral range.The difficulties associated with the Newton-Ralphson method are best illustrated in thespectral region around some multiple of the half-wave thickness. At the half-wave thickness,Eqs. 3.46a and 3.46b are independent of n, resulting in an infmite continuum of multiplesolutions.’°2 As a result, in the neighborhood around the half-wave thickness, the solution of nis highly sensitive to small measurement errors. In nonlinear optimization these factors arecompensated for by the regions around the quarter-wave thickness where a R/an and aare large. This property allows for an accurate determination of n over the entire of spectralregion, providing the choice of model is a good one.Despite the problems in determining the value of n at specific wavenumbers using theNewton-Ralphson method, it is still possible to investigate the bonding structure in theseregions. This is accomplished through fitting the chosen model to the absorption coefficient,ot, given byCL= 4tk(3.50)which is inherently less sensitive to measurement errors and film imperfections. This techniqueis discussed in the next section.3.4.5 Optical models in the Mid-InfraredFor non-metallic materials, the primary absorption mechanisms in the mid-infrared areChapter 4DIAMOND-LIKE FILMS4.1 IntroductionThis chapter provides a thorough investigation of the diamond-like films to be used asa protective overlayer for infrared multilayer coatings. The main goals of this chapter are toallow for a comprehensive understanding of the basic mechanisms of the deposition processwhich affect the properties of the diamond-like films and to provide a set of physicalmeasurements useful to the optical designer.The ii-iitial set of films studied were deposited in an argon atmosphere. This processsimplified the analysis and allowed for a comparison with previously published works. Thisalso served as a guide for the films studied later in the chapter. In addition, it was felt thatthese potentially useful films had not been examined in enough detail in the literature. Theoptical, infrared, electronic, tribological and microstructural properties of the films wereinvestigated.Once the films deposited in a argon atmosphere were characterized, the effects of theaddition of reactive gases of H2, 02 and N2 during the sputter process were investigated.The same analytical methods used for the amorphous carbon films were employed.The final section of the chapter discusses the feasibility of using the investigatedmaterials in infrared optics.Diamond-like Thin Films / 594.2 Amorphous Carbon Films4.2.1 introductionA study was undertaken to understand the properties of amorphous carbon (a-C) filmsas a function of pressure and substrate bias.105 The goals of this study were twofold. The firstwas to allow for a comparison with the results in the literature and to provide a more completeknowledge of the film properties relevant to protective optical coatings The second goal wasto provide a better understanding of how the individual deposition mechanisms affected theproperties of the films. A number of the more important studies in the literature of this natureare outlined below.Rossnagel et at)°6 studied the optical and electrical properties of carbon as a functionof deposition pressure. This was correlated with an in depth study of the plasmacharacteristics of the sputter gas. Their results showed that there was an increase in thetransparency and the resistivity of the films with increasing pressure accompanied by adecrease in the plasma density and the electron temperature at the substrate. These effectswere attributed to a decrease in the deposition energetics with increasing pressure. The paperdid not investigate the infrared properties of the materials nor did it give any indication of therelative hardness of the films.I. Petrov et al107 performed a comprehensive study of the effects of the substrate biasand the deposition pressure on the resistivity of carbon films. It was found that the resistivityof the films was maximized at the highest deposition pressures and when the substrate bias wasDiamond-like Thin Films I 60at the electrically floating potential. When the substrates were grounded during the depositionprocess, the film resistivity was on the order of 1 Q -cm over the entire range of pressuresexamined (0.8 to 4 Pa). There was a small decrease in the film resistivity when the magnitudeof the negative substrate bias was greater than that of the floating potential.A detailed investigation was performed by Window and Savvides.108 In this study, theproperties of diamond-like films were examined as a function of deposition power. In theirresults, the films became more transparent and nonconducting with decreasing power. Thiseffect was attributed to an increase in the bombarding ion/deposition flux ratio, which, in turn,increased the amount of energy delivered to each arriving atom. Preliminary tests of thisnature were performed during the course of this thesis with comparable results. However, dueto the extremely low deposition rates at the lower powers, it was felt that this technique wasimpractical and it was not pursued further.Though the studies in the literature showed that changes in the sputtering gas pressureand the substrate bias altered the film properties, there was no clear understanding of howeach of the individual deposition mechanisms affected the properties of the diamond-like films.Also, the studies were not comprehensive enough for the purpose of this thesis; in particular,there was a serious lack of information on the infrared properties.The initial tests performed in this thesis were centered about the ellipsometric results.Once the necessary analytical software was written, the ellipsometric analysis could beperformed with relative ease compared to the complementary techniques. This factor allowedfor an extensive study. The complementary methods used were scanning and transmissionDiamond-like Thin Films / 61microscopy (SEM and TEM), electron diffraction (ED), and hardness and resistivitymeasurements. Infrared measurements were not included in the initial investigations for tworeasons. The first was that the IR measurements and analysis routines were quite timeconsuming compared to the ellipsometric methods. It was felt it was better to use the abovetechniques to determine which of the deposition conditions warranted further study. Also, atthe time of this study, the infrared measurements were being set up as a collaborative effortand could not be performed until a later date.4.2.2 ExperimentalThe planar magnetron system described in section 3.2 was used for the diamond-likefilm deposition. The target material was pyrolytic graphite. An unbalanced magnetron wasemployed in order to supply a substantial ion current at the substrate.109All of the films were deposited at a 100 W sputtering power. The substrate to targetdistance was 8 cm. As carbon has the ability to absorb large quantities of impurity gases,’1°thetarget was presputtered for 1 hour before each deposition run. The base pressure prior tosputtering was below 2 x104 Pa. During the sputter process, the argon gas pressure wasincreased by varying the argon flow rate while keeping the pumping speed fixed. This helpedto keep the base pressure constant at all times. In addition, the back pressure of the diffusionpump was kept below 60 mTorr at all times. This consideration is important as the pumpingefficiency can drop dramatically if the back pressure goes above 100 mTorr. Wheneverpossible all the films used in a study, such as ellipsometric measurements as a function ofDiamond-like Thin Films I 62pressure, were deposited in the same run. This procedure helped eliminate such possiblesources of nonrepeatabiity as drifts in the pressure gauges, differences in the target thicknessand differences in the base pressure.Highly polished silicon substrates, with a manufacturers’1’specified “roughness” of 4Angstroms, were used for the ellipsometric, SEM, and the hardness measurements. Comingglass substrates, 1 inch in diameter, were used for the resistivity measurements. For the TEMmeasurements, the films were deposited onto freshly cleaved NaC1, floated off in distilledwater and placed onto copper grids.An important factor in thin film deposition is the cleanliness of the substrate. To ensureclean substrates the following procedure was used. First the substrates were mechanicallypolished by hand using methanol and lens paper for approximately 1 minute. Next, ultrasoniccleaning was employed. In this procedure the substrates were first immersed in a beaker ofacetone, then trichiorylethelene, followed by methanol for approximately 3 minutes each.After each step the substrates were rinsed with de—ionized water then blown dry with N2 gas.Euipsometric measurements revealed this to be a more effective cleaning method than that ofmechanical polishing alone. Cleaning was not necessary for the freshly cleaved NaClsubstrates.Ellipsometric measurements were performed on the spectroscopic rotating analyzerellipsometer described in section 3.3. The films were analyzed immediately upon removalfrom the deposition chamber in order to help reduce any error in measurement resulting from ahydrocarbon overlayer buildup from the atmosphere.”2 Ifmore than one sample was removedDiamond-like Thin Films / 63from the chamber at a time, the remainder of the samples were stored in containers containingpure N2 until measurement.The hardness measurements were determined through the scratch method.113 In thisprocedure, the films were scratched with an indenter under increasing loads. The depths ofthe scratches were then measured through profiometry. The rate of increase in scratch depthvs. load gave an indication of the relative hardness between the films. The depth of thescratches did not exceed more than 10% of the film thickness (1.5 ± .1 rim) in order to preventthe substrate from influencing the results.114Initially, the substrate adhesion was poor for the films deposited at the higherpressures. As a result, the scratch method would remove the films from the substrate. Inaddition, the films deposited at higher pressures failed the tape test.”3 However, if the filmswere initially deposited at a pressure of 0.5 Pa for approximately 1 minute, all of the filmsshowed excellent adhesion. This effect was attributed to an increase in the bombardment fromthe reflected neutrals, which has been shown to be beneficial for this aspect.115Resistivity measurements were made with a four point probe.’6 Ion currents at thesubstrate were determined by biasing a 2.5 cm diameter probe,117 centred on the magnetronaxis, at —100 V. The probe was placed on the substrate table which was also biased at —100V during the measurements. The same probe was also used to determine the floating voltageof an electrically isolated substrate. The significance of these measurements is explainedbelow.Diamond-like Thin Films I 64For a floating surface in a plasma, an electron and ion flux impinges upon the surface.Initially the magnitude of the flux of each species, J, , is given as1’8= .6nj —i- I (4.1)m)where fle is the electron density in cm3, Te the electron temperature in degrees Kelvin and mthe mass of the species, s, in grams. As the initial electron flux is greater than the ion flux, thesurface will charge negative with respect to the plasma until the two fluxes are equal. At thispoint the voltage of the surface reaches a value Vf , typically between —10 to —35 V, wherev —v =—-ln m , (4.2)2e 2.31fle)where V is the plasma potential, which is typically on the order of a few volts, if a voltageon the order of —100 V is placed on the detector it has a sufficient negative bias to repelnearly all of the electrons in the plasma but not enough to cause a significant secondaryelectron emission from the bombarding ions.63 At this voltage, the current is equal to the ioncurrent, giving a measurement of the magnitude of the ion bombardment. The determinationof the floating voltage, in turn, gives a measurement of the average energy of the bombardingspecies.Diamond-like Thin Films I 654.2.3 Resultsa) PressureDiamond-like thin films were investigated over the pressure range of 1 to 8 Pa. Thefilms were deposited onto electhcally isolated (floating) substrates. Below 1 Pa it was foundthat the films were under considerable compressive stress and would delaminate from thesubstrate when the thickness was over 0.5 pm.The deposition parameters are shown in Table 4.1. The magnitude of both the targetvoltage and the substrate floating voltage decreases with increasing pressure. The decrease inthe target voltage is due to an increase in the sputtering efficiency at the higher pressures. Thedecrease in the substrate voltage is attributed to a lower electron temperature; the result ofscattering. A lower electron temperature is also one possible reason for the decrease in theion current (Eq. 4.2), though a reduction in the plasma density could also be a contributingfactor (Eq. 4.1). The deposition rate first increases then decreases with pressure which iscommon for films deposited at the same power.”9The optical constants and the individual thickness of the films were determined byfitting the ellipsometric measurements to the Forouhi and Bloomer interband model describedin section 3.3 which has been shown in the literature to be appropriate for diamond-likefilms.’20 In addition to solving for the optical constants, the model can determine additionalinformation about the bandstructure. This ability is best illustrated by considering themechanisms for absorption in carbon in the visible-UV range as illustrated below.Diamond-like Thin Films I 66Table 4.1 Deposition parameters of films deposited as a function of pressure onto electricallyisolated substrates.Pressure Target Voltage Substrate Ion Current Deposition(Pa) (V) Voltage (mA) Rate(V) (nm/mm)1 -531 -25 0.53 4.22 -516 -23 0.51 4.74 -499 -18 0.45 4.68 -479 -12 0.43 3.3A schematic of the theoretical band structure12’ for diamond-like carbon is shown inFig. 4.1, with contributions from both the bonding and the antibonding it and a bands. The acontribution comes from both sp2 and sp3 hybridized bonds and is usually centered around 15eV. The it bands have lower transition energy which can range from 0 to 5 eV. The originsof the different bonding structures in carbon are described below.In its ground state the carbon atom has the electronic configuration 2s 2p. Indiamond, 4 sp3 hybridized bonds form a tetrahedral structure. In graphite, there are threehybridized sp2 orbitals and one Pz orbital. The sp2 orbitals lie in a plane at 1200 from eachother. The electrons in the Pz orbitals between the graphite sheets overlap and formdelocalized it bonds. The bonding and antibonding it bands in turn overlap, which is the causeof the opaque nature of graphite. Disorder in the graphitic structure is thought to lead to boththe creation of sp3 bonds and the localization of the it electrons.’22 The localization of theelectrons can result in a separation of the it bands creating a bandgap. Ultimately, anincreasing number of sp3 bonds would result in a material whose properties were close toDiamond-like Thin Films I 67Valence Bands Conduction Bands///NY.NEnergyFigure 4.1 Schematic representation of the bandstructure of amorphous carbon.diamond.In this study, the only absorption mechanism considered was interband transitionsbetween the bonding and the antibonding it bands. It was assumed that the a bands wouldhave a negligible contribution over the photon energy range measured (1.5 to 6 eV) and theaddition of five extra parameters in the model would cause an unnecessary complication.The experimentally determined and the theoretically calculated values of the complexreflectance ratio, p, are shown in Fig. 4.2 for the films deposited at 1, 4 and 8 Pa. Theoptical constants derived from the interband model are shown in Fig. 4.3 for the filmsdeposited at 1, 2, 4 and 8 Pa. Table 4.2 shows the thickness, model parameters and theunbiased estimator for each of the films. The thickness of the films were also measuredthrough profilometry to within ± 5 nm and in each case the measurements agreed to withinerror with the results shown in Table 4.2.Diamond-like Thin Films I 681.501.251.000.75C0.250.000.750.500.250.00—0.25—0.50—0.75—1.001.5 5.0 5.5 6.0E(eV)Figure 4.2 Experimentally determined and theoretically calculated values of the real (a)and imaginary (b) parts of the complex reflectance ratio for films deposited at 1, 4 and 8Pa.2.0 2.5 3.0 3.5 4.0 4.5Diamond-like Thin Films / 69Table 4.2 Farouhi and Bloomer interband model parameters and the unbiased estimators forfilms deposited as a function of pressure onto electrically isolated substrates.Pressure Thickness n a b c(Pa) (nm)1 72.0 ± 2.1 1.75 ± .04 .51 ± .05 2.2 ± .4 3.9 ± .8 .0302 78.3 ± 1.7 1.64 ± .03 .42 ± .03 2.0 ± .2 3.2 ± .5 .0244 84.2 ± 1.3 1.52 ± .01 .32 ± .02 2.3 ± .3 5.2 ± .7 .0268 76.4 ± 0.8 1.40 ± .01 .23 ± .01 3.9 ± .5 15 ± 1 .024Table 4.2 omits the parameter Eg in the modeling results. It was found that the value ofEg was highly correlated with the values of B and C resulting in large errors in all threeparameters. In each optimization, the value of Eg was close to zero so it was subsequentlyset to zero and treated as a constant during the fitting procedure. This discrepancy withrespect to the theoretical development in section 3.3 is due to a breakdown in the parabolicband assumption close to the minimum and the maximum of the conduction and valence bandsrespectively. For amorphous solids, below the expected optical bandgap, there exist a series oflocalized tail states which increase exponentially with photon energy.’23Though a well defmed bandgap does not exist for amorphous semiconductors a“pseudo-bandgap” can be deduced through the fitting of the imaginary part of the dielectricfunction in the linear region above the tail states to the relation(4.3)where B is a constant and ET the pseudo-bandgap. The above equation is known as the Taucrelation.’24 Tauc plots for the above films are shown in Fig. 4.4. The tail states are clearlyDiamond-like Thin Films / 70Table 4.3 Measured properties of films deposited as a function of pressure onto electricallyisolated substrates.Pressure(Pa)Pseudo - Bandgap Resistivity Relative Hardness(eV) (ohm-cm)1 0.3 30 12 0.4 400 .544 0.7 2000 .288 1.2 .14visible for the film deposited at 8 Pa. The least squares fit lines are extrapolated back to the xaxis in order to determine the values of ET which are presented in the second column of Table4.3 along with the resistivity of the films in the third column.The plots of the scratch depth vs. load are shown in Fig. 4.5 along with thecorresponding least squares fit. The relative hardness between the films, which is the ratio ofthe slopes, is given in the last column of Table 4.3.Scanning electron micrographs of fracture cross-sections and transmission electronmicrographs of films deposited at 1 and 8 Pa are shown in Fig. 4.6. and in Fig. 4.7 respectively.The thickness of the TEM films is approximately 600 Angstroms. The films deposited at 1 Paappear dense and featureless. For the 8 Pa films there is direct evidence of columnar growthand an open voided structure. The films deposited at 4 Pa appeared very similar to thosedeposited at 8 Pa. The films deposited at 2 Pa were intermediate in microstructure comparedto those deposited at 1 and 4 Pa.I‘3*Figure 4.3 Tauc plots as a function of pressure for the amorphous carbon films. The linearfits have been extrapolated back to the origin in order to determine the pseudo-bandgap.Diamond-like Thin Films / 71r—— 11111, I3.01 Pa1.51.0kI I I I1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0E(eV)Figure 4.4 Real (n) and imaginary (k) refractive indices for films deposited at 1, 2, 4 and 8Pa.43210.0 0.5 1.0 1.5 2.0 2.5 3.0E(eV)3.5Diamond-like Thin Films I 72160 I I IiPa140- 2Pa4 Pa120o 8Pa100 °C80 - 0C)40-0 100 200 300 400 500 600 700 800Load (grams)Figure 4.5 Scratch depth vs. load for films deposited at 1,2, 4 and 8 Pa. The correspondinglinear least squares fit is also shown.Diamond-like Thin Films I 73(a)(b)Figure 4.6 SEM fracture cross-section photographs of films deposited at (a) 1 Pa, and(b) 8 Pa. The scale is indicated on the figures.Diamond-like Thin Films I 74(a)(b)Figure 4.7 TEM photos of films deposited at (a) 1 Pa, and (b) 8 Pa. The films wereapproximately 600 angstroms thick. The scale is approximately 50 nm/inch.Diamond-like Thin Films / 75The electron diffraction results for all of the films appeared identical and featured twobroad diffuse rings. This property indicated that all of the films were amorphous without anylong range order.b) Substrate Bias.Two sets of films deposited at argon pressures of 1 and 8 Pa were studied as a functionof substrate bias. For each set of fthns it was found that above a substrate bias of —50 V thefilms appeared to be under considerable compressive stress and would delaminate from thesubstrate upon removal from the deposition chamber.Ellipsometric studies of the films deposited at 1 Pa were shown to be identical in termsof there optical properties. There was no discernible difference in the optical properties of thefilms deposited at 8 Pa at substrate biases greater than —30 V.The refractive indices of two 8 Pa films, one deposited at —1 2V (floating potential)and one at —30 V bias, are shown in Fig. 4.8. The SEM photo of the film deposited at —30 Vappeared very similar to that of the film deposited at 1 Pa and at a floating potential. Thehardness of the film deposited at —30 V was to within error (10%), the same as that at —12 V.The substrate bias and ion currents were also altered by changing the magnetics of thesputter source through the use of a balanced magnetron. Over the pressure range of interest,the replacement of the magnetics caused an increase in the magnitude of the target voltage of10 to 20 V. The ion currents decreased on average by a factor of 2, and the floating voltageDiamond-like Thin Films I 76I I I I I In1.5-12V—30V1.0a)a)I0.052.02.53.03.54.04.55.05.56.0E(eV)Figure 4.8 Real and imaginary refractive indices for films deposited at 8 Pa with substratebiases of (a) —12 V and (b) — 30 V.by a factor of 20%. A set of films were deposited as function of pressure and their opticalproperties determined through ellipsometry. After depositing the films the unbalancedmagnetron was replaced and the above measurements were repeated. The ellipsometric modelparameters for both sets of measurements agreed to within error.4.2.4 DiscussionThe electron microscopy results show that with increasing pressure the turns develop amore voided microstructure. This trend is well known for magnetron sputtered films and isattributed to a decrease in the deposition energetics. At low pressures there is a considerableDiamond-like Thin Films I 77energy flux resulting from the reflected neutrals at the target surface, and the bombarding ionsfrom the plasma in the vicinity of the substrate. As discussed in section 3.2.2, the bombardingparticles both impart energy into the growing film, which increases the adatom mobility andforward sputter the film material into voids and interstitial sites. The sputtered atoms alsoarrive directly at the substrate with several eV’s of energy. These factors result in a denselypacked film. At higher pressures, increased gas scattering results in a more thermalized andoblique deposition flux as well as a reduction in the energy of the neutrals due to a lower targetvoltage. In addition, there is a decrease in the energy of the ions due to a reduction in thefloating potential of the substrate.With increasing pressure there is also a substantial change in the ellipsometricmeasurements. Microstructural changes alone can result in large changes in the opticalproperties of thin films and this effect is often used to deduce such factors as void fractions andsurface roughness through ellipsometric modeling.125 For carbon films, however, there is theadded complexity of the possibility of a change in the chemical bonding configuration or thelocalization of the t bonds. For example, energetic particle bombardment results in hightemperature/pressure “spikes” which are believed to result in the creation of sp3 bonds.126It was attempted to determine whether the changes in optical properties for filmsdeposited at different pressures could be explained solely in terms of microstructure alone or ifan accompanying change in the molecular bonding configuration was also necessary. Toaccomplish this, the ellipsometric data at 8 Pa was fit to an N-layer model where theBruggman effective medium approximation was used to determine the dielectric function ofDiamond-like Thin Films / 78each layer. Both a 3 dimensional and a 2 dimensional isotropy were considered. The dielectricfunction of the film deposited at 1 Pa was used as the reference data. All of the modelsattempted predicted void fractions in excess of 50 %, which seemed large given the electronmicroscopy results, and unbiased estimators an order of magnitude larger than that for theinterband model.For metallic films deposited at high pressures, the SSC model is a often a more suitablechoice than the Bruggman effective medium approximation.89 At higher deposition pressures,voids in the film can become connected, enhancing the screening of the metallic phase. As thefilms deposited at low pressures were reasonably conducting, the above study was repeatedusing the SSC model. However, it was found that with this technique there was at best a fewpercent improvement in the unbiased estimator and about a 5 % reduction in the void fraction.It was felt that this relatively small effect was the result of the dielectric contrast between thefilm material and the ambient being small compared to that with a metal.Though a suitable model for the dielectric function of the 8 Pa film could not be found,this does not necessarily mean that the resultant dielectric function cannot be arrived at fromthe chosen set of phases. To investigate the this factor further, the Wiener bounds (Section3.3.5) to the resultant dielectric function were applied at three separate photon energies: 1.5,3.5 and 6 eV’s. The results are shown in Fig. 4.9. Also shown are the bounds between theEMA and SSC models for a film with a 2 dimensional isotropy. It can be seen that the valuefor the 8 Pa film lies within the dielectric bounds for the last case only and in this instance stillDiamond-like Thin Films / 79I I I I(1,0)‘ I I I I I I IEMAsscWeiner8 Pa FilmFigure 4.9 Theoretical Wiener bounds when the two phases are the ambient and theamorphous carbon film deposited at 1 Pa (Ar) at the photon energies 1.5, 3.5 and 6 eV. TheThe data points are spaced at intervals corresponding to a 20 % change in the constituents.The bounds at each energy have been displaced for presentation purposes. Also shown are thedielectric functions for the EMA and SSC models. In addition, the dielectric values for the filmdeposited at 8 Pa at the above photon energies are presented.(3.2,2.6)(3.7, 2.9)3.5eV-(1,0)(5.3, 2.6)(1,0) 1.5eVI I IDiamond-like Thin Films I 80lies outside the region expected for an isotropic film. Hence, it can be concluded that thedifference in the optical properties between the 8 Pa and 1 Pa film can not be explained interms of the difference in the microstructure alone. This result correlates well with largevariations in the resistivity and hardness measurements.One other factor which can influence the ellipsomethc results is surface roughness.The Farouhi-Bloomer model was used to determine the dielectric function of the individualfilms when surface roughness was included in the film structure model. In this case a twolayer model was used. The top roughness layer contained 50 % voids and the Bruggmaneffective medium approximation was used to determine the resultant dielectric function. Thethickness of both layers was allowed to vary.It was found that the inclusion of surface roughness into the model for the highpressure film did not result in a reduction of the unbiased estimator and caused only minutechanges in the dielectric function. This factor was attributed to the small dielectric contrastbetween the film and the ambient. For the low pressure film the inclusion of surface roughnessresulted in a 20 % improvement in the unbiased estimator ( for a surface roughness of 30Angstroms) and the general effect of increasing the real part of the dielectric function andlowering the imaginary part. However, when the Wiener bounds were examined it was foundthat this was not enough of a change for the results of the 8 Pa film to lie within the requireddielectric bounds.Though it can be concluded that the changes as a function of pressure are the result ofa change in the bandstructure, it cannot be said, at this point, whether or not the changes areDiamond-like Thin Films I 81the result of an increase in the number of sp3 bonds. Though this is often cited as the reasonfor more diamond-like properties126”27another valid reason is the localization of the itelectrons. One other important consideration is that the above diamond-like properties do notnecessarily indicate a large fraction of sp3 bonds. These two factors are best understood byconsidering a number of the theoretical studies in the literature, which are outlined below.An excellent theoretical discussion of the properties of amorphous carbon is given by J.Robertson.’28 In this study, he compares the difference between a number of randomnetwork models with different sp2 Isp3 bonding ratios and models which consist primarily ofgraphitic islands linked by sp3 bonds. The graphitic island structure was chosen as it wasfound that the formation of 6-fold rings during the deposition process was thermodynamicallyfavourable over a number of other naturally occurring configurations. The chosenmicrostructure consisted of graphitic islands with complete breaks in the it bonding at theedges.The optical properties of the models were determined through a tight-bindingapproximation,129 which included both the first and the second nearest neighbour interactions.In addition, the optical properties for the diamond and graphite structures were also predictedthrough the above method. The tight-binding approximation gave reasonable results for boththe diamond and graphite bandstructures and predicted the values for the optical bandgaps ofthese materials.There was a distinct difference in the optical properties of the random network and thegraphitic island models. It was shown for the random networks that, even for the 100% sp3Diamond-like Thin Films I 82bond model, an optical bandgap did not exist. For the graphitic island structure, however, thepresence of medium range order in the material resulted in a bandgap which was inverselyproportional to the island size.Hence, according to Robertson’s study, an increasing bandgap alone does notnecessarily indicate an increase in the number of sp3 bonds. The results in this thesis wouldseem to support this as the films become softer as the optical bandgap increases.Another theoretical study of amorphous carbon was performed by Tamor and Wu.’3°Their assumption was that the diamond-like properties of a—C resulted from imperfections inthe graphite lattice. In their model, the parallel graphite sheets were linked by sp3 bonds.Percolation theory 131 was used to determine the percentage of sp3 bonds required for thematerial to change from a metal to an insulator, which was found to be 8.3 %. The maximumallowed number of diamond bonds in the above model was shown to be approximately 10%.A theoretical simulation which complements the above studies was performed byG.Gali et al. 132 In this study, the structural and electronic properties of amorphous carbonare generated through a molecular-dynamics method.’33 The model starts with a random arrayof carbon atoms at 5000K which are subsequently quenched to room temperature. This modelsimulates the effects of ion bombardment which causes high temperature/pressure spikes.The theoretical results predicted 85% sp2 sites and 15% sp3 sites. The generalstructure was one of intersecting planes of 5, 6 and 7 fold rings. These properties correlatewell with the two models above. In addition, the theoretical electronic density of states was ingood agreement with experimental values in the literature.Diamond-like Thin Films I 83It should be noted that the above discussion is not meant to show that a large degree ofsp3 bonding cannot exist in amorphous carbon films, only to point out they are not necessarilyrequired to explain what are commonly referred to as “diamond-like” characteristics.One method for determining the presence of it electrons in carbon is through theexamination of the energy loss function, —Im(1IE), where’34—Im(1/E) =E2/(E+), (4.4)Peaks in the energy loss function occur for plasma oscillations when both E1 and E2 are small,as is the case for carbon. For amorphous carbon there are generally two peaks, a lower peakwhich results from the it electrons and one which includes the effects of all of the valenceelectrons (it + ). To a first order approximation, the position of the peaks, ho ,. is given bythe relation 135Ci) p=(ne2/Em) (4.5)where n is the electron density, e the electron charge, E the permativity of free space and m theelectron mass.Figure 4.10 The energy loss function Im (-l/e(o)) vs. photon energy for the films deposited at1 and 8 Pa. Also included is the loss function for diamond and graphite (E..Lc).()0.200.160.120.080.040.00Diamond-like Thin Films / 841.51.20.90.60.30 5 10E(eV)0.015Fig. 4.10 gives the energy loss functions for both graphite and diamond along withthe loss function for the films deposited at 1 and 8 Pa. The it plasmon peak for graphite iscentered around 7 eV which is beyond the range of the instrumentation used in this thesis.However, from a visible inspection of Fig. 4.10, it can be seen that the energy loss functionsfor both the 1 and the 8 Pa films have not reached a maximum by 6 eV. This factor indicates asubstantial amount of sp2 bonding in the films. In addition, there does not appear to be anappreciable difference in the peak positions, suggesting that there is not a large difference inthe density of the it electrons in the two materials.Diamond-like Thin Films I 852.01.51.0C0.50.0—0.5—1.0E(eV)Figure 4.11 Real and imaginary values of the experimentally determined complex reflectanceratio of a film deposited at 8 Pa on an electrically isolated substrate and two theoreticallymodeled fits. The first model assumes no voids while the second contains 10% voids.Unlike the films deposited as a function of pressure, the films deposited as a function ofsubstrate bias do not exhibit large differences in their optical properties. For the filmsdeposited at 8 Pa there is, however, a substantial change in the microstructure which appearsto undergo a transition from zone-i to zone-T with an increasing substrate bias. This effect isattributed to the bombarding ions. Ellipsometric modeling was once again used to determine ifthe difference in optical constants could be explained solely in terms of changes in themicrostructure of the films. In this case, the dielectric function of the film deposited at —30 Vbias was used to fit the ellipsometric data of the film deposited at the floating potential. Theresults for two different EMA models are shown in Fig. 4.11. The first model assumed no1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Diamond-like Thin Films / 86voids and allowed the thickness of the film to vary. The introduction of voids into the secondmodel resulted in a relatively good fit withan unbiased estimator of 0.06 and a void fraction of0.1 ± .01. Given the good correlation between the electron microscopy and the ellipsomet.ricresults, it would appear that an increase in the energy of the bombarding ions over the rangestudied results in a change in the microstructure only. This result correlates well with theresults of I. Petrov et al.’°7 which showed a small increase in the conductivity of their filmswith an increasingly negative substrate bias indicating an increase in the density of their films.Table 4.1 shows that the magnitude of the floating voltage and the energy of the argonions increases with decreasing pressure. However, given the results for films as a function ofsubstrate bias, it appears unlikely that this effect alone would explain the large change in thefilm properties. One other possible mechanism is the difference in the energetics of thereflected neutrals. As discussed in section 3.2, unlike the relatively low energy ions, theseparticles can have energies up to the target voltage. Few studies have been performed ondetennining the magnitude of the reflected neutrals but it appears to be an approximately anorder of magnitude lower than that of the ions.’36 The energy of the bombarding particles inother deposition methods such as chemical vapour deposition2’ (> 100 eV) and laserablation’37 (>50 eV) indicate that relatively high energies are required for the formation ofdiamond-like films.Diamond-like Thin Films / 874.3 Infrared Studies ofAmorphous Carbon Films4.3.1 IntroductionTo understand the nature of the amorphous carbon films further a study wasundertaken where the infrared properties were measured as a function of depositionpressure.138 The effects of substrate bias on the infrared properties was not investigated as itwas felt that this procedure resulted in an increase in the film density only.The goal of this study was two—fold. The first was to measure the absorptioncoefficient in the infrared in order to detennine if the films were suitable for opticalapplications. The second goal was to perform a chemical analysis of the films through theexamination of the nature of the molecular bond vibrations.4.3.2 ExperimentalThe films to be investigated through infrared spectroscopy were deposited onto doublepolished semi-insulating GaAs substrates, which were transparent in the range of 700 to10,000 cm1 . The measured infrared reflection and transmission spectra for a GaAs substrateis presented in Fig. 4.12. Also shown in this figure is the residue (1—R—T). As the idealabsorption is zero, the residue, with a range from —l % to 0%, gives an indication of theaccuracy of the method.The reflection measurements were made in reference to an aluminum mirror adjacentto the sample of interest. As the aluminum mirror would cloud easily when the samples wereDiamond-like Thin Films / 880.70.60.50.40.30.20.1Figure 4.12 Mid-infrared reflection (R) and transmission (7) spectra for a semi-insulatingGaAs substrate. Also shown is the residue: l-R -T.changed between measurements, this presented another potential source of error. As theadherence of the aluminum film to the glass substrate was poor, cleaning the minor proveddifficult and often resulted in a small degree of scratching. The solution to the above problemwas to include a third surface in the measurements, that of a GaAs substrate. As the surfaceof the GaAs substrate was highly polished and easily cleaned, it provided a reliable check forthe reflection measurements.The samples were measured over the range of 800 to 9000 cm’ . In this thesis, therange from 800 to 4000 cm’ is denoted as the mid-infrared and from 4000 to 9000 cm’ the0.8 0.030.020.010.00—0.0140000.0800 1600 2400 3200Wavenumber (crrrl)Diamond-like Thin Films / 890.75 I I IGaAs— — —— DispersionlessDispersionk=.0251::0.00 I4000 5000 6000 7000 8000 9000Wavenumber (cnn)Figure 4.13 Theoretical reflection spectra of a 1.25 pm thick film with a refractive index of 2on GaAs along with the reflection spectra of the substrate. Also shown is the reflectionspectra of a film with dispersion and one that in addition has a value of k = .025. The value ofAv represents the distance between the reflectance maxima.near-infrared. For carbon films, absorption peaks due to molecular resonance vibrations lieprimarily in the mid infrared. Though the near-infrared does not provide information aboutthe chemical bonding structure, it can be used to deduce the film thickness. The techniqueused to determine the thickness of the film is described below.For a transparent film on a substrate, the envelope method139 is often used to deducethe value of n and the film thickness, d. Fig. 4.13 shows the theoretical reflection spectra of a1.25 im thick film with a refractive index of 2 on GaAs along with the reflection spectra of theDiamond-like Thin Films / 90substrate. Also included is the theoretical reflection spectra for a film with a linear dispersionofn =2+ (V — 4000)/9000 cm (4.6)and a film with the above dispersion which also has a value of k equal to 0.025. For thetransparent dispersionless film, the solution of n and d is quite straightforward. The value ofthe optical thickness, nd, can be determined through the relationnd=—, (4.7)where Av is the difference in wavenumber between the reflectance maxima. The value of n canthen be determined by examining the difference in intensity, Al, between the minimum andmaximum values through the relation:f \2 “ 2In_—l in —nAl = I s —S, (4.8)n3+1) Lj3Jwhere flf and n are refractive indices of the film and the substrate respectively.The above method becomes more complicated when dispersion is included in therefractive index. However, if a suitable model for the refractive index is chosen, the envelopemethod can be used to determine an appropriate set of starting values for the fitting routines.Fig. 4.13 shows that the additional presence of absorption in the films does not, in thiscase, visibly affect the distance between the interference maximum but has the general effect oflowering the overall reflectance of the film/substrate system. The inclusion of absorption canDiamond-like Thin Films / 91also affect the value of A!, ultimately reducing it to zero. However, as long as a significantamount of interference remains in the films, it should still be possible to deduce the opticalconstants and the film thickness from the choice of an appropriate model.Ideally, then, the films should be thick enough to ensure interference fringes in the nearinfrared, but not so thick as to be completely opaque. Another limiting factor for thethickness is the problem of multiple solutions to the optical constants in the mid-infrared. Ingeneral, the thicker the film, the greater the number of possible solutions.’°2 At the otherextreme, the limits to the instrumentation accuracy require total absorption levels of at leastseveral percent in order to guarantee an accurate determination of the absorption coefficient.The optimum thickness range was determined to be approximately 0.8 im for the mostabsorbing films and 1.4 tm for the most transparent ones.A set of films were deposited as a function of pressure for the purpose of infraredmeasurements. The films were deposited at argon pressures of 1, 2, 4 and 8 Pa in order toallow for a comparison with the experimental results in the previous section.4.3.3 ResultsThe reflection (R) and transmission (7) measurements for the film deposited at 1 Pa isshown in Fig. 4.14. Also included is the calculated value of the absorbance (1-R-T). Thepeaks due to molecular vibrations can be seen in the region between 900 and 1700 cm1.Interference effects in the absorption spectrum are also present. The elimination of this artifactDiamond-like Thin Films / 920.75Reflection0 60 — — — — Transmission- Absorption- 0.45 - —-0.150.00800 1200 1600 2000 2400 2800 3200 3600 4000Wavenumber (cm-i)Figure 4.14 The mid-infrared reflection and transmission spectra for a film deposited at 1 Pain argon. Also included is the calculated value of the absorbance (1-R-T).in the solution of the absorption coefficient provides a check on the accuracy of the thicknessdetermination.The Forouhi—Bloomer model was chosen to determine the optical constants and filmthickness in the near-infrared. The reflection measurements and the modeled fits are shownfor the films deposited at 1 and 8 Pa in Fig. 4.15. The modeling results appear to accountfor the dispersion in both n and k for the two films.The values of k for the films in the near- infrared are given in Fig. 4.16. The values ofn are essentially those in the infrared region of Fig. 4.5. The results show a general reduction0C?C)C)Figure 4.15 The near-infrared reflection measurements and the modeledthe films deposited at 1 and 8 Pa.010010-110-2 —fits are shown for4000 5000 6000 7000 8000 9000Wavenumber (cm’)Figure 4.16 Log of k vs. wavenumber for films deposited at 1,2,4 and 8 Pa in the nearinfrared. The values of k were determined through fitting the reflection spectra to the FarouhiDiamond-like Films I 930.50.40.30.20.14000 5000 6000 7000 8000Wavenumber (cm)9000I —1 Pa2Pa4PaOPaBloomer model.Diamond-like Thin Films I 94of absorption with increasing pressure. A notable exception to this trend is observedfor the 2 Pa film where the absorption is greater than the 1 Pa film at the higherwavenumbers. This anomaly is also observed for the optical constants in Fig. 4.5 at the lowerend of the energy spectrum.Once the thickness of each of the films was determined, the optical constants could besolved for in the mid-infrared. This procedure proved to be somewhat difficult due to thepresence of multiple solutions. The most effective way found to solve for the optical constantsof the films is outlined below.In order to employ the Newton-Rhaphson method, an initial guess of the solution setmust be supplied. In the procedure used in this thesis, the initial value of k at eachwavenumber, v, is determined through the relationk—ln(l—A)(49)4it v dwhere A is the measured absorption and d is the thickness of the film. Equation 4.9 is derivedby ignoring interference effects in the film and the reflection off the back of the substrate. Aset of solutions is then found at each wavenumber using the above value of k and a range of nvalues centered about that derived in the near infrared. The correct solutions at eachwavenumber can then be determined by looking for a continuum across the entire spectrum.In general, the errors in n were quite large, so a continuum was sought in the values ofk only. However, there were still regions where a solution could not be found. In order toDiamond-like Thin Films I 95remedy the above situation, a new set of initial values was determined by interpolatingbetween the accepted values of k and the above procedure was repeated. After one or twoiterations a solution for the entire range could be found.Once the absorption coefficient as a function of wavenumber was determined, atheoretical fit to the data was performed using Eq. 3.53. The experimentally determinedabsorption coefficient and the corresponding theoretical fit as a function of wavenumber forthe films deposited at 1, 2, 4 and 8 Pa are shown in Figs. 4.17 through 4.20. The modelingparameters are given in Table 4.5.An important factor is the overall accuracy of the absorption coefficient. Using Eq.4.9 we can estimate the error as(4.10)(l-A).dwhere \A is the uncertainty in the absorption. Equation 4.10 tends to overestimate the errorin c as it ignores the effect of multiple reflections in the film which enhances the overallabsorption (except at the quarterwave thickness) for a given absorption coefficient. Thelowest measured amount of absorption in the films is approximately 5 %. Given a maximumvalue of 1% for z\A (Fig 4.13) this results in an absolute error of 70 cm1. It is important tonote that this is a systematic error rather than a random one and hence will tend to offset agood part of the spectrum. As a result the error in the terms in Table 4.4 wifi partially beabsorbed by the Urbach tail. However this value does place a limit on how accurately one canmeasure the optical window where no molecular absorptions are present.C)00.1->0rj0Diamond-like Thin Films / 961600 2400 3200Wavenumber (cm4)900060004-40U0—430000U).0800 4000Figure 4.17 Experimentally determined and theoretically calculated absorption coefficient ofthe film deposited at 1 Pa in argon. The theoretical fit was determined through equations 3.51and 3.52600050004000300020001000800 1200 1600 2000 4000Figure 4.18 Experimentally determined and theoretically calculated absorption coefficient ofthe film deposited at 2 Pa in argon. The theoretical fit was determined through equations 3.512400 2800 3200 3600Wavenuinber (cm1)and 3.52.I2000160012008004008001600SC)C)C.)00U)Wavenumber (cnr1)Diamond-like Thin Films / 9740001600 2400 3200Figure 4.19 Experimentally determined and theoretically calculated absorption coefficient ofthe film deposited at 4 Pa in argon. The theoretical fit was determined through equations 3.51and 3.52.200012008004000800 1600 2400 3200Wavenumber (cnr’)Figure 4.20 Experimentally determined and theoretically calculated absorption coefficient ofthe film deposited at 8 Pa in argon. The theoretical fit was determined through equations 3.514000and 3.52.Table4-4:FittingParametersandPossibleBondingConfigurationsforFilmsDepositedinArgonasaFunctionofPressurePossibleiPa2Pa4Pa8PaBondingV0JFV0JFV0JFV0JF(1)35302.1942.635141.3838.034711.5039.234592.1646.534093.6067.8(2)33005.90112.133243.7287.2(3)31411.7265.6312911.6156.1(4)29750.266.429513.2733.329315.4560.529108.2359.428604.8256.428580.2915.2(5)20990.4012.521060.134.7921100.0050.6(6)17073.9521.4170720.043.1170817.838.9(7)15853.9125.7158533.361.4159726.664.9160422.166.915238.6638.0(8)143722.968.9144840.376.0144714.361.914394.8537.9(9)138210.942.4137216.449.913787.5639.1(10)129076.6127.4128081.491.7129028.263.5130617.660.31112133.5133.4119542.386.2120632.277.7106741.7202.4105775.8102.8105953.3108.281075.5107.282353.8103.979347.8122.0LDiamond-like Thin Films / 99For the samples deposited at higher pressures, the mid-infrared can be divided intothree regions. The first is the C—C network and CH deformation region at wavenumbersbelow 1700 cm1. Aside from the CtC stretch at around 1600 cm1 it is difficult to identifyany particular resonance. Hence the assignment of the bonding configurations given in Table4.4 in this region are not the only possible ones. Adjacent to this region is a strong C=0resonance at around 1700 cm’.The second region is a low absorption window between 1900 and 2700 cm1. Thisregion is of interest for optical applications. The small peak at around 2100 cm’ is attributedto nitrogen impurities. The third region is the result of CH and 0—H stretch modes. There isalso evidence of a weak Urbach tail.The films deposited at lower pressures show evidence of a much stronger Urbach tail.This factor correlates well with the high absorption values in the visible regions. For the filmdeposited at 1 Pa there is no evidence of any CH, CO or OH bonds.4.3.4 DiscussionThe JR results show that with increasing pressure there is a general trend towards alower overall absorption in the films. The spectroscopic results also show that there isunintentional hydrogen and oxygen incorporation in the films.The most probable source of the impurities is the finite base pressure, which in turn, isprimarily due to outgassing from the surfaces in the chamber. After several hours of diffusionDiamond-like Thin Films /100pumping, the outgassing consists predominately of water vapour (assuming good care is takento keep the chamber clean which was the case during the course of this thesis). This factorwould explain the presence of both oxygen and hydrogen in the films.The incorporation of impurities at higher pressures is attributed to a change in theenergetics at the substrate surface. It is not attributed to a change in the base pressure as carewas taken to ensure that this was constant over the entire pressure range. At lower pressuresthe impurity atoms may be sputtered off due to the energetic impacts from the reflectedneutrals. The carbon atoms remain due to the higher C-C bond strength (607 KJ/mol) thanthat of the C—H (338 KJ/mol) or the C=0 bond (532 KJ/mol in 0=C0).’4° The impurities dueto nitrogen are still present due to the CN bond having a strength (754 KJ/mol) which isgreater than the C—C bond.A number of attempts were made to lower the impurity level of the depositionchamber, through baking and longer pumping times (several days). However, it was foundthat the system was operating at the optimum conditions.Table 4.4 divides the possible bonding configurations into 10 separate types. In theregion between 2700 cm and 3350 cm there are the resonance vibrations due to CH stretchmodes. Configuration 2 is contributed to hydrogen bonded to sp’ (acetlynic) carbon.’41which is present in the films deposited at 4 and 8 Pa. Lower in wavenwnber are a number ofresonance vibrations due to hydrogen bonded to sp2 carbon (configuration 3 )142 In addition,there are a number of vibrations at wavenumbers usually assigned to either CH2 and CH3stretch modes in organic molecules or hydrogen bonded to sp3 carbon.’43Diamond-like Thin Films /101There are also two indications of oxygen in the films. The first is due to H—Oresonance vibrations in the region from 3400 to 3550 cm1 , which are present in the filmsdeposited at 4 and 8 Pa. Values in this region are more typical of those found for bonding inorganic molecules than that for H20 (3675 cm1 symmetric and 3756 cm’ antisymmetric).There is also a strong peak in the higher pressure fthns at around 1700 cm’ due to C=Obonding and a relatively low one for the film deposited at 2 Pa.Of particular interest is the C=C bond around 1600 cm’. This has two possiblesources. The first is from the presence of organic molecules in the film matrix. The secondpossible source is the single phonon vibration in graphite.34The last three assignments, configurations 8,9 and 10 are somewhat arbitrary as there isa high degree of overlapping between the various resonances. Hence it is difficult to performany type of analysis with the results in these regions.The infrared results for the films deposited at high pressures have a number ofsimilarities with those in the literature deposited under different deposition conditions butwhich also exhibit low absorption in the visible.1’34 In all of these cases there is the presence ofhydrogen in the films. The effects of hydrogen incorporation in diamond-like films is explainedbelow.In amorphic 4-fold coordinated solids such as silicon and germanium, the incorporationof hydrogen is thought to passify dangling bonds.’ As a result, hydrogenated forms of thesematerials are generally less optically absorbing. Amorphous carbon films are inherently morecomplicated than silicon and germanium due to the additional ability of the material to formDiamond-like Thin Films /102sp2 type bonds. In this case an additional role for hydrogen is to allow for different sp3 Isp2bonding ratios.A theoretical study was performed by J. Angus and F. Jansen’45 where the amount ofhydrogen incorporation in carbon was predicted using a random covalent network. In this casethe role of the hydrogen was to ensure that the network was properly constrained, that its thenumber of constraints per atom equaled the number of degrees of freedom: 3.The results of the model gave an upper limit and lower limit for hydrogen incorporationof 60% and 20 % respectively. Above 60 % the carbon matrix would be underconstrainedresulting in a soft polymer-like material. Below 20 % hydrogen incorporation, the materialwould be overstrained and reconstruct, possibly into graphitic clusters. Therefore withdecreasing percentage of hydrogen the graphitic island model of Robertson would appear tobe more appropriate.The theoretical results matched those in the literature quite well for films with a higherhydrogen content.’46 However, for the lower hydrogen films, the films were less graphiticthan predicted. It was felt that this was the result of the presence of medium range order in thematerials which would also reduce the stress in the films.The incorporation of hydrogen at low levels is also thought to reduce the number ofdangling bonds in sp3 carbon and reduce the bonding between the graphitic clusters.147 This,in turn, would also reduce the mobility of the it electrons. The resulting material would bemore transparent, have an increase in the resistivity and be softer. It would also allow for aDiamond-like Thin Films /103smaller island size, by allowing for the creation of more sp3 bonds, increasing the opticalbandgap.One possibility for the increase in transparency for the films deposited at higherpressures, then, is the incorporation of hydrogen. This factor is also a possible explanation forthe observed decrease in hardness and the increase in the resistivity. However from Table 4.4and from Figs. 4.18 to 4.20 there does not appear to be a large degree of difference in thedegree of hydrogen concentration if the integrated area under the absorption curves for the C-H stretch vibrations between the films deposited at 2, 4 and 8 Pa are considered. Hence it isdifficult to say if the change in the transparency is the result of hydrogen incorporation alone.A set of experiments which were complementary to the ones in this thesis wasperformed by J. Uliman et.al. •148 In this study, carbon films were deposited through r.fsputtering in a pure argon atmosphere at approximately 1.3 Pa. The target voltage wasvaried over the range from —1500 to —2900 V.Ullman’s results showed that the IR transparency of the films increased with decreasingtarget voltage. However the hydrogen concentration in the films was relatively constant ataround 8 %. This level is much lower than those typically found in the literature whenhydrogen is intentionally incorporated (20 to 60 %).Uliman argued that the reason for the increase in transparency was the reduction inenergy of the target reflected neutrals and of the secondary electrons. It was felt that the lowerof the energetics at the substrate resulted in a reduction in the graphitic island size (assumingRobertson’s model) . A lower energy environment would lead to a faster quenching timeDiamond-like Thin Films /104which could possibly result in a smaller over grain size. An increase in the optical bandgap hasalso been observed in the literature when the substrate temperature was lowered duringdeposition to 77 K.’49The films deposited as a function of pressure in this study are consistent with the aboveresults. The decrease in hardness could also be explained through the lowering of thebombardment energies. As the formation of sp3 bonds is thought to be the result of ionbombardment, a reduction in this factor could decrease the amount of linking between thegraphitic islands.In addition to hydrogen there is also the incorporation of oxygen in the films. Theoxygen is bonded both to hydrogen and to carbon. This factor is relatively low for the filmsdeposited at 2 Pa but increases for the films deposited at a higher pressure. This factorsuggests the presence of organic molecules bonded onto the carbon matrix or some form ofpolymer phase in the film which grows with increasing pressure. The latter result would beconsistent with those for films deposited from chemical vapour deposition (CVD) under lowenergy conditions.’5°In the CVD process the energetic bombardment is controlled entirely by the biasing ofthe substrate through the bombardment of ionized particles. Below approximately —100V apolymer is deposited. Above —100 V a diamond-like film is deposited with a decreasinghydrogen content with increasing bias. At approximately —600 V the bombardment energy isenough to drive off all of the hydrogen and an opaque film is deposited as a result.Diamond-like Thin Films /105The results in this study are consistent with those of the CVD process if we considerthe primary source of energetics to be the reflected neutrals. At low pressures there is noevidence of hydrogen in the films. The presence of the C=C resonance vibration is most likelydue to the single phonon process of graphite. As the pressure increases this vibration increasesrelative to the other vibrations in the region. As it is unlikely the amount of sp2 bonding isincreasing to a large degree, this factor is most likely due to the growth of an organic phase inthe material. At 8 Pa the film is not completely polymerized, however, as there are stifiresonances associated with sp3 carbon. This is probably due to the relatively small amount ofhydrogen present compared to the CVD method.Polymer materials deposited in CVD processes are highly transparent and have arefractive index between 1.5 and 1.8. One possibility considered was that the 8 Pa film was acombination of the material deposited at 1 Pa and a polymer. This can be discounted throughthe re-examination of the Wiener-bounds. In this case the dielectric function for the 8 Pa filmdoes not lie in the boundaries required for an isotropic material. This factor is enhanced if weconsider the additional effects of voids in the higher pressure films. Hence, if a polymericphase is present, there must also be a change in the bonding configuration of the diamond-likephase.Therefore, at this point, there appear to be three possibilities for the change in theproperties of the diamond-like films as a function of pressure. The first is the incorporationof hydrogen which pacifies the dangling bonds. The second is the growth of a separate soft,Diamond-like Thin Films /106transparent polymer phase. The third is a reduction in the graphitic island size. It is possiblethat all three processes are happening concurrently.4.4 Amorphous Carbon Films with Oxygen, Nitrogen and Hydrogen.4.4.1 IntroductionA series of studies similar to those performed in the last section were undertaken for anumber of films deposited in an argon/reactant gas mix. The purpose of this investigation wastwo-fold. The first reason was to allow for a better understanding of how the impuritiesobserved in the infrared spectra in the previous section affected the properties of the films. Inthis case, the “impurities” were to be added intentionally and primarily at pressures lowenough to prevent the inclusion of additional background gases. The second reason was tocompare the resultant properties with those films deposited inpure argon. This would allowfor a determination of the optimum deposition conditions for infrared optical applications.The initial tests were again centered around ellipsometry, due to the relative ease of thistechnique at this point in the thesis. However, the complementary techniques used to analyzethe films were more selective in this section. Once these were undertaken, infrared analysiswas performed when deemed necessary.The first section looks at the effects of intentionally introducing oxygen into thesputtering gas. This section is fairly brief and is intended to complement the next section.0.-40Diamond-like Thin Films /1070.1 0.2 0.3 0.4 0.502 Partial Pressure (Z)543210.0Figure 4.21 Deposition rate vs. 02 partial pressure for amorphous carbon films deposited in a02 / Ar mix. The total deposition pressure was 1 Pa.which examines the effects of hydrogen. The fmal section investigates the properties of filmsdeposited in argon/nitrogen sputter gas mix.4.4.2 Amorphous Carbon Films with OxygenAn ellipsometric study of set of films deposited in a argon/oxygen mix was performed.The total deposition pressure was 1 Pa. The 02 partial pressure was varied from 0.0 to 0.5Pa.Diamond-like Thin Films /108There was a small increase in the transparency of the films with an increasing 02 partialpressure; with approximately a 10% overall increase in the pseudo-bandgap. A more dramaticeffect was observed for the deposition rate (Fig 4.21) which experienced an order ofmagnitude reduction at the highest partial pressure.There are two possible explanations for the decrease in the deposition rate. The firstpossibility is that the oxygen is reacting with the loosely bound surface atoms at the substrateto form carbon monoxide or carbon dioxide. It has been shown that the presence of 02 andoxygen atoms can etch away diamond-like films deposited through r.f. plasmadecomposition.’5’A preferential etching could also be the reason for the small increase in thetransparency of the film. The second reason is that the oxygen is reacting with the targetsurface. It is unlikely that this phenomena has any effect on the films deposited in intentionallypure argon due to the relatively low levels of the oxygen.Infrared measurements of a film deposited in an 0.1 Pa 02 / 0.9 Pa Ar mix were taken.The results were similar to those for the film deposited in a pure argon atmosphere at the sametotal pressure (Fig 4.18) , with no evidence of CO or OH bonds.It would appear, then, that oxygen is only incorporated when there is the additionalpresence of hydrogen. This observation lends weight to the argument in section 4.3.4 thatthere are organic molecules bonded onto the carbon matrix or a polymer phase in the filmsdeposited at high pressures in intentionally pure argon.Diamond-like Thin Films /1094.4.3 Amorphous carbon with hydrogen (a-C:H)a) Experimental and ResultsTwo sets of ellipsometric measurements were performed in this section. In bothcases, the optical constants of the materials were determined as a function of H2 partialpressure. The first set of films were deposited at a total pressure of 1 Pa and the second set ata total pressure of 8 Pa. The Farouhi-Bloomer model was used to determine the opticalproperties of the films.Electron diffraction results showed that the hydrogenated carbon films wereamorphous. The resistivity of the films deposited at the highest hydrogen concentration ineach case was greater than the maximum limit of the 4-point probe (10 - cm1). The filmdeposited at a total pressure of 8 Pa, and a hydrogen partial pressure of .03 Pa appeared tobe relatively soft compared to the other films. Infrared analysis of a film deposited in a 0.9 PaAr and 0.1 Pa H2 mix was performed. The experimentally determined and theoreticallycalculated mid-infrared absorption coefficient as a function of wavenumber is given in Fig.4.23. The model parameters are given in Table 4.5 along with those for the films deposited inpure argon at 1 and 8 Pa. The near infrared k values of this set of three films are given inFig 4.24.Diamond-like Thin Films /1103.0 I I I IOPafl .OlPa1.0iPa Ar/H2•.0E(eV)Figure 4.22 Real (n) and imaginary (k) refractive indices vs. photon energy for carbon filmsdeposited in an Ar/H2 mix for a number of different partial pressures of hydrogen. The totaldeposition pressure was 1 Pa.1000800600400200800Diamond-like Thin Films /1114000Figure 4.23 Absorption coefficient of the film deposited in 0.1 Pa H2 and 0.9 Pa Ar. Thetheoretical fit was determined through equations 3.52 and 3.53.4000 5000 6000 7000 8000 9000Wavenumber (cmi)Figure 4.24 Log of k vs. wavenumber for films deposited at 1 and 8 Pa in pure argon and fora film deposited in 0.1 Pa H2 and 0.9 Pa in argon. The values of k were determined throughfitting the reflection spectra to the Farouhi-Bloomer model.1600 2400 3200Wavenumber (cnr1)10010-110—2I 0—lPaAr8PaAriPa Ar/H?)I-Diamond-like Thin Films /112Table 4.5 Fitting Parameters and Possible Bonding Configurations for Films Deposited inArgon and in an Argon / Hydrogen Mix.Possible 1 Pa (Ar)BondingV0 J I- V0(1) 35143459(2) 3324(3)(4) 29312858(5) 2099 0.40 12.5 2110(6) 1708(7) 1585 3.91 25.7 16041523 8.66 38.0(8) 1437 22.9 68.9 1439(8) 1378(9) 1290 76.6 127.4 1306(10) 12061067 41.7 202.4 10597931 Pa (Ar/H2)V0 J8 Pa (Ar)J 1’1.38 38.02.16 46.53.72 87.23012 1.69 39.25.45 60.5 2911 9.65 56.40.29 15.20.005 0.6 2095 0.16 6.817.8 38.9 1680 1.84 32.622.1 66.9 1599 6.22 41.91541 1.69 27.44.85 37.9 1439 5.61 28.97.56 39.117.6 60.3 1303 21.5 89.932.2 77.7 1175 24.1 118.753.3 108.2 985 1.42 21.247.8 122.0 847 49.5 78.01): H-O (sretch) (2): hydrogen bonded to sp1 hybridized carbon (stretch) (3):hydrogenbonded to sp2 hyberdized carbon (stretch) (4): hydrogen bonded to sp3 hyberdized carbon(stretch) (5) CEN (6): C=O stretch (7): C=Cstretch (8): C-H rock or CH2 deformation (9):CH2 symmetric bending (10): sp2 - and sp3 - hybridized carbon.The optical constants for the films deposited at 1 Pa total pressure are presented in Fig4.23. The pseudo-bandgap increased from 0.3 to 1.4 eV over the range of H2 partialpressures. The maximum bandgap was achieved at a hydrogen partial pressure of 0.1 Pa.For the set of films deposited at 8 Pa the maximum bandgap was achieved at ahydrogen partial pressure of .03 Pa, increasing from 1.2 to 1.5 eV. A higher hydrogen partialpressure did not result in a change in the optical properties of the films.Diamond-like Thin Films /113b) DiscussionThe infrared results for the film deposited in an argon/hydrogen mix differ in naturefrom those for the films deposited in the last section which also show the presence ofhydrogen. A comparison of the C—H stretch bands for these films is given in Fig 4.25 wherethe spectrum for each film has been displaced by a constant amount for comparison purposes.An important criteria is the integrated area under the absorption spectra,152 ot:a0=CJa(v)dv (4.11)where a is the absorption due to the C—H bonds and C0 a proportionality constant. The valueof a0 gives the amount of bonded hydrogen in the films.The value of a0 for the individual films has not been calculated for two reasons. Thefirst is that the constant of proportionality is difficult to determine and there is somecontroversy over its exact value, due to various types of carbon bonding.153 The secondreason is that the additional presence of a strong Urbach tail for a number of the films makesthe evaluation of the integral quite difficult. However, a visual inspection of the spectra showsthat there is a larger amount of hydrogen present in the film deposited in a Ar / H2atmosphere than the other films, all which appear to have roughly the same amount of C—Hbonds in the sp3 region.Diamond-like Thin Films /114‘.4-C0—40($2•02400 2700 3000 3300 3600Wavenumber (cm-i)Figure 4.25 C—H stretch vibrations for films deposited in pure argon at a) 2 Pa, b) 4 Pa c)Pa and d) 0.1 Pa H2 and 0.9 Pa argon. The spectra has been shifted for comparisonpurposes.One other feature of interest in this region is the nature of the stretch vibrations.Unlike the films deposited at 4 and 8 Pa in argon, there are no resonaces due to sp’ bonding inthe films deposited in an H2 /Ar atmosphere (Tables 4.4 and 4.5). In addition, the low ratio ofhydrogen bonded to sp2 and sp3 carbon respectively appears closer to that of the 2 Pa filmrather than the films deposited at higher pressures.From Tables 4.4 and 4.5 it can be seen that the degree of oxygen incorporation iS muchless for the film deposited in a hydrogen/argon mix than that of the high pressure films. InacdDiamond-like Thin Films /115addition the peak due to the C=C bond is also smaller and comparable to the film deposited atI Pa in pure argon.The above results indicate that either a polymer phase is not present in the filmdeposited in an H2 I Ar atmosphere or that it is much less than that in the higher pressurefilms. In addition, most the hydrogen appears to be bonded to sp3 carbon. Therefore, underthese conditions, the hydrogen appears to be the reason for the more diamond-like propertiesof the films.The ellipsometric results indicate that the incorporation of hydrogen is more easilyachieved at higher pressures. This observation lends weight to the argument that the presenceof hydrogen is due to a change in energetics at the substrate rather than an increase in the basepressure. In addition, the softness of the film deposited with intentional hydrogenincorporation at high pressures indicates that a polymer phase does grow under low energyconditions.A similar study was performed in the literature for magnetron sputtered films wherehydrogen was intentionally introduced at low overall pressures (though without the midinfrared results).6 It was found that there were no measurable changes in the properties of thefilms when the H2 partial pressure was greater than 5 %. In addition there was a reductionby a factor of three in the hardness between the a-C and a-C:H films. As the hardness ofthe films in this thesis decreased by a factor of about 7 when the pressure was varied between 1and 8 Pa, this would also indicate that there is a softer phase in the high pressure films.Diamond-like Thin Films /116One possible explanation for the trend observed for the films deposited as a function ofpressure is as follows. At low pressures, hydrogen is not easily incorporated into the film dueto the highly energetic reflected neutrals. However, a limited amount of sp3 bonding occursdue to high pressure/temperature spikes. As the pressure increases the hydrogen present in thechamber can now be incorporated into the film. As the majority of the hydrogen initiallyappears to be bonded to sp3 carbon, this is similar to the case where hydrogen is purposelyintroduced at lower pressures. However the lower amount of hydrogen present prevents thesame degree of change in the optical properties of the film.As the pressure increases further, it becomes increasingly easy to incorporate hydrogen,which can further stabilize sp3 bonding. However the lower energetics at the substrate resultin a decrease in the probability of the creation of diamond bonds. As a result, an organic orpolymer phase also occurs due to the presence of hydrogen and oxygen.4.4.4 Carbon Nitride Filmsa) IntroductionRecently there has been good deal of interest in the ability to deposit carbon nitridefilms. This interest is primarily due to a theoretical study by A.Y.Liu and M.LCohen154which predicted that the hardness and thennal conductivity of the phase 3-CN4 was on theorder of that of diamond. At the time of the writing of this thesis the above material had notDiamond-like Thin Films /117been synthesized though a number of attempts to deposit thin films of f-C3N4had been made.A number of the studies in the literature relevant to this thesis are outlined below.A comprehensive investigation was performed by C.J. Torn et. al. In this study,the properties of the films deposited through r.f. sputtering were examined as a function of N2partial pressure. The optical band-gap was observed to increase from 1.1 to 1.4 eV for amaximum nitrogen incorporation of 10%. An internal reduction in stress was also reportedfor the films.An increased incorporation of nitrogen of up to 40 % was reported for films depositedthrough dc sputtering’56 and through ion assisted deposition.157 In addition, the hardness ofthe films was shown to be comparable to the a-C:H films in the literature.’56One additional study showed that the nitrogen in the a-C:N films was chemicallybonded to the carbon atoms through both infrared and Raman spectroscopy.8However, theoptical constants in the infrared were not determined.A study was undertaken in this thesis to examine the optical properties of a-C:N filmsin more detail. The properties of the films were investigated as a function of N2 partialpressure and total deposition pressure.b) ExperimentalA set of ellipsometric studies was performed both as a function of N2 partial pressureand total pressure. The preparation techniques were the same as outlined in section 4.2.2. Theoptical constants were determined through the Forouhi-Bloomer model.Diamond-like Thin Films /118The films deposited at high N2 partial pressures exhibited poor adhesion on both sfficonand gallium arsenide substrates. By introducing a carbon intermediate layer between thesubstrate and the film, the overall adhesion could be improved. However, films on the orderof a micron could still not be grown on the GaAs substrates, which prevented JRmeasurements from being performed for this material.c) Results and DiscussionThe optical constants for a number of films deposited in Ar and N2 are presented inFig. 4.26. Shown are the values as a function of photon energy for a film deposited at 1 Pa inpure argon and for films deposited in pure nitrogen at 1, 2 and 4 Pa.For the films deposited as a function of N2 partial pressure at low overall pressuresthere was a noticeable change in the optical properties as illustrated in Fig. 4.26. However itwas found that at 50 % partial pressure the pseudo-bandgap had increased to 90 % of its fmalvalue. The relative change in the optical properties as a function of nitrogen partial pressuredecreased with increasing overall pressure until at 8 Pa no difference could be observed.One noticeable effect was a dramatic increase in the deposition rate as a function ofnitrogen partial pressure. This factor is illustrated in Fig. 4.27 for a set of films deposited at 1Pa overall pressure where an eight-fold increase in the deposition rate is observed. This factoris an important technological advantage as the deposition rate of sputtered carbon is relativelylow when compared to the more predominate CVD process.a)a)C)a)CI-,Ca)Diamond-like Thin Films /119Figure 4.27 Deposition rates vs. N2 partial pressure for films deposited in a nitrogen / argonmix. The deposition power was 100 W and the total pressure was 1 Pa.3.0iPa Ar)25 1PaN2:zzjr0.52— —I • I I I I I I1.5 2.0 2.5 .0 3.5 4.0 4.5 5.0 5.5 6.0Energy (eV)Figure 4.26 Refractive index measurements for films deposited in argon and N2 . Therefractive indices were determined through the Forouhi-Bloomer model.2.52.01.51.00.50.00 0.25 0.50 0.75Nitrogen Partial Pressure (Z)1.00Diamond-like Thin Films /120As the maximum degree of nitrogen incorporation observed in the literature isapproximately 40 %, the above increase can not be explained in terms of nitrogenincorporation alone. The increase in the deposition rate is also attributed to chemicalsputtering of the target.158 In this method, the bombarding ions react with the target atoms,increasing the overall sputter rate.From the above ellipsometric results it would appear that the incorporation of nitrogendoes not result in same degree of change in the optical properties as that of hydrogen at lowerpressures. In addition, from the results at higher pressures, it would appear that nitrogen doesnot enhance the optical properties once hydrogen is also present. This is in good agreementwith a study in the literature which showed that the presence of nitrogen caused a smalldecrease in the optical bandgap for diamond-like films deposited through chemical vapourdeposition.’59The main advantage of a-C:N films, then, appears to be the relatively high depositionrates. However, the additional presence of a large CN resonance at 2100 cm1 in the middleof the optical window could also be problematic.4.5 Technical Feasibility -One of the most important coatings is the single layer anti-reflection coating (Eq. 2.29).As discussed previously, diamond-like carbon films are well suited as anti-reflection coatingson germanium optics as the latter material has a refractive index of approximately 4.1 in theinfrared.’60Diamond-like Thin Films /121A theoretical study was undertaken to examine the feasibility of using the films studiedin this chapter for the above purpose. The model assumed a single layer coating on one side ofa germanium window. The thickness, d, at each wavelength, . was given byd=— (4.11)4nwhere n is the refractive index of the given material. The value of n for each material wasessentially a constant and equal to that in the near infrared red.The reflection, transmission and absorption at the quarter-wave thickness at eachwavelength was calculated for the films deposited at 1, 2 , 4 and 8 Pa in argon, and for thefilm deposited at 1 Pa in an argon/hydrogen mix. One problem for the last two films was thatthere was a discontinuity in the k-values at the boundary between the near and mid-infrared.This was attributed to the small error in the fit for the model in the near infrared. As thevalue of k is very sensitive to this factor when its overall value is small, this leads to largerelative errors. The near infrared values of k for these two films were then determined byinterpolating between the value measured at 4000 cm’ in mid infrared studies and the valuemeasured at 9000 cm’ in near infrared ones.As the films were antireflecting, the value of R at each wavelength was approximatelythat of the back surface of the germanium substrate, 37 %. The absorption values (1—R—T) aregiven in Fig. 4.28., except for the 2 Pa film which were very similar to the those for the filmdeposited at 1 Pa.5 6 7 8 9 10 11 12Wavelength (microns)Figure 4.28 Theoretical absorption as a function of wavelength for quarter-wave carbon filmson germanium. Note that the thickness is not constant as a function of wavelength but that ofEq. 4.11.Aside from the film deposited at 1 Pa, there is a relatively low absorption windowbetween 2 to 5 Pa, discounting the C-H absorptions around 3 .tm. The lowest values are forthe film deposited in a Ar! H2 atmosphere. Aside from the previously mentioned film, theabsorptions are approximately equal in the region between 8 to 12 I.Lm. Though the value ofthe absorption coefficient is higher in Fig. 4.17 than in Figs. 4.19 and 4.20, this factor ispartially offset by the larger refractive index which decreases the necessary physical thicknessrequired for quarter-wave conditions.Diamond-like Thin Films /122C—I0U2-C1 Pa4Pa8PaiPa0.40.30.20.10.0..rSI.3 41 2-FDiamond-like Thin Films /123if the main criterion is the maximum possible transmission, then the fi]m deposited in aAr! H2 atmosphere is clearly the ideal choice. As the reflection from a germanium surface isapproximately 37 %, the film will enhance the transmission over the entire wavelength range.This film is also well suited to be used as termination layer for a broadband anti-reflectioncoatings on infrared materials in the range from approximately 1 to 6 tm.Though the film deposited at 1 Pa appears unsuitable for optical applications, it shouldnot be dismissed. If a 20 % reduction in transmission is acceptable, then the hardness of thematerial may make it the ideal choice. Many current commercially available optical filtershave relatively low transmissions; typically on the order of 60% or less.161Chapter S J2..L1-GERMANIUM CARBIDE5.1 IntroductionOnce the diamond-like films were characterized the next step was to be able to depositthe intermediate materials for the optical multilayers. A suitable choice for the mid-infrared isgermanium carbide, which is sometimes used in protective optical multilayers which employdiamond-like films.14’62 Germanium carbide is an alloy which can range from pure carbon topure germanium. The desirable properties of this matetial are outlined below.The most important property of germanium carbide is its tunable refractive index,which varies almost linearly with the carbon fraction from 4.1 to 1.8.163 This factor allows fora good deal of flexibility in the design of optical coatings. Infrared studies have shown thatthere is Ge-C bonding over the entire alloy range,’TM indicating that this property is not merelythe result of a dielectric average of the individual carbon and germanium phases. The materialis also quite hard if a sufficient fraction of the material is carbon.’TMThere are two main methods for depositing germanium carbide, plasma assistedchemical vapour deposition (PACVD)’65 and reactive sputtering.’66 In the PACVD method,germane (GeH4) and a hydrocarbon gas, typically methane, are used as the source ofgermanium and carbon. The main disadvantage of this method is the very high toxicity of thegermane gas. In the reactive sputtering method, a germanium target is sputtered in anargon/hydrocarbon mix. A serious drawback to this method is that an increasing methanefraction will ultimately poison the target, leading to the deposition of either diamond-likeGermanium Carbide I 125carbon or a polymer. This factor limits the attainable refractive index range from 4.1 toapproximately 3.As the goal of this thesis is to develop the ability to deposit multilayers throughmagnetron sputtering alone, the restriction on the refractive indices is a potential problem.One possible solution is through co-sputtering of two targets of carbon and germaniumoriented at an angle.’67 One can then tune the refractive index through adjusting the powerratio to the targets. if absorption due to dangling bonds is a problem, then hydrogen gas canbe introduced into the chamber.Despite its simplicity, there are a number of drawbacks to the above configuration.The oblique angle of incidence of the deposition flux results in shadowing effects. In additionthe deposition rate is reduced under these conditions. Finally, this method makes the design oflarger systems quite complicated.An alternative method, which is examined in this thesis, is to deposit alternate layers ofgermanium and carbon. if the layers are thin enough, interdiffusion between the layers shouldresult in the formation of germanium carbide. This method would lend itself well to a systemwith either rotating substrates or targets. The same chamber could also be used to deposit thediamond-like films. This technique can also compensate for the relatively low sputter rate forcarbon compared to germanium by having a greater number of carbon targets. In addition, thedeposition rate could be enhanced by introducing methane into the sputter gas which woulddecrease the required thickness of the carbon layers.Germanium Carbide /126Interdiffusion between the individual layers has been studied extensively in x-raymultilayer systems.168”69 However, the focus of these studies has been to have as sharp aninterface as possible.Two factors have been found which affect the amount of diffusion between theindividual materials in multilayer systems. The first is the degree of energetic particlebombardment. In general, an increase in the deposition energetics results in an increase in theamount of diffusion. The second factor is surface roughness. An increase in surfaceroughness in one material results in a mixed layer as the second material is deposited. Theatoms in this mixed layer can then interdiffuse.A study was performed to examine the degree of interdiffusion as a function ofsubstrate bias and deposition pressure. An increase in substrate bias increases the energy ofthe bombarding ions, but reduces the amount of surface roughness. In turn, an increase inpressure results in a larger degree of surface roughness but reduces the energy of the reflectedneutrals. Therefore, in both cases, there are two competing factors which can effect theamount of diffusion.The germanium and carbon multilayers were analyzed through in-situ ellipsometry.The significance of these techniques with respect to the above systems is discussed in the nextsection.Germanium Carbide I 1270.025—0.025-—0.075A—0.125—0.175—0.225 — -—0.425 —0.375 —0.325 —0.275Rho (real)Figure 5.1 Theoretical trajectory for a germanium/carbon multilayer deposited onto silicon.The thickness of the individual layers is 2.0 nm. The inset shows the difference between a sharpand diffuse layer.-0.0 10-0.025-0.040 ——0.30 —0.27000g000000 SiC (Diffusion)80Si0 0 000 00 0oooooo0000 GermaniumCarbonGermanium Carbide! 1282016128402 6 10 14 18 22(real)Figure 5.2 Wiener bounds for the germanium and carbon phases in Fig. 1. The data pointscorrespond to a 5% change in the constituents. Also shown is the expected dielectric valuesassuming the Bruggman effective medium theory with a three dimensional isotropy. The insetshows the ellipsometric trajectory of Fig 5.1 along with that for a film with the same pseudo-dielectric function. The value of the pseudo-dielectric function, GeC, is also shown on the mainI IGeWeinerEmaGeCCfigure.Germanium Carbide /1295.2 Analytical MethodsFig. 5.1 shows the theoretical effipsometric trajectory as a function of thickness for aneighty layer stack with alternating layers of germanium and carbon at the HeNe wavelength.The complex refractive index is taken to be (4.8, 1.78) for the germanium layers and thatfor the carbon layers, (2.52, 0.56). Each layer is 2 nm thick and the data points are spaced0.2 nm apart. The angle of incidence is 67.8°. Hence the trajectory is simulating whatone would expect to see through in-situ ellipsometry.There is, initially, a good deal of contrast between the carbon and the germaniumlayers. As more layers are deposited, this contrast decreases and the trajectory appears toconverge, if the system is thick enough to be opaque at the wavelength of interest, theellipsometric trajectory will form a closed path between the endpoints of the germanium andthe carbon layers.One advantage to the above technique is that there is marked difference between asharp and diffuse interface in the ellipsometric trajectory in the p plane. This effect isillustrated in the inset of Fig. 5.1. Here the data points are spaced 0.1 nm apart. The initialcarbon layer on germanium is shown for the case of a perfect interface. In addition, thetrajectory for an intermediate layer, 0.5 nm thick, with a linear diffusion gradient between thecarbon and germanium layers is also shown. The model assumes that the carbon smoothes outthe surface roughness of the germanium layer. Hence, the overall thickness of the multilayerdoes not increase for the first 5 data points. Other forms of diffusion wifi have differenttrajectories in the complex plane and this factor is exploited in the later sections.Germanium Carbide! 130An infinite amount of layers wifi form a closed path in the ellipsometric planeapproximately around the value of p equal to (-.286,-. 158). This corresponds to value of pgiven by a semi-infinite substrate with a dielectric function of (13.5, 10.2) at the wavelengthof interest. Fig. 5.2 shows the Wiener bounds for the range of dielectric functions which canresult when the constituents of germanium and carbon have the optical constants given above.It is assumed that there is no chemical bonding between the individual materials, as this couldaffect the dielectric functions. The data points are spaced at intervals corresponding to a 5 %change in the amount of each constituent. Also shown is the resultant dielectric function for athree dimensional isotropy when the Bruggman effective medium approximation is assumed.The value corresponding to the pseudo-dielectric function of an infinite stack is given as thedata point GeC. The pseudo-dielectric function of a multilayer structure is defmed as that of asemi-infinite substrate which would give the same complex reflectance ratio at the angle ofincidence of interest.The pseudo-dielectric function of an infinite stack lies between the EMA and theWiener bound corresponding to minimum screening. This is to be expected due to the angleof incidence and the anisotropic nature of the material. At an angle of incidence ofapproximately 68° the larger of the electric field components is aligned parallel to the grains(in this case the individual layers). Hence the overall screening is reduced from that of arandom three dimensional structure.Ideally, one would expect the pseudo-dielectric function to be aligned aside the pointcorresponding to an equal fraction of germanium and carbon, given that the volume fractionsGermanium Carbide! 131of the constituents are equal. However, the theoretical data point is a few percentage pointsaway from this value, indicating a greater amount of germanium in the system than is present.This anomaly is due to the arbitrary choice of choosing a point in the middle of a layerdeposition. As a result the top bilayer, which has the largest effect on the measured value ofp. is germanium rich.The above analysis does not apply when the thickness of the layers become appreciableon the order of the wavelength of the light. In this case the infinite wavelength approximationused in the determination of the effective medium theories breaks down and interferenceeffects between the layers must be considered.If there is mixing between the constituents, without a change in the chemical bondingconfiguration, then the multilayer will become more isotropic and the pseudo-dielectric datapoint will move towards the value given by the Bruggman effective medium theory. Ifchemical bonding occurs and results in an overall change in the dielectric function, then thedata point may not lie within the expected dielectric bounds.The inset of Fig. 5.2 shows the stack of Fig. 5.1 with the data points spaced 0.5 nmapart. In addition, the theoretical trajectory of a uniform layer of GeC with a dielectricfunction of (13.5, 10.2) is shown. It can be seen that the trajectory of the uniform layerfollows that of the stack quite closely, especially as an increasing number of layers aredeposited. Hence one can determine the pseudo-dielectric function of the stack to a good dealof accuracy without depositing an infinite amount of layers.Germanium Carbide /132The above theory can be applied to spectroscopic ellipsometry. The modelingtechniques used the previous section can be used to determine the nature of the multilayer. Inthis case an 2 or 3 dimensional isotropy can not be assumed and the screening parameter, lc,must be allowed to vary. If a good degree of chemical mixing is present, then the ForouhiBloomer model may provide a better fit to the ellipsometric data.5.3 ExperimentalThe germanium carbide films were deposited in the chamber with the rotating targetsand the fixed substrate holder. This system is described in greater detail in section 3.3. Agermanium and a pyrolytic carbon target were used. The substrate holder was electricallyisolated from the grounded chamber in order to allow for the application of a substrate bias.The substrate preparation techniques were the same as those described in section 4.2.2.Diffusion pumping with a liquid nitrogen cold trap was used to maintain a low base pressureduring the deposition process.The films were monitored during the deposition process through in-situ ellipsometry.During the ellipsometric monitoring of the film growth, it was desired to take a data-point ateach Angstrom of film growth in order to observe the effects of diffusion to a good deal ofprecision. However, it was initially found that the deposition rate of germanium was too highto accomplish this given that the data collection and process time for the in-situ ellipsometerwas on the order of 3 seconds. In order to reduce the deposition rate of germanium, a maskGermanium Carbide /133was placed in front of the target. The deposition rate of carbon was low enough not to requirethis procedure.The “target” thickness of the individual layers in the stacks was approximately 2.0 nm.Forty layers were deposited in all. In addition, individual layers and bilayers several tens ofnanometers in thickness were also deposited in order to determine the dielectric functions ofthe individual materials.Two sets of experiments were conducted, one as a function of pressure and the otheras a function of substrate bias. The deposition pressures were 0.5, 1.0 and 2.0 Pa. In thesystem used in this study, it was necessary to achieve these pressures by increasing thethrottling of the diffusion pump. Hence, there was an increase in the base pressure by a factorof 2—3 from 2 x i04 Pa over the experimental range. During the deposition process, thesubstrates were electrically isolated. Balanced magnetrons were employed in order to reducethe effects of the plasma ions.A set of individual films and multilayers were also deposited as a function of substratebias. In this case, the pressure was held constant at 1.0 Pa and the films were deposited atsubstrate biases of —22 V (floating) , —50 V and —100V. In this set of experiments,unbalanced magnetrons were used in order to ensure a good ion flux at the substrate.Germanium Carbide! 1345.4 Films Deposited as a Function of Pressure.5.4.1 ResultsFig. 5.3 shows the experimentally measured and the theoretically detenninedellipsomethc data points for a germanium/carbon bilayer deposited at 0.5 Pa in argon. Theoptical constants were found to be (4.8, 1.78) for the germanium layer and (2.52, 0.56) for thecarbon layer. The data were fit using the projection method, which is explained in detail inchapter 6. Essentially, in this technique, the distance in the complex plane between theexperimental data points and the theoretical trajectory is minimized. The main advantage ofthis method is that one need not know the thickness of the film at each data point apriori tothe optimization procedure. The above procedure was repeated for films deposited at 1 and 2Pa. The optical constants for the films deposited at 1 Pa were, to within a fitting error of ±.02, the same as those for the 0.5 Pa film for both germanium and carbon.For the germanium film deposited at 2 Pa a single layer model could not be used todescribe the ellipsometric trajectory of the film. In this case a three layer model with anincreasing void fraction was used which assumed that the optical constants of the bulkmaterial are the same as those for the film deposited at 0.5 Pa. The results of the fit arepresented as the inhomogenous line in Fig. 5.4 while the void fractions, thicknesses and theresulting optical constants of the individual layers are given in Table 5.1. For comparisonpurposes, a homogenous model with the same optical constants as layer 1 in Table 5.1 is alsoshown in the figure. Finally the ellipsometric trajectory of a film with surface roughness layer90.0—0.1—0.2—0.3—0.4—0.5—0.5rho (real)Germanium Carbide / 135—0.2Figure 5.3 Experimental data and theoretical fit to a germanium/carbon bilayer on a siliconsubstrate deposited at 0.5 Pa. The optical constants were determined to be (4.78,1.78) for thegermanium layer and (2.52, 0.56) for the carbon.I I IFigure 5.4 Experimental data and three theoretical models for a germanium layer depositedon silicon at 2.0 Pa. The parameters for the inhomogenous layer are given in Table 5.1Si00 GermaniumCarbonTheor. Fit0.5 Pa—0.4 —0.32PaI0.00—0.05—0.10—0.15—0.20—0.25 ——0.42\° Exper. DataInhomogenous— — — HomogenousRoughness—0.38 —0.34 —0.30 —0.26rho (real)—0.22Germanium Carbide / 136Table 5.1 Parameters for inhomogeneous model in Fig. 5.4. The bulk optical constants arethat of the germanium film deposited at 0.5Layer Thickness (nm) Void Fraction Optical Constants1 4.0 .15 (4.14, 1.49)2 5.0 .21 (3.78, 1.32)3 24.0 .24 (3.62, 1.24)which initially follows the same ellipsometric trajectory as the homogenous film is presented.The model is based on the observation that a roughness layer generally evolves as17°dr=dS (5.1)where d is the total film thickness, dr is the thickness of the top roughness layer and s is amodel parameter with a value between 0.25 and 0.50. In Fig. 5.4, the value of s = 0.5 andthe optical constants are assumed to be those of the film deposited at .5 Pa with a 12% voidfraction. The optical constants for the carbon layer deposited at 2 Pa were determined to be(2.1, 0.42).The ellipsometric trajectories for the germaniumlcarbon multilayers deposited at 0.5,1.0 and 2.0 Pa are shown in Figs. 5.5, 5.6 and 5.7. Also shown is the theoretical ellipsometrictrajectory for a material with the same pseudo-dielectric function as the stack. The opticalconstants for the material are also shown on the plots and presented in Table 5.2, along withthe optical constants of the single layer films.. For the multilayer deposited at 1 Pa a twolayer model was required, indicating a inhomogeneous growth pattern. The differenceGermanium Carbide / 137Table 5.2 Optical constants vs. pressure for single layers and multilayers. More than 1 set ofoptical constants indicates inhomogeneities in the films.Pressure (Pa) Germanium0.5 (4.78, 1.78)1.0 (4.78, 1.78)Carbon Ge/C Multilayer(2.52, 0.56) (4.23, 1.34)(2.52, 0.56) (4.0, 1.30)(3.7, 1. 15)2.0 (4.14, 1.49) (2.1, 0.42) (2.48,0.44)(3.78, 1.32)(3.62, 1.24)between the two sets of optical constants indicates approximately a 15% increase in voids.Due to the large degree of inbornogenities in the films, an analysis with the Wienerbounds was not performed for the films deposited as a function of pressure.5.4.2 DiscussionThe results show that there is an increasing amount of inhomogeneity in the germaniumfilms as the pressure of the sputter gas is increased. As discussed in section 3.2.2, this isattributed to a reduction in the energy of the reflected neutrals. It should be noted that the 3-layer model used to predict the ellipsometric trajectory of the film deposited at 2 Pa is notnecessarily unique and other factors, such as the presence of impurities, could also be affectingthe optical properties of the film.Germanium Carbide /138Rho (real)Figure 5.5 Ellipsometric trajectoly of a germaniumlcarbonfloating substrate at 0.5 Pa. Also shown is the theoreticalmaterial with the pseudo-dielectric function as the stack.multilayer deposited onto aellipsometric trajectory for aI I I0.5 Pa10 00000.025—0.025- —0.075—0.125—0.175Si000GermaniumCarbon(4.23, 1.34)I I—0.225 ——0.425 —0.375 —0.325 —0.275 —0.225Germanium Carbide /1390.0001100 01 Pa °°00Si—0.050—100GermaniumCarbon(4.0,1.3)(3.7,1.15)E 00—0.1500o0’Of-0.200—0.250 I I I—0.400 —0.350 —0.300 —0.250 —0.200Rho (real)Figure 5.6 Effipsometric trajectory of a germanium/carbon multilayer deposited onto afloating substrate at 1.0 Pa. Also shown is the theoretical ellipsometric trajectory for amaterial with the pseudo-dielectric function as the stack. In this case a two layer model isrequired.I0.000—0.100—0.200—0.300 ——0.350Rho (real)Germanium Carbide / 140Figure 5.7 Ellipsometric trajectory of a germanium/carbon multilayer deposited onto afloating substrate at 2.0 Pa. Also shown is the theoretical ellipsometric trajectory for amaterial with the pseudo-dielectric function as the stack.2PaI I I0CGermaniumCarbon(2 . 48, . 44 )—0.250 —0.150 —0.050 0.050Germanium Carbide /141Inhomogeneities were not detected in the carbon films. Though thin films of carbonhave been observed to be quite smooth,171 it is also possible that inhomogenities are notdetected due to the reduced dielectric contrast between carbon and the ambient. This is also aprobable reason for the ability of a one layer model to describe the dielectric function of themultilayer deposited at 2 Pa.Interdiffusion between the individual layers is clearly visible in the ellipsometrictrajectories of the germanium/carbon multilayers shown in Figs 5.5, 5.6 and 5.7. The mixing ofthe individual layers is observed to increase as the argon pressure is increased from 0.5 to 2.0Pa.Fig. 5.8 shows the ellipsometric data for the first few layers of the system deposited at1 Pa. Also shown is a theoretical simulation for the 3rd, 4th and 5th layers. Both sets of datahave been displaced for comparison purposes.The theoretical model has assumed diffusion between the 3rd and 4th and the 4th and5th layers. The thickness of each diffusion layer is 6 Angstroms and a linear gradientbetween the dielectric functions of the two materials is assumed. However, the nature of thediffusion is assumed to differ at the Ge/C and at the C/Ge interface.For the interface where carbon is deposited onto germanium, the model assumes thatthe germanium layer is rough and the carbon atoms initially smooth out the surface. Themodel simulates this effect by having the carbon atoms diffuse into the germanium layerwithout an overall increase in the thickness of the stack. As a result, the six initial data pointsCGermanium Carbide I 142Figure 5.8 Experimental data for the first few layers of the multilayer deposited at 1 Pa. Alsoshown is a theoretical simulation of layers 3, 4 and 5 with diffusion between the layers. Bothsets of data have been displaced for comparison purposes.of the simulation represent an additional Angstrom of diffusion rather than one of layergrowth. As the atoms diffuse into germanium, the surface becomes more carbon-rich. Theoverall thickness of the stack increases after the sixth data point, where a pure carbon layer isthen deposited.The theoretical results match the experimental trajectory fairly well, though the anglebetween the germanium trajectory and the trajectory of the diffusion layer appears to be moreoblique in the former case. This could be the result of a non-linear diffusion gradient.SimulationSi000OOOQ Exp. Data0 Germanium0 Carbon5rho.r (arb. units)Germanium Carbide! 143The nature of the interface where germanium has been deposited onto carbon isassumed to be differ from the above case. In x-ray multilayer systems it has been shown thatthe deposition of carbon tends to smooth out the surface of a multilayer.54 As a result,physical intermixing is more likely due to pure diffusion and one expects the overall thicknessof the multilayer to increase during the initial deposition process.The model which most closely matched the experimental results was carbon diffusinginto the newly deposited germanium layer, as shown in Fig. 5.8. In this case, each data pointindicates an additional Angstrom of thickness. A linear gradient between the dielectricfunctions was once again assumed.An increase in carbon diffusing into the germanium layer with increasing pressure ismost likely the result of a more open voided structure in the later. The smaller carbon atomscan then readily diffuse into the germanium. This theory is supported by the modeling resultsfor the thick germanium film deposited at 2 Pa. Models which also included germaniumdiffusing into the carbon layer resulted in a poorer agreement with the experimental data.The theoretical model shows a smaller radius of curvature for the intermediate layerbetween layers 4 and 5 than that for the experimental data. The reason for this can be, in part,explained through an examination of the first layer of the experimental data. Ideally, thetrajectory should have the same form as that of layer 3 in the simulation. However, the pathinitially departs from this with a small degree of curvature. This thickness, termed the criticalthickness,’72 is the result of an initial anisotropic film growth. After this point the depositionbecomes more uniform and the curve is closer to the ideal.Germanium Carbide /144The multilayer deposited at 2 Pa appears to be fairly homogeneous with a large degreeof mixing between the carbon and germanium layers. However, due to the observed voidedstructure for germanium (and for carbon at this pressure in chapter 4), the optical constants ofthe resulting film are likely to change over time due to moisture penetration. Henceincreasing the degree of mixing through altering the sputter gas pressure appears impracticalfor optical applications.5.5 Films Deposited as a Function of Substrate Bias5.5.1 ResultsThe optical constants for carbon and germanium were determined for a set of singlelayer films on silicon substrates which were biased at —22 V (electrically floating), —50 V, and—100 V respectively. The deposition pressure was 1 Pa.The thickness of the individual germanium fthns grown as a function of substrate biaswas approximately 40 nm. To within a modeling error of ± .015 for n and k, no difference inthe optical properties of the above films could be observed. The complex refractive index wasdetermined to be (4.92, 1.70).Fig. 5.9 presents the ellipsometric trajectories for three carbon films deposited atdifferent substrate biases along with the accompanying theoretical fits. The thickness of thefilms decreases from approximately 28.5 nm at the floating potential to 23.5 nm at a —100 VGermanium Carbide I 1450.00___________________________—0.05- —0.10__ __ _ __—0.20—0.25—0.30 ——0.26 —0.24 —0.22 —0.20 —0.18 —0.16 —0.14rho (real)Figure 5.9 Experimental data and theoretical fits for carbon films deposited as a function ofsubstrate bias. The optical constants of the 1 layer theoretical models are given. The insetshows two of the experimental trajectories and two theoretical models which assume the bulkmaterial is that of the film deposited at —100 V.substrate bias. This could be, in part, the result of an increase in the density of the film. Thetheoretically determined optical constants are also given in Fig 5.9 and in Table 5.3. It can beseen that the general trend with increasing substrate bias is an increase in the refractive indexn, along with a decrease in the absorption and deposition rate.The inset of Fig. 5.9 shows the films deposited at —22 V (floating) and —100 Vsubstrate bias along with the theoretical trajectories of two models. Both models assume thatthe bulk material has the same optical properties as the film deposited at —100V and in eachcase the Bruggman effective medium approximation is used to determine the resultantFloating (—22V)a —100VRou,ghnesVoids—22V (2.28, .61° —50 V (2.36, .54—100 V(2.54, .38)Germanium Carbide I 146Carbon Ge/C Multilayer(2.28, 0.61) (3.76, 1.13)(3.62, 1.09)—50 (4.92, 1.70) (2.36, 0.54) (3.76, 1.13)(3.76, 1.21)—100 (4.92, 1.70) (2.54, 0.38) (3.84, 1.10)dielectric function of the individual layers. The first model has a single layer trajectory with a20 % void fraction. The second model has a surface roughness layer with a thickness given byEq. 5.1 where the roughness parameter, s, is equal to 0.5. The roughness layer consists of aneven mixture of bulk material and voids. It is clear from the resulting trajectories that theellipsometric properties of the carbon films deposited at lower substrate biases cannot beexplained through microstructural changes alone.Figs. 5.10, 5.10 and 5.12 show the ellipsometric trajectory of the germanium/carbonmultilayers deposited at a substrate bias of —22 V, —50 V and —100 V respectively. Everysecond data point collected is shown. The thickness of the germanium and the carbon layersis approximately 2 nm.Table 5.3 Optical constants vs. substrate bias for single layers and multilayers. More than 1 setof optical constants indicate inhomogeneities in the films.Substrate Bias (V) Germanium—22 (4.92, 1.70)Germanium Carbide / 1470.000—0.045—0.090—0.135—0.180—0.225—0.35 —0.32 —0.29 —0.26 —0.23 —0.20Figure 5.10 Efflpsomethc trajectory of a germanium/carbon multilayer deposited onto afloating substrate (—22 V). Also shown is the theoretical ellipsometric trajectory for amaterial with the pseudo-dielecthc function as the stack.I I I I I-22V000 Si0000germaniumcarbon(3.76,1. 13(3.62,1.09I i I I IGermanium Carbide / 1480.000—0.045—0.090—0.135—0.180—0.225 ——0.35 —0.32 —0.29 —0.26 —0.23 —0.20Figure 5.11 Effipsomeiric trajectory of a germanium/carbon multilayer deposited onto asubstrate biased at —50 V. Also shown is the theoretical ellipsometric trajectory for amaterial with the pseudo-dielectric function as the stack.-Soy 0 Si000D‘ I I I I I I I IGermaniumCarbon(3.76,1.13(3.76, 1.210.000—0.045—0.090- —0.135—0.180—0.225Germanium Carbide I 149—0.35 —0.32 —0.29 —0.26 —0.23 —0.20rho (real)Figure 5.12 Ellipsometric trajectory of a germanium/carbon multilayer deposited onto asubstrate biased at —100 V. Also shown is the theoretical ellipsometric trajectory for amaterial with the pseudo-dielectric function as the stack.— boy 0 0 Si—— F____GermaniumCarbon(3.84,1. 10)0000000Germanium Carbide! 150(21.3, 16.7)Figure 5.13 Wiener bounds for the multilayer stacks deposited as a function of substrate bias.The optical constants are determined from the single layer films. The data have been offset ineach case for comparison purposes.•GeC(21.3, 16.7)(21.3, 16.7)-22V- (5.28, 2.55)(4.83,2.78)Germanium Carbide! 151Also presented in the figures is the theoretical ellipsometric trajectory of a material thatfollows the trajectory of each multilayer. Inhomogenaties must be taken into account for themultilayers deposited at —22 V and at —50 V. The density of the system appears to bedecreasing with increasing thickness for a floating bias and increasing at a bias of —50 V. Theoptical constants for the multilayers are presented on the figures and along with those for thesingle layers in Table 5.3.It can be seen that the diffusion of carbon into the germanium layer increases with agreater substrate bias. However, the germanium/carbon interface appears to become sharper.The Wiener bounds for the three multilayers are given in Fig 5.13 along with thepseudo-dielectric function of each system. The optical constants of the constituents areassumed to be those for the single layer films deposited at the corresponding substrate bias.The data points on the bounds represent a 10 % change in the fraction of the constituents. Thethree sets of bounds have been displaced for comparison purposes. Error bars are included forthe dielectric function of the multilayer deposited at a floating bias. The error range for theother multilayers is on the same order as that of the previous data point. This degree of errorcompensates for the inhomogeneities in the films.5.5.2 DiscussionThe results for the single layers of germanium indicate that the density of the films doesnot change with an increase in the substrate bias. This observation correlates well with theresults for the films deposited as at the lower pressures in the previous section. Hence, oneGermanium Carbide /152can conclude that germanium films with a zone-T microstructure are deposited at 1 Pa and ata floating potential.Fig 5.9 indicates that the optical properties of the carbon films change with anincreasing substrate bias. This effect cannot be attributed to an increase in the film densityalone due to the increase in the transparency of the film material. This property was notobserved in chapter 4 due to the inability to grow films under the above conditions withthickness greater than 50 - 70 nm. Carbon films in this thickness range (>70 nm) are requiredfor analysis by the ex-situ ellipsometer as the film thickness and the optical constants forthinner films. are highly correlated.’73The resulting optical constants at high substrate biases are closer to those of theamorphic diamond films produced through high energy arc deposition. Films of this natureare thought to contain a large percentage of sp3 bonds.’74 As with the above case it is alsodifficult to grow relatively thick films through this technique,’75 which is a major problem ininfrared applications.Figs. 5.10 through 5.12 show that the diffusion of carbon into the underlyinggermanium layer increases with a greater substrate bias. However, the nature of theellipsometric path differs from that of the films deposited as a function of pressure. In thiscase there appears to be a small amount of curvature outwards before the trajectory bendsback in the opposite direction of the underlying layer. This is attributed to a small increase inthe overall thickness of the multilayer, indicating that the germanium layer is smoother than inthe previous section.Germanium Carbide / 153The degree of interdiffusion between the germanium/carbon boundary appears todecrease with increasing substrate bias. This is attributed to an increase in the density of thelayers and overall smoother films. It is unlikely that the increase in bias will result in thegermanium diffusing into the carbon due to the relatively large atomic size of the former.Fig. 5.13 shows that in all three instances the pseudo-dielectric function of themultilayer lies within the corresponding Wiener bounds. It should also be noted that theexperimental value lies very close to the expected one and within the boundaries of error.Therefore chemical mixing between carbon and germanium does not appear to effect thedielectric properties of the material.Substrate bias which are much greater than —100 V are usually not applied in practicedue to the problems of resputtenng and the formation of a high compressive stress in thefilms. Therefore it would appear that biasing the substrate does not result in enoughinterdiffusion to make the deposition of alternate layers of germanium and carbon practical foroptical coatings.One potential solution to the above problems can be found through the observation thatthe effective medium theories apply to layers which are thin compared to the wavelength ofinterest. Hence, one should still be able to achieve the desired refractive index if the longwavelength approximation applies to the stack.. It should be noted that at a normal incidencemaximum screening occurs and the resultant dielectric function is found through Eq. 3.11. Asthe two materials should be relatively transparent at the wavelength of interest the effectiverefractive index of the stack, n, can approximated through the relationGermanium Carbide I 154nefffn+n(5.2)where f. n and f8, fl are the volume fractions and refractive indices of the carbon and thegermanium phases respectively. One potential problem to the above solution is interdiffusionbetween the layers over time, as this would reduce the overall screening and change theeffective refractive index5.6 ConclusionsAn increase in the pressure and an increase in the substrate bias results in an increase inthe interdiffusion between the carbon and germanium layers in a multilayer stack.. However,only an increase in pressure appears to allow for the required degree of mixing necessary toproduce germanium carbide. Unfortunately, this also results in a film with a Zone- 1microstmcture (section 3.2.2), making these coatings unsuitable for optical applications.The results and analysis show that the required refractive index can still be achieved ifthe layers are thin enough for the long wavelength approximation to apply. However, thisvalue could change over time if enough diffusion results. Therefore, one would like to makethe individual layers relatively thick in order to reduce this effect.Chapter 6 L5SOPTICAL MULTILAYERS6.1 IntroductionOnce the diamond-like and the germanium carbide films were characterized, a controlsystem was required that would allow for the deposition of multilayers of these materials. Itwas also desired to be able to deposit dielectric multilayers in the near infrared region.In order to deposit multilayers with the desired reflection and/or transmissioncharacteristics, it is necessary to control the thickness of each layer to the required degree ofaccuracy. The simplest method of control is that of timing.66 In this technique, the depositionrates and the optical constants are obtained from previous runs and an assumption is made thatthey wifi remain constant over the current run. As the optical constants of the diamond-likeand germanium carbide films are highly dependent upon the deposition conditions, this methodis inadequate for the purposes of this thesis.A more precise form of control for the deposition of dielectric multilayers istransmission monitoring.176 In this method, the transmittance of the multilayer is measured insitu. As the intensity can be calculated as a function of layer thickness through the matrixmethod, the deposition process is halted when the desired value is obtained.There are a number of drawbacks to the above method. As the transmission ismonitored at normal incidence, for a large number of systems the intensity cannot be measuredunless the deposition process is halted. A possible solution to this problem would be toOptical Multilayers /156_kt.010.410000 15000 20000 25000 30000Wavenumbers (cmt)Figure 6. iTheoretical reflection and transmission characteristics for two anti-reflectioncoatings on a transparent substrate with a refractive index of 4. The first film has an n and kvalue of (2,0) while the second has a value of (2,.01)design a system with the targets oriented at an angle, however, as discussed in Chap 5, thisresults in shadowing effects. Another potential complication is caused by undesired and oftenunpredictable amounts of absorption in the films. Even for dielecthc materials, residualimpurities in the deposition chamber can result in a small value of k, typically between a valueof l0 and 10g. This factor results in an overall reduction in the transmission values whichincreases with the number of layers. To help compensate for this effect, adaptive routines areoften required which recalculate the necessary thicknesses of the remaining layers after eachOptical Mu:ltilayers /157individual layer deposition.’77 This problem is intensified when absorbing films such as carbonor metals are deposited.As transmission monitoring appeared quite problematic for the purposes of this thesis,in-situ ellipsometry was chosen as the method for controlling the individual layer thickness.One advantage to this technique is that the optical properties are measured at a non-normalangle of incidence. Therefore, constant monitoring of the film growth is possible. Also,reflection measurements are inherently less sensitive to absorption in the films thantransmission measurements. This property is demonstrated in Fig. 6.1 for an antireflectioncoating (n = 2) on a substrate (n = 4) of infmite thickness. Two cases are shown, one for atransparent film and one for a film with a value of k equal to 0.01. If we compare the maximaand minima in the intensities it can clearly be seen that the transmission is affected by a factorof at least 3 over the reflection spectra.Another important consideration is that each ellipsometric measurement results in twopieces of information as opposed to a transmission measurement which results in only one.For dielectric coatings, this allows for a solution of n and d, giving information on both theoptical thickness and the quality of the film. Ideally, for partially absorbing coatings, we wouldlike solve for the two unknowns nd and k. Unfortunately this is not possible in practice as thecomplex reflectance ratio cannot written as a function of the above variables. However, asillustrated in Chapter 5, the solution of n, k and d can determined through the observation ofthe ellipsometric trajectory in the complex p plane. One fmal advantage is that ellipsometricOptical Multilayers /158measurements are inherently more precise than intensity measurements as they are self-referencing.At the start of this project, aside from the added instrumental complexity, the potentialdrawbacks to this technique were not obvious as, for optical films, this method had only beenused to control the thickness of a single layer on a substrate.178’9 There were a number ofdevelopments in the x-ray multilayer field;72’18° but, to date, there had been no improvementover the previously mentioned timing method. Also the x-ray films were thin compared to themonitoring wavelength and highly absorbing, which made a comparison with the films used inthis thesis difficult. However, given the potential applications, it was felt that this was aworthwhile project for a Ph.D. thesis.The remainder of the chapter is as follows. The methods used to determine theoptimum deposition conditions for single layer Si02 and Ta2O5 films are discussed in section6.2. These films are to be used to test the initial control routines. The section starts with anoverview of reactive sputtering, then discusses how in-situ ellipsometry was used tocharacterize the films. In section 6.3, the development of an optical multilayer control systemfor dielectric films is examined. Several iterations were required before a successful routinewas implemented. In the final section the routines are extended to absorbing films.-.‘CI.F—Optical Multilayers /159Figure 6.2 Typical target voltage vs. 02 flow rate for reactive sputtering of silicon. Themetallic mode corresponds to the region where the target is partially covered with an oxide.6.2 Single Layer Films6.2.1 Reactive Sputtering.The dielectric materials used in the course of this thesis were deposited through theprocess of reactive sputtering.181 In this technique, a metallic target is sputtered in an Ar102gas mix resulting in the deposition of an oxide of the target material. One of the main02 Flow RateOptical Multilayers /160advantages of this method is the high operational powers possible due to the great thermalconductivity of the metal. One other advantage is that, for conducting targets, a dc rather thanan if bias can be used; simplifying the procedure and allowing for a larger degree of scale up.’82Fig. 6.2 shows a typical target voltage vs. 02 flow rate for the reactive sputtering ofa silicon target. Here the flow rate of the inert gas, the sputtering power and the pumpingspeed are constant. In region 1, the target voltage is essentially constant and an increasing 02flow rate does not result in an increase in the overall pressure. These effects are due to thesputtered metal flux reacting with all of the oxygen. Typically, the film deposited in thisregion is a suboxide of the desired material. In region 2, the flow rate has increased to thepoint where all of the sputtered metal reacts with the oxygen. Under these conditions, thedeposited material is either stoichiometric or very close to it. In addition the overall pressurebegins to rise and the target becomes partially covered with an oxide, resulting in a drop inboth the target voltage and the deposition rate. This region of operation is known as the metalmode. In region 3 the target is fully covered with an oxide, the deposition rates are fairly lowand the excess oxygen results in an increase in the pressure. The excess oxygen can, forcertain materials, such as titanium oxide, result in a degradation of the film quality.183 Thismode is known as the covered or dielectric mode.The optimum deposition region then typically lies somewhere in the metal mode.However, there is a drawback to working in this region for optical coatings due to the changesin the deposition rate which result from variations in the amount of target coverage. As thisregion is not wide in terms of 02 flow rate, small fluctuations in the oxygen partial pressureOptical Multilayers /161can result in large changes in the deposition rate. Hence monitoring is crucial in this region ifhigh quality optical multilayers are desired.6.2.2 In -Situ MonitoringFig. 6.3 shows the ellipsometric path as a function of thickness for a number ofdielectric films with different refractive indices in the complex p plane. The substrate materialis silicon. For a dielectric film of a given refractive index, the path will follow the sametrajectory each time ndcosØ, where 0 is the angle of incidence, reaches a multiple of the half-wave thickness. If the film is absorbing, the path will eventually spiral around then reach thevalue of p for an infmitely thick layer of the deposited material. This effect is shown in Fig.6.4 for a film with refractive index of (2.0, 0.1). Hence monitoring during the film growth canbe used to determine both the optical constants and the quality of the deposited material.Inhomegeneaties and surface roughness will also result in a non-closed trajectory.’84The ellipsometric properties described above also hold if the film is deposited onto anoptical multilayer. This factor allows for a “quick and dirty” method of determining theoptimum conditions. One can monitor a multilayer where the individual films are grown undera number of different deposition conditions. If the ellipsometric trajectory for a given layerreturns to the sane point on the complex plane, then the deposited material is of a highquality.Optical Multilayers /1621.4\1.8 1.6IN//—6 —4 —2 0 2 4321C—1—2—36Rho (Real)Figure 6.3 Theoretical ellipsometric trajectories for a number of dielectric films in thecomplex p plane. For a given refractive index the trajectory wifi follow the same spiral eachtime a multiple of the half-wave thickness is reached.0.50.30.1-0.1—0.3—0,5 I—0.4Rho (real)Figure 6.4 Theoretical ellipsometric trajectory for a film with a refractive index of (2.0,0.1)on silicon. Also shown are values of p for a silicon substrate and an infmitely thick film.• Si• Film—0.2 0.0 0.2— I__ I0.4 0.6 0.8Optical Multilayers 11636.2.3 Silicon OxideThe silicon target used in this study contained 5% aluminum in order to increase theelectrical conductivity of the material and, therefore, allow for a more stable operation with adc sputter source. As the refractive index of Si02 and Al2 03 are both “low”, 1.45 for Si02,and 1.62 for Al2 03, the addition of aluminum had only a small effect on the optical propertiesof the deposited material.Initially the films were deposited using a dc power source. However, the resulting filmquality was poor with macroscopically visible pinholes. This result was attributed tooccasional arcing during the film deposition, which could be observed through the portwindows and through the monitoring of the output of the power supply. Arcing is caused by athick oxide buildup on regions of the target where the sputter rate is low. During the sputterprocess, these regions charge up until a dielectric break-down occurs, creating an arc and oftenresulting in the deposition of an inferior quality film.A solution to the above problem was found through the use of a low frequency powersupply which operated at 40 kHz. Under these conditions, the bias on the target is positivefor half the cycle. The period is long enough to discharge the oxide buildup but short enoughnot to extinguish the plasma. It should be noted that at this operating frequency the systemcan essentially be treated as dc because the ions are able to move completely across the plasmaregion within a half-period.’85Initial tests showed that the best films in terms of the magnitude of the refractive indexwere deposited at the lowest possible operating pressures. This was attributed to energeticOptical Multilayers /164particle bombardment which increased the density of the film. In addition, the films appearedto be quite transparent if they were deposited in either the metal or the dielectric modes.A set of three films were deposited onto silicon substrates to allow for a more precisestudy of the optical constants. The system was operated at three different points on the curveof Fig. 6.2; approximately at the boundary of the metal mode and region 1, in the middle ofthe metal mode, and approximately at the boundary of the dielectric and metal modes. Duringthe deposition runs the films were monitored through in-situ ellipsometry. The operatingpressure was 0.35 Pa and the sputter power was 100 Watts.Fig. 6.5 shows the ellipsometric trajectory of the film deposited at the boundary ofregion 1 and the metal mode. Also included is a theoretical fit to the data assuming ahomogeneous film. The theoretically determined values of the optical constants were n =1.474 and k = 3 x 1O. Fig. 6.6 shows the ellipsometric data for the film deposited in themiddle of the metal mode. The results show that the film is clearly less absorbing in thisregion, with a value of k determined to be less than 1 x i(i. Also the value of n appearsto be almost identical to the previous sample. However, the deposition rate under theseconditions is reduced from approximately 3 A/s to 1.5 A/s.For the sample deposited at the boundary of the metal and the dielectric modes, nodifference in the optical constants was observed when compared to the previous sample.However, there was a further decrease in the deposition rate. Hence the deposition conditionsappeared to be optimized at low pressures and in the middle of the metal mode.66420—2—4—6—8 I •—17 —15 —13 —11rho (real)Optical Multilayers /165o Exp.Data— Theor. Fit—9 —7 —5 —3 —1 1Figure 6.6 Experimental data and theoretical fit for silicon oxide on a silicon substrate as afunction of film thickness. The value of k was determined to be equal to 3x 1O. The film wasdeposited at the boundaries of region I and the metal mode.864.2.—C2—6—8 I I I—17 —15 —13 —11 —9 —7 —5 —3 —1 1Rho (real)Figure 6.5 Experimental data and theoretical fit for silicon oxide on a silicon substrate as afunction of film thickness. The value of k was determined to be less than lx10. The film wasdeposited in the middle of the metal mode.Optical Multilayers /166Once the optimum conditions for film growth were determined, it was possible tomake a comparison between the in-situ and the ex-situ ellipsometer. This allowed for anaccurate determination of the window correction factor x (see appendix A, Eq. A.12).A Si02 film was deposited while being monitored by the in-situ ellipsometer. When theoptical thickness was approximately 120 nm thick, the deposition was halted and the filmimmediately removed from the chamber and measured on the ex-situ ellipsometer at the HeNewavelength (632.8 nm). The value of p measured on the ex-situ ellipsometer is shown in Fig.6.7. From this measurement the refractive index of the film was determined to be 1.472. Thedotted line shows the trajectory a film of this refractive index would have if the angle ofincidence of the in situ ellipsometer was the same as that of the ex-situ instrument, 67.50°.As the complex reflectance ratio is a function of the angle of incidence it is important todetermine this parameter to a high degree of accuracy. This criterion can be achieved bymeasuring the complex reflectance ratio of the Si substrate before deposition. In this particularcase, the real part of p is essentially independent of small changes in the overlayer thickness,but highly dependent upon the angle of incidence. Also, as the imaginary component of p issmall, from Eq. A.12 in the appendix, it can be shown that the real part of the complexreflectance ratio is not subject to the effects of the vacuum port windows.The angle of incidence was determined to be 67.94 ± .03 O Fig. 6.7 shows thetheoretical ellipsometric trajectory of film with a refractive index of 1.472 at this angle. Thewindow parameter a was adjusted until the optimum fit was achieved as shown in the graph.The value of cx was determined to be .006 ±. .0005.Optical Mukilayers /167b—0.2 —0.1 0.00.00—0.25—0.50—0.75—1.00—1.25—0.3 0.1Rho (real)Figure 6.7 Comparison between the ex-situ and in-situ ellipsometer. Presented are the in-situreadings during the growth of a silicon layer on silicon, the ex-situ measurement of the film andthe theoretical trajectories at each of the instruments angle of incidence.It should be noted that the fmal n and k values given in this section were determinedafter all of the window correction factors were obtained.6.2.4 Tantalum OxideTantalum oxide films were investigated in order to determine the optimum depositionconditions. The method of investigation was the same as that for the Si02 films.Optical Multilayers /1680.50.30.1-0.1—0.3—0.5 ——0.3 0.9Rho (real)Figure 6.8 Ellipsometric trajectory for a tantalum oxide film. The results indicate very littleabsorption in the film.The voltage vs. oxygen flow rate shown for silicon in Fig. 6.2 differs for tantalum. Inthis case there is an initial rise in the target voltage as the metal mode is approached followedby a drop as the target becomes covered with an oxide.The refractive indices of the tantalum oxide films also increased with a decreasingpressure. However as the target voltage increases at lower pressures, the power supply, with amaximum voltage output of 500 V, limited the range of possible pressures. The operatingpressure was chosen to be 0.35 Pa.A study similar to the one performed for the Si02 films was undertaken for thetantalum oxide films. No measurable change in the optical constants was measured after the0.0 0.3 0.6Optical Multilayers /169target voltage had reached a maximum, however there was a decrease in the deposition ratewith an increasing 02 flow rate. Before the maximum in the target voltage was reached, thesputtered films were highly absorbing. Hence the optimum deposition region was found to bejust after the peak in the voltage where the deposition rate was approximately 3 A/s.The ellipsometric measurement of a film deposited under the optimum conditions isshown in Fig. 6.8. The data indicate that there is very little absorption in the film.6.3 Optical Multilayers6.3.1 Multilayer Control DevelopmentOnce the single layer films were optimized, it was necessary to develop a controlroutine in order to deposit the optical multilayers. As discussed previously, the individual filmthicknesses were to be determined through the method of in-situ ellipsometry.To aid in the development of the software routines, two multilayers were depositedthrough the timing method while being monitored by the in-situ ellipsometer. Theellipsometric data were then used to test the subroutines before they were implemented inthe control procedure.The two multilayers deposited were quarter-wave stacks of Si02 and Ta205 with a‘target’ wavelength of 300 nm and 632.8 nm (HeNe) respectively. The form of each of thestacks was1.51.00.50.0—0.5—1.0—1.5rho (real)Optical Multilayers /1702.0 2.5Figure 6.9 Ellipsomethc trajectory of a 300 nm quarter-wave stack onthe He Ne (632.8 nm) wavelength..0Figure 6.10 Ellipsometricwavelength of 632.8 nm.beyond the asterisksa silicon substrate attrajectory of a 632.8 nm quarter-wave stack on a silicon at aThe trajectory has a maximum magnitude of approximately 200I-Lowlndex (1.47) IIHighlndex(2.1) nd=300/4nm—0.5 0.0 0.5 1.0 1.5Low index(1.46)High index (2.1)2.01.51,00.50.0—0.5—1.0—1.5—2.0nd = 632.8/4 nm—2.0 —1.5 —1.0 —0.5 0.0 0.5Rho (real)1.0Optical Multilayers /171Air / HLHLFILRLHL / SiThe theoretical values of p for the two multilayers are shown in Figs. 6.9 and 6.10. Thethinner of the stacks provided a relatively ‘well behaved’ ellipsometric trajectory to test theinitial subroutines. The thicker stack allowed for the development of more robust algorithms.Once the subroutines were developed, they were implemented in the main programwhich was subsequently used to control the deposition of a new quarter-wave stack at theHeNe wavelength. The reflection and transmission spectra of the stack were then measuredand compared with theory. -The quarter-wave stack was deposited onto a glass substrate. As this was difficult tomonitor with the in-situ ellipsometer, due to the incoherent reflections off the back of theglass, the layer thickness was monitored off an adjacent Si substrate. To ensure that thedeposition was the same for each substrate the target was toggled at ± 20° or equivalentlyover an arc length of 14 cm. The length of the two substrates was on the order of 2 cm andthey were evenly spaced about an angle of 0° with respect to the toggle.There were a number of iterations to the control routines until a method was found thatworked with a good degree of success. The next three sections outline the various methodstried and discuss the problems associated with each routine.6.3.2 Matrix MethodThe first method used to control the optical thickness of the individual layers was thedirect solution of the mathx equations. As discussed in the introduction, a singleOptical Multilayers /172measurement of p allows for the solution of two unknowns. Unfortunately, the equations forp can not be inverted in terms of the optical constants and the film thickness and therefore areusually solved numerically through the Newton-Raphson method. As discussed in section 3.4,this method usually requires highly accurate initial values. The procedure is also timeconsuming, which is a potential problem for real time applications.For a transparent film, an alternative method of solution exists which was initiallydeveloped for a single layer on a substrate.186 For an ambient/film/substrate system thecomplex reflectance ratio can be written as— rp — r01 +r12 exp(2if3 d) 1 +r01r12, exp(2if d)r 1+r01r2exp(2if3d) r013 +r12 exp(2i(d)‘ (6.1)where d is the film thickness and r01 and r12 are the reflection coefficients at the ambient/filmand the film/substrate interfaces respectively. The value of is given by=21tf—sin2Ø , (6.2)where N is the complex refractive index, 0 is the angle of incidence and ? is the wavelengthof interest. For a dielectric film, where [3 is real, Eq. 6.1 can be separated into two functionswhereF (n) =0, (6.3a)F2(n,d) = 0. (6.3b)Equations 6.3a and 6.3b are given in full detail in reference 186. Equation 6.3a can be solvedOptical Multilayers /173numerically through the use of the single variable Newton’s method. Once the value of n isobtained, Eq. 6.3b can then be determined analytically for d, allowing for a solution of theoptical thickness.The above method can also be used to determine the optical thickness of a film on aknown multilayer. For a multilayer system the derivation of the reflection coefficients is givenbyr 1 r,j] Fexp(i13d) 0 1 F 1 7j2p,$ B,3= [r 1 j [ 0 exp(—id)J [ri2p 1 J [c(6.4)where the right most matrix is the product of all of the underlying matrices up to but excludingthe second last interface. The complex reflectance ratio can then be written as— r +r1’2exp(2if3 d) 1+ iij’ exp(2if3 d)1+ rr’ exp(2if d) z + ij exp(2if3 d)(6.5)where(Ti2ps +Ti2p,s= (1 + 2p,s C/A)(6.6)As Eq. 6.5 is identical in form to Eq. 6.1., Eq. 6.3a and 6.3b can also be applied to muhilayerfilms.One potential problem considered before the routine was implemented was the effect ofa finite amount of absorption in the films. As more layers were deposited, neglecting thisfactor would result in an increasing error in the calculated values of A,5 and C. This, inOptical Multilayers /174turn, would result in a large error in the determination of the optical thickness. In order tocompensate for this effect, an additional routine was developed that was performed after eachlayer was deposited. In this procedure, nonlinear optimization was used to determine theoptical constants of the deposited materials using the previous data.The above routine has two basic assumptions. The first is that n and k for eachmaterial remains constant over the entire multilayer. The second assumption is that thedeposition rate, d, remains constant over an individual layer. This allows for a determinationof the thickness for each measured value of p through the relationd1=dQ —ta) (6.7)where t, is the time the data point of interest was taken and t a critical time period whichallows for the substrates to rotate into position and for the initial nucleation process on thesurface. The deposition rate can be determined by dividing the fmal thickness of a layer by thetotal deposition time minus the critical time. For an N-layer multilayer, the parameters to befit are thenj=1..rn, (6.8)where m is the number of different materials.The fmal algorithm for the control routines is shown in Fig. 6.11. At specific timeintervals a measurement of p is made. The value of nd is then determined through the useof Eqs. 6.3a and 6.3b. The procedure is then repeated until the user specified opticalthickness, nd1, is reached. The deposition is then halted by rotating the targets to anOptical Multilayers /175Figure 6.11 Flow diagram for the matrix method of controffing the deposition of opticalmultilayersOptical Multilayers /176intermediate position. The nonlinear optimization routines are then performed and the valuesof and C are updated for the next layer. The current target is then rotated into positionand the above procedure is repeated until the final layer, N, is deposited.Despite the simplicity of the above routines they were found to be inadequate as theoptical thickness for the HeNe quarterwave stack could not be determined to any degree ofaccuracy beyond 4 layers. One problem was the large degree of error in the calculated valuesof and If the coefficients are accurate, then the solution for the initial measurementof a layer should result in an optical thickness close to zero. However, these measurementsincreasingly deviated from this value until at the fifth layer the error was on the order of 10 nm.As the deposition rate was on the order of 0.2 nm/s and measurements were takenapproximately every 3 seconds, this large of an offset was highly unlikely.Further investigations revealed that the assumption of a constant deposition rate overthe growth of a single layer was not a good one. This was attributed to operating in themetallic mode. As a result the optimization fits were poor, resulting in a large uncertainty inthe optical constants.One further problem was that there was a large amount of noise in the calculated valuesof iid for certain regions, typically on the order of 1 nm. This degree of noise was notobserved in the measured values of p. It was concluded that the method was too sensitive tosmall imperfections in the deposited material and small amounts of misalignment in the in-situellipsometer. To illustrate these factors, consider Fig. 6.3 again. During the initial growth ofan oxide on silicon the ellipsometric path is practically independent of n. It is not, however,Optical Multilayers /177simply dependent on nd but on fd. As a result an error p, which can be caused by aninadequate model, miscalibration or simply noise in the system, results on an error in ndthrough the relation6ndsin2Øsiano (6.9)nd n2 n2 apTherefore, in regions where anmp is large, the uncertainty in the optical thickness is also large.It should be noted that Sp is in a direction perpendicular to the trajectory for a constantrefractive index in Eq. 6.9.6.3.3 Projection Method.Though direct use of the matrix equations did not result in a workable control routineit was observed that the experimental data followed the theoretical trajectory quite closely.Hence the deviations from the ideal model were small. It was also noted that the refractiveindices of the deposited materials were very repeatable between different runs.The above observations led to the development of the next control routine referred toas the projection method. In this technique the optical constants determined from previousruns are specified at the beginning of the deposition of the multilayer. The optical thickness isthen determined during the layer deposition by projecting the experimental value onto theclosest point of the theoretical curve. As with the previous method after the individual layerdeposition is completed, nonlinear optimization is performed to determine the actual opticalOptical Multilayers /178Figure 6.12 Flow diagram for the projection method for the control of the depositionmethod.Optical Multilayers /179constants. These constants can then be used to calculate the theoretical trajectory oncethe particular layer material is deposited again. It should be noted that this method lends itselfwell to absorbing films. The algorithm for the projection method is shown in Fig. 6.12. It canbe observed that the overall method is quite similar to the matrix method aside from having tospecify the initial values of the optical constants. The theory for determining the opticalthickness from a measurement of p is given below.The difference, D, between the theoretical curve and an experimental value isD(d)=pT(d)—pE, (6.10)where p7(d) is the theoretical value as a function of thickness and PE the experimentallymeasured data point. Rather than minimizing the absolute value of Eq. 6.10 it is simpler tominimize its square1D12= D*, (6.11)and hence find the zero of*d=D*+Di=0. (6.12)Observation of the right hand side of 6.12 shows that we want to solveRe- D*) = 0, (6.13)orR (apre---•PT — Prncas) ) — . (6.14)Optical Multilayers /180The projection method deals effectively with the two main problems cited in the previoussection. Equation 6.9 shows that as the optical constants are determined to a good deal ofaccuracy, the overall error in nd should be small. Also no assumptions need to be made aboutthe deposition rate in the optimization routines. In this case the function to be minimized isa = ID12 (6.15)where N is the number of measured data points. If the number of data points becomes toolarge, then a fraction can be selected at some chosen interval. The parameters to be adjustedto minimize Eq. 6.15 are then{n3,k) j=1,m (6.16)where in is the number of material types.The projection method worked well when analyzing the 300 nm quarter-wave stackbut developed difficulties with the one deposited at the HeNe wavelength. There wereproblems due to inaccuracies when calculating the substrate coefficients as before, though notas serious. At the eighth layer the initial measurement of p gave an nd value of approximately4 nm. This indicated that the simple model used to describe the stack was not sufficient.Potential deviations from the chosen model include interdiffusion between the layersand inhomogeneities in the layers themselves. One other potential problem results fromchanges in the optical constants over the deposition run. This effect is possible, for example, ifthe base pressure does not remain constant, which can alter the value of k. Also drifts in theoverall pressure can affect the value of n, though this factor is expected to be small.Optical Multilayers /181Aside from the non-idealities in the films, another potential source of error ismisalignment and miscalibration of the ellipsometer itself. This wifi also contribute to errors inthe deduced values of the substrate coefficients.Aside from problems with the chosen model another error arises from the nature of thefunction in Eq. 6.5 These errors result from problems with projecting onto the abrupt turns inthe ellipsometric trajectory shown in Fig. 6.9. This problem is better ifiustrated through theexamination of the eighth layer of the HeNe quarter-wave stack presented in Fig. 6.13. Herethe experimental data points are shown on the continuous line at intervals of approximately 4nm (every fifth data point measured is shown). Also shown is the theoretical trajectorypredicted from the previous optimization routines. It can be seen that the experimental resultsfollow the theoretical trend fairly closely aside from an offset that appears in part due to asmall error in the determination of the substrate optical properties. However, at the pointwhere the trajectory makes a sharp turn a more serious problem arises. Here the experimentalcurve intersects the theoretical one at the wrong branch. If the minimal distance method wereused the resulting optical thickness would appear to initially be getting smaller after reachingthis point. We have found that, depending on the exact orientation of the two curves, theexperimental data can continue to be projected onto the wrong branch of the theoreticalcurve. Also, it can be seen that the change in p is relatively insensitive to thickness after theturn, hence the offset error in this situation can be quite problematic. The nature of the path ofp can also be a problem during the optimization routines. From Fig. 6.13 it is evident that theOptical Multilayers /1821.00.70.4E0.=0.1-0.2-0.5 —-0.8 0.1 0.4 0.7rho (real)Figure 6.13 Experimentally measured and theoretically predicted ellipsometrictrajectories for the eighth layer of the quarter-wave stack controlled by the projectionmethod.Exper. Data.— —- Theor. Pred.0.80.70.60.50.40.30.1Start-0.5 -0.20.2 0.3 0.4 0.5 0.6Optical Multilayers I 183that the program can easily converge to a local rather than the global minima. This, in turnwould lead in an error in the determined values of n and k.An 8 layer quarter-wave (HeNe) stack was deposited through this method and itsreflection and transmission spectra measured. The maximum in reflectance was found to be atapproximately 580 nm indicating an average layer optical thickness of 145 nm rather than158.2 nm6.3.4 Transform methodThe projection method discussed above appeared to be too sensitive to theaccumulative errors in the substrate parameters. Also the ellipsomethc trajectory of thecomplex reflectance ratio was both difficult to fit through nonlinear optimization due to thepresence of local minima and to project onto for the determination of the optical thickness, nd.What was needed was a method that could accommodate the imperfections in thesubstrate. Also, it was desired to be able to transform p into a form that could easily beoptimized. A solution was found through a transform method for a single layer on a substratedeveloped by Yousef and Zaghloul.187 Through Eq. 6.5 , the above method can be extended tomultilayers. The transform is described below.From Eq. 6.5, the thickness of the topmost layer affects the complex reflectance ratiothrough the termx exp(2if3 d). (6.17)Optical Multilayers I 184For a transparent film, Eq. 6.17 is that of a unit circle with a phase factor of 2(3d. For anabsorbing film, Eq. 6.17 will spiral in towards the origin. Equation 6.5 can be thought of as atransform that maps a value from the complex x plane onto to the complex p plane. As Eq.6.17 is a much more “well behaved” function than Eq. 6.5, one possibility is to use an inversetransformation to project a measured value of p back to the x plane and determine the phasefactor directly. This can be done in practice however it turns out to be preferable to workthrough an intermediate transformation given byz=c+gx(6.18)1+ abxwherea=r(1, bij’25, c—r, g=’i’• (6.19)The value of z is then mapped onto the p plane through the transformp =Wz++Y, (6.20)where=b’(a2—1)(ab—cg)(6.21a)— abc=g2 1)(’cag),(6.21b)4g — abc= (g +abc)(b+acg)— 2bg .(a2 +c2) (621c)..Jg — abcOptical Multilayers I 185Equation 6.18 is a linear fractional or MObius transform which has the importantproperty of mapping circles onto circles.’88 Hence, for a dielectric film, the transform of themeasured data points back to the z plane should result in a circular arc.If one assumes a perfect alignment and calibration then deviations from a circular arcfor an experimentally measured set of data are the result in an error in the calculated values ofW, X and Y. The data can then be fit to Eq 6.20 through an adjustment of{n, ,n2c; , c;}, (6.22)where n1 and 122 are the refractive indices of the topmost and the second topmost layer andC’ =--, C’ =.-. (6.23)P S Ap SThe main problems discussed in the last section have now been addressed. Rather thanadjusting the optical constants to fit all of the preceding data, the values of n and thecoefficients of the product of the matrices are adjusted until the spectra of the topmost layerhas the proper form. This factor helps prevent a propagation of the errors of the substrate.Also, as the data is presented in the form of a circular arc, it is relatively simple to project ontothe theoretical curve and to fit through nonlinear optimization.As previously mentioned, the above method can be applied to Eq. 6.17 rather than Eq.6.18. However, one advantage to the using the z transformation is illustrated in Fig. 6.14.Here the z-transforms of the values of p in Fig. 6.10 are presented. It can be seen that there isgraphical representation for a quarter-wave stack at this wavelength in the z- plane. This0.3N—0.2—0.7Figure 6.14 Projection of the theoretical data of Fig. 6.10 onto the z plane. The data alwaysprogress counter clockwise. The radius of the curves increase with a greater number ofdeposited layers. The value of the Si substrate is also shown.Optical Multilayers / 1861.30.8SiLow IndexHigh Index—I I I I—1.2—1.8 —1.3 —0.8 —0.3 0.2 0.7z (real)Optical Multilayers I 187representation differs for alternate forms of multilayer coatings. Hence the z-plane providesinformation on the nature of the multilayer and its imperfections. This cannot be said forworking in the x -plane which provides information on the arc length only.Fig. 6.15 shows the algorithm used for the solution of the optical thickness of eachlayer. This routine contains one more step than the previous one with the transformation ontothe z-plane. The routine was found to be successful when tested on the sample data. Themethod was then used to control the deposition of a quarter-wave stack at the HeNewavelength of the formAir I HLHLHLHLH I GlassThe target optical thickness of each layer was 158.2 nm.The ellipsometric results in the z-plane are shown in Fig. 6.16. The agreementbetween the experimental and theoretical curves is quite good even at the ninth layer. Table6.1 gives the determined values of the film thickness, refractive indices, and substrateparameters before and after the fitting the data after each layer deposition. The initial opticalthicknesses are all greater than 158.2 nm due to the finite time taken to rotate the targets outof position. The largest adjustment in the optical thickness occurs for the first layer. This isalso accompanied with a relatively large alteration in the substrate parameters. This affect isattributed in part to the initial deposition of an absorbing layer several monolayers thick ontothe silicon substrate, which we have observed through the ellipsometric trajectory.Another reason for the large adjustment is illustrated in Fig. 6.17. Here we present thecurves for the first three layers. By examining the beginning of the first arc we can see thatOptical Multilayers I 188Figure 6.15 Flow diagram for the first iteration of the z-transform method for the control ofthe deposition of optical multilayers.Optical Multilayers / 189EN0 S102Ta205Theor. Fit1.20.80.40.0-0.4-0.8-1.2 —-1.8Figure 6.16 Ellipsometric data in the z-planedeposited through the z-transform method.-1.4 -1.0 -02-0.6z (real)0.2 0.6for the layers in the quarter-wave stackTable6.1Initialandfinalopticalthicknesses,refractiveindicesandsubstrateparametersforaquarterwavestackdepositedattheHeNewavelength.TheellipsometrictransformisshowninFig6.160 = cI:LayerMaterialThicknessn(Si02)n(Ta205)C’s,C’C’(nm)I(initial)Ta205158.41.4722.1000.0000.0000.0000.0001(final)Ta205153.71.4722.096-0.027-0.0280.013-0.0142(initial)Si02158.31.4722.0960.342-0.112-0.2490.1142(final)Si02159.71.4742.0960.340-0.143-0.2500.1293(initial)Ta205159.01.4742.0960.022-0.1870.0310.1983(final)Ta205159.81.4742.0960.031-0.1780.0320.1894(initial)Si02158.41.4742.096-0.314-0.0760.1280.1574(final)Si02159.01.4712.096-0.292-0.0350.1290.1495(initial)Ta205159.11.4712.0960.405-0.297-0.2700.0385(final)Ta205159.41.4712.0710.406-0.289-0.2680.0356(initial)Si02158.71.4712.071-0.5030.3990.331-0.1416(final)Si02160.01.4712.071-0.4960.4060.330-0.1417(initial)Ta205160.41.4712.0710.342-0.665-0.2440.3637(final)Ta205162.71.4712.0500.337-0.663-0.2410.3718(initial)Si02158.81.4712.050-0.4460.6660.240-0.4278(final)S102159.51.4712.050-0.4410.6810.239-0.4279(initial)Ta205159.21.4712.0500.203-0.835-0.0120.5309(final)Ta205160.31.4712.0500.192-0.829-0.0040.534Optical Multilayers I 1910.50.30.10,EN-0.1-0.3 --0.5 —-1.2 -0.2z (real)Figure 6.17 Effipsometric data in the z-plane for the first three layers in the quarter-wavestack deposited through the z-transform method.the experimental points do not coincide with the start of the theoretical trajectory but at arelative angle of x. This is one drawback to the fitting routines in that as we are projectingo Si02D Tap5a-1.0 -0.8 -0.6 -0.4Optical Multilayers / 1921 .00.80.604-.C)a)a)0.20.07500 10000 12500 15000 17500 20000 22500 25000Wavenumber (cm-i)Figure 6.18 Experimentally measured and theoretically determined reflection spectrafor a 5 period (HeNe-15,800 cni1 ) quarter-wave stack deposited through the transformmethod. The theoretical curve is calculated using the final thickness for layer in Table6.1. Also shown is the theoretical spectra for an ideal stack.onto the theoretical curve, the radius of curvature is correct but not necessarily the arc length.This wifi manifest itself in a non-zero original reading. This effect is still seen in the secondtrajectory but not the third, indicating that the error is not necessarily propagating.The reflectance of the dielecthc mirror is presented in Fig. 6.18 along with twotheoretical spectra. The dashed line represents the target reflectance assuming all the opticalthicknesses were 158.2 nm. The solid line is calculated using the final theoretical values inTable 6.1. The theoretical curve is shifted downwards slightly towards the infrared, which is tobe expected given that the majority of the optical thicknesses are greater than 158.2 nm.Optical Multilayers I 193The theoretical spectra matches the experimental data quite well in the infrared and upto the HeNe wavelength (15,800 cm’). Above this point, the experimental curve appears tobe shifted downward at an increasing rate as we go into the ultraviolet (UV). This effect isattributed to dispersion in the optical constants which was neglected in the theoreticalcalculations. As dispersion is negligible in these materials in the near infrared, the resultsagree well in this region. In the visible-UV regions the value of n increases with increasingwavenumber resulting in a larger value of nd. This results in the side bands being spacedcloser together.At this point the z-transform method appeared to be much more successful than theprevious two methods. However it was felt that there were still two improvements whichcould be made. The first was to optimize the transform parameters at some point during thelayer deposition rather than at the end of the run. This would result in a final optical thicknessthat was closer to the target thickness. The second was to determine the optical thicknessfrom the experimental arc length, rather than from the theoretical curve. This would helpreduce the error resulting from a different starting angle. To simplify the procedure, the offseterror was simply subtracted off the determined value of nd. Though this is not strictly valid,as arc length is not conserved when transforming from the x to the z-plane, this should result ina first order improvement.The final algorithm for the control routines is shown in Fig. 6.19. In this case the userdecides at what point, fldm, during the growth of an individual layer that the deposition isOptical Multilayers I 194Figure 6.19 Flow diagram for the second iteration of the z-transform method for the controlof the deposition of optical multilayers.Optical Multilayers I 1951.00.80.60C)0•1-00.20.07500 10000 12500 15000 17500 20000 22500 25000Wavenumber (cm.1)Figure 6.20 Experimentally measured and theoretically determined reflection spectra for a 5period (HeNe- 15,800 ciii’) quarter-wave stack deposited through the revised z-transformmethod. The theoretical curve is calculated assuming a perfect stack.halted and the model parameters updated. The refinement procedure is repeated at theendpoint in order to update the substrate coefficients for the next layer.The experimental reflectance spectra for a quarter-wave stack identical in design to theprevious sample but deposited through the final control routine is shown in Fig. 6.20. Alsoshown is the theoretical spectra for a perfect stack. In this case, the reflection spectra is closerto the ideal than that in Fig. 6.18, indicating that the final algorithm is an improvement overthe previous one.In order to test the routines further, a Fabry-Perot filter was deposited. As discussed inChapter 2, a Fabry-Perot filter consists of a half-wave layer sandwiched between twoOptical Multilayers / 196quarter-wave stacks. As a result, the conditions for high transmission at the desiredwavelength require a high degree of matching between the two stacks.’89The design of the Fabry-Perot filter wasAir/UI!5LL/HL ,4 H/Glass.Hence the subroutines had to control the deposition of 21 quarterwave layers.The Fabry-Perot filter was deposited under the same conditions as the quarter-wavestack. Once the filter was removed from the deposition chamber, a colour shift along onedirection of the sample was observed. This effect was attributed to a non-uniform thicknesswhich, in turn, was attributed to a non-uniform deposition flux which is inherent in magnetronsputtering.’90 This effect was not noticeable to the same degree for the quarter-wave stack dueto the lower number of layers.One solution to the above problem would be to design a mask to allow for a uniformdeposition across the surface. As this would result in a decreased deposition rate, anotherpossible solution would be to have the targets also move along the radial direction of thechamber. However both these procedures would be quite time consuming.As the beam-width of the spectrophotometer was approximately 7 mm the non-uniformthickness had the effect of broadening the transmission peak in the measured spectra. Inorder to compensate for this factor, a 2 mm wide slit was placed in front of the filter. Theslit was positioned relative to the sample by finding the maximum transmission through thefilter for a HeNe laser. The resulting position on the filter corresponded, within a 2 mm error,to that of the monitoring laser.Optical Multilayers / 1971.00.80riCl)IE0.40.20.07500 11000 14500 18000 21500 25000Wavenumber (cnr)Figure 6.21 Experimentally measured and theoretically determined transmission spectra for a5 period (HeNe- 15,800 cm’) Fabry-Perot filter deposited through the revised z-transformmethod. The theoretical curve is calculated assuming a perfect stack.The experimental and the theoretical spectra for the Fabry-Perot filter are shown in Fig.6.21. The fit between the two spectra is fairly good, however, there are a number ofdiscrepancies, the most important being those at the HeNe wavelength (632.8 nm). Oneproblem is that the peak transmission is too low, 66 % rather than the theoretical 95 % (theideal transmission is less than 100 % due to the glass substrate). This can be in part attributedto the non-uniformity of the sample and the finite bandwidth of the spectrophotometer (1 nm)given that a measurement with a .5 mm beam-width HeNe laser resulted in a transmission of75 %. The measured FWHM of 17 nm is also larger than the ideal 6 nm.Optical Multilayers I 198One potential source of the above errors can be observed by examining a number ofthe theoretical fits in the z-plane to the experimental data (Fig. 6.22). The first layer presentedis the tenth which, ideally, is a half-wave (316.4 nni) thick. A good theoretical fit to the datais achieved for this important layer. However, a problem arises with the next layer. At onepoint along the trajectory, the experimental data points can be seen to increase in radius thencurl back along the theoretical curve.In order to compensate for the above problem, the routines reject transformed datapoints which are a percentage greater than the theoretical radius. Under these circumstancesthe routines revert to the timing method until the data points fall back onto the theoreticalcurve. From Fig. 6.22, it can be seen that for the high index of refraction layers thisproblem becomes more serious with an increasing number of layers. For the fmal layer (Si02), however, the data is continuous along the entire theoretical curve.The source of the error illustrated in Fig. 6.22. can be understood by examining thetheoretical trajectory of the last two layers of the Fabry-Perot filter in the complex p plane(Fig. 6.23). The data points are spaced 4 nm apart and the positions on the high refractiveindex trajectory corresponding to four different optical thickness are also presented.Fig. 6.23 shows that there are two regions of insensitivity in terms of ap/and; the firstis approximately between 8 and 36 nm, and the second approximately between 96 and 140nm. As the absolute rate of change of z with respect to optical thickness is practicallyconstant in these regions, the value of z/ap is expected to be large. Hence smallOptical Multilayers I 199b1Figure 6.22 Ellipsometric data in the z-plane for a number of the layers of the Fabry-Perotfilter deposited through the revised z-transform method. The theoretical curve is calculated1.751.250.750.25—0.25—0.75—1.25—2.00 —1.50 —1.00 —0.50 0.00z (real)0.50 1.00assuming a perfect stack.Optical Multilayers I 200o Ta205o Si0236-8-0.0 0.2 0.4 0.60.800.650.500.350.200.05—0.10 ——0.8 —0.6 —0.4 —0.2 0.8Rho (real)Figure 6.23 The theoretical trajectory in the p plane of the last two layers of the Fabry-Perotfilter. The data points are spaced 4 urn apart. The optical thickness of the tantalum oxidelayer is presented at a number of points along the curve.measurement errors, small errors in the model parameters or film imperfections wifi lead tolarge errors in the value of z. These effects can clearly be seen in Fig. 6.22. The fmal Si02layer is free of these regions resulting in good overall fit.Though one of the main problems cited in the section on the projection method appearsto be carried through in the z-transform, it is less problematic in this technique. Oneadvantage of the z-transform method for dielectric films is that the data points should ideally alllie on the same circle. As a result, one can reject data points whose radius is greater or lessthan the theoretical value by some predetermined value. This simplifies the optimizationOptical Multilayers I 201procedure due to the reduced number of local minima. Therefore reasonable values could stifibe achieved allowing for the good fits of the low index of refraction layers.Since, however, an ideal fit is never achieved, Fig. 6.22 shows that the possibilityexists of errors in the model parameters or misalignment and calibration errors. One otherpossible source of error which also must be considered is the effects of imperfections in thefilm itself. In order to determine this, a number of sets of data for the nineteenth layer weregenerated assuming a linearly decreasing refractive index gradient or some degree of surfaceroughness. The data were then fit to a theoretical curve in the z-plane using the aboveroutines. The starting parameters where those used to generate the theoretical data. In thecase of the inhomogeneous films the refractive index at the midpoint of the layer was used.Fig. 6.24 shows the optimization results for a set of data with a refractive indexgradient from 2.15 to 2.05. The data sets with less inhomogeneity resulted in better fits. Alsoshown is the actual data for the nineteenth layer, displaced by a constant factor for comparisonpurposes.The above set of tests were reperformed on a number of sets of data with a surfaceroughness which was a percentage of the total thickness. The void fraction of the surfacelayer was 50 %. One set of results are also shown in Fig. 6.24 for the case where the surfaceroughness was 10 % of the total thickness. In this case the above effects are less than that forexperimental case.Optical Multilayers / 2021.501.000.500.00—0.50—1.00—1.50—1.75 —1.25 —0.75 —0.25 1.25z (real)Figure 6.24 The optimized fits to two generated sets of data in the z-plane for the nineteenthlayer of the Fabry-Perot filter. The first assumes 10 % inhomogeneities and the second has asurface roughness layer equal to 10 % of the total thickness. The optimization model assumesan ideal film. Also shown is the experimental data. The curves have been offset forI I I ICCExper. Data.Inhomeg.RoughnessTheor. FitI I0.25 0.75presentation purposes.Optical Multilayers I 203The imperfections in the two models shown in Fig. 6.24 are somewhat large for amaterial such as tantalum oxide especially considering that the layer was deposited underconditions where a zone-T microstructure would be expected. As a result, it is possible thatthe errors in the fit are in part due to imperfections in the instrumentation or problems in thealgorithms.Miscalibration or misalignment errors are the result of limitations in the design of thein-situ ellipsometer. One improvement in the instrumentation would be to increase the angularresolution of the polarizers to that of the ex-situ machine (.005°). Another possible source oferror is the birefringence of the port windows. Though this effect is reduced through thecalibration routines, it would be better to deal with the problem at the source. Since thedevelopment of the in-situ ellipsometer, a low birefringent window material developed atAT&T labs’9’ has become commercially available. One fmal improvement to the instrumentwould be to have the angle of incidence determined through some method other than ameasurement off the Si substrate, as this procedure does not allow for an independentcalibration check.Another possible source of error are the optimization routines themselves. Thetechniques used in this project were kept fairly simple as the goal was to demonstrate a proofof principle, rather than deposit state of the art optical coatings. One disadvantage to the abovetechnique is that the outlier points are ignored. More robust routines and careful weightingcould be applied to achieve a more realistic fit. Also, we have not taken full advantage of theform of the z-transform in the optimization routines. A more sophisticated mathematicalOptical Multilayers I 204treatment could be used to eliminate more of the local minima ( such as when the phase angleis incorrect).Even if the above improvements are implemented they cannot handle the case where anendpoint lies in the a region of insensitivity. Though the timing method can in part compensatefor this factor, as previously discussed, the assumption of a constant deposition is not alwaysvalid. A potential solution is to use more than one wavelength. At the beginning of each layerdeposition the software can choose the optimum monitoring wavelength. Multiwavelength in-situ effipsometers are now commercially available.’92One final note should be made on the lack of adaptive routines which are often requiredto deposit high quality optical multilayers. As previously mentioned, each type of opticalmultilayer system has its own set of curves in the z-plane. It would interesting to see aftereach layer deposition, if it would be possible to recalculate the required thicknesses of theremaining layers in order to achieve the final trajectory and if this correspondingly would givethe correct reflection and/or transmission characteristics for the system.6.4 Optical Monitoring of Absorbing CoatingsOnce the algorithms were developed for dielectric routines, it was necessary to extendthe routines in order to be able to monitor and control absorbing layers. As discussedpreviously, determining the layer thickness and optical constants for absorbing films isinherently more difficult than that for dielectric coatings due to the additional unknown at eachdata point.Optical Multilayers I 205For single layers on a substrate a technique that is often used is to solve for two datapoints at once.193’4 In this case, there are an equal number of equations and unknownsallowing for the employment of such numerical techniques as the Newton-Raphson method.These techniques are time consuming and often highly sensitive to noise. In addition, theygenerally require a knowledge of the substrate to a high degree of precision making thetechniques unsuitable for multilayers.A method has been developed for superlattices which allows for the solution of boththe optical constants and the layer thickness.195 This technique has been applied primarily fordetermining alloy fractions in such materials as aluminum gallium arsenide. However thetechnique requires prior knowledge of the optical constants as a function of alloy compositionand cannot deduce these values independently. As a result, this method is not suitable for suchmaterials such as carbon which can take on a wide range of values.The method for determining the optical constants and the thickness of the films used inthis thesis was essentially the same as that for the transparent films, that is project onto thetheoretical curve then use an optimization routine to determine the optical constants moreprecisely. Of course this requires some estimate of the optical constants prior to deposition,however, with a well controlled system, this should not present a problem.Though the above technique proved problematic for dielectric multilayers with morethan ten layers, the same difficulties do not exist for 3 to 4 layers of partially absorbingmaterials. In this case the path in the p plane is generally more well behaved due to thedampening of the interference effects. The use of z-transforms is often unnecessary underOptical Multilayers / 206these conditions and a modified version of the projection method can be used. In thistechnique one projects onto the theoretical curve generated by Eqs. 6.5 and 6.6 and performsthe optimization on a single layer using the set of parameters given in Eq. 6.22.The method was tested using two carbon films deposited onto silicon. The first filmwas deposited at 1 Pa in argon at 100 W while the second was deposited at the same pressureand power but with a 33% CH4 I 67% Ar sputter gas mix.Fig. 6.25 shows the experimental data and theoretical fit for the carbon film depositedin pure argon. The resulting optical thickness was determined to be 160.9 nm and the opticalconstants (2. 19,.337). In addition, theoretical trajectories for dielectric films of the sameoptical thickness with refractive indices of 2.1, 2.19 and 2.3 are also shown. The trajectoryof the absorbing coating is clearly distinct from the three dielectric curves, indicating that thepresence of absorption can be detected by observing the trajectory in the complex plane.Fig. 6.26 shows the initial trajectories of Fig. 6.25 in greater detail. The first datapoint is not that of the silicon substrate due to the presputtering of the target before deposition.Initially all of the dielectric trajectories essentially lie on the same curve. However theabsorbing film has a clearly distinct initial path. Hence the effects of absorption can bedetected for relatively thin coatings.Initially, the experimental trajectory of Fig 6.26 does not follow the theoretical curve.This factor is attributed to an intermediate layer between the silicon and carbon, possibly ofsilicon carbide.COptical Multilayers I 207a Exper. Data2.19,.377)2.1,0.0)— —— 2.19,0.0)2.3,0.0)0.0—0.1—0.2—0.3—0.4 -—0.5 ——0.30/—0.15 0.00rho (real)0.15 0.30 0.45 0.60 0.75Figure 6.25 Experimental data and theoretical fit with a refractive index of (2.19, .377) for acarbon film deposited in argon. Also shown are the theoretical trajectories for three dielectricfilms.0.00—0.05—0.10—0.15—0.20—0.25 —0.24 —0.23 —0.22 —0.21rho (real)—0.20Figure 6.26 The initial values of the data and models presented in Fig. 6.26.—0.0 ——0.1_____—0.2—0.3—0.4—0.5—0.6—0.7—0.8—0.9 ——0.3Figure 6.27 Experimental data and two theoretical fits to a carbon film deposited in 33 %CH4/67%Ar.Fig 6.27 shows the experimental ellipsometric trajectory of the film deposited in a 33%CH4 I 67% Ar sputter gas mix. Also show are two theoretical fits. One was accomplished bysetting the value of k equal to zero and the other through allowing k to vary.It is interesting to take note of the difference in the optical thickness of the two layers,1547 vs. 1569 angstroms, which is just over a percent difference. This illustrates howellipsometric measurements are relatively insensitive to small amounts of absorption in thefilms. However, due to the difference in the optical constants, the difference in the physicalthickness is closer to four percent.Optical Multilayers / 208I I I° Exper. DataTheor. Fit (1.75,.0168)— —- Theor.Fit(1.792,0.0)—0.1 0.1 0.3rho (real)0.5 0.7 0.9Optical Multilayers I 2096.5 ConclusionsA unique control routine has been developed which uses in-situ ellipsometry tomonitor and control the thickness of the individual layers. This technique can be used for bothdielectric and absorbing films. However, at this point, the routine develops problems fordielectric coatings with more than ten layers.This routine is well suited for the deposition of germanium carbide as it can alsomonitor the refractive index of the individual layers. This should allow for better qualitycontrol of films of this nature.One area of research that the above methods could be extended to is the study ofrnetal-dielecthc multilayers. This technique could be used both for control, and as a monitor todetermine effects of oxidation of the metal films.Chapter 7CONCLUSIONTwo of the stated objectives of this thesis were achieved: 1) the determination of theoptimum conditions for the deposition of diamond-like films through magnetron sputtering and2) the development of a control system for optical multilayers which can determine both thethickness of the individual layers and their corresponding optical constants. The third objectivewas not completely achieved in that a method to deposit germanium carbide over the entirealloy range was not accomplished. As a result, the refractive index range of this material waslimited from 4.1 to 3. However, a potential solution to this problem was found throughdepositing alternating layers of carbon and germanium which are thin on the order of thewavelength of interest.The thesis results showed that the best diamond-like films were deposited at the lowerdeposition pressures. The increase in transparency at the higher pressures appeared to be, inpart, due to hydrogen incorporation and the presence of a polymer phase in the films. Inaddition, these films were relatively soft and were porous if a substrate bias was not applied. Itwas determined that the amount of hydrogen incorporation required for the lower pressurefilms depended upon the degree of trade-off between the hardness and the transparency.The optical properties of the carbon nitride films were intermediate to those of thehydrogenated and unhydrogenated films. Since these films have a hardness comparable to thehydrogenated films, they do not appear to have any special advantage. However, given theConclusion /211relatively high deposition rates of these films they may ultimately prove to be the most usefulfrom a commercial point of view; assuming that the adhesion problems can be overcome.The work on the in-situ ellipsometric monitoring and control of films should bedeveloped further. One area of development would be to increase the robustness of theoptimization routines. This would allow for the deposition of more layers and relax thetolerances on the initial guesses of the optical constants. 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Aspnes, L.T. Florez, B.J. Wilkens, J.P. Harbison, and R.E.Ryan, J.Vac. Sci. Technol. A 7, 3291 (1989).191 G.N. Maracus, J.L. Edwards, K.Shiralagi, K.Y. Choi, R. Droopad, B. Johs andJ.A.Woollam, J. Vac. Sci. Technol. A 10, 1832 (1992).192 M.Yamamoto and T. Namioka, Appi. Opt. 31, 1612 (1992).193 S. Sarvada, M.D. Himel, K.H. Guether and F.K. Urban, Proc. Soc. Photo-Opt. Instrum.Eng. 1270, 133 (1990).194 D.E. Aspnes, J. of the Opt. Soc. Am. A 10,974(1993).195 P.S. Hauge, Surf. Sci. 56, 148 (1976).196 P.S. Hauge and RH. Dill, Optical Communications 14,431(1975).Appendix AIN-SITU ELLIPSOMETER ALIGNMENT AND CALIBRATIONA.1 Alignment and CalibrationFor a rotating compensator ellipsometer the light intensity incident upon thephotodetector can be written as195I(t)=10(1+a2cos2o t+b2 sin2ot+a4•cos4cot+b4sin4ot), (A.1)where (X, is the frequency of rotation of the compensator and 1 the dc intensity. Theharmonic coefficients can be written in tenns of the anayizer angle A and compensator defectparameters, q,r and s through the relations:’96-2r(vtanA)sin2A + 2s(cos2A + p.)a2 = (A.2a)2 + q(vsin2A + p.cos2A)— 2r(vtanA)cos2A + 2s(sin2A + v)b2 — , (A.2b)2 + q(vsin2A + j.tcos2A)(2-q)(p.cos2A - vsin2A)a4 = , (A.2c)2 + q(vsin2A + p.cos2A)(2-q)(p.sin2A + vcos2A)b4 = (A.2d)2 + q(vsin2A + p.cos2A)whereAppendix /224= cos2P — COS2NI, (A.3a)1 —cos2Pcos2’qi= sin 2P sin 2rqi COSA(A.3b)1 - cos2P•cos2qcand where P is the polarizer angle and qr and z\ the ellipsometric parameters.The calibration routine used in this thesis requires a metallic sample. In this caselinearly polarized light wifi have its polarization preserved upon reflection if and only if it isaligned to the p or s axis. Under these circumstances the paramenters (ii,) = (± 1,0) and themagnitude of the coeffiecents can be written asI 2 2 4s(l+2II+.L)(A4a)(2+qicos2A)Ja +b= (2— q)22(A 4b)(2+qjicos2A)The calibration routine is then as follows. The polarizer is first aligned to the p-axiswhere the magnitude of the second harmonic is at a minimum and equal to zero. Next theanalyzer is aligned to the s-axis where the magnitude of the fourth harmonic is at a maximumand ideally equal to one. The minimum in the second harmonic is sharp and can be foundsimply by searching for it. The maximum in the fourth is broad and a quadratic fit is applied todata points about the maxiumum.Appendix /225Once the polaizer and analyzer angles have been determined the compensatorextraordinary axis must be calibrated. This is detemined by adjusting the compensator axisuntilb4 =0.A.2 Window CorrectionsThe inclusion of vacuum port windows causes complications due to the stessbirefrengence in the window material. If this factor is assumed to be small the Jones matrix ofeach window in the sample p and s axis orientation is given asT=+ia 1, (A.S)L i3 1—ia]where a and 3 represent first order effects. As the sample itself can be represented asEP.c 01S= Lo iI’ (A.6)the combined window sample system is written asS’ = T01 S .T(A.7)To the first order, equation A.7 can be written in matrix form as=p.(l+ia) i.(p,.131+13j1 (A.8)(1—ia) jAppendix /226In Eq. A.8, [3 and I3 represent the terms for the input and output windows respectivily and ois equal to a + c. Through the use of a bilinear transformation, the exit polarization canbe written asxSo= (l—k)•x3+i.(p51013) (A.9)i(pj31 + + p(1+zx)where= TanP.(A.1O)By expanding and retaining terms to the first order the actual complex reflectance ratio can bewritten as=—i0x51+ p+i(I31/x—13x — 2x). p; + i(130/x5)p2, (A.11)where s’ is the measured complex reflectance ratio. If the polarizer is aligned to 45° thenthe above equation can be simplified to=5—iI302icp+ ,12. (A.12)The presence of the windows can also affect the calibration results. To illustrate this,consider the case where the polarizer angle is close to zero. Under these circumstancesequation A.9 can be written as—p5P+ipf31+i30— 1—ia (A.13)Appendix I 227which, to the first order, can be simplified top3,.P+ pJ, + i(p3P+pj + I3). (A.14)For light with its major axis close to the s-axis and which is only slightly effiptically polarizedEq. 2.4 can be writen asX0+i. (A.15)Therefore Eq. A.15 can be represented through(A.16a)(A.16b)Therefore, as one searches for a zero in Eq. A.4a the calibration routine will give improperangles for A and P. The angles will deviate from the actual angles A0 and P0 by the amounts(A.17a)(A.17b)As the above equations are sample dependant the system can stifi be calibrated through asuitable choice of two different substrates. If the difference in the complex reflectance ratios islarge, then one does not need to be able to measure these values to a great deal of precisionand the system can be calibrated through solving the following matrix:[_Psli 0 Psir ii—p31 1 p11 01I P2I 0 p2T 1[_p 1 P321 ojThis procedure also solves for f.Appendix /228P0A0— psli P1A1— Psir—p32iP2—ps2rP_(A.18)

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