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Characterization of inconel/carbon multilayer mirrors for 45 Å wavelength Aouadi, Mohamed Samir 1994

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CHARACTERIZATION OF INCONELICARBONMULTILAYER MIRRORSFOR 45 A WAVELENGTHbyMOHAMED SAMIR AQUADIB.Sc., University of Constantine, 1986M.Sc., University of Ottawa, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDepartment of PhysicsWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIADecember 1994© Mohamed Samir Aouadi, 1994In 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.Department of Pi-)’)S Ic ,(Signature)The University of British ColumbiaVancouver, CanadaDate b?cei I ‘1’19-DE-6 (2/88)ABSTRACTThis thesis reports on the study of x-ray mirrors that operate at normal incidencefor 45 A wavelength used in applications such as x-ray microscopy, x-ray astronomy, xray lithography, x-ray imaging, and x-ray lasers. These mirrors are fabricated byalternately depositing two materials of different scattering factors to form a multilayerstructure. A theoretical treatment to identify new combinations of materials for thesemirrors was provided. Carbon and inconel were then selected for ‘low index’ and ‘highindex’ layers, respectively, in the multilayer system.The thin film laboratory at U.B.C. was set-up for x-ray multilayer research byautomating a sputter coater to allow for the deposition of multilayers and by developingthe appropriate software for data analysis. The optical and structural properties, thechemical composition, and the thermal stability of the deposited materials were measuredas a function of argon pressure and substrate bias voltage using X-ray PhotoelectronSpectroscopy (XPS), X-ray Diffraction (XRD), Grazing X-ray Reflectometry (GXR), andSpectroscopic Ellipsometry (SE). Multilayers grown at a low pressure and a moderatesubstrate bias (—40 to —80 V) were found to be the most suitable for x-ray reflectors.Also, samples for second order reflection (period = 45 A) were found to be more stablethan samples for first order reflection (period = 22.5 A).In situ ellipsometry was used to monitor the deposition of single layers andmultilayers of inconel and carbon. Valuable information was obtained regarding the earlystages of film growth, interdiffusion at the interfaces, porosity of the films, etc. Thecoalescence thickness of inconel was found to be 10 A. Interdiffusion was found to occurat the ‘carbon-on-inconel’ interlace because of the rough underlying inconel layer but notat the ‘inconel-on-carbon’ interface because of the smooth underlying carbon layer.Interdifusion at the ‘carbon-on-inconel’ layer was also found to increase with the numberof layers. The control routine worked well. However, timing was found to better controlthe reproducibility of the thickness.IIITABLE OF CONTENTSAbstract iiTable of Contents ivList of Tables viiiList of Figures xList of Symbols xixAcknowledgements XWChapter 1 Introduction to X-Ray Multilayers 11.1 General 11.2 Review 11.3 Goal of this work 41.4 Main contribution of this thesis 61.5 Chapter organization 6Chapter 2 Selection of Materials for Deposition 82.1 Introduction 82.2 X-Ray mutlialyer theory 82.2.1 Interaction of soft x-rays with matter 82.2.2 Calculation of multilayer reflectivity 92.2.3 Rough interfaces and transition layers 132.3 Selection of materials for x-ray multilayers 14Chapter 3 Experimental Procedure 21iv3.1 Introduction 213.2 Sputtering 213.2.1 Processes involved in sputtering 223.2.2 Description of sputter apparatus 233.3 X-ray photoelectron spectroscopy and Augerelectron spectroscopy 273.3.1 Description of apparatus 303.4 Ellipsometry 333.4.1 Polarized light 343.4.2 Description of ex situ ellipsometer 403.4.3 Description of in situ ellipsometer 433.5 X-ray diffractometer 473.6 Nonlinear optimization 513.7 Linear regression analysis 56Chapter 4 Tungsten Films 584.1 Introduction 584.2 Experiment 594.3 Results and discussion 594.3.1 X-ray phototelectron spectrocopy 594.3.2 X-ray diffraction 684.3.3 Grazing x-ray reflection 684.3.4 Spectroscopic ellipsomety 74v4.3.4.1 Effective medium theory 754.3.4.2 Results and discussion 834.4 Conclusions 94Chapter 5 InconellCarbon Multilayers 975.1 Introduction 975.2 Experiment 975.3 Results and discussion 985.4 Conclusions 128Chapter 6 Optimization of Deposition Conditions 1296.1 Introduction 1296.2 Experiment 1296.3 Results 1306.4 Discussion 1496.5 Conclusions 154Chapter 7 In situ Ellipsometry 1557.1 Introduction 1557.2 Single layers of inconel 1587.3 Single layers of carbon 1657.4 Description of monitoring and control routine 1657.5 Multilayer deposition 1727.6 Conclusions 185Chapter 8 Conclusion 186viReferences 189vHLIST OF TABLESTable Page1.1 Largest experimental reflectivities for x-ray multilayer systems with anincident radiation of 45 A wavelength. 52.1 Optimized first order reflectivities of 300-layer multilayers of carbon/metalcompound with an incident radiation of 45 A wavelength (d=22.6 A). 192.2 Optimized second order refleotivities of 300-layer multilayers ofcarbon/metal compound with an incident radiation of 45 A wavelength(d=45.2 A). 204.1 Oxide thickness deduced from deconvoluted XPS spectra for tungsten films0.4 Pa, 2.0 Pa, and 4.0 Pa. 684.2 Properties of tungsten obtained from GXR analysis of a set of filmsprepared at 0.4, 2.0, and 4.0 Pa. 744.3 Properties of tungsten obtained from GXR analysis of a set of filmsprepared at 0.4, 2.0, and 4.0 Pa, but thinner than those in Table 4.2. 754.4 Spectroellipsometric results for films grown at 0.4 Pa. 874.5 Spectroellipsometry analysis of “thick” sample with a two layer modelconsisting of an oxide layer on top of a tungsten layer. 944.6 Spectroellipsometry analysis of “thin” sample with a two layer modelconsisting of an oxide layer on top of a tungsten layer. 954.7 XPS curved resolved data for thick samples grown at 0.4, 2.0, and 4.0 Pataken 1 1/2 months after deposition. 96yin4.8 XPS curved resolved data for thick samples grown at 0.4, 2.0, and 4.0 Pataken 3 months after deposition. 965.1 Properties of carbon and inconel layers obtained from GXR. 1025.2 Spectroscopic results for inconel films grown at 0.4 Pa. 1095.3 SE results for inconel film grown at 0.4 Pa, 1105.4 Spectroellipsometry analysis of “thin” and “thick” C samples with a two-layermodel consisting of a bulk layer and surface microroughness. 1125.5 Properties of inconel/carbon multilayers obtained from GXR analysis. 1236.1 Properties of carbon layers as a function of bias voltage, obtained fromGXR analysis. 1336.2 Spectroelllipsometry analysis of inconel samples as a function of biasvoltage, with a one-layer model. 1376.3 Spectroelllipsometry analysis of carbon samples as a function of biasvoltage, with a one-layer model. 1406.4 Measured first order reflectivities for 60-layer multilayers with a period of45 A deposited with different bias voltages. 1476.5 Measured first order reflectivities for 60-layer multilayers with a period of22.5 A deposited with different bias voltages. 149LIST OF FIGURESFigure Page2.1 Atomic scattering factors f1 and f2 for the elements in the soft x-rayrange. 102.2 Schematic cross-section of a multilayer structure. 112.3 Calculated reflectivities versus grazing angle of incidence for a 100 A thicktungsten film. 153.1 Cross-sectional view of planar magnetron sputter source used in thisstudy. 243.2 Diagram of the sputtering system, viewed from the front with the front door,substrate table, and shutter removed. 253.3 Schematic diagram of the photoemission process. 283.4 Schematic diagram of the Auger process. 293.5 Schematic diagram of (a) the side view and (b) the individual parts ofLeybold MAX 200 system. 313.6 Schematic diagram of the concentric hemispherical analyzer. 323.7 (a) A typical polarization ellipse. (b) Reflection and refraction of a planewave at a boundary between two dielectric media. 353.8 Optical layout of the spectroscopic ellipsometer. 413.9 Ellipsometer and its attachement to the sputtering chamber. 443.10 Functional block diagram of a rotating compensator ellipsometer. 453.11 Ellipsometric trajectory during the growth of a 300-layer inconel/carbonxmultilayer (15 A inconel, 30 A carbon). 483.12 Geometry of the Rigaku x-ray diffractometer. 504.1 XPS spectra for tungsten films prepared at (a) 0.4, (b) 2.0, and 4.0 Pa,associated with photoelectrons from the 4f712 and 4f512 shells using Al Koc xrays taken at a take-off angle of 90°. 604.2 Sampling depth versus take-off angle; 90° and 20°. 614.3 XPS spectrum for tungsten film prepared at 0.4 Pa associated withphotoelectrons from the 4rn and 4f shells using Al Koc x-rays taken at atake-off of 20°. 624.4 Deconvolution of the XPS spectra of tungsten films prepared at a pressureof 0.4 Pa. Data were taken with Al Koc x-rays taken at a take-off of 90°. 644.5 Structural model deduced for the tungsten film from XPS study. 664.6 Normalized grazing incidence reflectivity data for W films grown at 0.4, 2.0,and 4.0 Pa. 694.7 Experimentaly determined and theoretically calculated normalized grazingincidence reflectivity for W film grown at 0.4 Pa. 714.8 Experimentaly determined and theoretically calculated normalized grazingincidence reflectivity for W film grown at 2.0 Pa. 724.9 Experimentaly determined and theoretically calculated normalized grazingincidence reflectivity for W films grown at 4.0 Pa. 734.10 Normalized grazing incidence reflectivity data for a set of W films grown at0.4 Pa, 2.0 Pa, and 4.0 Pa, which are thinner than those in Fig. 4.8. 76xi4.11 Experimentaly determined and theoretically calculated normalized grazingincidence reflectivity for ‘thin’ W film grown at 0.4 Pa. 774.12 Experimentaly determined and theoretically calculated normalized grazingincidence reflectivity for ‘thin’ W film grown at 2.0 Pa. 784.13 Experimentaly determined and theoretically calculated normalized grazingincidence reflectivity for W films grown at 4.0 Pa. 794.14 Pseudodielectric function of a tungsten thin film grown at 0.4 Pa, referencedto as “thick” in the text. 804.15 Pseudodielectric function of a tungsten thin film grown at 0.4 Pa, referencedto as “thin” in the text. 814.16 Overlayer model used in the SE study. 844.17 Dielectric function (a) of thin ‘tungsten’ film obtained from the SE study; and(b) of bulk single crystalline tungsten. 864.18 Experimentally determined and theoretically calculated complex reflectanceratio for ‘thick’ W film grown at 0.4 Pa. 894.19 Experimentally determined and theoretically calculated complex reflectanceratio for ‘thick’ W film grown at 2.0 Pa. 904.20 Experimentally determined and theoretically calculated complex reflectanceratio for ‘thick’ W film grown at 4.0 Pa. 914.21 Experimentally determined and theoretically calculated complex reflectanceratio for ‘thin’ W film grown at 0.4 Pa. 924.22 Experimentally determined and theoretically calculated complex reflectancexnratio for ‘thin’ W film grown at 2.0 Pa. 935.1 Schematic of the 3-zone Lindberg tube furnace. 995.2 Experimentally determined and theoretically calculated normalized grazingincidence reflectivity data for two carbon samples of differentthicknesses. 1005.3 Experimentally determined and theoretically calculated normalized grazingincidence reflectivity data for two inconel samples of differentthicknesses. 1015.4 Experimentally determined and theoretically calculated normalized grazingincidence reflectivity data for two inconel samples using a three-layermodel. 1035.5 Pseudodielectric function of a carbon thin film referenced as “thick” in thetext. 1045.6 Pseudodielectric function of a carbon thin film referenced as “thin” in thetext. 1055.7 Pseudodielectric function of a inconel thin film referenced as “thin” in thetext. 1065.8 Pseudodielectric function of a inconel thin film referenced as “thick” in thetext. 1075.9 XPS spectra of Ni2 and C1 shells of as-deposited inconel/C bilayer usingAl Koc x-rays taken at a take-off angle of 90°. 1115.10 XPS spectra of Ni2 and C1 of as-deposited inconel/C bilayer using Al KocXIIIx-rays taken at a take-oft angle of 300. 1135.11 XPS spectra of Ni2 and C1 of as-deposited C/inconel bilayer using Al Kox-rays taken at a take-off angle of 90°. 1145.12 AES spectra of inconel/C bilayer after ion sputtering. The spectra depictsa KLL transition from C atoms in a carbide environment. 1155.13 Intensity of different x-ray photoelectron peaks normalized to silicon peakas a function of 1/sine for inconel/C bilayer after ion sputtering, where e isthe take-off angle. 1165.14 Overlayer model for inconel/C sample. 1185.15 Overlayer model for C/inconel sample. 1195.16 XPS spectra of Ni2 and C1 of C/inconel bilayer using Al Kc x-rays takenat a take-off angle of 90° after 5 minutes of ion bombardment. 1205.17 AES spectra of C/inconel bilayer after ion sputtering. The spectra depictsa KLL transition from C atoms in a pure graphite environment. 1215.18 XPS spectra of Ni2 and C1 of C/inconel bilayer using Al Kc x-rays takenat a take-off angle of 90° after 5 minutes of ion bombardment. 1225.19 Normalized grazing incidence reflectivity data for a 10-layer multilayer asdeposited and at different annealing temperatures. 1245.20 GXR data for a 30-period multilayer (a) in the theoretical ideal case, (b) forthe theoretical fit, and (c) for the experimental data. The curves werearbitrarily shifted for the sake of viewing. 1255.21 Theoretical reflectivity of multilayers for 45 A radiation as a function of thexivnumber of periods. 1276.1 Normalized grazing incidence reflectivity data for inconel samples grownwith different bias voltages. 1316.2 Normalized grazing incidence reflectivity data for carbon samples grownwith different bias voltages. 1326.3 Measured (full curve) and calculated (dashed curve) reflectivity versusgrazing angle for an inconel film grown with a substrate bias of —40 V. 1346.4 Real part of pseudodielectric function of inconel thin films grown withdifferent bias voltages. 1356.5 Imaginary part of pseudodielectric function of inconel thin films grown withdifferent bias voltages. 1366.6 Real part of pseudodielectric function of carbon films grown with differentbias voltages. 1386.7 Imaginary part of pseudodielectric function of carbon films grown withdifferent bias voltages. 1396.8 XPS spectra of Ni28 of as-deposited C/inconel bilayers grown with a biasvoltage of (a) —40 V and (b) —130 V using Al Koc x-rays taken at a take-offangle of 90°, and (c) —130 V at a take-off angle of 300. 1416.9 Plot of the Ni/Cr composition ratio deduced from XPS measurements as afunction of bias voltage for C/inconel bilayers whose period is 22.5 A. 1436.10 Normalized grazing incidence reflectivity data for 60-layer multilayer mirrorswith a period of 45 A, deposited with different bias voltages. 146xv6.11 Normalized grazing incidence reflectivity data for 60-layer multilayer mirrorswith a period of 22.5 A and deposited with different bias voltages. 1487.1 Real-time ellipsometric trajectory recorded during the deposition of inconellayers grown with a substrate bias of —40 V. 1597.2 Plots of n and k versus thickness for an inconel layer grown with asubstrate bias of —40 V. These results were obtained by fitting theellipsometric data using Yamamoto’s routine. 1607.3 Film thickness versus time for an inconel layer grown with a substrate biasof —40 V. These results were obtained by fitting the ellipsometric data usingYamamoto’s routine. 1617.4 Volume fraction versus time for an inconel layer grown with a substrate biasof —40 V. These results were obtained by fitting the ellipsometric data usingan EMA model. 1627.5 Thickness versus time for an inconel layer grown with a substrate bias of—40 V. These results were obtained by fitting the ellipsometric data usingan EMA model. 1637.6 Real-time ellipsometric trajectory recorded at the early stages of thedeposition of an inconel layer with a substrate bias of —40 V. The solid lineis the theoretical trajectory assuming the growth of a homogeneouslayer. 1647.7 Real-time ellipsometric trajectory recorded during the deposition of inconellayers with different substrate bias voltages. 166xvi7.8 Volume fraction versus time for an inconel layer grown with differentsubstrate bias voltages. 1677.9 Real-time ellipsometry data for carbon layers. 1687.10 Schematic diagram of the sputtering system. 1707.11 Real-time ellipsometric trajectory recorded during the deposition of a 10-layer inconellcarbon multilayer. 1737.12 Enlargments of the ellipsometric trajectory in Fig. 7.11 showing (a) thecarbon-on-inconel interface and (b) the inconel-on-carbon interface. 1747.13 Real-time ellipsometry trajectory recorded during the controlled depositionof a 100-layer inconel/carbon multilayer. 1767.14 Thickness determined from ellipsometric data in Fig. 7.13. 1777.15 Experimental and theoretical GXR measurements for a 100-layerinconel/carbon multilayer. 1787.16 Real-time ellipsometric trajectory recorded during the deposition of a 100-layer inconel/carbon multilayer by timing. 1807.17 Thicknesses obtained from ellipsometric data as a function of the layerposition in the stack. 1817.18 GXR measurements recorded for a 100-layer inconel/carbon multilayerdeposited by timing. 1827.19 Theoretical GXR data for a 100-layer inconel/carbon multilayer depositedby timing. The GXR data was simulated with the thicknesses obtained fromellipsometric data. 183xvii7.20 Theoretical GXR data of a 100.1ayer inconel/crbon multilayer. 184xviiiLIST OF SYMBOLSA Complex field vectorA0 Avogadro’s numberAES Auger Electron SpectroscopyB Ellipticity of polarized lightC Covariance matrixD Displacement fieldDW Debye-Waller factorE EnergyEMA Effective Medium ApproximationF Surface height distributionFe Fraction of photoelectrons detectedG HessianGXR Grazing X-ray ReflectionIntensityJ Fraction of electrons detected by the analyzerK Correlation matrixL High index materialL’ Low index materialM Concentration of atoms/cm3M0 Molecular weightN Complex refractive indexxixNmjn Minimum number of periods to obtain a useful normal incidence reeflectivityP Dipole momentQ Azimuthal angleR ReflectivityS Atomic sensitivity factorSE Spectroscopic EllipsometryTb Student t numberU Number of data pointsV Electric Potential (Voltage)Spectrometer work functionX Electric field vectorXPS X-ray Photoelectron SpectroscopyXRD X-Ray DiffractionY X-ray fluxZ Atomic numbera Model parameter in curve-fittingcoefficient used to calculate azimuthal angle Qcoefficient used to calculate azimuthal angle 0bk coefficient used to calculate ellipticity Bc Speed of lightd Period of multilayer coatingxxd0 Thickness of oxide top layerd1 Thickness of high index layerd2 Thickness of low index layere Charge of electronem Measurement errorf Atomic scattering factorf1 Real part of atomic scattering factorImaginary part of atomic scattering factorg Principal axis of the ellipseh Planck’s constantComplex number J(-i)Labelk Absorption coefficient (imaginary part of N)m Order of reflectionn Index of refraction (real part of N)o Gradientp1 Number of substrate passes for carboni2 Number of substrate passes for inconelq Lorentz depolarization factorInner radius of the concentric hemispherical analyzer in XPS apparatusOuter radius of the concentric hemispherical analyzer in XPS apparatusre Classical radius of an electron (2.82x1013cm)xxir12s Fresnel expression for reflection for s polarized lightr12 Fresnel expression for reflection for p polarized lightt Timeu Electron mean free pathv Number of parametersw Volume fractionx x-coordinatey y-coordinatez z-coordinate, measured perpendicular to substratez0 Mean surface heightF Standard deviationA Relative phase changeAa Average constant in expression for index of refraction of multilayer structure (fla1 -a)tan’P Relative phase attenuationNumber of degrees of freedomcx Angle of incidencex2 Angle of refractionCCB Pseudo-Brewster anglec, Principle anglexxiiDerivative of minimization functionf3 Thickness ratio in a multilayer structurePhotoexcitation probabilityConstant in expression for index of refraction (n=1-)Dielectric functionC Error tolerance11 Density8 Polarization of electric fieldTake-off angle for XPS detectort CoverageScreening parameterWavelength of radiationm Mean free path for photoelectronConstant in Levenberg-Marquardt methodIa Atomic photoionization cross-sectionv FrequencySecond derivative of minimization functionp Complex reflectance ratioa Root-mean square roughness of surfaceat Root-mean square roughness of surface for filma Root-mean square roughness of surface for substratePhase constantsxxiiiFilm phase thicknessx Square root of minimization functionNumber of atoms in a moleculeAngular frequencyxxivACKNOWLEDGEM ENTSFirst, I would like to express my sincere gratitude to my thesis supervisor Dr. R. R.Parsons for his continual guidance, support, encouragement and help during the courseof this work. It is also a pleasure to acknowledge all the support and help I have receivedover the years from my lab colleagues, especially Norman Osborne for emparting histechnical expertise to me, Glenn Clarke for his productive discussions related tospectroscopic ellipsometry, and Al Kleindschmit for his technical help with the in-situellipsometer.I am also grateful to the following parties for their collaboration in the completionof this thesis: Dr. P. C. Wong and Dr. K. A. R. Mitchell at the Department of Chemistry,UBC, for XPS measurements; and Dr. L. Da Silva at the Lawrence Livermore NationalLaboratories, Berkeley, for normal incidence reflectivity measurements at 45 Awavelength.Acknowledgement is also extended to all my friends for their continual support,especially Fionn Horgan, Naomi Richardson, Mohamed Boulfiza, and Anthony Clarke.I would like to express my deep gratitude to my parents, my sister Amina, and mybrother Riadh who have provided unfailing support and patience throughout the years.Finally, I would like to acknowledge the financial assistance of R. R. Parsons andof The University of British Columbia.xxvChapter 1Introduction to X-ray Multilayers1.1 GeneralThe need for devices with high reflectivities at soft x-ray wavelengths for newapplications such as x-ray microscopy, x-ray astronomy, x-ray lithography, x-ray imaging,and x-ray lasers has provided the impetus for intensive research and development in thefield of x-ray optics.1 However, at angles other than grazing angles, x-ray reflectivity fromthe surface of any material is negligible because the refractive index at x-ray wavelengthsis close to unity for all materials. Recent advances in thin film deposition technology haveenabled the fabrication of synthetic lattices consisting of alternating layers of very thin(<100 A) ‘high’ and ‘low’ index materials. Such multilayer structures provide highref lectivities due to constructive interference effects when the Bragg condition is satisfiedand may be regarded as artificial crystals having large spacings between the diffractingplanes.1.2 ReviewSoon after Von Laue discovered the diffraction of x-rays by crystals in 1912 thepotential of multilayer structures to extend the range of this phenomenon to longerwavelengths was proposed. In 1929 and 1930 the first attempts to fabricate x-ray mirrorswere unsuccessful because of technical limitations in producing high vacuums for thin filmdeposition.23 In 1935 and 1940 some of these limitations were overcome and Cu/Au1multilayer structures with periods of 100 A were fabricated.45 However, these structuresdecayed within a week due to interdiffusion of the layers. It was not until 1967 that thefirst stable reflectors were fabricated.6 These reflectors consisted of a stack of 200evaporated layers of Fe and Mg having periods of 30—50 A. Since then a large numberof material combinations have been used for the fabrication of x-ray mirrors with highref lectivities.The selection of a material combination for x-ray mirrors is guided by; (1) theresults of theoretical modelling in terms of the theoretical performance at the wavelengthof interest, and (2) the practical realization of the layered structure, since the constituentlayers need to be uniform in their thickness and composition and have sharp and stableinterfaces. High index materials that have been investigated include: tungsten, rhenium,platinum, rhodium, molybdenum, and alloys of these. The commonly selected low indexmaterials include: carbon, boron, silicon, and various compounds of these. Up to now,carbon/tungsten and carbon/tungsten-rhenium alloy were the most extensivelyinvestigated structures since they form very stable and smooth interfaces.79X-ray multilayer mirrors are usually fabricated by physical vapour depositiontechniques, i.e., electron beam evaporation ,b012 sputtering,13 laser evaporation, andmolecular beam epitaxy.’5 Amorphous films are usually associated with the smoothestsurfaces. The fabrication of fully crystalline multilayers by molecular beam epitaxy wassuggested as a means to produce stable interfaces which are essentially roughnessfree.15 However, no epitaxial grown multilayer structure is presently known whereby thetwo components have sufficient contrast to produce high reflectivity for soft x-rays.2In sputtering systems the reproducibility of layer thicknesses is usually controlledby timing. X—ray reflectometry11’18was used to control the thickness of the layers butwas only successful for a limited number of layers in a multilayer system.18 Morerecently, kinetic ellipsometry’9was used for closed loop control of film thickness but failedto achieve better accuracy than timing. Kinetic ellipsometry1922 was also used tounderstand the evolution of film growth and to obtain more detailed information on filmproperties. For example the coalescence thickness of tungsten was found to be about9A.Several groups have reported reflectivities of 50% at near-normal incidence forwavelengths greater than 120 A using Mo/Si multilayers.’5’225 Such reflectivities areclose to the theoretical values for an ideal structure with parallel, smooth, and sharpinterfaces. Multilayer mirrors operating at these wavelengths are presently fabricated invarious laboratories and have become commercially available (e.g., Energy ConversionDevices, USA).26 However, at shorter wavelengths (20—80 A) multilayer performance ismuch lower than that predicted from theoretical values for an ideal structure.27At the present time the main thrust of research appears to be towards (1)identifying practical applications for x-ray multilayer technology at large wavelengths, (2)pursuing basic research to improve the performance of multilayer structures at shortwavelengths, and (3) improving the quality of these structures for applications that requirehigh stablity when subjected to a large thermal load. Significant contributions to the fieldof x-ray multilayers have been made by dominant research centres, such as theLawrence Livermore National Laboratory (LLNL), the Lawrence Berkeley Laboratories3(LBL), the Ovonic Synthetic Materials Company (OSMC), the Optical Sciences Center atthe University of Arizona, AT&T Bell Laboratories, and the FOM Institute for Atomic andMolecular Physics, the Netherlands. Reviews of the work done at these centres andother centres have been published by Chakraborty,1 Barbee,28 Rosenbluth,29 andMichette.3°1.3 Goal of this workThe purpose of this thesis is to fabricate x-ray mirrors for operation at 45 Awavelength. The predicted theoretical reflectivity at normal incidence varies from 25%to 35% for 300-layer multilayers depending on the combination of materials. Table 1.1gives the largest experimental reflectivities obtained to date. These values are muchlower than the theoretical values which suggests that there is room for improvment. Ourlaboratory became interested in this particular wavelength through collaborative projectswith Dr. Luiz Da Silva at the LLNL, who is developing x-ray laser cavities. Recentexperiments at the LLNL have demonstrated the possibility of significantly amplifying theemission of soft x-rays.31 Calculations and preliminary tests have indicated that improvedmultilayer cavity mirrors would provide significant enhancement of x-ray laser output.32This thesis is divided into three major sections. The first section reports on thegrowth and analysis of tungsten which has been widely used for the high index layer inx-ray multilayers.28 The main reasons for this investigation were; (1) to develop myanalytical techniques for measuring the important parameters for x-ray multilayers(reflectivity, layer thickness, layer roughness, optical constants, chemical content, etc.),4Table 1.1: Largest experimental reflectivities for x-ray multilayer systems with anincident radiation of 45 A wavelength. This data was collected at the OSA topicalmeeting of x-ray multilayer structures, Jackson Hole, WY 1994.Affiliation Layer N umber ReflectivityCombination OfB i-layersLBL Cr/C 150 7.0%LBL NiCr/C 50 6.0%LBL Ge/C 200 5.0%LBL Ru/C 150 4.5%LBL Cr23/C 100 4.0%OSMC W/B4C 250 2.8%and (2) to devise computer programmes for data analysis. In the second section,ref lectivities of new pairs of materials are calculated at 45 A wavelength. lnconel (inconelis a nickel based alloy which has the following composition (by weight): Ni 57.7 (mm), Cr22.0, Mo 9.0 (max), Fe 5.0 (max), Nb and Ta 3.7 (max), Co 1.0 (max), Mn 0.5 (max), Ti0.4 (max), Si 0.4 (max), Al 0.4 (max), C 0.1 (max)) and carbon were selected fordeposition because of their theoretically high performance and their stability at elevatedtemperatures. Single layers, bilayers, and multilayers of these materials were depositedby dc magnetron sputtering and the physical and optical properties of the films weredetermined with the use of grazing x-ray reflectometry (GXR) and spectroscopicellipsometry (SE). These films were further investigated with x-ray photoelectronspectroscopy (XPS) and Auger electron spectroscopy (AES) to determine their chemicalcontent and to examine their interfaces. The effects of sputter pressure, substrate bias5voltage, and annealing temperature on the film properties were also investigated. In thethird section, in situ ellipsometry was used to (1) monitor and control film thickness and(2) to understand the growth process of inconel and carbon. Multilayer samples werethen sent to LLNL for reflectivity measurements at 45 A.1.4 Main contribution of this thesisThis main contributions of this thesis are listed below:(1) It provides a theoretical treatment to identify new materials for x-ray mirrors withparticular interest in operation at 45 A.(2) It develops the appropriate experimental and analytical techniques to set up thethin film laboratory at U.B.C. for x-ray multilayer research.(3) It presents a comprehensive study of the optical, chemical, and structuralproperties of single layers of tungsten, carbon, and inconel.(4) It presents a systematic investigation of the optical, chemical, thermal, andstructural properties of inconel/carbon multilayers as a function of the depositionconditions to optimize their performance.(5) It explores the capabilities of kinetic ellipsometry as a technique for closed loopcontrol of film thickness.1.5 Chapter OrganizationThis thesis is divided into eight chapters. Chapter I provides an introduction to thisstudy. Chapter II gives an introduction to x-ray multilayer theory. It also presents6theoretical modelling of the performance of new pairs of materials for short wavelengths(45 A) applications. Inconel was selected for a high index material because of its goodstability under high temperature conditions and because of its superior theoreticalperformance. Carbon was selected for a low index material because of very lowabsorption coefficient at 45 A and because it can be deposited as very smooth layers.Chapter lii describes the experimental procedures used in this investigation, It alsodiscusses the theoretical background of these procedures. Specific attention is given to;(1) the processes involved in planar magnetron sputtering, including thin film growth, (2)SE, XPS, and AES with an emphasis on the quantities of interest to the analysis of thedata provided by these techniques, (3) in situ ellipsometry equipment and the softwareroutines related to it, and (4) nonlinear optimization methodology used in data analysiscomputer programmes. In chapter IV the properties of tungsten films prepared by dcmagnetron sputtering are studied as a function of working pressure. In chapter V, singlelayers, bilayers, and multilayers of these materials, fabricated by sputtering, and theeffects of post-deposition annealing are investigated. In chapter VI single layers, bilayers,and multilayers of inconel and carbon fabricated with different bias voltages arecharacterized and the optimum deposition conditions for inconel/carbon are developed.The effect of ion bombardment during multilayer growth is discussed. In chapter VII, theresults of in situ ellipsometry are explored. In chapter VIII, the conclusions of this workare presented and suggestions for future work are given.7Chapter 2Selection of Materials for Deposition2.1 IntroductionThis chapter is divided into two major sections. In the first section, the theory ofthe interaction of soft x-rays with matter is briefly reviewed. This theory is used tocalculate the reflectivity of a multilayer structure at short wavelengths ( 45 A) in the idealcase of parallel, smooth, and sharp interfaces and then extended to the more realisticcase of rough and interdiffusing interfaces. The general criteria to obtain structures withhigh reflectivity are examined. In the second section, materials which have good stabilityat elevated temperatures are considered for x-ray multilayers. A pair of materials is thenselected for experimental study.2.2 X-ray multilayer theory2.2.1 Interaction of soft x-rays with matterThe optical properties of a material are characterized by the complex refractiveindex N defined in terms of its index of refraction n and its absorption coefficient k asfollowsN—ri—ik (2.1)In the x-ray region, the index of refraction n is slightly less than one and, therefore, N isusually written as8Mr A2N = 1-8÷1k = 1—2iu(f1÷1f2) (2.2)where M is the concentration of atoms/cm3,re=2.82x1013cm is the classical radius of anelectron, the wavelength of the radiation, and f1 and f2 are wavelength dependentatomic scattering factors given by33’4f (E)=z÷ 1__________(2.3)1 7t10hc E2—E’f (E)a (2.4)2 2trhcHere J.ta(E) is the atomic photoionization cross-section, Z is the atomic number, h isPlanck’s constant, and E is the the photon energy. The atomic scattering factor f=f1+i2is defined as the ratio of the amplitude of the electric vector scattered by an atom overthat scattered by a free electron. Values of the atomic scattering factors for the elementshave been tabulated by Henke35 for photon energies between 100 and 2000 eV. Thesevalues are plotted in Fig. 2.1.2.2.2 Calculation of multilayer reflectivityFigure 2.2 depicts an ideal multilayer structure with parallel, smooth, and sharpinterfaces. This structure is fabricated by alternately depositing two materials L and V90.01Figure 2.1: Atomic scattering factors f1 and f2 for the elements in the soft x-ray range.3540ATOMIC NUMBER100100.110Figure 2.2: Schematic cross-section of a multilayer structure.d111of different scattering factors. In Fig. 2.2, d1 and d2 designate the thickness of layers Land L’, respectively, and d is the period of the multi layer (d=d1+d2). The calculation of thereflectivity of such a multilayer structure has been treated in many textbooks on opticalfilms.3639 For completeness, the basic concepts are reviewed here.An electromagnetic wave incident on an interface is split into two waves: atransmitted wave propagating in the second medium (complex refractive index N2) anda reflected wave propagating back to the first medium (complex refractive index NJ. Thereflected amplitudes for polarizations perpendicular (r12) and parallel (r12s) to the planeof incidence are defined as follows:N1coseL-N2cccosa+N1cosa2-tco cccosa+Nwhere cx1 is the angle of incidence and a2 is the angle of refraction at the interfacebetween media 1 and 2, respectively. These angles are related by Snell’s lawIsina2N1si (2.7)The reflectivity from a multilayer system is calculated by applying recursively thefollowing expression for the amplitude reflectance of a single layer, for the s and ppolarizations:124’+rexp(2i4) (2.8)1+rr9’exp (2.z4)where r and rb are the amplitude reflectances of the top and bottom boundaries of thelayer, respectively. The film phase thickness 0 is given by27iNd1cosa (2 9)where d1 is the film thickness; and a1, the angle of refraction in the film.2.2.3 Rough interfaces and transition layersThe above theory is suitable for multilayer structures with parallel, sharp, andsmooth interfaces. However, in a real multilayer structure adjacent layers are separatedby a transition layer associated with interfacial roughness and interdiffusion between itsconstituting materials. For layer interfaces generated by sputtering, a good representationof the surface height distribution F(z) of a transition layer is given by a Gaussian profile401 e__z0)2/2 (2.10)v[2-awhere z is measured perpendicular to the sample surface, ; is the mean surface height,and a is the root-mean square roughness or “interface roughness.The reflected amplitude R from an interface with a transition layer is calculated bymultiplying the amplitude reflectances in Eqn. 2.8 by the Debye-Waller factor (DW), which13is obtained by taking the Fourier transform of F(z)4147EosinDW—exp(-( 1)2) (2.11)Eqn. 2.11 is valid under the assumption that the surface height distribution has agaussian profile and the slope of the surface irregularities are sufficiently small that effectssuch as shadowing and multiple scattering between irregularities at the same interfaceand polarization effects due to local variations in the angle of incidence can beneglected.1 The theory discussed above has been adopted by researchers”47thoughno systematic study was conducted to compare experimental data to the detailed theory.Fig. 2.3 shows the calculated reflectivities versus grazing angle of incidence for a100 A thick W film on a Si substrate for three (top) surface roughnesses: a=0, 4, and 8 A.The bottom surface is assumed to be sharp and smooth. In this thesis, interfacialroughness will be determined from GXR measurements. As we will see in a late chapter,GXR is a precise technique for the determination of roughness, film thickness, and opticalconstants.44472.3 Selection of materials for x-ray multilayersAs mentioned in the previous section, the ideal materials constituting a multilayerhave parallel, sharp, and smooth interfaces. In addition, these materials need to havea large difference in their refractive index to maximize the reflectivity at each interface.Also, materials should be chosen with melting points well above the operating14106 ISURFACE ROUGHNESS10 --____0 ANGSTROMS—— 4 ANGSTROMS104 8 ANGSTROMS103 - .Cl)C *.S102-- ..-....-*. . . .. . -100 -I I I I0 1 2 3 4 5 6Grazing Angle (Degrees)Figure 2.3: Calculated reflectivities versus grazing angle of incidence for a 100 A thicktungsten film.15temperature of the application. The performance of x-ray multilayers used as reflectorsof intense synchrotron radiation is greatly affected by the power load they are subjectedto, which may exceed 100 W/mm2 in the case of high-brilliance storage rings.48 Suchhigh power loads can increase roughness at the interfaces (usually throughcrystallization), cause interdiffusion of the layers, and alter the thickness of the layersthrough expansion or contraction. Preliminary results of Ziegler et al.48 have shown thatin the absence of active cooling the exposure of various multilayers to a power densityof 1 W/mm2 raises the temperature to 500°C and reduces the reflectivity by about a factorof two.Carbon has been widely used as the low index material in x-ray multilayers.Carbon is very stable at high temperature and it can be deposited with very littleroughness. Silicon has also been used by many groups; however, it is not appropriatefor synchrotron radiation applications since it melts at a relatively low temperature.49Multilayer combinations made of carbon and pure metallic elements have beengrown. However, in thermal treatment studies48 these multilayer structures weredestroyed due to interdiffusion and/or crystallization when annealed at temperaturesranging from 400°C to 700°C, depending on the materials used.46’5°In my search for new material pairs I considered various compounds and alloysfor the high index layers and, for the above-mentioned reasons, kept carbon for the lowindex layers. My search for suitable high index materials was biased towards alloys andcompounds for three reasons. First, alloys can have superior stability at high temperaturecompared to the elements which constitute them. Second, most of the previously16repeated work has concentrated on pure elements and, therefore, I felt there was agreater chance of making a significant advancement by exploring compounds and alloys.Third, thin films of alloys tend to be amorphous, and thereby, are expected to besmoother than polycrystalline pure metal films.17’51In the remaining chapter I give the results of calculated reflectivities of multilayerstructures where the low index material is carbon and the high index material is acompound or an alloy. I confined my computations to compounds and alloys which areknown to be stable at high temperature.49’52 Compound materials include carbides,nitrides, or suicides. Alloy materials include a mixture of the following transition metals:Cr, Mn, Fe, Co, Ni, and Cu. Multilayers whose high index material is one of thesetransition metals exhibit large reflectivities at 45 A and it is therefore expected thatmultilayers made of alloys of these materials would have a comparable reflectivity sincethe refractive index of the alloy would be a weighted average of the refractive indices ofthe constituent atoms.27I restrict my calculations to 300-layer multilayers which seems to be an adequatenumber of layers for two reasons: (1) good quality multilayers with reproducible layerthicknesses are practically achievable for this number of layers, and (2) this number islarger than the estimated minimum number Nmin (typically Nmjn = 100 at 45 A) of periodsrequired to obtain a substantial normal incidence reflectivity (> 15%). Nmin is given by53(2.12)Here, An and Ak are the differences in the optical components of the coating materials.17The reflectivity from a multilayer system is calculated by applying recursively thegeneral solution for the amplitude reflectance of a single film given by Eqn. 2.8. Therefractive index of each layer is calculated from Eqn. 2.2. At our wavelength of interest(45 A) the scattering factor of a compound is a weighted average of the scattering factorof the constituent atoms,27 which is given by Henke et al.54For normal incidence, the positions of maximum reflectivity are given by552d(1AaYfl7A (2.13)Here, d is the period of the multilayer; m, the order of the reflection; ?, the wavelengthof radiation; and Aa is given by55aPt6i(113t)82 (2.14)where & and 2 are factors that represent scattering by the metallic layer and carbon,respectively, and are defined in Eqn. 2.2; and is the thickness ratiod1(d-i-2). Theanalytical formula for the optimum thickness ratio I3 of a periodic structure wascalculated by Vinogradov and Zeldovich for an infinite number of layers. For a finitenumber of layers the optimum values of d and are found numerically using an algorithmthat scans through all of their possible values.55 Tables 2.1 and 2.2 list the thicknesseswhich give the largest reflectivities for first and second order reflectivities, respectively.I have listed only the multilayers with reflectivities larger than 25 % for first orderref lectivities and larger than 20% for second order ref lectivities.18Table 2.1: Optimized first order reflectivities of 300-layer multilayers of carbon/metalcompound with an incident radiation of 45 A wavelength (d=22.6 A).Metal Thickness Thickness ReflectivityCompound Of Metal Of CarbonCompoundCrN 9.5 A 13.1 A 42.4 %VN 9.5 A 13.1 A 39.7 %Cr32 9.3 A 13.3 A 37.2 %Inconel 625 7.7 A 14.9 A 36.9 %TiN 10.2 A 12.4 A 34.0 %Ta2N 6.3 A 16.3 A 27.6 %VC 10.0 A 12.6 A 27.4 %WC 6.3 A 16.3 A 27.3 %TaC 6.6 A 16.0 A 26.6 %In my thesis, I have decided to deposit inconel/carbon multilayers which, to myknowledge, is the first attempt to fabricate a layered structure with this combination ofmaterials. Inconel 625 is a nickel based alloy which has the following composition (byweight): Ni 57.7 (mm), Cr 22.0, Mo 9.0 (max), Fe 5.0 (max), Nb and Ta 3.7 (max), Co 1.0(max), Mn 0.5 (max), Ti 0.4 (max), Si 0.4 (max), Al 0.4 (max), C 0.1 (max).57 The reasonfor the choice of carbon has already been discussed. The choice of inconel is due to thefact that it is an alloy with excellent properties at high temperature. lnconel ischaracterized by good corrosion and oxidation resistance, and by high mechanicalstrength at elevated temperature (up to about 1000 °C).19Table 2.2: Optimized second order reflectivities of 300-layer multilayers ofcarbon/metal compound with an incident radiation of 45 A wavelength (d=45.2 A).Metal Thickness Thickness ReflectivityCompound Of Metal Of CarbonCompoundCrN 10.3 A 34.9 A 37.1 %VN 10.1 A 35.1 A 34.7%Cr32 9.8 A 35.4 A 32.7 %Inconel 625 8.6 A 36.6 A 31.4 %TiN 10.6 A 34.6 A 29.1 %VC 10.7 A 34.5 A 22.6 %Ta2N 8.0 A 37.2 A 20.2 %20Chapter 3Experimental Procedure3.1 IntroductionThis chapter describes the experimental procedures and equipment used in thisinvestigation. Section 3.2 describes the dc planar magnetron sputtering systems usedto fabricate samples. Sections 3.3, 3.4, and 3.5 report on the experimental proceduresinvolved in x-ray photoelectron spectroscopy, ellipsometry, and x-ray diffractometry.These techniques are used for the following reasons: (1) XPS to evaluate the chemicalcontent of the layers; (2) SE to determine the thickness of the layers and theirmicrostructural properties; (3) in situ ellipsometry to understand the growth process of thelayers and to control the thickness of the layers; (4) GXR to determine the thickness androughness of the layers and to test the performance of the films at 1.54 A wavelength.The last two sections, 3.6 and 3.7, discuss the theoretical models used in analyzing theXPS, GXR, and SE data; Section 3.6 reviews nonlinear optimization; section 3.7discusses linear regression analysis.3.2 SputteringMy film samples were fabricated by dc planar magnetron sputtering.13 Sputtering13and electron beam evaporation1012 are the two most commonly used techniques for thedeposition of x-ray multilayer coatings. Each method has advantages and disadvantages;however, in the case of x-ray multilayer deposition, sputtering is usually the method of21choice because it offers very reproducible and well controlled deposition rates. In generalsputter deposition is associated with the following advantages:* Excellent film uniformity.* Good adhesion at the substrate.* Smooth filmsIn the next section I give a brief review of the processes involved in do magnetronsputtering, followed by a description of the sputter apparatus.3.2.1 Processes involved in sputteringSputtering is a process whereby material is ejected from a ‘target’ surface as aresult of bombardment of the target by energetic particles. In the case of planarmagnetron sputtering, energetic ions are drawn to the target from a glow dischargeplasma by the application of a negative potential to the target. Secondary electronsejected during ion bombardment are accelerated away from the negative target surfaceand, thereby, acquire sufficient energy to ionize the sputter gas, in our case argon. Thisimpact ionization produces ions, thus leading to a self-sustained glow discharge.Momentum transfer from the argon ions to the target surface results in some of the targetatoms being ejected or “sputtered”. A substrate is positioned in front of the target tointercept sputtered atoms. The trajectory of the sputtered species from the target to thesubstrate depends on the pressure used during deposition. At low pressures (O.5 Pa)the mean free path in the sputter gas is between 10 to 15 mm and the trajectory of thesputtered species to the substrate is line-of-sight (essentially collisionless). At relatively22high pressures (3 Pa) the mean free path in the sputter gas is about 1 mm and thetransport of the sputtered species is a diffusive (random walk) process.Fig. 3.1 shows a cross-sectional view of the planar magnetron source used here.A magnet placed behind the target creates a magnetic field of about 300 Gauss parallelto the target surface. A negative voltage is applied to the target, with the chamber beingthe ground return. Electrons emitted from the cathode target are accelerated away fromthe cathode; but, due to the magnetic field, they are bent back towards the target. Thiselectron confinement near cathode surface significantly increases the ionization of argonnear the target, thus leading to much higher efficiency (i.e. source operates at low voltageand pressure). A further benefit of the magnetic confinement is reduced bombardmentof the substrate by energetic electrons and, therefore, the substrate temperature duringdeposition does not rise more than about 50 °C above the ambient temperature.Three sputter target materials were used; carbon, tungsten, and inconel. Thecarbon target was a disk of 99.99% purity pyrolitic carbon;58 the tungsten target, a diskof 99.99% purity super-high temperature and pressure pressed tungsten;58 and theinconel target was made out of a 3 mm sheet of inconel.59 The targets were bonded toa water-cooled copper backing plate with the use of silver epoxy.3.2.2 Description of sputter apparatusTwo sputter coaters were used for this study. The first one, schematically shownin Fig 3.2, consists of a 55 cm diameter stainless steel chamber with four 5 cm diameter23WATERFigure 3.1: Cross-sectional view of planar magnetron sputter source used in thisstudy.planar magnetron sputter sources. Substrates were placed on an annular table 7.8 cmin front of the sputter target. The targets and the substrate table were vertical. Thesubstrate table was rotated continuously at 3 rpm during deposition to improve filmuniformity. A shutter was situated between the substrate holder and the sources to allowsputter cleaning of targets prior film deposition. The substrate table was electricallyisolated from the grounded chamber. An external dc power supply was used to put avoltage (“bias”) on the substrate table during film deposition. The process parameterswhich were varied, i.e. power levels, sputter pressure, and substrate bias, will bediscussed in subsequent chapters. The vacuum chamber was pumped by a diffusionpump backed by a mechanical rotary pump. A liquid nitrogen trap was used to preventbackstreaming of oil into the chamber and to pump water vapour. The base pressure ofthe system was 2.Oxl 06 Torr after an overnight pumpdown. Power to the sputter24Gas InletGate ValveColc TrapThrottleDiffusionPumpFigure 3.2: Diagram of the sputtering system, viewed from the front with the front door,substrate table, and shutter removed.GaugeSputter SourceCapacitanceManometerMechan;ca( Roughing Pump25sources was supplied by Advanced Energy MDX-1 K dc supplies. The sputter gas wasultra high purity Ar (99.998 %). The gasflow was controlled by an MKSmass flowcontroller and the pressure was read by an MKS capacitance manometer. Duringsputtering, a variable orifice device (“throttle) above the diffusion pumpwas partly closedin order to increase the argonpressure in the chamber withoutexcessively loading thediffusion pump.The sputtering apparatus wasautomated to improve the reproducibility of layerthicknesses in the sequentialdeposition of carbon/inconel multilayer structures. Thesubstrate was first moved infront of the carbon target to allow for the deposition ofcarbon for p1 substrate passes.The substrate was then movedin front of the inconeltarget to allow for the deposition of inconel for p2 substrate passes. These steps wererepeated until the desired number of layers is reached. The number of substrate passesp1 and p2 depended on the desired thicknesses of the inconel and carbon layers. Typicalvalues of p1 and p2 were 12and 2, respectively. Details onpower levels and othersputter parameters are givenin sections to follow.The second sputter coater wassimilar to the above-described system, except forthe differences discussed below. This sputter coater wasespecially designed toaccommodate an in situ ellipsometer and was only used in the seventh chapter pertainingto thickness control studies.The description of the in situellipsometer will fllow insection 3.4.3. The samples areplaced on a fixed sample holdermounted on the backwall of the chamber. The targets are placed on an annular table in front of th e sampleholder. The motion of this annular table and therefore thedeposition process are26controlled by a routine discussed in great detail in chapter 7.The substrates were polished (111) Si wafers with a manufacturer’s6°specifiedroughness of ±4 A. Prior to deposition, the substrates were cleaned by ultrasonicagitation in an acetone bath followed by rinses in trichioroethylene and ethanol. Thesubstrates were dried with a jet of pure nitrogen gas. Adhesive tape was used to attachthe substrate to the substrate table.3.3 X-ray Photoelectron Spectroscopy and Auger Electron SpectroscopyXPS is a technique for chemical surface characterization which consists ofdetecting and analyzing photoelectrons produced by irradiating a sample with a soft x-raybeam of known photon energy hv. The photoemission transition is shown in Fig. 3.3. Acore electron absorbs an x-ray photon and is ejected from the solid with a kinetic energyEk, given byEk=hv—EB—W$p (3.1)where EB is the electron binding energy and is the spectrometer work function. Thelatter energy is the combination of the work function for the materials, and the workfunction induced by the analyzer. A photoelectron spectrum is generated by recordingthe photoelectron current as a function of Ek. From these results, peaks associated withthe binding energies for each element present in the sample (to a depth of about 60 A)are obtained. Published tables of photoelectron binding energies for all elements areused to identify peaks in x-ray photoelectron spectra. The integrated area under a peak27hi’— _4wspX-R&y — EBPho toUFigure 3.3: Schematic diagram of the photoemission process.is a direct determination of the relative number of atoms in a particular orbital state.In AES a specimen is bombarded with electrons with known energy, usuallybetween 3 to 10 keV, and secondary (or “Auger”) electrons emitted from the sample aredetected. The basic transition processes are depicted in Fig. 3.4. A non-radiativereadjustment to an inner shell may take place by having an electron from a tightly boundorbital fall from a higher level X of energy E to the core level vacancy W of energy E(Fig. 3.4). The excess energy (E—E) is used to eject an electron from level Y of energyE1. This last electron, known as “Auger” electron, is emitted from the sample underinvestigation with a given kinetic energy Ek given by the following expressionEkEwExEyEOEE (3 • 2)The energy Eeff is associated with the extra energy needed to remove an electron from28Figure 3.4: Schematic diagram of the Auger process.electronvacuumelectron Auger29a doubly ionized atom, and the dynamic relaxation of the electrons during the two electronemission process. Since the kinetic energy of the Auger electron is related to the bindingenergies of the electronic levels which took part in the Auger process, it is unique to eachelement and, therefore, the distribution of Auger electrons can be used in AES todetermine surface composition ( top 60 A of film). A review of these effects is given byWeissmann and Muller.613.3.1 Description of apparatusThe XPS and AES spectra were recorded with a Leybold MAX200 system, whoseside view is schematically shown in Fig. 3.5(a). The chamber of the spectrometer isconstructed of stainless steel. Samples are mounted on sample holders and locked ona sample magazine (Fig. 3.5(b)) which can hold up to seven sample holders. The samplemagazine is then moved to the transfer chamber. After the transfer chamber is pumpeddown to 108 Torr with a turbomolecular pump, a gate valve is opened and the sampleholder is transferred to the analysis chamber and locked to the manipulator. Themanipulator allows the sample to have five degrees of movement, three for linear motionand two for rotation. This setup enables positioning of the sample and the ability to makemeasurements as a function of angle of incidence for the x-ray beam.A AlF source is used to provide an x-ray beam with an energy of 1486.6±0.43 eV.A 2 tm thick Al foil (window) is interposed between the anode and the sample to screenout any stray radiation.Photoelectrons are detected by a concentric hemispherical analyzer (CHA). As30Energy Analyzer (EA 200)Analysis(a)X-ray monochromator (RMC1O)Energy Analyzer (EA 200)Manipulator(b)Transfer ChamberSample MagazineFigure 3.5: Schematic diagram of (a) the side view and (b) the individual parts of LeyboldMAX 200 system.Detector (MC 18)X-Ray source (XR 200)Sample Holder,j31—1/2vFigure 3.6: Schematic diagram of the concentric hemispherical analyzer.illustrated in Fig. 3.6, a potential is applied across the hemispheres such that the outerone (radius r2) is negative (—1/2AV) and the inner one (radius r1) is positive (-i-1/2AV).The condition for an electron of kinetic energy E0, injected tangentially at the source, togo through the analyzer is given byeV=E0(rJr1-r12) (3.3)By a sweep of the bias potential, AV, on the analyzer, an energy spectrum for theelectrons is obtained.The XPS system is equipped with an ion gun for depth profiling analysis and anelectron gun for AES measurements. The ion source employs an argon gas pipeddirectly into the back of the gun and a discharge is initiated by a high-voltage to ionizethe gas. This gun operates at accelerating voltages between 2 and 10 kV. The electron+1/2 t V32source is based on the thermionic emission of electrons from a heated tungsten filament.This filament is biased negatively with respect to a nearby grounded anode in the rangefrom 4 to 20 kV to accelerate the emitted electrons.The XPS spectrometer is interfaced to a Hewlett-Packard 1000 basedmicroprocessor using Data System DS 100 software. The computer controls most of thespectrometer functions and the operations of data acquisition and data processing. TheXPS spectrometer is provided with an integrated software package to analyze the datait collects.Before performing any data collection, photoemission peaks from a gold sampleare used to calibrate the system. The gold 4f712 photoemission peak at 83.8 eV is usedas a reference. For non-conducting materials, photoemission spectra are calibratedagainst the carbon is photoemission peak at 285.0 eV,3.4 EllipsometryEllipsometry is the measurement of the change in the state of polarization of a lightwave upon reflection at the interface between two media with different dielectricconstants. Ellipsometry is widely used to investigate the optical and microstructuralproperties of thin films and to measure film thickness. In the present study, ellipsometryis used (1) in situ to control film thickness and (2) ex situ to investigate the optical andmicrostructural properties of these materials.This section is divided into three subsections. The first subsection reviewspolarized light and its mathematical representation and defines the complex reflectance33ratio which is the experimental quantity of interest in ellipsometry; and the second andthird subsections describe the ex situ and in situ ellipsometers used in this thesis study.3.4.1 Polarized lightThe electric field vector of a monochromatic plane wave of angular frequency opropagating in direction z is given by62X(z, O=RAet) (3.4)where A is the complex field vector that lies in the xy plane. X can be written in termsof its x and y coordinatesX=A,cos(ø t- kz+r) (3.5)andX=Acos(w t- kz÷r) (3.6)where we have defined the complex vector A asA=xAei-yAeh (3.7)where A and A are positive numbers, x and y are unit vectors, and ; and are phaseconstants.34a)b)xR;ght Hand PotoHzotlonFigure 3.7: (a) A typical polarization ellipse. (b) Reflection and refraction of a plane waveat a boundary between two dielectric media.y,QQ = Azimuthal AngleB = Xy’ / Xx’35In general the resultant electric field vector X will trace out an ellipse in a fixedplane normal to the propagation direction, as shown in Fig. 3.7. The equation of theellipse can be obtained by eliminating ot—kz in Eqns. 3.5 and 3.6. After several algebraicsteps one obtains(X)2tXrcsin2t (3.8)where(3.9)Defining x’ and y’ to be a new set of axes along the principal axes of the ellipse,the equation of the ellipse in the new coordinate system becomes.,,2.,2÷ (3.10)gwhere g and g’ are the principal axes of the ellipse and E and E, are the componentsof the electric field vector in this principal coordinate system.The parameters that describe the ellipse polarization in its plane are as follows:(1) The azimuthal angle Q between the major axis of the ellipse and the positivedirection of the X axis;(2) The ellipticity, B, which is the minor/major axis ratio; and36(3) The handedness of the ellipse of polarization, which is defined as right-handed(B<O) if the electric field rotates clockwise (cw) and is left-handed (B>O) if theelectric field rotates counterclockwise (ccw), when looking into the source of light.It is convenient to define the plane of incidence by the direction of propagation zand the normal to the surface. The electric field components parallel and perpendicularto the plane of incidence are denoted by X (TM mode) and X (TE mode), respectively.The polarization of the electric field is defined as:0= “c’ IXsI’9kt,_1p) (3.11))) IkI)0 is real for linearly polarized light, and purely imaginary for circularly polarized light. Thepolarization state can also be written in terms of the azimuthal angle and the ellipticity,63tan Q-’-iB (3.12)1 -!B(tanQ)The Fresnel complex reflectance coefficients, R and R, for the parallel (p) andperpendicular (s) polarizations are defined byR (3.13)37(3.14)where superscripts i and r denote the incident and reflected quantities, respectively.Fig. 3.7 displays the convention used for incident, reflected, and transmitted electric fields.In ellipsometry, the measured value is the complex reflectance ratio p is definedby63(3.15)0’where 8’ and 8’ are the polarization states of the incident and reflected light, respectively.It is often convenient to write p in the formp = tan’!’ e (3.16)where tan’P is the relative amplitude attenuation and A is the relative phase changebetween the incident and reflected polarization states. Values for tanNf and A are listedby Azzam and Bashara for various bulk materials.63 For a bare substrate, the pseudoBrewster angle c8 is defined as the azimuthal angle when tanNf is minimum. Also, theprincipal angle oc1 is defined as the azimuthal angle for which A=—7t12. For a dielectricmaterial c and cx are equal. In general, a change in the state of polarization is obtainedupon reflection of light. By measurement of p, these changes in polarization contain38information about the film’s microstructural properties, as discussed herein.If linearly polarized light with an azimuthal angle Qi is incident on a surface, thenfrom (3.12) and (3.15) the following expression for the experimental complex reflectanceratio64 in terms of the quantities (Qr,B) is obtainedp=tanQ’. ootQr_IB (3.17)1 +!B(cotQr)In the case of an ambient-substrate system, the complex reflectance ratio is givenby= sin2cg— cOSa— sin czj (318)sin2cg + cOsa [(es Ie - sin2aI1where x is the angle of incidence, Ea and Eb are the effective dielectric functions for theambient and substrate, respectively. Thus, knowing p, can be solveds = sin2cc + sin2cc tan2cc [(1 — p) 1(1 + p)]2 (319)The value calculated in Eqn. 3.19 is known as the pseudodielectric function and isrepresentd by <> under the assumption that the substrate contains no overlayers,surface roughness, porosity, etc.393.4.2 Description of ex situ ellipsometerThe optical layout of the rotating analyzer ellipsometer (RAE) used in this study isshown in Fig. 3.8. This spectroellipsometer was designed and constructed byDr. B. Sullivan as part of his Ph.D. thesis at UBC. A brief description of the apparatusis given below. A detailed description is given in Dr. Sullivan’s thesis.65A current-stabilized, convection-cooled, 75 W Hamamatsu Xenon short-arc lampis used to provide a continuous broadband spectra from 1.2 to 6.6 eV. The light beamis then collected by a 20 cm focal mirror and focussed on the entrance slit of a double-prism Cary—15 monochromator. This type of monochromator is advantageous incomparison to a single element monochromator since it reduces the background signal.Quasi-monochromatic light exits the monochromator, is collected by transfer optics, entersthe ellipsometer chamber, goes through a MgF2 Rochon polarizer, and is reflected off asample with angle of incidence 67.500±0.020. The state of polarization of the incidentbeam is controlled by the rotational azimuth of the polarizer around the beam axis. Thetransfer optics consists of MgF2 coated Al concave mirrors. The overcoat preserves thehigh UV-reflectance properties of the Al mirror. After reflection off the sample, lightpasses through a crystal quartz Rochon analyzer, which is transparent from 0.2 eV to6.6 eV, and then detected by a 2.9 cm diameter Hamamatsu R-376HA photomultipliertube, with a spectral response from 1.4 eV to 7.7 eV.A vacuum chuck on top of a rotatable base in the center of the chamber is usedto hold the sample. A computer controlled stepping motor is attached to an anti-backlashworm/worm gear combination, and, via a feedthrough, rotates the sample holder with a40Figure 3.8: Optical layout of the spectroscopic ellipsometer.65TALIGNb€NTLASERDOUBLEPRISMMONDCWROI4ATOR41step resolution of 0.009°. A He-Ne laser has been set up to properly align the samplewith respect to all the optical components in the system. The laser light enters thechamber through a port and is reflected off the sample. The sample holder is rotated andtilted until the beam spot is reflected back towards the laser; thereby aligning the verticalplane of the sample.During polarization state measurement the analyzer is rotating at a constantangular frequency o and, as a result of the symmetry of the analyzer, the detected lightsignal is modulated at 2o. The sinusoidal modulation of the signal depends on thepolarization of the reflected light; it is maximum for linearly polarized light and is zero forcircularly polarized or totally unpolarized light.The electric field transmitted by the analyzer is given by:65XA = X [cos (Q-Q’)+iB sin (Q-Q’)] (3.20)Here Q’=ot is the azimuthal angle of the analyzer with respect to the plane of incidence.From Eqn. 3.20 the transmitted intensity is:‘A = I (1 ÷bpos2Q’+bpin2Q’) (3.21)where2Q = arctan(bjb? (3.22)42B ±[(1 —b,)J(1 +b,)J112 (3.23)bk..b,2+bJ2 (3.24)values for bE and b1 are obtained by computing the Fourier transform of the detectedsignal. Values for Q and B are then calculated from Eqns. 3.20 and 3.21.3.4.3 Description of in situ ellipsometerIn situ ellipsometric measurements during thin film deposition were recorded withthe rotating compensator ellipsometer shown in Fig. 3.9. This in situ ellipsometer wasdesigned and constructed by A. Kleinschmidt as part of his M.A.Sc. thesis at UBC. Abrief description of the apparatus is given below. A detailed description is given inKleinschmidt’s thesis.The ellipsometer is made of three modules: (1) a source arm, (2) an adjustablesample holder, and (3) a detector arm. The source and the detector arms are clampedonto vacuum ports of the sputtering chamber. The sample holder is mounted on the backwall of the chamber.Figure 3.10 illustrates the inter-relation of the major components of the in situellipsometer. In the source arm, a 5 mW HeNe laser (6328 A) is used to generate theincident beam. The light beam then goes through a rotatable Glan-Thompson polarizercoated with an anti-reflection film and mounted inside a drum assembly. The incidentbeam exits the source arm through a NW25 vacuum port adapter mounted on the43cr4w0D0U)w4IC.)wI-ID0U)40I0wFwUuJ0IUiIFigure 3.9: Ellipsometer and its attachement to the sputtering chamber.44T1CD CD Ci30 -n C 0 0 0 C) 0.CD -‘ 3 0 -I’cn—I.CD C) 0 3 CD D Cn 0 -I CD 0 0 3 CD CD 0) 0)DETECTORANALYZERROTATIrK;Cc*4PENSATORHeNeLASERSHUTTERPOLARIZERENTRANCEANDEXITWINDOWSI.VTORCONTROLLERLASERPOWERSUPPLYELECTRONICSINTERIACEPCWITHDATAACQU131TIONCARDsputtering chamber and is reflected off a sample with an angle of incidence of68.20±0.02°. The sample is taped on the sample holder. The reflected beam enters thedetector arm through another vacuum port adapter mounted on the chamber, and thengoes through a rotating compensator followed by a GIan-Thompson analyzer identical tothe polarizer and a photodetector which consists of a photodiode and its associatedelectronics. A narrow band filter which corresponds to the HeNe frequency is placed infront of the photodiode to cut out stray ambient radiation. The in situ ellipsometer iscontrolled by an IBM compatible PC through a Labmaster DMA data acquisition systemand I/O interface board.To align the sample, the reflected beam is adjusted parallel to the optic axis of thedetector arm via three vacuum feed-through micrometer screws accessible from the backof the chamber. The program ADCrun.pas66 is used to read the photodetector outputwhile slowly adjusting the sample stage until the maximum output is found. A routine waswritten to utilize the in situ ellipsometer for closed loop control of layer thickness. Thisroutine will be discussed in detail in chapter 7.The accuracy of the ellipsometer was increased by averaging raw data from 40compensator rotations which correspond to a duration of about 3 seconds. This accuracywas determined by measuring the complex reflectance ratio of a silicon sample a hundredtimes and by calculating the standard deviation of the data. The complex reflectance ratiowas found to be p=(—O.2364±O.0001 , —0.0158±0.0001). The accuracy of the ellipsometeris therefore APrAPi±O.0001 The accuracy in thickness was estimated from theaccuracy in the complex reflectance ratio by simulating the ellipsometric trajectory of the46multilayer system I intend to fabricate in chapter 7. This multilayer system consists of300-layers of alternately deposited inconel and carbon layers. The inconel layers are15 A in thickness and have a complex refractive index of (2.94,3.02). The carbon layersare 30 A in thickness and have a complex refractive index of (2.40,0.57). The simulationwas determined by calculating the reflectivity from a multilayer system by applyingrecursively Eqn. 2.8 and translating this reflectivity into a complex reflectance ratio usingEqn. 3.15. Fig. 3.11 gives the result of this simulation. After the deposition of 50 layersthe ellipsometric trajectory varies between two fixed data points for which the differencein complex reflectance ratio is APr0.016755 for the real part and Ap=0.026434 for theimaginary part. Form this simulation an accuracy of Ap=Ap=±O.OOOl translates to athickness accuracy of ±0.15A.The reflectivity of a 300-layer multilayer system operating at 45A at normalincidence was then calculated in the case of an ideal multilayer with smooth, uniform, andnon-interdiffusing layers (1) with no thickness error and (2) with a random thickness errorof ±0.1 5A. This error was found to decrease the total reflectivity from an ideal of 20% to18%.3.5 X-Ray DiffractometerGXR spectra were recorded with the use of a Rigaku RU-200 rotating anode x-raydiffractometer operated with a (1.54 A wavelength) CuK source. All of the spectra weretaken with an accelerating voltage of 50 kV and a current of 100 mA. As indicated inFig. 3.12, the x-ray beam passed through a 0.05 mm divergence slit (DS) and was474.704.450-c4.200L3.453.20 -0.23 0.48Figure 3.11: Ellipsometric trajectory during the growth of a 300-layer inconel/carbonmultilayer (15 A inconel, 30 A carbon).I -0.28 0.33 0.38 0.43Real port of rho48diffracted by the specimen to form a diffracted beam which came to focus at a 0.15 mmreceiving slit (RS). The diffracted beam was filtered by a graphite crystal monochromatorwith a 112 mm radius of curvature. The x-rays then entered a Nal scintillation counterwhose response was linear up to 30,000 counts/s. Since the reflectivities varied over arange of 106 in the angular region of interest, GXR measurements were divided intoseveral regions by using different filters which attenuated the signal to accommodate forthe counter’s limitations. The sub-divided spectra overlapped and, therefore, by scalingand matching the overlap regions, a continuous reflectivity spectrum was obtained overthe angular range of interest. The intensity changed by about six orders of magnitudeover the angle range used (0.4O4.0).The x-ray system is equipped with an x-ray goniometer unit which was remotelycontrolled at the operating panel. The goniometer consists of two rotating axes: the 0-axis, and the 9’-axis as shown in Fig. 3.12. The detector rotates along the 8’ axiswhereas the sample rotates along the 8 axis.X-ray scans could be taken in three modes: (1) 8 scan, (2) 0’ scan, and (3) 0/0’scan. The third mode is the one used in GXR studies with the proviso that the systemsatisfies the Bragg-Brentano condition which consists in scanning the 0-axis and the0’—axis together such that 0=20. The system is therefore aligned to make sure that thefront surface of the sample satisfies the Bragg-Brentano condition before any GXRmeasurements are recorded. The alignment hinges upon the fact that for a given angleof incidence 8 the maximum reflectivity should be observed for 8’=28. The alignmentprocedure consists in moving the counter (0’-axis) to 9’=2°, rotating the sample (0-axis)49X—roy tubeFigure 3.12: Geometry of the Rigaku x-ray diffractometer.ScimpteDSCounterCrystci1 ronochromcitor’50from 0 to 4°, recording O for which a reflection peak is observed, and moving the sampleby (e—O) to adjust the goniometer so that 0 is half 8’.In the analysis of the GXR data I assume that the x-ray beam is parallel andmonochromatic, that the slits and sample do not fluoresce, that the collimators have afinite divergency, and the monochromators have a finite band pass. At very low angles(grazing angles) the measurements require high angular resolution (± 0.002°) of thegoniometer and very precise mechanical adjustment of the sample on the center ofradiation.3.6 Nonlinear OptimizationIn this thesis nonlinear optimization and linear regression analysis techniques arevery important for fitting theoretical models to the GXR and SE data. The first step in theanalysis is a suitable choice for a merit function, which can be minimized and used as ameasure of the goodness of the fitting procedure.The following minimization function was constructed to fit the data (y1,x) j=1,...,Uto a model described by a functional relationship y(x,) where a=(a1,a2...,a)Tare themodel parameters:x2(a) - Y G’ (3.25)emjwhere erni is the measurement error (standard deviation) of the jth data point. The optimal51values of the parameters a were obtained by minimizing x2(.) with respect to each of theparameters simultaneously.Since the models used in this thesis have a nonlinear dependence on theadjustable parameters, the minimization procedure proceeds through numerical iteration.Given trial values of the parameters, solutions are attempted until the minimum value ofx2 is reached. Close to this minimum, the x2 function is approximated by a quadratic formx2(a)“X2(ff)-.a+-a..G.a (3.26)The gradient (2) of x2 with respect to the parameters , which is equal to zero at theminimum of x2 (Eqn. 3.26), has components= -2 - q; a)Iay(x,; a) (3.27)aak 0m,iTaking an additional partial derivative gives the Hessian of x2a(2 2y18Y(xi;a) ay(x,;a)-[y-y(x,;a) 8Y(x,;a)1 (3.28)8ak8a, i-i em,, 8a aapakIf the approximation in Eqn. 3.26 is a good one, the minimized parameters may beobtained from the current trial parameters ur as follows52=(3.29)If Eqn. 3.26 is a poor approximation to the shape of the function to be minimized at ur’the steepest descent method67 is usedconstantxVx2( (3.30)where the constant is small enough not to exhaust the downhill direction. It is aconvention to define the following parametersp (3.31)IC2âaka2x (3.32)2 8a,Oa,making []=1I2 in Eqn. 3.29 which can be rewritten as a set of linear equations>,,Jarpk (3.33)This set is solved for the increment 8a1 that, added to the current approximation, give thenext approximation. The steepest descent formula in Eqn. 3.31 is rewritten as53öa,=constantxf3, (3.34)The convergence criteria can be stated as followsI (3.35)andIL1XtL(I C2 (3.36)where and C are specified tolerances. Usually, the above conditions are modifiedslightly so as to be independent of scaling in x2 and .There are numerous nonlinear optimization techniques available and they all haveadvantages and disadvantages depending on the minimization function. They usuallydiffer in how to update the Hessian from one iteration step to the next and in the searchdirection and search length algorithms. In this study, we have opted for the LevenbergMarquardt method.67 In this case, Eqn. 3.31 is rewritten as6a,= 1 13, (3.37)where is a constant. A new matrix ‘ is defined by+j (3.38)54jk &i (339)so as to combine Eqns. 3.33 and 338 into a single equationM(3.40)Given an initial guess for , the following list of steps is the recommended LevenbergMarquardt recipe67(1) Compute x2().(2) Pick a value for,say 2=0.OO1.(3) Solve the linear equations 3.26 for 8a and evaluatex2(.+).(4) Ifx2(÷)x increase A by a factor of 10 and go back to (3).(5) If decrease by a factor of 10, update the trial solutionand go back to (3).Once a satisfactory minimum has been found, i.e. once the best-fit parameters areobtained, 2 is set to zero and the following matrix is computed(3.41)which is the estimated covariance matrix of the standard errors in the fitted parameters a.553.7 Linear Regression AnalysisHaving obtained the best-fit parameters for a certain model, it is then necessaryto determine the uncertainty associated with each deduced parameter. These parameteruncertainties, along with x2C helped judge the suitability of the model.The standard error on each fitted parameter is given by(3.42)Assuming that the optimization parameters are normally distributed, one canestablish confidence limits from the student-t distribution for (U—U’—l) degrees of freedom.The 100(1—b)% confidence limits are given by6arsjTb (343)where Tb is the student-t number. For a confidence limit of 90 %, Tb=l .67 and there isa 90% probability that the true parameter value aitrue lies in the intervalLflf8a,m+8i (3.44)Confidence limits are obtained by using contours of constant t2 as the boundary of ourconfidence region. Let be the optimized parameters of the fit, If we change oneparameter akfI by an amount Aa and optimize all the other parameters for minimum 2,then the new value of x2 will be Tb greater than the old value56x2(a÷Aa)=x17) Tb (3.45)A correlation matrix is defined byKr “ (3.46)yIp,where the diagonal elements of this matrix are equal to unity. If any off-diagonal elementK11 approaches ±1, then the parameters a1 and a have a strong cross-correlation betweenthem. As a consequence, the uncertainties in these parameters will be very large as agood fit can be obtained while varying these two parameters together over a largeparameter space. If the measurement errors are not normally distributed, C,1 cannot beinterpreted as the actual squared standard errors of the parameter estimation.57Chapter 4Tungsten films4.1 IntroductionI started my research with a comprehensive study of the properties of tungstensingle layer thin films since tungsten is widely used for the high index layer in x-raymultilayers.28 Through this study I developed the necessary experimental and analyticaltechniques to set up our laboratory for x-ray multilayer research. The tungsten films werecharacterized with GXR, XPS, AES, and SE; GXR was used to determine the thickness,roughness, and optical constants of the films; XPS and AES were used to study thechemical composition of the layers; and SE was used to determine the thickness of thelayers and to investigate their microstructural and optical properties.The investigated tungsten single layers were about ten times thicker than those(10—20 A) used in my multilayer study. Single layer thin films with these thicknesses aremuch easier to characterize with GXR and SE than single layers 10—20 A thick. Thegeneral properties of these relatively thick layers are very similar to those of thin layersin a multilayer structure except for the surface roughness which is expected to be largerfor thicker layers. A comparison between the properties of the relatively thick layers andthose of very thin layers, in particular the surface roughness, is discussed in chapter 6.The results of this study are also of use in other applications of very thin films oftungsten, such as x-ray masks in microelectronics.68’9584.2 ExperimentTungsten films were deposited with the first sputter deposition system describedin chapter 3. All of the investigated films were grown at a dc sputter power of 40 W.Sets of films were prepared with Ar pressures of 0.4, 2.0, and 4.0 Pa. The substrate totarget distance was 7.8 cm. The substrate table was electrically floating and was rotatedcontinuously at 3 rpm during deposition. Deposition rates were determined by measuringthe thickness of a thick film deposited for a number of substrate passes with a stylusprofilometer. The material deposited per substrate pass at Ar pressures of 0.4, 2.0, and4.0 Pa was 5.2, 5.7, and 7.8 A, respectively.4.3 Results and discussion4.3.1 X-ray Photoelectron SpectroscopyFig. 4.1 shows XPS spectra taken with take-off angle of 900 (Fig. 4.2) for samplesgrown at (a) 0.4, (b) 2.0, and (c) 4.0 Pa. The spectra can be interpreted in terms of twodoublets associated with W (zero oxidation state or W°) and W03 (+6 oxidation state orW”).70’1 The peaks in each doublet correspond to photoemission from the 4f712 and 4f512levels. As shown in Fig. 4.3, the intensities of the W peaks are significantly reducedcompared to those seen in Fig. 4.1, when the take-off angle (Fig. 4.2) is reduced to 20°.The mean free path for a photoelectron is about 30 A; therefore the sampling depthdecreases with more oblique take-off angles. Thus, the above results indicate that thetop surface layer of the W film is oxidized. Such oxidation in air is expected.71’2For a homogeneous sample the signal strength detected in XPS is given by73’459D>C’)Ca)4-’&40Binding Energy (eV)Figure 4.1: XPS spectra for tungsten films prepared at (a) 0.4, (b) 2.0, and 4.0 Pa,associated with photoelectrons from the 4f7, and 4f shells using Al Kc x-rays taken ata take-off angle of 900.36 32 2860zFigure 4.2: Sampling depth versus take-off angIe; 900 and 20°.onoJyser200x—raysourceanalyzer=90°samplex—raysourcesample61cr3>%(1)G).940Binding Energy (eV)Figure 4.3: XPS spectrum for tungsten film prepared at 4.0 Pa, associated withphotoelectrons from the 4f712 and 4f512 shells using Al Kc x-rays taken at a take-off angleof 200.36 32 28621j 4’ i11YA,,,(E) Fe(E? (4.1)Here, c1 is the x-ray flux, i is the density of atoms of type i, - is the photoexcitationprobability which depends on the solid angle of the emitted electrons and on thesensitivity of the detector, m(Ej) is the mean free path of an excited electron with energyE1, and Fe(Ei) is the fraction of electrons detected by the analyzer. The values for theatomic sensitivity factor S1 defined by the following equation are produced for variouscommon materials by the manufacturer (Leybold):S, 4’ Yi’mW? F0(E? (4.2)From Eqns. 4.1 and 4.2 the partial densities for the constituents in a homogeneoussample are obtained. In the case of a layered structure, such as the above-describedtungsten film with an oxide layer, the partial densities have to be corrected for the changein sampling depth with take-off angle, e.The electron flux reduction from atoms a distance z below the sample surface isassumed to vary with 8 as exp[—(zIsinOj/?e} where is the mean free path length for thephotoelectrons. The photoelectron current reaching the detector is, thereby, obtained byintegration of the above exponential function, to giveId=Id(l (4.3)where‘d is the detected current; Id°, the current at normal take-off angle; and d0, the63CoCl)a)-I-’CFigure 4.4: Deconvolution of the XPS spectra of tungsten films prepared at apressure of 4.0 Pa. Data were taken with Al Koc x-rays at a take-off angle of 90°.thickness of the layer. A smooth curve was fit to the baseline and subtracted from thespectra. A reasonable fit to the resulting peaks was obtained by assuming a LorentzGauss profile75’6 fraction of 0.6 and by variation of the heights and widths of the 4f712peaks. The intensity of the 4f512 was taken to be 3/4 that of the 4f712 photoelectron line fora W atom in the same chemical state.75As shown in Fig. 4.4 for a film prepared at 4.0 Pa, a very good deconvolution wasobtained by assuming the presence of an additional doublet associated with W02 (+4oxidation state or Wi”). The chi-square was improved by a factor of 3 over the model36Binding Energy (eV)64assuming only doublets associated with W and W03. The relative intensities of the W02peaks compared to the W03 peaks decreased when the take-off angle was changed from900 to 20°. This suggests a gradient in the oxygen content as a function of depth into thesample. The extra broadening of the W02 compared to the W03 and W peaks in Fig. 4.4could be associated with incompletely oxided atoms in W02 ‘layer’.From the above analysis of the XPS results, I obtain the three layer model shownin Fig. 4.5, for the tungsten films. The thicknesses of the oxide layers can be related bythe following equations for the integrated intensities (Eqn. 4.3) of the photoemissionpeaks, assuming that the thickness of the W layer is very large compared to the meanfree path in W774Y02 = 1 W02 Yw02 1•‘l w w e -((dJsh6!A“wos 1 W03 Ywos 19-((dnJsinOIL 5)Iw 11 w Y w e -((dsinO?!A,9-((djsin6)IAJThe mean free paths in W and W03 have been experimentally determined:78? = 12.8 Aand X03 = 26.3 A. Since the thickness of the W layer (1 50 A) is large compared to A,the factor 1—exp[—(d/sin9jflj was approximated by unity in Eqns. 4.4 and 4.5. Sincemeasurements of the mean free path in W02 were not found in the literature, I used thefollowing semi-empirical expressions79to calculate O265Figure 4.5: Structural model deduced for the tungsten films from XPS study.66A W02 = 0.72 d,1,5 E°5 (4.6)where dm is the monolayer thickness in nm; and E, the photoelectron energy in eV abovethe Fermi level. The monolayer thickness is given byM 1024d,= ox (4.7)rpA0where M0 is the molecular weight, N’ is the number of atoms in the molecule, A0 isAvogadro’s number, and i is the bulk density in kg/rn3. From the above Eqns. 4.6 and4.7 I obtain ?o2=28.7 A, X03=31 .9 A. While the calculated mean free path for W03 islarger than the experimental one (26.3 A), the relative ratio is expected to be sufficientlyaccurate to calculate X02‘WO2____(4.8)WO3 experimental AFrom the above equations I obtain X02 = 23.7 A. Using the above mean free paths, theoxide layer thicknesses were deduced from Eqns. 4.4 and 4.5, applied to the O=9O0 and=2O° data. In the calculations, the densities 1w03’ flwo2’ and i1 were assumed to beequal to the bulk values, 7.2, 10.9, and 14.1 g/cm3, respectively.20 The results of thecalculation are summarized in Table 4.1.67Table 4.1: Oxide thickness deduced from deconvoluted XPS spectra for tungstenfilms 0.4 Pa, 2.0 Pa, and 4.0 Pa.Pressure‘wcd’w I/1 Thickness ThicknessFor Film of W02 of W03Growth(Pa) (A) (A)0.4 0.379 0.846 7 162.0 0.307 1.079 6 194.0 0.830 1.332 19 104.3.2 X-ray DiffractionSince no peaks were observed in XRD spectra, the films were assumed to beeither amorphous or composed of very small crystallites with grain size < 100 A.4.3.3 Grazing X-ray ReflectionFig. 4.6 gives the GXR pattern of a set of tungsten samples depicted in Table 4.1.The extended interference pattern for the film prepared at 0.4 Pa indicates that depositionat lower pressure produces smoother films. The GXR data were curve-fitted using theprocedure outlined in section 3.6 to determine the optical constants, film thickness, andsurface roughness. The reflected intensities at each interface were calculated withFresnel equations (Eqns. 2.5 and 2.6). The reflectivity from a multilayer system isdetermined by applying recursively the general solution for the amplitude reflectance ofa single layer given by Eqn. 2.8. Imperfect boundaries were incorporated in thecalculation by multiplying the amplitude reflectances in Eqn. 2.8 by the Debye-Wallerfactor (Eqn. 2.11).6810010-110-2104104100Figure 4.6: Normalized grazing incidence2.0, and 4.0 Pa.reflectivity data for W films grown at 0.4,1 2 3 4Grazing angle (degrees)69The uniformity of the GXR interference pattern in Fig. 4.6 indicates that the filmconsists of a uniform single layer, rather than a three layer structure (Fig. 4.5). Applyingthe three layer model and the above equations to the GXR data, I deduced a total oxidethickness of 7 A for the film grown at 0.4 Pa, and < 2 A for films grown at higherpressure. These thicknesses are significantly less than the XPS obtained thicknessesshown in Table 4.1. These results suggest that the roughness of the oxide layers isgreater than 2.Jcosx, which causes a smearing of the interference effects in the oxidelayers.In fitting the GXR spectra, the following adjustable parameters were used: the layerthickness d1, roughness at the film-substrate interface a, roughness at the film-ambientinterface a, the scattering factor 6, and a scale factor m that matches the intensity unitsof the data to that of the theoretical intensity profile. The results of this curve-fitting areshown in Figs. 4.7, 4.8, and 4.9 for the samples grown at 0.4, 2.0, and 4.0 Pa,respectively. The best-fit parameters are presented in Table 4.2. The deduced filmdensities using Eqn. 2.2 and the 6 values in Table 4.2 are 13±2, 14±1, and 14±1 g/cm3.The film densities are less than the bulk value 19.3 g/cm3 which suggests that the“tungsten” layer is made of slightly porous (W30) since the film density of a bulk W30 is15.0 g/cm3.71 This result was not confirmed by the XPS analysis because the chemicalshift of W30 is expected to be small and, as a result, the W and W30 peaks cannot beresolved.Fig. 4.10 shows GXR spectra for another set of films grown at 0.4, 2.0, and 4.0 Pa,but thinner than the first set. The results of the curve-fitting of their GXR data are shown70103 -Fit102-o Data10° -goCw 010-1 -010-2 -1O- -0 1 2 3 4Grazing angle (degrees)Figure 4.7: Experimentally determined and theoretically calculated normalized grazingincidence reflectivity for W film grown at 0.4 Pa.71I 03102— 1011 004-15C.I0-11 0-210-s10-i I0 1 23Grazing angle (degrees)Figure 4.8: Experimentally determined and theoretically calculated normalized grazingincidence reflectivity for W film grown at 2.0 Pa.721 041 03102101cd 10010-1tC1 0-31 0-41 0-50Figure 4.9: Experimentally determined and theoretically calculated normalized grazingincidence reflectivity for W film grown at 4.0 Pa.1 2 3Grazing angle (degrees)73Table 4.2: Properties of tungsten obtained from GXR analysis of a set of filmsprepared at 0.4, 2.0, and 4.0 Pa.Pressure d1 a 6(Pa) (A) (A) (A)0.4 117.2±0.1 3.1±0.1 1.7±0.2 31±42.0 122±1 13±2 2.9±0.6 35±24.0 113±1 14±2 3.5±0.2 35±2in Figs. 4.11, 4.12, and 4.13. The best-fit parameters are presented in Tables 4.3.These results are similar to the ones obtained for the thicker films.43.4 Spectroscopic EllipsometryTo characterize the microstructure of my films, the SE data were analyzed usinga standard procedure derived by Aspnes.8° In this method, an n-layer model of the filmis constructed where each individual layer represents a certain aspect of the film, i.e.surface roughness, film porosity, oxide layers, etc. The dielectric function of each layerdepends upon the composition and volume fraction of the phases present in it.8083 Thisdielectric function is determined by the appropriate effective medium theory (EMT) forcharge screening effects between these phases.81’2 A necessary prerequisite for thisanalysis is the availability of bulk or reference dielectric data for all the constituent phasescomprising the film.74Table 4.3: Properties of tungsten obtained from GXR analysis of a set of filmsprepared at 0.4, 2.0, and 4.0 Pa, but thinner than those in Table 4.2.Pressure d1 at as(Pa) (A) (A) (A)0.4 80.8±0.1 4.1±0.7 2.9±0.1 31±42.0 82.4±0.4 9.2±0.8 3.0±0.3 40±64.0 80.0±0.3 11.3±0.3 4.3±0.2 37±2Wavelength-independent parameters such as the thickness of each layer and thevolume fraction of each phase, are then used in the model to calculate the theoreticalcomplex reflectance ratio Pcaic’ throughout the spectral range of interest (using Eqns. 2.8and 3.15). These wavelength-independent parameters are determined by fitting Pcaic toPexp’ the theoretical and experimental complex reflectance ratios, respectively, using thenonlinear optimization technique discussed in section 3.6.In the rest of this section, the EMTs will be reviewed and the results anddiscussions of my SE measurements will be given.4.3.4.1 Effective Medium TheoryThe effective dielectric function of a layer composed of two or more phases iscalculated through EMT. This effective dielectric function depends on the filmcomposition, the volume fraction of each phase, and the size and shape of the grains.7510010-110-2101CQ1010410-’0Figure 4.10: Normalized grazing incidence reflectivity data for a set of W films grownat 0.4, 2.0, and 4.0 Pa, which are thinner than those in Fig. 4.8.1 2 3 4Grazing angle (degroes)761 01 0—. 1 02zCu>14-CO 1001 0-1 0-2I 0-0Figure 4.11: Experimentally determined and theoretically calculated normalized grazingincidence reflectivity for ‘thin’ W film grown at 0.4 Pa.1 2 3 4Grazing angle (degrees)771041 03— 102—. 1 01U)10°1 0-110-21 0-3Fit0 Data0 1 2Grazing angle (degrees)Figure 4.12: Experimentally determined and theoretically calculated normalized grazingincidence reflectivity for ‘thin’ W film grown at 2.0 Pa.78,‘ita11O2 VIC101-1 0010.-I — I0 1 2 3Grazing angle (degrees)Figure 4.13: Experimentally determined and theoretically calculated normalized grazingincidence reflectivity for ‘thin’ W film grown at 4.0 Pa.7935302520ca 151050-51.50 4.00 4.50 5.00 5.50Figure 4.14: Pseudodielectric functionreferenced to as “thick” in the text.of a tungsten thin film grown at 0.4 Pa,2.00 2.50 3.00 3.50E (eV)803004.00 4.50 5.00 5.50Figure 4.15: Pseudodielectric functionreferenced as “thin” in the text.of a tungsten thin film grown at 0.4 Pa,252015I50-51.50 2.00 2.50 3.00 3.50E (eV)81In this section a brief discussion of the most important EMT’s will be given.The dielectric function,=1+i, of a material is defined asDeX=X+4itP (4.9)where D, X, and P are the average (macroscopic) displacement field, electric field, anddipole moment per unit volume, respectively. In the visible near-uv spectral region, thedominant contribution to comes from the electric polarizability which is determined bythe type of atoms present, their bonding configurations, their density, and the presenceor absence of long-range order. Thus, solving the microscopic fields for a certainmicrostructure and then averaging leads to the macroscopic dielectric function. DifferentEMT’s are used for different microstructural configurations.Aspnes developed several of the more common EMT’s. For two-phase mixtures,these theories have the general form8185Wa +Wb (4.10)+1(€a+KFh€bFhwhere Ea, Eb, and Eh are the dielectric functions of the a, b, and “host” phases,respectively, Wa and wb are the volume fractions of a and b, is the dielectric function ofthe composite, and ic is the screening parameter. The Lorentz depolarization factorq=1/(1-i-is) determines the geometrical screening effect of the grains depending on theorientation of the applied field where Oq1. For spherical grains or a 3—dimensionalisotropic microstructure q=1/3. Similarly, q=1/2 would be appropriate for a822—dimensional isotropic m icrostructu re which describes columnar film morphology.The Maxwell Garnett87’theory, which describes a cermet type of structure whereone phase is encapsulated by the other phase, follows when ha or EhEb in (4.10). TheBruggeman89 effective medium approximation (EMA), which describes a randomaggregate microstructure, follows for a self-consistent solution, i.e., when Eh=E in (4.10).Many different films prepared by evaporation or sputtering are best described by theEMA.4.3.4.2 Results and Discussions:The dielectric function of my tungsten films was obtained from the analysis of theSE data for two samples prepared at 0.4 Pa, with different thicknesses. Figs. 4.14 and4.15 give the real and imaginary parts of the pseudodielectric data for these two samples.To construct my n-layer model I made the following assumptions:(1) As shown in Fig. 4.16, I modelled my films as two layers: a W layer and a W03oxide layer. I have chosen a relatively simple model with the two oxide layers(Fig. 4.5) approximated by a single oxide layer (the W02 layer in Fig. 4.5 being agraded transition layer WON).(2) The dielectric function of the oxide layer was taken from the literature.20 Thecomplex reflectance ratio of a bare Si substrate was measured and its dielectricfunction calculated from its pseudodielectric function.(3) The porosity in any of the two layers shown in Fig. 4.16 was incorporated in theprogram with an EMA. The dielectric response of a given layer is determined83Figure 4.16: Overlayer model used in the SE study.d1d 284from Eqn. 4.10W3 =0 (4.11)€8+lCZ€ €,+K€I assumed a two-dimensional isotropy characterized by i=1, which is the case forcolumnar film morphology. The W layer in the thicker film was taken to be the Wreference with the porosity found by GXR. Consequently, the porosity in any other Wlayer was measured with respect to that layer. The porosity in the bulk region of theother layers involved in our analysis were variable parameters.The following chi-square was then minimized:x2=D[ Ie4(EP_e(EPI21 (4.12)where and are the dielectric functions of two W layers of same density; U, thenumber of data points; and E., the energy of the incident beam.Fig. 4.17 is a plot of the dielectric function of a non-porous ‘tungsten’ layerobtained from the above least-squares curve fitting program assuming that the base layerin Fig. 4.16 is slightly oxidized tungsten, i.e. W30. The parameters which best fit thetheoretical curve are shown in Table 4.4. The deduced thicknesses of the W layers areapproximately the same as that obtained from the GXR analysis. The thickness of theoxide layer in Table 4.4 is approximately equal to the total oxide thickness found by XPS(Table 4.1). The volume fraction for Win the thinner film is found to be less than that for85403530252010504—1.50 2.00 2.50 3.00 3.50E(eV)k00 4.50 5.00 5.50Real part— —— Imaginary partE(eV)Figure 4.17: Dielectric function (a) of thin tungsten film obtained from the SE study;and (b) of bulk single crystalline tungsten.4% Reel —4%——- Imaglnarypert40 I I I35______30254%— — —— 4% — —152.0 2.5 3.0 3.5 4.0 4.5 5.0 5.586Table 4.4: Spectroellipsometric results for films grown at 0.4 Pa. These results arebased on the minimization of the difference between the dielectric function of twoequally dense W layers of different thicknesses.Sample Thickness Thickness Volume VolumeOf Oxide Of Fraction FractionLayer Tungsten Of Of(A) Layer Oxide Tungsten(A) Layer LayerThick 29 115 0.95 1.00SampleThin 28 84 0.94 0.95Samplethe thicker one. This may result from the non-parallel columnar growth of the film alongthe direction of growth9°and/or interfacial inhomogeneities.The SE spectra of the samples prepared at higher pressure were fitted using theoptical microstructural analysis described by Aspnes,80’91given that the reference dielectricfunction for W is the one found above (for the thick sample deposited at 0.4 Pa). A four-parameter model based on Fig. 4.16 was used and the thickness and the porosity of eachlayer was varied to obtain a best fit. The porosity of the layers was incorporated in themodel with the EMA theory, assuming a two-dimensional isotropy (ic = 1). The best-fitparameters for the theoretical model were obtained by minimizing the unbiased estimatorxu,1, D (4.13)(U-U -1)j-i87through nonlinear optimization and linear regression analysis, where U and U’ are thenumber of data points and wavelength-independent parameters, respectively, and a thewavelength-independent parameters in the model.The experimentally determined and theoretically calculated values of the complexreflectance ratio are shown in Figs. 4.18, 4.19, and 4.20 for the ‘thick’ samples grown at0.4, 2.0, and 4.0 Pa, respectively, and in Figs. 4.21 and 4.22 for the ‘thin’ films grown at0.4 and 2.0 Pa, respectively. The parameters which best fit the data are shown inTables 4.5 and 4.6. The thick film grown at 4.0 Pa is found to be more porous than thefilms grown at lower pressure in agreement with previous findings. A satisfactory fitcould not be obtained in the case of the thin sample grown at 4.0 Pa (Table 4.6).Presumably, the porosity became so large that the theoretical model was no longerapplicable.For thin films prepared by sputtering, Thornton92 devised a structure zone modelwhere the film microstructure was classified as a function of substrate temperature andargon working pressure. At low Ar pressures, there is considerable energeticbombardment of the growing film by Ar ions which are neutralized and reflected at thetarget.93 The transfer of momentum to the growing film from this energetic bombardmentpromotes a more densely packed structure and a smoother surface. At higher Arpressures, however, increased scattering of the sputtered species results in a moreoblique incident deposition flux, and, as a result, a more voided columnar structure dueto enhanced atomic shadowing develops. Also, a lower target voltage decreases theenergy of the primary neutrals which reduces the energy flux to the substrate.94 This88I I-0.10a,h.a,C,CCoC,0,.4-a,Ixa’-0.3a.E0C,04-1.. -CO0.Coa,0.1CoE0 DataFit-0.51.5-0.12.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)Figure 4.18: Experimentally determined and theoretically calculated complexreflectance ratio for ‘thick’ W film grown at 0.4 Pa.89-0.10Ia,0C-.Ca0a,•1-a,I-.xa’-0.30.E000-0.40.Caa,a:-0.5 —1.5-0.10L.a,EFigure 4.19: Experimentally determined and theoretically calculated complexreflectance ratio for ‘thick’ W film grown at 2.0 Pa.0 DataFit00000000000 00 0000 000000 00000000I I2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)1.5 2.0 2.5 3.0 3.5 4.0Energy (eV)4.5 5.0 5.590.2 0.084-cuI-a,0-0.02-0.1 2[.22-0.321 .5-0.10 —04-Cua,-0.204-0a,a,-0.30a,0.E0. -0.4004-.Cu0.50—-0.60 3.5 4.01. Energy (eV)Figure 4.20: Experimentally determined and theoretically calculated complexreflectance ratio for ‘thick’ W film grown at 4.0 Pa.2.0 2.5 3.0 3.5 4.0 4.5 5.05.5Energy (eV)I I I0 DataFitI • II I II2.0 2.5 3.0 4.5 5.0 5.591-0.10.100x0-0.30.E0004-I.. -0.a,-0.51.5I:::•t -0.4a,0.Figure 4.21: Experimentally determined and theoretically calculated complexreflectance ratio for ‘thin’ W film grown at 0.4 Pa.0 DataFit2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)92-0.104-a,1a,0C-a,4-0a,a,Ix. -0.30.E0004--a,0.a,a,-0.51.54;0.1EFigure 4.22: Experimentally determined and theoretically calculated complexreflectance ratio for ‘thin’ W film grown at 2.0 Pa.2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Energy (eV)93Table 4.5: Spectroellipsometry analysis of “thick” sample with a two layer modelconsisting of an oxide layer on top of a tungsten layer. Porosities were incorporatedin both layers with EMA.Pressure Thickness Thickness Volume Volume(Pa) Of Oxide Of W Fraction FractionLayer Layer Of Of W(A) (A) Oxide0.4 30±1 115±2 0.94±0.04 1.002.0 31±3 123±7 0.98±0.12 0.96±0.034.0 27±14 149±16 0.63±0.40 0.62±0.04region is characterized by rough surfaces, poor stability, and properties that are far frombulk properties.95XPS measurements were repeated a few months after the film deposition in orderto study the effect of air exposure on these films (1 1/2 months later for one set of films,and 3 months for a second set). Comparing Tables 4.7 and 4.8 with Table 4.1, weobserve that all films further oxidized with time, with the films grown at higher pressure,oxidizing faster. The increased oxidization rate for the higher pressure films can beassociated with the increased porosity.4.4 ConclusionsIn this study, do magnetron sputter deposited thin films of tungsten were grown at0.4, 2.0, and 4.0 Pa. These films were found to be either amorphous or composed ofvery small crystallites with grain size < 100 A. The samples consisted of three layers: a94Table 4.6: Spectroellipsometry analysis of “thin’1 sample with a two layer modelconsisting of an oxide layer on top of a tungsten layer. Porosities were incorporatedin both layers with EMA.Pressure Thickness Thickness Volume Volume(Pa) Of Oxide Of W Fraction FractionLayer Layer Of Of W(A) (A) Oxide0.4 29±2 83±3 0.92±0.06 0.95±0.022.0 30±3 80±4 0.86±0.07 0.95±0.034.0 Unable Unable Unable Unableto fit to fit to fit to fitbase layer of tungsten; a graded transition layer whose average stoichiometry is WO2;and a surface layer of WO3. The thickness of the oxide layers further increased withtime. The roughness and porosity of the films were found to increase with increasing Arpressure, in agreement with Thornton’s92 structure zone model. These results suggestthat the tungsten layers prepared at lower pressures are the most appropriate for use as‘high index’ layers for x-ray mirrors. The dielectric function of non-porous tungsten wasdetermined and may be used as a reference in fitting the SE spectra of thin films oftungsten with different porosities using the optical microstructural analysis described byAspnes.80’91Experimental and analytical techniques were successfully developed to set up ourlaboratory for x-ray multilayer research. XPS, GXR, and SE have been shown to becomplementary techniques that have allowed the determination of the thickness andporosity of the component layers of the samples. The overlayer model was deduced from95Table 4.7: XPS curved resolved data for thick samples grown at 0.4 Pa, 2.0 Pa, and4.0 Pa, taken 1 1/2 months after deposition.Pressure lwdI lwcd1 Thickness Thicknessof W02 of W03(Pa) (A) (A)0.4 0.415 1.850 8 262.0 0.411 1.725 8 254.0 0.931 2.301 15 25angle resolved XPS measurements. The thickness of the oxide layer was found fromanalyzing the XPS and SE data. The thickness of the base tungsten layer wasdetermined from GXR and SE data. Finally, the roughness of the films was obtained fromGXR data.Table 4.8: XPS curved resolved data for thin samples grown at 0.4 Pa, 2.0 Pa, and4.0 Pa, taken 3 months after deposition.Pressure‘w02”w 1ic/lw Thickness Thicknessof W02 of W03(Pa) (A) (A)0.4 0.788 1.258 13 172.0 0.457 1.519 9 234.0 1.326 3.597 19 3096Chapter 5Inconel/Carbon Multilayers5.1 IntroductionIn this chapter single layers, bilayers, and multilayers of carbon and inconel,selected as low and high index materials in chapter 2 for their theoretical performanceand their expected stablity at high temperature, are deposited and then analyzed with thecharacterization and analytical techniques developed in chapter 4. GXR and SE are usedto determine the physical and optical properties of the layers; and, XPS and AES todefine their chemical content and to examine their interface. Multilayers are furthermorestudied as a function of annealing temperature to study the layer and interface stabilityas a function of temperature. A 30-period multilayer was then sent to the LLNL to betested at 45 A wavelength.5.2 ExperimentThin films of carbon and inconel were grown with the first sputter deposition systemdescribed in section 3.2.2. The deposition conditions of these films were similar to thedeposition conditions of tungsten thin films (chapter 4) except for the following differences.The Ar pressure was 0.4 Pa for all of the samples. Single layer films were grown witha stationary substrate. The deposition rates of C and inconel (sputter power of 40 W)were 0.7 and 2.7 Ads, respectively. The multilayer samples were deposited at a sputterpower of 62 W for inconel and 72 W for C. Inconel samples were grown with a substrate97bias voltage of —100 V. The application of a substrate bias is known to enhance thesmoothness of thin films and will be discussed in great detail in chapter 6. The materialdeposited per substrate pass was about 5.5 A for inconel and 1.2 A for C.After measurement, the samples were annealed in a 3-zone Lindberg tube furnace(Fig. 5.1) in an Ar environment to avoid oxygen contamination. Samples were placed filmside up on a flat piece of alumina. After loading the sample, the tube was sealed withendcaps and thoroughly flushed with Ar prior to turning on the furnace. A ramp rate of10 °C/min was maintained during heating. The bilayer samples were annealed for 3hours at 500°C and the XPS measurements were repeated. The multilayer samples wereannealed for 3 hours at 300, 400, 500, and 600°C, respectively. The reflectivitymeasurements were then repeated.5.3 Results and discussionsFigure 5.2 gives the GXR pattern of two carbon samples deposited for 4 and 6minutes, respectively. Fig. 5.3 is the GXR pattern of two inconel samples grown for 50and 70 seconds, respectively. The extended interference patterns indicate that thesefilms are smooth. The GXR data were curve-fitted with the one-layer model describedin the previous chapter to determine the optical constants, thicknesses, and interlacialroughnesses of the component layers. The results of this curve-fitting are shown inFigs. 5.2 and 5.3. The best-fit parameters are presented in Table 5.1. This one-layermodel gave very large x2 for inconel layers, between 1600 and 2000. An acceptable fitshould result in a x2 of the order of the number of data points,67 i.e. 700. However, this98Zone I______Quartz TubeGas InFigure 5.1: Schematic of the 3-zone Lindberg tube furnace.model gave satisfactory results for carbon since the x2 was of the order of the numberof data points,87 i.e. 700.A three-layer model with five variable parameters improved the fit of the GXR datafor inconel. The three layers consist of (1) a top layer of thickness d1 with (in Eqn. 2.2)linearly varying from min to 6max (linearly varying refractive index), (2) a bulk layer ofthickness d2 with 88max (constant refractive index), and (3) a bottom layer of thicknessd3 with S linearly varying from max to 8min Layers (1) and (3) were modelled as a stackof 0.5 A thick layers. The best-fit parameters using this model were: (a) for the thicksample: d16.5±0.4 A, d2=161.0±0.3 A, d3=11.5±0.2 A, 5max25±1>(10,Zone 2 HeaterZone 2 TherrocoupeZone 3Boat With Sap1e99105104103>Cl)a)1021 011 00Figure 5.2: Experimentally determined and theoretically calculated normalizedgrazing incidence reflectivity data for two carbon samples of different thicknesses.0.0 0.5 1.0 1.5 2.0 2.5 3.0Grazing Angle (Degrees)1001 051041 03- 1 02>‘Co10°1 0-11 0-210-sFigure 5.3: Experimentally determined and theoretically calculated normalizedgrazing incidence reflectivity data for two inconel samples of different thicknesses.0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Grazing angle (Degrees)101Table 5.1: Properties of Carbon and Inconel layers obtained from GXR analysis.Sample Layer Film &<106 f3x106Thickness Roughness(A) (A)Thin 170±2 11±2 6.2±0.6 0.1±0.3carbonThick 238±1 8±2 6.4±0.7 0.2±0.2carbonThin 121.6±0.4 7±2 20±4 2.2±0.8inconelThick 173.8±0.4 7±3 21±3 1.0±0.5inconel6m1n2.2±O.5X10, and (b) for the thin sample: d1=18.4±0.7 A, d2=103.1±0.6 A,d316.3±0.4 A, maF2l±)<l0_6, 6minl .0±0.4x106 The results of this curve-fitting for thethick sample are shown in Fig. 5.4. The x2 was substantially improved(28OO)The SE data for two samples of inconel and two samples of carbon prepared at0.4 Pa, with different thicknesses, were used to determine the dielectric function for bulkinconel and carbon, respectively. Figs. 5.5 and 5.6 give the real and imaginary parts ofthe complex reflectance ratio for the C samples. Figs. 5.7 and 5.8 display the real andimaginary parts of the complex reflectance ratio of the inconel films. To fit the data I haveused the same procedure as in section 4.3.4. Two models were used in analysing thedata: a single layer model which consists of a bulk region and a smooth surface and amodel that assumes surface roughness. In analysing the data I used the following points:(1) The reflectance ratio of a bare Si substrate was measured and its dielectric functioncalculated from Eqn. 3.1.1021051 04103I::10010-11 0-2Figure 5.4: Experimentally determined and theoretically calculated normalizedgrazing incidence reflectivity data for the ‘thick’ inconel sample using a three-layermodel.0 DataFit• I I—-- I •0_______________________________0000 0 0o o 0I000000 00 00 000.0 0.5 1.0 1.5 2.0 2.5Grazing Angle (Degrees)3.0 3.5 4.01030.300.1a,0CCa4-0C,a,a-.xa’-0.30E0C)-0.51.5Figure 5.5: Pseudodielectric function of a carbon thin film denoted as “thick” in thetext.2.0 2.5 3.0 3.5 4.0 4.5Energy (eV)1040.20.0I.-0.10C-0.2a)-0.3E0C.)-0.5-0.6-0.7 —_______________________1.5Figure 5.6: Pseudodielectric function of a carbon thin film denoted as “thin” in thetext.0.1 r Real partI — — Imaginary part\- — —2.0 2.5I I3.0 3.5Energy (eV)4.0 4.5 5.0105-0.1-0.20.1(U-0.30CCU.10-0.4a)I‘Ca)E0C)-0.6-0.71 .5Figure 5.7: Pseudodielectric functiontext.2.0 2.5 3.0 3.5 4.0 4.5Energy (eV)5.0of an inconel thin film denoted as “thin” in the106-0.1-0.20-0.3C)4-C)-0.4a)I[C:-0.71.5 5.0Figure 5.8: Pseudodielectric function of an inconel thin film denoted as Hthickl in thetext.2.0 2.5 3.0 3.5 4.0 4.5Energy (eV)107(2) The film porosity was incorporated in the program with an EMA (Eqn. 4.11). Iassumed a two-dimensional isotropy which describes columnar film morphologycharacterized by K=1.(3) The surface microroughness was incorporated into the second film model byassuming that it consists of a layer made of 50 % bulk and 50 % voids.Table 5.2 and 5.3 show the best fit parameters and 90% confidence limits for theinconel films for the first and second model, respectively. The unbiased estimators infitting the inconel samples were 0.38 and 0.18 for the first and second model,respectively. A decrease in the unbiased estimator indicates that the second model isa better theoretical model.I was unable to determine the dielectric function for bulk carbon using the methoddiscussed in section 4.3.4. A second approach was successfully attempted: a ‘thick’ Csample was deposited for four hours under the above conditions. The pseudodielectricof this sample was measured and was then assumed to represent the dielectric functionof carbon films. The SE spectra of thin C samples were then fitted using the opticalmicrostructural analysis described by Aspnes,80’91 given that the reference dielectricfunction for C is the pseudodielectric function of the thick sample. A one-layer model wasused, with its thickness and porosity varied to obtain the best I it. The porosity of the layerwas incorporated in the model with the EMA theory, assuming a two-dimensional isotropy(K = 1). The best-fit parameters for the theoretical model were obtained by minimizingthe unbiased estimator in Eqn. 4.13. The parameters which best fit the data are shownin Table 5.4.108Table 5.2: Spectroscopic results for inconel films grown at 0.4 Pa based on theminimization of the difference between the dielectric function of two inconel layersof different thicknesses with no surface roughness.Sample Thickness ofinconel layer(A)Thick sample 181±3Thin sample 128±2X-ray photoelectron spectra of inconel/carbon bilayers (the inconel layer being ontop of the C layer) were taken for photoelectrons associated with Ni2, Cr,, Mo, C1, andO., orbitals. Fig. 5.9 shows the Ni2 and C1 spectra for normal take-off angle. Theelectron binding energy profile of each metallic element in the inconel environment showsan oxide peak and a metallic peak; specifically for Ni2 (j=312) the metallic peak is at853.5 eV and the oxide peak at 856.7 eV. Incidentally O shows the two regular bindingenergies corresponding to oxide and OH. The carbon spectra require five differentcomponent binding energies corresponding to C—O single bond (e.g., C—O—H and/orC—O—C) at 286.5 eV, double bond C=O at 288.6 eV, hydrocarbon contamination at285.0 eV, graphitic C at 284.1 eV, and C bonded to metal (i.e. carbide) at 283.2 eV. Theexistence of the latter component suggests that there is interdiffusion between inconeland carbon. With a take-off angle of 30° (Fig. 5.10), the XPS intensities of the metalpeaks are significantly reduced compared to the metal oxide peaks; also 0 peaks andC structure associated with oxygen and hydrocarbons are enhanced, while the metal109Table 5.3: SE results for inconel film grown at 0.4 Pa based on the minimization ofthe difference between the dielectric function of two equally dense layers of differentthicknesses assuming a bulk layer and surface roughness.Sample Thickness of Thickness ofrough layer bulk layer(A) (A)Thick sample 5±5 186±7Thin sample 7±5 127±5carbide and graphitic carbon structures are reduced. Taking into account the increasedsurface sensitivity for small take-off angles, we conclude from a comparison of the abovedata that the top surface layer of the sample is a contamination layer followed by a verythin oxidized inconel layer. Fig. 5.11 shows photoelectron spectra for Ni2 and C1 froma C/inconel bilayer (the C layer being on top of the inconel layer). In contrast withFig. 5.9, no metal oxide peaks are now observed, which indicates that inconel is protectedby the C layer and that the oxidation in the previous sample is due to contact with airafter removal from the deposition system.The inconel/C sample was studied after a series of bombardments with Ar ions.After a few minutes of bombardment, the C peaks related to contamination, the metaloxide peaks, and the oxygen peaks disappeared, thereby supporting the model that thecontamination layer and oxide layer are uppermost. Simultaneously, the intensities of thegraphitic C—C and C—metal peaks increased, and the metal peaks in the inconelenvironment are still observed. Fig. 5.12 shows the KLL Auger spectrum at this stage110>U)a)CDU,C0)CFigure 5.9: XPS spectra of Ni2 and C1 of as-deposited inconel/C bitayer using AL Kcx-rays taken at a take-off angle of 900.111Binding Energy (eV)Binding Energy (eV)Table 5.4: Spectroellipsometry analysis of “thin” and “thick” C samples with a two-layer model consisting of a bulk layer and surface microroughness. Porosities wereincorporated in both layers with EMA.Sample Unbiased Thickness Of VolumeEstimator Bulk Layer Fraction Of(A) Bulk LayerThin 0.03 171±3 0.99±0.04Thick 0.02 239±3 1.00±0.03of bombardment; the fine structure at 271.6 and 275.8 eV is characteristic of thepresence of carbide (Ni3C)96 and hence is consistent with the concept of carboninterdiffusion into the inconel.With further ion bombardment, a stage could be reached where the only XPSpeaks observed are those due to carbide, graphite, silicon and its oxide. This providesa direct probe of the inconel/carbon interface, an observation that is further supported byan enhancement in the fine structure in the carbon AES spectrum.Fig. 5.13 displays the intensity of different photoelectron peaks for the inconel/Cbilayers normalized to the intensity of the Si peaks as a function of 1/sinO, where 8 is the(take-off) angle between the plane of the sample surface and the axis of the detector.The different variations for the metallic peaks suggests that these elements are notuniformly distributed in the inconel layer.From the XPS results, we obtained the multilayer models shown in Figs. 5.14 and5.15 for our two bilayer samples. For the inconel/C bilayer, the intensity of the C and the112(I)a)(I,Ca)CFigure 5i0: XPS spectra of Ni2 and C1 of as-deposited inconel/C bilayer using Al Kox-rays taken at a take-off angle of 300.113Binding Energy (eV)286 284Binding Energy (eV)D(1>(I)CCDCoca)CFigure 5.11: XPS spectra of Ni2 and C1 of as-deposited C/inconel bilayer using Al Kocx-rays taken at a take-off angle of 9Q0Binding Energy (eV)292 290 288 286 284 282 280Binding Energy (eV)114-%0Figure 5.12: AES spectra of inconel/C bilayer after ion sputtering. The spectrumdepicts a KLL transition from C in a carbide environment.Si peaks is calculated fromI i (i-exp(—d/1sinO)) (5.1)I9- I exp(—d/1sinO) (5.2)I is the intensity of photoelectrons coming from the300Binding Energy (&d)where 0 is the take off angle,atomic level Y of the element X in the material of interest, 1 is the intensity of the11512-NH- o Cr‘00 MoAC! 40z20 l I I I1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.01 /sinOFigure 5.13: Intensity of different x-ray photoelectron peaks normalized to silicon peakas a function of 1/sine for inconel/C bilayer after ion sputtering, where 8 is the take offangle.116reference spectra coming from the atomic level Y of the pure element X, d is thethickness of the carbon layer, and I is the mean free path of the electrons in carbon.The thickness of the graphite layer in the first sample was deduced by plotting theleft-hand side of the following equation, which was obtained from taking the ratio of theabove equations, as a function of 1/sin 9:‘C I’S -Iln( is ‘4 (5.3)I ir 4,sino‘Cu’s’I used the semi-empirical expression (4.6) to calculate the mean free path in C and Siand obtained 1= 15.4 A and I=22.3 A. The deduced graphite layer thickness is 13±2 A.Fig. 5.16 shows the Ni2 and C1 spectra of the C/inconel sample after 5 minutesof ion bombardment. Only two C peaks are observed: graphitic C, and metal carbide.AES measurement confirms the presence of graphite in its pure form since there is nosplitting of the C peak97 (Fig. 5.17). Fig. 5.18 shows XPS spectra from the same sampleat a take-off angle of 3Q0• The intensity of C in its pure form has increased significantlycompared to the other peaks indicating that the top layer consists of pure carbon (forexample the intensity of the metallic Ni2 (j=312) peak is reduced by a factor of 3.1compared with the situation in Fig. 5.16).After annealing both bilayers, the 0 and Si peaks were significantly enhancedwhereas the C peaks totally disappeared. The disappearance of C could be the resultof diffusion of C atoms into the substrate and reaction with oxygen which is present insmall amounts in the furnace table.117ContaminationI !°‘oxideFigure 5.14: Overlayer model for inconel/C sample.118Inconel,. C -I CD CJ1a’ 0 CD CD -I 3 0 ci CD 0 3-D CD>‘0CD>.(I)a)CFigure 5.16: XPS spectra of Ni2 and C1 of C/inconel bilayer usingA1 Ko x-rays takenat a take-off angle of 900 after 5 minutes of ion bombardment.120Binding Energy (eV)Binding Energy (eV)(I,CCBinding Energy (eV)Figure 5.17: AES spectra of inconellC bilayer after ion sputtering. The spectradepicts a KLL transition from C atoms in a pure graphite environment.Fig. 5.19 gives the GXR patterns of a 5-period multilayer as-deposited andannealed at various temperatures. Multilayer structures represent a composite of all thespecific characteristics of the individual component elements. The as-deposited GXRpattern was curve-fitted to determine the thickness and interfacial roughness of thecomponent layers. The optical constants were assumed to be the ones obtained fromthe GXR analysis of single layers. Five adjustable parameters were used to fit the GXRspectra: the layer thicknesses, roughness, and a scale factor m which was discussedearlier. The results of this curve-fitting are shown in Table 5.5. Annealing up to 300°Cdid not show any noticeable change in the spectrum. Above 300°C several changes inthe GXR spectrum were observed; (i) the peaks shifted to higher angles, (ii) theirlinewidth broadened, and (iii) the interference pattern became less extended. These121>‘Li)Li)a)Figure 5.18: XPS spectra of Ni2 and C1 of C/inconel bilayer using Al KcL x-rays takenat a take-off angle of 3Q0 after 5 minutes of ion bombardment.122Binding Energy (eV)Binding Energy (eV)Table 5.5: Properties of inconel/carbon multilayers obtained from GXR analysis.Thickness Thickness Roughness Roughnessof C of inconel of C of inconel(A) (A) (A) (A)15±1 17±1 2.8±0.1 6±1changes in the GXR pattern are attributed to interdiffusion between subsequent layers.Interdiffusion results in a decrease of the difference in electron densities between theconstituting layers and the roughening at the interfaces. As a consequence, the numberof the interference peaks and their intensities significantly decrease.98 The peak shift tohigher angles can also be interpreted in terms of an increase in the period of themultilayer which may occur as a result of crystallization.99 The considerable broadeningof the linewidth of the interference peaks also suggests that there is a large fluctuationof the period of the multilayer.98 Annealing at about 600°C completely destroys theinterference pattern. The same results were obtained for 5-period multilayer samples withslightly different thicknesses.Fig. 5.20 gives the GXR pattern of a 30-period multilayer (a) in the ideal case ofa periodic multilayer structure with parallel, sharp, and smooth interfaces, (b) for thetheoretical fit of my experimental data, and (c) as measured for one of my sputterdeposited samples. The measured first order reflectivity was 15% of the theoretical one(1.7% compared to a theoretical 6.5%). The secondary peaks of the experimental GXR12310-1 - \....._.. .10-2 - \.10 rI 0 I I1O-2 3 4 5 6 7 820Figure 5.19: Normalized grazing incidence reflectivity data for a ten-layer multilayer as-deposited and at different annealing temperatures.124L()liii I 1111111 I 11(1111 I 1111111 I I 11111 I I 1111111 I I liII I I I4III I I I II I lI1r_____‘a,004-._ _ _CN40—4.’oc)U,-CO_ _4-•—00I s d:00II I $ U,I a,I U)_I s- U__C4Jf.__0)ON, h_.__ _0r_•10C. -.SS“I I 1111111 I I III I I hiii miii I I lillill I IIIIIii I Iiiiiil I I hiIi0C,,Lg) * C, C4 . 0 V0 0 0 0 0 0 0 0 0 0,- - - ‘-,-- 1 1(ne) AI!sueuIFigure 5.20: GXR data for a 30-period multilayer (a) in the theoretical ideal case, (b) forthe theoretical fit, and (c) for the experimental data. The curves were arbitrarily shiftedfor the sake of viewing.125curve (Fig. 5.20(c)) are regularly spaced which suggests that my multilayer has a verysmall thickness error (<0.5 A). The amplitude of these secondary peaks decreasesrapidly with increasing the grazing angle which indicates that the roughness is increasingwith the number of layers. Fig. 5.20(b) shows a simulated curve assuming a constantroughness of 2.5 A for the carbon layer and a linear increase of the roughness of theinoonel layer from 2.5 A to 5.2 A throughout the stack.This sample was then tested at the LLNL with synchrotron radiation at 45 Awavelength. The measured reflectivity was 0.3% compared to a theoretical 5.5% (6% ofthe theoretical reflectivity). Fig. 5.21 gives the theoretical reflectivity at 45 A as a functionof the number of periods. This figure indicates that a high reflectivity would only beachieved by growing a multilayer with more than 100 periods. The theoretical reflectivityfor a 150-period multilayer is 36.9% compared to 5.5% for a 30-period multilayer. I didnot grow samples with a larger number of periods because my sputtering system is notstable enough to be operated for several hours. If I had grown a 150-period multilayerand if I assume that the relative ratio of experimental and theoretical ref lectivities is thesame(54‘ R lexpenmenta!‘3O 30then I would have obtained a reflectivity of 2.0% which is comparable to the values shownin Table 1.1.126Figure 5.21: Theoretical reflectivity of multilayers for 45 A radiation as a function of thenumber of periods.403530>N>C-)0)‘4-0)10500 15 30 60 7590 105N Limber of perods120 135 1501275.4 ConclusionsIn this chapter, magnetron sputtering was used to fabricate single layer films,bilayers, and multilayers of carbon/inconel. The refractive indices of inconel and carbonlayers at 1.54 A were determined. Interdiffusion occurred between the carbon and theinconel layers and inconel oxidized when exposed to air. When annealed, theinterference pattern of the GXR spectra of carbon/inconel multilayers broadened until itdisappeared at about 600 °C. This is attributed to interdiffusion between layers and tolarge fluctuation of the period of the multilayer.This preliminary study indicates that inconel/carbon has potential to be a goodcombination for x-ray multilayers since the interference pattern of C/inconel multilayersis extended at 1.54 A. However, the new combination does not seem suitable for intensesynchrotron radiation since it is destroyed at a relatively low annealing temperature(600 °C). More work needs to be done in order to enhance the performance of thismultilayer system. In this thesis I will try to enhance two aspects of the deposition ofthese multilayers: (1) decrease the roughness of the multilayers by bombarding the layersduring growth in chapter 6 and (2) control the reproducibility of the thickness of the layersusing an in situ ellipsometer in chapter 7.128Chapter 6Optimization of Deposition Conditions6.1 IntroductionProperties of optical thin films can be improved by ion bombardment of a growingfilm.86 Ion bombardment enhances the surface mobility of adatoms and, thereby,promotes faster coalescence of the island structure in the early stage of a growing film.It also results in the densification of the film by disruption of columnar growth. However,in the case of a multilayer structure, bombardment can enhance diffusion between layers.The degree of intermixing depends on the energy and mass of the bombarding ions.In this chapter, I provide a comprehensive characterization of inconel/carbonmultilayers as a function of substrate bias voltage in order to optimize the depositionconditions of this system and, therefore, enhance its performance. Single layers, bilayers,and multilayers of inconel and carbon are grown and analyzed with the samecharacterization techniques used in the two previous chapters. Two sets of bilayer andmultilayer samples are analyzed: one set with a period of 22.5 A and the other set witha period of 45 A, which correspond to first-order and second-order reflections of 45 A atnormal incidence, respectively.6.2 ExperimentCarbon and inconel were grown with the first sputter deposition system describedin chapter 3. The deposition conditions were similar to the ones in the previous chapter129except for the few following differences. The samples were deposited at a sputter powerof 40 W for inconel and 58 W for C. Samples were produced with substrate bias voltagesin the range from a floating potential (—15 V for inconel and —30 V for carbon) to —130 V.For bilayers and multilayers we will denote by (V1,2)the substrate voltages during thedeposition of inconel (V1) and carbon (V2). The average amount of material deposited persubstrate pass was about 5.5 A for inconel and 0.9 A for C.6.3 ResultsFigs. 6.1 and 6.2 give the GXR patterns of inconel and carbon samples depositedafter 44 and 160 substrate passes, respectively. The intensity of these peaks was shiftedin these figures for the sake of clarity. For inconel samples, the effect of applying anegative bias is to enhance the interference pattern with the most pronounced patternsobtained for samples grown with a bias voltage between —40 V and —60 V. For carbonsamples, the interference pattern is very evident even at low bias, —30 V (floatingpotential), and no additional improvement is observed with the application of a largerexternal bias. Greater biases (e.g. —130 V) appear to roughen both inconel and carbonfilms.The GXR data were curve-fitted using the same procedure discussed in theprevious chapter to determine the optical constants, thicknesses, and interfacialroughness of the component layers. The carbon data were curve-fitted using the onelayer model whereas the inconel data were curve-fitted using the three-layer model. Theresults of this curve-fitting are presented in Table 6.1 for carbon layers. The best-fit1301 0515V1 041 03D 1021 01Ca) ‘J \;4P•\’/10° %f /\p110-I \.% ‘ V‘ —.‘I10-2 \.• 410-3..I I .b0 1 2 3 4Grazing Angle (Degrees)Figure 6.1: Normalized grazing incidence reflectivity data for inconel samples grownwith different bias voltages.131-40 V1 04-80 V10I_______103>\1102C4-C— 101_••\.100...‘.0, 5’.f1 0-10.0 0.5 1.0 1.5 2.0 2.5Grazing Angle (Degrees)Figure 6.2: Normalized grazing incidence reflectivity data for carbon samples grownwith different bias voltages.132Table 6.1: Properties of carbon layers as a function of bias voltage, obtained fromGXR analysis.Bias Layer Roughness Roughness 6x10Voltage Thickness at Top At BottomSurface Surface(V) (A) (A) (A)-30 162.7±0.2 7.0±0.4 1.7±0.4 5.9±0.7-40 202.4±0.2 3.2±0.4 5±1 4.8±0.8-80 197.2±0.2 4.1±0.2 1±1 6.1±0.7-130 184.0±2.0 6.0±0.8 10±3 6.0±0.6parameters for inconel were: (a) for the —40 V sample: d1=1 6.2 A, d2=1 34.5 A, d3=1 0.0 A,2Ox1O6,min2X1O6,and (b) for the —60 V sample:d1=30.3 A, d2=1 42.0 A, d3=7.9A, max20><1 6, min2><1 Fig. 6.3 shows the fit obtained with these parameters forinconel and carbon samples grown with a bias voltage of —40 V.Figs. 6.4 and 6.5 give the real and imaginary parts of the pseudodielectric data forinconel layers grown with different bias voltages. Figs. 6.6 and 6.7 give the real andimaginary parts of the pseudodielectric data for carbon layers grown with different biasvoltages. The SE data for the incone and carbon samples were fitted using the opticalmicrostructural analysis described by Aspnes et al.80’91 The reference dielectric functionsfor carbon and inconel used in the fitting procedure are the ones found in chapter 5. Ihave assumed that the morphological and optical properties of inconel thin films do notchange significantly with the application of a substrate bias since the pseudodielectric1331O104103Lu. 102C04-& 10110010-1021 Q52—1 07C2103ci)C21 Q221 Q10.0 0.5 1 .0 1 .5 2.0 2.5 3.0 3.5 4.0 4.5 5 0Gro7ng onge (Degrees)Figure 6.3: Measured (full curve) and calculated (dashed curve) reflectivity versusgrazing angle for an inconel and a carbon film grown with a substrate bias of -40 V.1 2 3 4Grazing Angle (Degrees)134CC-)C.)C)q)0IDD(nci00C0a)\\\\—1 5 V———40V—80V—100 V—130 V1 5.01 0.05.00.0—5.0—10.0—1 .5Figure 6.4: Real part of pseudodielectricdifferent bias voltages1352.0 2.5 3.0 3.5 4.0 4.5Fnergy (eV) 5.0function of inconel thin films grown with• 40.035.0____0- 30.025.020.0(I)0Ci1 0.0>C 50C1.55.0Figure 6.5: Imaginary part of pseudodielectriC function of inconel thin films grown withdifferent bias voltages.—isv—40 V—60V—100 V—130 V-—-——- ——-— I2.0 2.5 .0 3.5 4.0 4.5Energy (eV)136Table 6.2: Spectroellipsometry analysis of inconel samples as a function of biasvoltage, with a one-layer model.Bias Unbiased Thickness VolumeVoltage Estimator Fraction(V) (A)-15 0.0091 190±15 0.92±0.02-40 0.0083 167±10 0.97±0.02-60 0.0048 170±6 0.95±0.01-100 0.0047 175±7 0.96±0.01-130 0.0031 171±4 0.98±0.01data were very similar for all of the studied samples. A two-parameter model based ona one-layer model was used, with the film thickness and porosity varied to obtain the bestfit. The porosity of the layer was incorporated in the model with the EMA theory89 relevantfor a random aggregate structure. The parameters which best fit the data and theunbiased estimators are shown in Tables 6.2 and 6.3 for inconel and carbon layers,respectively. The thicknesses given in 6.2 are in good agreement with the GXR resultsin Table 6.1, for carbon layers. In 6.2 and 6.3 the volume fractions of both carbon andinconel increase with the application of a substrate bias in agreement with previous workon ion bombardment effects on sputter-deposited thin films.100’1X-ray photoelectron spectra of inconel/carbon bilayers (with the carbon layer beingon top of the inconel layer) were taken for photoelectrons associated with Ni2,Cr2,M03d,C1, and O orbitals. Fig. 6.8 shows XPS spectra of Ni2 for samples grown with a biasvoltage of (a) —40 V and (b) —130 V for 90° take-off angle, and (c) —130 V for 30° take-off1371 2.00C-)C:3U6.0o 0.0 -aaci-)ft:—3.0 -1.5 5.0FIgure 6.6: Real part of pseudodielectric function of carbon films grown with differentbias voltages.S—30V—— —40V—80v—130 V20 2.5 3.0 3.5 4.0 4.5Energy (eV)1381 2.0UCD(-)9.0UV001::E 0.0— 1.5 5.0Figure 6.7: Imaginary part of pseudodielectric function of carbon films grown withdifferent bias voltages.1392.0 2.5 3.0 3.5 4.0 4.5Energy (eV)Table 6.3: Spectroellipsometry analysis of carbon samples as a function of biasvoltage, with a one-layer model,Bias Unbiased Thickness VolumeVoltage Estimator Fraction(V) (A)-30 0.022 167±14 0.93±0.14-40 0.021 201±13 0.95±0.09-80 0.022 202±14 0.96±0.09-130 0.033 199±24 0.97±0.14angle. The photoelectron spectra of Ni2, Cr2, and Mo3d show an oxide peak and ametallic peak for the sample subjected to a —130 V substrate bias; for example, themetallic and oxide peaks for Ni2 0=3/2) are at 853.5 eV and 856.7 eV, respectively.Other XPS spectra were also taken but were not included in this thesis. The carbon C1spectra revealed the five different component binding energies obtained in chapter 5. TheO., structure has the two regular binding energies corresponding to oxide and hydroxide(OH).By comparing the XPS spectra of different samples, it was found that the Ni peakshowed no trace of oxide for the (—40 V,—40 V) sample, very little oxide for the(—15 V,—30 V) and (—100 V,—100 V) samples, and large amounts of oxygen for the(—130 V,—130 V) sample. To understand the source of oxide we grew a set of sampleswith layers twice as thick as the layers of the previous set. No trace of oxide wasdetected in any of these samples, which suggests that carbon provided a diffusion barrierto oxygen. For the first set of samples the presence of oxide peaks in the bilayers can140(a)(b) /(c)8”’D 35- (,O 55 SOBinding Energy (cv)Figure 6.8: XPS spectra of Ni2 of as-deposited C/inconel bilayers grown with a biasvoltage of (a) -40 V and (b) -130 V using Al Kc x-rays taken at a take off angle of 900,and (0) -130 V at a take off angle of 300.141be correlated to the roughness of the inconel layer. From the GXR measurements, it wasshown that the roughness of the inconel layer was affected by the substrate bias and thatthe smoothest samples were grown with a bias between —40 V and —60 V. As we moveaway from this optimal range of bias values the inconel layer becomes rougher which inturn roughens the thin carbon layer and provides holes or cracks through which oxygendiffuses. In other words, the carbon layer formed a continuous film only for the(—40 V,—40 V) sample. The coalescence thickness of a carbon layer is therefore of theorder of 10 A and depends on three major parameters: (1) the roughness of theunderlying layer, (2) the growth process of carbon which depends on the depositionconditions, and (3) the degree of interdiffusion between carbon and inconel. As shownby curve (c) in Fig. 6.5, the intensity of the oxide peak associated with Ni2 significantlyincreased when the take-off angle was changed from 900 to 30° for a C/inconel bilayergrown with a substrate bias of —130 V. This result indicates that the concentration ofoxygen in the inconel layer is largest at the top, which suggests that the presence ofoxygen in the inconel layer is due to contact with air after removal from the depositionsystem. From these XPS measurements, a substrate bias of about —40 V seems to beoptimal for the fabrication of inconel/carbon multilayer mirrors with a period of 22.5 A.In Fig. 6.9, the ratio Ni/Cr determined by XPS is plotted as a function of substratebias. These results show that the Ni/Cr atomic ratio is lower in the film than in the targetwhere it is equal to The rate K at which component n of the deposited alloy isbeing incorporated into the film is given by102K — (6.1)1422.22.00Cu1.8C0Co016£0C.)I0z1.21.0 1500Figure 6.9: PJot of the Ni/Cr composition ratio deduced from XPS measurements asa function of bias voltage for C/inconel bilayers whose period is 22.5 A.30 60 90 120Substrate bias (-V)143Here, Rn is the rate that the nth component is condensing at the film surface, S is theresputtering rate, and V,1 is the re-evaporation rate. At very low bias voltages resputteringis negligible (S0) since there is very little bombardment of ions and neutrals at thesubstrate. The spatial distribution of the sputtered atoms and, hence, the rate ofcondensation of each of the alloy components at the substrate are strongly dominated bythe relative masses and numbers of the cathode and gas atom species since thesputtered atoms change energy and direction whenever they undergo a collision. Theyundergo about 3 to 5 collisions at our working pressure (0.4 Pa). Unfortunately, data onthe spatial distribution profiles of alloy species have been collected only for a few alloysystems, and not generally under the types of high flux conditions consistent withmagnetron sputtering. However, lighter elements are generally expected to undergo morescattering than heavier ones resulting in a reduced deposition rate of the lighter elementat the substrate.103 Our XPS results indicate a larger content of the lighter element (Cr)in our films excluding spatial distribution to be the cause of our findings. Eqn. 6.1suggests that a low content of Ni in the film in comparison to the target is due to a largerevaporation rate for Ni than for Cr. Considerable evaporation occurs from the substrateat initial stages of film condensation and the sticking coefficients of the different elementsare therefore small.104 Re-evaporation is also enhanced because of our low depositionrate. 102In Fig. 6.9 the ratio Ni/Cr appears to increase with the application of a substratebias. Biasing the substrate results in its bombardment with energetic species which144consist of the condensing film atoms, gas atoms from the working gas, or impurity atomsfrom the chamber walls or the background gas.105 The energetic bombardment mayoriginate from a variety of sources, including reflected neutralized primary ions from thetarget surface, energetic ions and electrons from the plasma, negative ions created at thetarget surface during sputtering, charge exchange neutrals, and energetic sputteredatoms from the target.105 The bombardment of a multicomponent solid surface with ionsor neutral atoms alters the chemical composition of the surface due to the difference inthe sputtering yield of the constituents.106 The constituent with the largest sputter yield,Cr in our case, is preferentially removed from the surface, enriching the surface layer inthe lower sputter yield material, Ni. The species which is deficient in the biased filmappears as surplus in films which are deposited at surfaces with less bias such as theanode or the chamber walls.107 To confirm that Cr is preferentially sputtered in an inconelenvironment, I have grown an inoonel/C bilayer (the inconel layer being on top of the Clayer). The sample composition was determined by XPS for as-deposited films and aftera series of bombardments with soft Ar ions, The Ni/Cr ratio significantly increased withthe bombardment which demonstrates that Cr is preferentially sputtered.Fig. 6.10 gives GXR patterns of 30-period multilayers whose period is 45 A, whichwere deposited with different bias voltages. Table 6,4 gives first order reflectivitiesmeasured at 1.54 A for the different samples. This table indicates that the performanceof my multilayers is optimized for —80 V bias voltages.Fig. 6.11 gives the GXR patterns of 30-period multilayers whose period is 22.5 A,which were deposited with different bias voltages. Table 6.4 gives first order reflectivities1451051 04103102Cd101Co1001 0-11 0-21 0-31 0-40Figure 6.10: Normalized grazing incidence reflectivity data for 60-layer multilayermirrors with a period of 45 A, deposited with different bias voltages.1 2 3 4Grazing Angle (Degrees)146Table 6.4: Measured first order reflectivities for 60-layer multilayers with a period of45 A deposited with different bias voltages.Bias ReflectivityVoltage(V)Ideal case 41%-15,-30 16%-60,-60 22%-80.-80 25%-130,-130 11%measured at 1.54 A for the different samples. This table indicates that the best reflectivityis obtained for a —40 V bias voltage.The difference between the optimal conditions of the two sets of samples may beexplained in terms of the two competitive processes that take place due to ion—induceddeposition of multilayers: (i) smoothing of the layers, and (ii) intermixing at the interface.The former enhances the reflectivity while the latter decreases it. The results obtainedwould indicate that the optimum trade-off depends on the thickness of the layers.Fig. 6.11 indicates that a multilayer coating fabricated with an electrically floatingbias (—15 V,—30 V) exhibits relatively sharp reflection peaks, whereas Fig. 6.1 indicatesthat the interference pattern of a single layer of inconel film produced under the samebias conditions is destroyed. To help explain these conflicting results we have grown inaddition to the (—15 V,—30 V) sample a (—15 V,—130 V) sample. Unlike the first sample,the second one did not exhibit sharp reflection peaks. For both samples, one would147104103105_102 ‘VA. 101 NU). 10°& .‘b10-11 0-2—10-3 •4%10-40 1 2 3 4Grazing Angle (Degrees)Figure 6.11: Normalized grazing incidence reflectivity data for 60-layer multilayermirrors with a period of 22.5 A and deposited with different bias voltages.-40 V,-40 V——-60V,-60V——- -80V,-80V-130 V.-130VA148Table 6.5: Measured first order reflectivities for 60-layer multilayers with a period of22.5 A deposited with different bias voltages.Bias ReflectivityVoltage(V)Ideal case 7.0%-40,-40 2.5%-60,-60 1.0%-80.-80 0.6%-130,-130 0.1%expect from our study of single layers a rough inconel layer to be first deposited.However, because of sequential deposition of the inconel and carbon layers, a freshlygrown inconel layer is bombarded by ions accelerated by the self-bias produced by thecarbon target. The ion bombardment caused by the self-bias (—30 V) in front of thecarbon target smooths the inconel layer in the early stages of carbon deposition, whilethe —130 V externally applied bias increased roughness.6.4 DiscussionThe results of the GXR data indicate that the roughness of relatively thick singlelayers is larger than that of thin layers in a multilayer structure with a similar totalthickness. These results are in agreement with the results found by Savage et al.108 Thesurface roughness of a single layer film increases with increasing thickness as dS where0.25<s<0.50. The parameter s takes on the value 0.5 in the extreme case where atoms149impinge on the substrate without subsequent surface diffusion resulting in an average filmthickness with a Poisson distribution. The film morphology depends only on the differentkinetic processes during film growth in terms of a competition between the arrival rate andthe diffusion rate of the impinging atoms. Another factor that contributes to surfaceroughness is shadowing.108 For a multilayer structure, Savage et al.’°8 have shown thatinterfacial roughness depends on the thickness of the individual layers. This phenomenonis attributed to the presence of interfaces between subsequent layers which suppressesthe increase in roughness that would occur in single layer growth.RMS values for the surface roughness at the inconel/carbon and carbon/inconelinterfaces are usually obtained by curve-fitting GXR data with a Debye-Waller factor. Thisfactor is equivalent to a transition layer with a continuously varying refractive index whoseprofile is an error function.44 Such a profile may also be used to model interdiffusionlayers.””°9 It is therefore very complex to differentiate between roughness andinterdiffusion in GXR measurements.Modification of the surface morphology by ion bombardment has been investigatedby many workers, but is still not fully understood.UO At low ion energies (<—100 eV)subsurface damage and gas incorporation are relatively low.1 At these energies thesputtering yields’°° are generally low (1 0-i 01) and the ions preferentially redistribute thedepositing species rather than resputter them. A low energy ion penetrates the film toa depth of 10—30 nm depending on the ion and film atomic masses.101 During penetrationthe ion loses energy by electronic excitation and kinetic energy transfer to knock-onatoms.214 Surface smoothing by low-energy ions is due to sputtering of weakly bonded150atoms from pointed surface formations and to an increase in surface diffusion. Filmdensities are observed to increase due to surface atoms being sputtered forward intovoids and local heating to fuse grains. The density increases rapidly at low ion energiesbecause a weakly bonded porous structure is easier to reorder and density than a moreclosely packed one.115 When sputtering begins to predominate over diffusion in adatommovement, surface roughness increases and etch patterns appear on the surface.’16Other workers have found optimal ion energies between 30 and 50 eV,7’8similar to ourresults.This study also re-emphasizes the need for understanding the earliest stages offilm formation in the optimization of multilayer coatings. In what follows, I give a briefreview of the different growth processes of thin films and discuss their relation tomultilayer performance. There are three thin film growth mechanisms:5°4(1) Island growth: It occurs when small stable clusters nucleate on the substrate andgrow in three dimensions to form islands. This takes place when atoms or molecules inthe deposit are more strongly bound to each other than to the substrate.(2) Layer growth: It occurs when the growth of small stable clusters is overwhelminglyin two dimensions resulting in the formation of planar sheets. This takes place when theatoms are more strongly bound to the substrate than to each other.(3) Stranski-Krastanov growth: Starts as layer growth but subsequent layer growthbecomes unfavorable and islands form.To grow good quality multilayer films, the growth mode should ideally be a layergrowth to minimize (1) the roughness and (2) the coalescence thickness of the layers.151The future of multilayer structures for normal incidence reflectivity at short wavelengthswill be set by the critical particle thickness dimension.103 Evans et al.103 showed that thereflectivity R’ of a 2N layer stack with the metal layer being covered by a fraction f is (f=1when the layer is fully covered):= f (j_fN) (6.2)R N (1-f)where R is the reflectivity of a multilayer with continuous metal layers (f=1). For example,for 2N=60 and f=0.9, then R’= 0.08 R. My XPS measurements revealed that coalescenceof 12 A thick carbon layers was only obtained for a substrate bias voltage of(—40 V,—40 V). A study of the growth process of inconel and carbon layers andmultilayers will be conducted under different deposition conditions with an in situellipsometer in chapter 7.The tendency to form a layer growth is increased by’°4 (1) a low substratetemperature, (2) a high boiling-point film material, (3) a high deposition rate, (4) strongbinding forces between film and substrate, (5) a low surface energy of the film material,and (6) a high surface energy of the substrate. This suggests that the growth of goodquality inconel/carbon multilayer mirrors requires the optimization of (1) the depositiontemperature, (2) the deposition rate, and (3) the adatom diffusion through ionbombardment of the substrate. These mechanisms are discussed below:(1) Substrate temperature: A low substrate temperature results in a small critical nucleusfor which coalescence occurs at a relatively low coverage. At very low temperatures,152however, surface mobility of adatoms is very low resulting in rougher films. An optimalsubstrate temperature is therefore required. Most workers have fabricated multilayermirrors at room temperature. The few temperature dependence studies conducted so farinvolve electron beam evaporated samples. Ogura et aL24 were the first group to reporton increased reflectivity at optimized substrate temperatures for Mo/Si multilayer coatings.More recently N jibe et aL’19 and Kloidt et al.12°observed a substantial enhancement in thereflectivity for Mo/Si coatings deposited at 150 °C. On the other hand, Puik et al.121observed an increase in reflectivity for Ni/Si and Ni/C at 100 °C and below roomtemperature, respectively.(2) Deposition rate: Increasing the deposition rate results in smaller islands and in higherrates of island formation. This means that a continuous film is produced at lower filmthicknesses. Higher deposition rates also decrease the number of impurities in the film.However, it is more difficult to control or monitor the thickness of the layers if thedeposition rate is too high.122 An optimal deposition condition is needed for which acompromise between both effects is found. To the author’s knowledge, there is nosystematic study of the properties of x-ray multilayers as a function of deposition rate.Most of the deposition rates used so far range from 0.2 to 2 /s.45’7222124(3) Ion bombardment of the substrate: As was mentioned in the introduction of thischapter, ion bombardment enhances the surface mobility of adatoms and promotes fastercoalescence of the island structure in the early stages of a growing film. However, ionbombardment also enhances interdiffusion of subsequently deposited layers. An optimalion bombardment is needed as demonstrated in this work. Puik et al.’2”5 used ion153bombardment both during (ion assisted deposition) and after deposition (ion etching) toreduce the roughness of electron beam deposited multilayers and therefore enhance theirreflectivity. Ion etching results in a higher reduction in roughness than ion assisteddeposition.121 Spiller et al.’26 enhanced the reflectivity of x-ray mirrors by ion polishingwhich consists in bombarding the surface of the growing film with an ion beam at grazingangle. This method minimizes momentum transfer normal to the surface and, therefore,does not enhance interdiffusion at the interface between the high and low index materials.6.5 ConclusionsIn this chapter, single layer films, bilayers, and multilayers of carbon/inconel weregrown with different substrate bias voltages. The application of a moderate substrate bias(—40 to —80 V) was found to optimize the deposition conditions of x-ray reflectors asshown from XPS and GXR measurements. It also resulted in the densification of the filmas confirmed by SE. Samples for second order reflection (period = 45 A) were found tobe more stable than samples for first order reflection (period = 22.5 A) and, therefore, areexpected to be more suitable as multilayer mirrors.154Chapter 7In situ Ellipsometry7.1 IntroductionIn this chapter in situ ellipsometry is used to (1) understand the evolution of filmgrowth of inconel/carbon multilayers and (2) to control the reproducibility of the thicknessof the layer throughout the multilayer stack. To achieve these two goals the complexreflectance ratio p, which is the measured value in ellipsometry, is fitted with a theoreticalmodel to determine the thickness d of the layers. The theoretical modelling wasdiscussed in detail in chapters 3 and 4. In the ideal case of a homogeneous, isotropic,and plane parallel layer there is a simple and direct relationship between the measuredquantity p and the layer parameters n, k, and d. This relationship was discussed in detailin chapter 4. It is however impossible to determine the three unknowns simultaneouslyfrom a single measurement of p which consists of two values, i.e. the real an imaginaryparts of p. Two groups involved in the research of very thin films (< 100 A in thickness)attempted to solve this problem. I will briefly discuss their approaches to this challengingproblem:7.1.1. Houdy et al.:19’21Houdy et al.9’21 assumed that n and k were equal to the bulk values of theinvestigated materials and ended up solving for one unknown, d. They have devised athickness control routine in which the difference between the theoretical and experimentalvalues of the distance between the point prior to deposition in the (tanNfA) plane,155designated by (tan’q,,A), and the point reached in the ellipsometric trajectory at time t ofthe deposition, designated by (tanqi4) was minimized:21/(tan4r—tan4r2+(A A? (7.1)Through ellipsometry this group has gained unprecedented knowledge on interfaceformation and on thin film nucleation processes192’722729 but was unable to achievebetter thickness control than simply by timing.The model they have used for thickness control had the following weaknesses:(1) The index of refraction of an ultra thin layer is not necessarily the same as theindex of refraction of a bulk material.(2) Porosity in very thin films should be included to account for their growth process.7.1.2. Yamamoto et aL’3°To determine n, k, and d from ellipsometric data, Yamamoto et al.’3°assumed thatn and k remain constant for two slightly different thicknesses of the order of a few tenthsof a nanometer. By measuring p for two thicknesses d1 and d2 data they were able tosolve for four unknowns, i.e. n, k, d1, and d2. This method is very sensitive to smallvariations in refractive index due to inhomogeneities and to errors in the data especiallyat early stages of film formation in which case there is a continuous increase of the filmdensity.131From the above-mentioned studies I feel that monitoring of the ellipsometrictrajectory should be achieved by fitting one data point at a time. My approach involvesthree steps:156(1) Accurately determine the bulk refractive index of the investigated materials, i.e.inconel and carbon.(2) Model the dielectric of a very thin film with an EMA (Eqn. 4.11) assuming that thefilm consists of two phases: bulk material and voids. This dielectric function willthen be converted to a refractive index (n,k) using the following equations:—(7.2)- 2nk (7.3)(3) From a single measurement of p solve for the thickness of the film and the volumefraction of the bulk material.This chapter is divided into six sections. Section 7.1 is an introduction. Sections7.2 and 7.3 present the study of single layers of inconel and carbon, respectively. Themain reasons for this investigation were; (1) determine the refractive index of bulk inconeland carbon, and (2) test the validity of the theory that will be used to monitor and controlthe thickness of multilayer structures in this thesis. In section 7.4, a routine for multilayerthickness control is devised. In section 7.5, bilayers and multilayers of inconel andcarbon are investigated. Finally, section 7.6 gives a conclusion to this ellipsometric study.1577.2 Single layers of inconelFig. 7.1 gives the ellipsometric parameters (tanNIA) evolution of a single layer ofinconel grown for four minutes with a substrate bias of —40 V. A routine based onYamamoto’s method13°was used to fit the ellipsometric data in Fig. 7.1 in order todetermine the complex refractive index of thin films of inconel. Fig. 7.2 is a plot of thecomplex refractive index as a function of thickness while Fig. 7.3 is a plot of the filmthickness as a function of time. Film thickness varies linearly with time since thedeposition rate is not expected to vary especially over such a short period of time. Theaverage refractive index is found to be equal to (2.94±0.03 , 3.02±0.10).The ellipsometric data in Fig. 7.1 was also fitted with a single layer model for whichthe refractive index is modelled with an EMA assuming that the film consists of bulkmaterial and voids. I assume that the bulk refractive index of inconel is (2.94,3.02).Fig. 7.4 is a plot of the volume fraction of inconel as a function of thickness. Fig. 7.5 isa plot of thickness as a function of time. There is less scattering in Fig. 7.5 than inFig. 7.3 indicating the superiority of the EMA model over the Yamamoto model.Fig. 7.6 gives the ellipsometric trajectory for the —40 V sample during the earlystages of growth. At this stage, n, k, and d experience marked changes. As thedeposition proceeds, n and k start from n0 and k0 of the substrate and monotonicallyincrease toward the values for the bulk. The beginning of the growth departs fromhomogeneous growth and then returns to it after a thickness of approximately 10 A hasbeen deposited. This thickness is usually termed critical thickness d0. Yamamoto13°claims that at d=d the film undergoes a transition from an optically anisotropic state to1583.8 I I3.73.63.53.43.33.2 I0.23 0.28 0.33 0.38 0.43 0.48 0.53tansFigure 7.1: Real-time ellipsometric trajectory recorded during the deposition of inconellayers grown with a substrate bias of -40 V.1593.5;, 3.3-DC3.2UCL0 Index of ref motion• Absorption coefficientFigure 7.2: Plots of n and k versus thickness for an inconel layer grown with a substratebias of -40 V. These results were obtained by fitting the ellipsometric data usingYamamoto’s routine.1311603.4. I I• II I .J.LJ 0 0•— •I I C) — ._2.9 OO I I I0 20 40 60 80 100 120 140 160THickness (A)1 601 401201 00CCC-)C604020Figure 7.3: Film thickness versus time for an inconel layer grown with a substrate biasof -40 V. These results were obtained by fitting the ellipsometric data using Yamamoto’sroutine.13’16100 20 40 60 80 100 120140 160 180 200‘I1.015 - I I I I1.01301 .0111.0091 .0071.005E2 1 .0030 0> 0 0 0 00 0I.LRJI 0 0 00.9990.9970.99520410 60 80 100 120 140 160Thickness ()Figure 7.4: Volume fraction versus thickness for an inconel layer grown with a substratebias of -40 V. These results were obtained by fitting the ellipsometric data using an EMAmodel.162160InU,wCC.)I-140.1201 008060402000 20 40 60 80 100 120 140 160 180 200Time (s)Figure 7.5: Thickness versus time for an inconel layer grown with a substrate bias of—40 V. These results were obtained by fitting the ellipsometric data using an EMA model.1633.323.303.283.263.243.223.200.23 0.27Figure 7.6: Real-time ellipsometry trajectory recorded at the early stages of the depositionof an inconel layer with a substrate bias of -40 V. The solid line is the theoreticaltrajectory assuming the growth of a homogeneous layer.0.24 0.25 0.26tan164an optically isotropic state. He also claims that the values found for n and k for d<d areapparent values resulting from treating the film as isotropic. However, Chu et aL131 claimthat the early stage of growth of a thin film can be simulated with a multilayer model witha continuously increasing density.Fig. 7.7 gives the ellipsometric parameters (tanNIA) evolution during the growth ofinconel layers as a function of substrate bias (—20 V to —130 V), Fig. 7.8 is a plot of thevolume fraction of inconel as a function of thickness for the different deposition conditions.From Fig. 7.8, ion bombardment of the films results in the densification of the film inagreement with the findings in chapter 6.7.3 Single layers of CarbonFig. 7.9 shows the experimental ellipsometrictrajectoryfor a carbon film grown witha bias voltage of —40 V for four minutes. The experimental data was simulated with atwo-layer model: the first layer is a 14 A thick composition gradient corresponding to aSi—C interface whose refractive index is (3.07,0.52); the second layer is a 45 A thickhomogeneous layer corresponding to pure carbon and whose refractive index is(2.40±0.13 , 0.57±0.18). The application of an external bias did not affect theellipsometric trajectory suggesting that the properties of the film do not vary with biasvoltage in agreement with the GXR data in chapter 6.7.4 Description of monitoring and control routineThis section is a detailed description of the routine I have developed to control the1653.8__‘V37 -20V -—--V.zzz :gV..3.6_ _ __________ __V‘—V3.4.3.3.r123 0.28 0.33 0.38 0.43 0.480.53tan *Figure 7.7: Real-time ellipsometry trajectory recorded during the deposition of inconellayers with different substrate bias voltages.1661 .081 .071 .061 .051 .02- 1 .01>1 .000.990.980.97—20 V—40 V—80V—100 VI • I • I • FV —V ——•1:V———140 160 1800 20 40 60 80 100 120 200Thickness (A)Figure 7.8: Volume fraction versus thickness for inconel layers deposited with differentsubstrate bias voltages.1673.50 —3.453.40,oJThcPcg4o°335 a0-o—43.303.25 -°- °3.200.237 0.239 0.241 0.243 0.245tan$Figure 7.9: Real-time ellipsometry data for carbon layers.168deposition of inconel/carbon multilayers. The aim of this routine is to reproduce thesequential deposition of 15 A of inconel and 30 A of carbon 50 times (deposition of a 100-layer multilayer). Each inconel and carbon layer is deposited by moving the appropriatetarget back and forth over the substrate 10 and 30 times, respectively (10 and 30‘sweeps’). The average deposition rate per substrate pass should be 1.5 A and 1.0 A forinconel and carbon, respectively. The different steps in the control routine are outlinedbelow:1. The first step is an initialization step. The position of the inconel target is 90°(Fig. 7.10). The current at the inconel and carbon targets are set to 63 mA and150 mA, respectively, since these values were found to give an average depostionper substrate pass of 1.5 A for inconel and 3.0 A for carbon.2. Collect data of bare substrate using the ellipsometer. Determine the dielectricfunction of my bare substrate using Eqn. 3.19. This dielectric function will then beconverted to a refractive index (n,k) using Eqns. 7.2 and 7.3.3. Move the inconel target back and forth over the substrate six times (six sweeps).4. Collect ellipsometric data. Fit the ellipsometric data with a single layer model andsolve for the thickness and the volume fraction of the bulk material. The quantityI have minimized in my fitting routine is/(tanipe-tanip2+(A AJ (7.4)where (tane,Aexp) and designate the experimental and theoreticaldata, respectively.169Figure 7.10: Schematic diagram of the sputtering system.170CarbonInconel5. Move the inconel target over the substrate and determine the new thickness dnew.Rename the previous thickness as dOld. The actual deposition rate per substratepass R1 is:(7.5)6. Adjust the current to the inconel target so that the new value of the current wouldin theory result in a 15 A thick layer at the end of the tenth sweep. The depositionrate per substrate pass R2 needed to obtain a 15 A thick inconel layer is:(7.6)where daim is the thickness aimed for, i.e. 15 A, s is the number of sweepsperformed at the time of the measurement, and 5aim is the total number of sweepsaimed for, i.e. 10. Adjust the current to the new value i1:X (7.7)where toId is the old value of the current at the inconel target.7. Move the inconel target over the substrate three times and repeat (4), (5), and (6)each time.8. After 10 sweeps, determine the actual thickness of the inconel layer dinconet andstart depositing carbon. To compensate for any thickness error in the inconel171layer, the new carbon thickness aimed for dcarbofl jS.d, d- dinconei (78)where d is the period of the multilayer, i.e. 45 A.9. Move the carbon target over the substrate eighteen times.10. Repeat steps (4) to (7) but for carbon.11. After 30 sweeps switch to the depositon of inconel.13. Repeat (3) to (11) 150 times.The above-described routine was used to control thickness during the depositionof my multilayers. Whenever needed, this routine was used to monitor the deposition ofthese multilayers by ignoring the steps that involve current adjustments.7.5 Multilayer depositionFig. 7.11 shows ellipsometric measurements A as a function tan’41 correspondingto the growth of a 10—layer (5-period) inconel/carbon multilayer. Fig. 7.12 showsenlargments of selected parts of the ellipsometric trajectory in the previous figure to studythe “carbon-on-inconel” and “inconel-on-carbon” interfaces, respectively.At the beginning of the deposition of carbon on inconel (Fig. 7.12(a)), theellipsometric trajectory makes a half turn before retracing the trajectory for the depositionof pure carbon. This ‘back-step’ is attributed to the roughness of the inconel surfacewhich is filled in by carbon atoms which are first deposited in the valleys of the underlyinginconel layer; thus, there is transition layer at the ucarbononinconelhI interface. This1723.9Figure 7.11: Real-time ellipsometric trajectory recorded during the deposition of a10—layer inconel/carbon multilayer.0 Deposition of inconelC Deposition of carbon3.87.J.‘ 3.6 V3•5 V3.43.3oo0000000000i0.25 0.30 0.35 0.40 0.45tanq173377 I0.435 0.4373.740.41 0.420.439 0.443 0.4450 Deposition of inconelci Deposition of carbonFigure 7.12: Enlargments of the ellipsometric trajectory in Fig. 7.-li showing (a) thecarbon-on-inconel interface and (b) the inconel-on-carbon interface.3.873.65383a)813.79ro Deposition of inconelO Deposition of carbonCCCCCCCCC0o Cotan *3.803.783.76ci 0 0 000ci 0cicicicici_______________________________ci0tan 4r0.43 0.44174trajectory is simulated by a 5 A thick gradient corresponding to a mixture of inconel andcarbon. As indicated in Fig. 7.11, the relative size of the ‘back-step’ increases with thenumber of layers in agreement with the GXR data in chapter 5. In the case of the‘1nconel-on-carbon” interface (Fig, 7.12(b)) this ‘back-step’ is not observed which indicatesthat it is a sharp interface. Sharp “metal-on-carbon” interlaces were observed by otherworkers21’44and was attributed to the smoothing effect of carbon even on very disturbedsurfaces.A 100-layer multilayer was grown using the routine described in section 7.4 forclosed loop control of thickness. The refractive indices of inconel and carbon weremodelled with an EMA where the bulk refractive were assumed to be the ones obtainedin sections 7.2 and 7.3. Fig. 7.13 gives the ellipsometric data obtained for this multilayer.Fig. 7.14 gives the thicknesses determined from fitting this ellipsometric data. Fig. 7.15gives the experimental GXR data for this multilayer and the theoretical GXR data obtainedwith a model in which the thickness of each layer was assumed to be the one obtainedfrom ellipsometry. The other parameters used in calculating the theoretical GXR data,i.e. layer roughness and the optical parameters and k were assumed to be the onesdetermined in chapters 5 and 6. The reflectivity peaks of the experimental and theoreticalGXR are the same suggesting that the average period obtained with the closed loopcontrol routine is correct. However, there is a discrepancy in the shape of the two curvesespecially for higher order peaks.A 100-layer multilayer was then grown by keeping the current at the targetsconstant and by using in situ ellipsometry as a monitor. Fig. 7.16 gives the ellipsometric1754.4Figure 7.13: Real-time ellipsometry trajectory recorded during the controlled depositionof a 100-layer inconel/carbon multillayer.4.24.03.83.63.43.20.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44tan $1766560 0 Thickness of inconel55 • Thickness Of carbonA Period50___________________A45 AAAAA 4AAAAiAAAAAAAA*AAAAAAAAAAAA AAAAAAAAAA& 4ucii-35ci30 a••••252001 5 •0ooooooooOooOoOoOoooooo0O 00000010 05 I I0 5 10 15 20 25 30 35 40 45 50Boyer numberFigure 7.14: Thicknesses determined from ellipsometric data in Fig. 7.13.177Q61 Q5Q41 Q3- 1 Q21 Q11 000.0Grazing angle (Degrees)Figure 7.15: Experimental and theoretical GXR measurements for a 100—layerinconel/carbon multilayer.1.0 2.0 3.0 4.0178trajectory for this multilayer. Fig. 7.17 gives a plot of the layer thickness as a function ofits position the stack as determined from the ellipsometric model discussed earlier. Theaverage thickness is 31.0±1.0 A for inconel and 27.5±2.5 A for carbon. The averageperiod is 58.0±2.0 A. Fig. 7.18 gives the experimental GXR data for such a multilayer.Fig. 7.19 gives the theoretical GXR data for this samples assuming the layer thicknessesobtained from the previous ellipsometric model (Fig. 7.17). A comparison betweenFigs. 718 and 7.19 indicate that there is a discrepancy between the experimental dataand the theoretical model.The GXR pattern in Fig. 7.18 was modeled assuming the presence of thicknesserrors whose distribution is Gaussian. The standard deviation of the thickness was foundto be 0.6 A. This value is an upper limit since the broadening of reflectivity peaks is alsodue to ‘roughness’ and non-uniformity of the layers (chapter 6). This value is much lowerthan the theoretical value determined in the previous paragraph.To enhance the ellipsometric model I have devised a routine that minimizes thethickness error in the ellipsometric data in Fig. 7.16. I have started with a very simplemodel which assumes each layer to be homogeneous and non-interdiffusing with theadjacent layers. The variable parameters were the bulk refractive indices. Theparameters that minimized the thickness errors are (3.20,3.83) for inconel and (2.40,0.75)for carbon. The thicknesses obtained from this model are: 15.53±0.43 A for inconel,32.08±1.12 A for carbon, and 47.1±1.3 A for the period. Fig. 7.20 gives the theoreticalGXR data obtained with these thickness, The theoretical error in the period is still larger1794.24.03.8 cruD3.6 c00D000003.4000003.2 I I I0.24 0.28 0.32 0.36 , 0.40 0.44 0.48tansFigure 7.16: Real-time ellipsometric trajectory recorded during the deposition of a 100-layer inconel/carbon multillayer by timing.1805045 000 Inconel40 • 0 • Carbon• 0 0U)35 00(I)cii 0- 30 •RI1 0000000000000000000000000000000ci25 0020 000015010I0 5 10 15 20 25 30 3540 45 50Layer postonFigure 7.17: Thicknesses obtained from euipsOmetric data as a function of the iayerposition in the stack.181I I I I I I1O104‘3’ 103102 -U)CC10°-10—1 I I I0.5 1.0 1.5 2.0 - 2.5 3.0 3.5 4.0 4.5Grazing angle (Degrees)Figure 7.18: GXR measurements recorded for a 100-layer inconel/carbon multillayerdeposited by timing.1821 081 07108>.105a)-I1041 03102Figure 7.19: Theoretical GXR data for a 100-layer inconel/carbon multilayer depositedby timing. The GXR data was simulated with the thicknesses obtained from ellipsometricdata.0.0 0.5 1 .0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Grazing angle (Degrees)183Il107- Ii______Theory106_____________/——— Experiment‘II.,10104 1’ tw4-.&103 IIl I102 1101I I I I I0.0 0.5 1 .0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Grazing angle (Degrees)Figure 7.20: Theoretical GXR data of a 100-layer inconel/carbon multilayer.184than the experimental one which suggests that the one-layer model needs to be refined.7.6 ConclusionsIn this chapter, in situ ellipsometry was used (1) to monitor the deposition of singlelayers and multilayers of inconel and carbon and (2) to control the thickness of the layersin a periodic multilayer structure. The optical constants of inconel and carbon weredetermined at 6328 A wavelength. The coalescence thickness of inconel was found tobe 10 A. The control routine was uncapable of achieving a better accuracy than simplyby timing. In virtually all of the applications of in situ ellipsometry the individual layershave traditionally been modeled solely in terms of two parameters (thickness andrefractive index). This simple approach is inadequate in advanced precision opticalsystems and the theory needs to be refined to include second order effects. Theseinclude:(1) Inhomogeneities resulting in the variation of refractive index throughout singlefilms. For instance, GXR data indicated the presence of inhomogeneities in singlelayers of inconel (chapter 5).(2) Anisotropy in the refractive index with direction of radiation.(3) Departures from perfectly planar interfaces.A great deal of work is therefore needed to improve the models used to fit theellipsometric data and therefore be able to control the thickness of the layers in a moreefficient way.185Chapter 8ConclusionIn this thesis, new materials and their optimum deposition conditions for thefabrication of x-ray mirrors that operate at 45 A were investigated.1321 These mirrorsare intended for applications such as x-ray microscopy, x-ray astronomy, x-raylithography, x-ray imaging, and x-ray lasers.A theoretical treatment to identify the appropriate materials for these mirrors wasprovided. The thin film laboratory at U.B.C. was then successfully set up to research xray multilayers: (1) a sputter coater was automated to enable the growth of periodicmultilayers of these materials; (2) software was developed for the analysis of experimentaldata.The optical, chemical, and structural parameters of the deposited materials(reflectivity, layer thickness, layer roughness, optical constants, chemical composition)were measured using three complementary techniques: GXR, SE, and XPS. Theseparameters were studied as a function of argon pressure and substrate bias voltage. Theresults of this study suggest that multilayers prepared at a low pressure and a moderatesubstrate bias (—40 to —80 V) are the most appropriate for x-ray mirrors. Also samplesfor second order reflection (period = 45 A) were found to be more stable than samplesfor first order reflection (period = 22.5 A). Also, surface roughness was found to increasewith the number of periods.In situ ellipsometry was shown to be a powerful technique for monitoring the186deposition of thin films. Through it I have obtained information on the early stages of filmgrowth, interdiffusion at the interfaces, porosity of the films, etc. Interdiffusion, forinstance, was found to occur at the ‘carbon-on-inconel’ interface but not at the ‘inconelon-carbon’ interface. Unfortunately, I was not able to control the reproducibility of thethickness of my layers better than by timing. A systematic study needs to be carried outto further test the capabilities of in situ ellipsometry. The model used to fit theellipsometric data should be improved by taking inhomogeneities and interdiffusion intoaccount.To improve the performance of my multilayers I suggest that the sputtering systemused in this thesis be upgraded. This upgrade may be achieved by using a computerroutine that ensures the stability of the deposition parameters (Ar pressure and power)and therefore allows the deposition of a larger number of periods (> 100 layers).From this thesis I would like to suggest the following avenues of research worthexploring:(1) To investigate the degree of intermixing at interfaces in a multilayer structure asa function of deposition conditions using in situ ellipsometry and AES. This studywould be valuable in microelectronics and optical materials industry.(2) To further explore alloy/carbon multilayers where the alloy material consists of twoelements. The properties and performance of such multilayers would be examinedas a function of the composition of the alloy material. Recently, Cr/C and Nb’Cmultilayers were studied and compared. 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