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Study of Reaction Pathways and Kinetics in Cu(InxGa1-x)Se2 Thin Film Growth


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STUDY OF REACTION PA THWAYS AND KINETICS IN Cu(InxGa1-x)Se2 THIN FILM GROWTH By WOO KYOUNG KIM A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Woo Kyoung Kim

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To my wife Eun Mi, lovely son Jin Woo and my parents.

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iv ACKNOWLEDGMENTS First of all, I would like to express my si ncere appreciation to my research advisor, Dr. Timothy J. Anderson. His academic encouragement and considerate support have inspired me to establish the capability to pe rform independent resear ch, which will be an invaluable asset to my future career. I also want to show my gratitude to my supervisory committee, Dr. Sheng S. Li, Dr. Oscar D. Crisalle and Dr. Valentin Craciun, for kind advice and helpful discussion. I also want to give my special thanks to Dr. E. Andrew Payzant in Oak Ridge National Laboratory for his generous assistance in high temperature X-ray diffraction experiments, and Dr. Jianyun Shen for her help in thermodynamic calculation. Many thanks should be returned to former members of the UF solar cell research team, Dr. Suku Kim, Dr. Serkan Kincal and Dr. Seokhyun Yoon, who instructed me how to operate the MEE system and how to conduct my research. It was also a great pleasure to work with Jiyon Song, Ryan Kaczynski, Ryan Acher, Xuege Wang, Andre Baran, Wei Liu and Matt Monroe in the UF solar ce ll research team, and many other graduate students in electronic material processing group. Finally, I w ould like to thank Gerald R. Bourne for teaching me how to use FIB, a nd Kerry Siebein for TEM-EDS analysis at Major Analytical Instrumentation Center.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................ix LIST OF FIGURES...........................................................................................................xi ABSTRACT...................................................................................................................xvii i CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Photovoltaic Devices..............................................................................................1 1.2 Fundamental Physics of Solar Cells.......................................................................2 1.3 Why CIGS ?............................................................................................................5 1.4 CIGS Deposition Processes....................................................................................8 1.5 MEE System Description.....................................................................................13 1.6 Statement of Thesis Work....................................................................................16 2 BINARY AND TERNARY PHAS E DIAGRAM ASSESSMENT...........................19 2.1 Cu-Se Binary Phase Diagram Assessment...........................................................19 2.1.1 Introduction................................................................................................19 2.1.2 Experimental Information..........................................................................20 2.1.3 Thermodynamic Optimization....................................................................22 2.1.4 Results and Discussion...............................................................................26 2.1.5 Summary.....................................................................................................28 2.2 Thermodynamic Description of Tern ary Compounds in Cu-In-Se System.........40 2.2.1 Introduction................................................................................................40 2.2.2 Extrapolation of Binary Gibbs Energy to Ternary.....................................41 2.2.3 Experimental Information..........................................................................44 2.2.3.1 Ternary compounds..........................................................................44 2.2.3.2 Thermodynamic properties..............................................................44 2.2.3.3 Phase diagrams.................................................................................45 2.2.4 Ab initio Calculation on the Ternary Cu-In-Se Compounds......................46 2.2.5 Establishment of Thermodynamic Descriptions........................................47 2.2.5.1 Sub-lattice model for different ternary compounds.........................47

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vi 2.2.5.2 Evaluation of Gibbs energies of end-members in the sub-lattice model......................................................................................................48 2.2.6 Summary.....................................................................................................52 2.3 Cu-Ga-In Ternary Phase Diagram Calculation.....................................................58 2.3.1 Introduction................................................................................................58 2.3.2 Review of Sub-binary Phase Diagrams......................................................58 2.3.3 Prediction of Cu-Ga-In Ternary Phase Diagrams......................................61 2.3.4 Modification of Cu-Ga-In Ternary Phase Diagrams..................................65 2.3.5 Summary and Future Work........................................................................67 3 METAL (CU, IN, GA)-SE REACTION PATHWAYS.............................................69 3.1 Introduction...........................................................................................................69 3.2 Experimental.........................................................................................................71 3.2.1 Precursor Preparation.................................................................................71 3.2.2 In situ high-temperature X-ray diffraction.................................................73 3.3 Cu-Se Binary Formation.......................................................................................74 3.3.1 Glass/Cu/Se Precursor................................................................................74 3.3.2 Glass/Cu-Se Precursor................................................................................75 3.4. In-Se Binary Formation.......................................................................................78 3.4.1 Glass/In/Se precursor..................................................................................78 3.4.2 Glass/In-Se Precursor.................................................................................80 3.5 Ga-Se Binary Formation.......................................................................................82 3.5.1 Glass/Ga/Se Precursor................................................................................82 3.5.2 Glass/Ga-Se Precursor................................................................................83 3.6 Summary...............................................................................................................85 4 CUINSE2 FORMATION PA THWAYS AND KINETICS.......................................86 4.1 Introduction...........................................................................................................86 4.2 Glass/In2Se3/CuSe Precursor................................................................................88 4.2.1 Precursor Preparation.................................................................................88 4.2.2 Temperature Ramp Annealing...................................................................90 4.2.3 Isothermal Annealing.................................................................................91 4.3 Glass/InSe/Cu-Se Precursor..................................................................................96 4.3.1 Precursor Preparation.................................................................................96 4.3.2 Temperature Ramp Annealing...................................................................97 4.4 Glass/CuSe/In-Se Precursor..................................................................................99 4.4.1 Precursor Preparation.................................................................................99 4.4.2 Temperature Ramp Annealing.................................................................100 4.5 Glass/Mo/Cu-In-Se Precursor.............................................................................101 4.5.1 Precursor Preparation...............................................................................101 4.5.2 Temperature Ramp Annealing.................................................................102 4.5.3 Isothermal Annealing...............................................................................102 4.6 Selenization of Glass/Mo/Cu-In Precursor.........................................................105 4.6.1 Precursor Preparation...............................................................................105 4.6.2 Selenization Chamber Design..................................................................107

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vii 4.6.3 Temperature Ramp Selenization..............................................................108 4.6.4 Isothermal Selenization............................................................................110 4.7 Summary.............................................................................................................115 5 CUGASE2 FORMATION PATHWAYS AND KINETICS...................................120 5.1 Introduction.........................................................................................................120 5.2 Glass/GaSe/CuSe Precursor................................................................................121 5.2.1 Precursor Preparation...............................................................................121 5.2.2 Temperature Ramp Annealing.................................................................122 5.2.3 Isothermal Annealing...............................................................................122 5.2.4 TEM-EDS Analysis..................................................................................133 5.3 Glass/Mo/Cu-Ga-Se Precursor...........................................................................135 5.3.1 Precursor Preparation...............................................................................135 5.3.2 Temperature Ramp Annealing.................................................................136 5.3.3 Isothermal Annealing...............................................................................138 5.4 Selenization of Glas s/Mo/Cu-Ga Precursor........................................................143 5.4.1 Precursor Preparation...............................................................................143 5.4.2 Selenization Chamber Design..................................................................143 5.4.3 Temperature Ramp Selenization..............................................................145 5.4.4 Isothermal Selenization............................................................................147 5.5 Summary.............................................................................................................152 6 CU(IN,GA)SE2 FORMATION FROM SELENIZATION OF METALLIC CUGA-IN.......................................................................................................................155 6.1 Introduction.........................................................................................................155 6.2 Experimental.......................................................................................................156 6.3 Results and Discussion.......................................................................................157 6.3.1 Precursor Characterization.......................................................................157 6.3.2 Temperature Ramp Annealing.................................................................158 6.3.3 Isothermal Annealing...............................................................................163 6.3.4 Comparison Between CIS, CGS, and CIGS Formation...........................167 6.4 Summary.............................................................................................................169 7 DIFFUSION MODELING OF Cu-In SELENIZATION.........................................170 7.1 Introduction.........................................................................................................170 7.2 Multi-component Diffusion Theory...................................................................171 7.3 Thermodynamic and Kinetic Basis for DICTRA...............................................174 7.4 Diffusion Modeling of Sele nization of Cu-In Precursor....................................176 7.4.1 Kinetic Experiments.................................................................................176 7.4.2 Diffusion Modeling Using DICTRA........................................................178 7.5 Summary.............................................................................................................181

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viii 8 DEFECT CHARACTERIZATION BY DEEP LEVEL TRANSIENT SPECTROSCOPY (DLTS) TECHNIQUE..............................................................182 8.1 Introduction.........................................................................................................182 8.2 Operation Principle of DLTS Technique............................................................183 8.3 Equipment Description of UF-DLTS System.....................................................185 8.4 DLTS Measurement of CIGS Cells....................................................................189 8.4.1 DLTS Scan...............................................................................................189 8.4.2 Estimation of Trap Activation En ergy and Capture Cross-section..........191 8.4.3 Estimation of Trap Density......................................................................192 8.5 Summary.............................................................................................................195 9 CONCLUSIONS AND FUTURE WORK...............................................................198 APPENDIX EXPLORATION OF ME DICI SIMULATION OF CIGS SOLAR CELLS......................................................................................................................201 A.1 Overview of Medici...........................................................................................201 A.2 Non-uniformity of Doping Concentration.........................................................202 A.3 Medici Simulation of C-V Profile.....................................................................203 A.4 Medici Simulation on Gr ading Band Gap CIGS Cell........................................206 LIST OF REFERENCES.................................................................................................209 BIOGRAPHICAL SKETCH...........................................................................................218

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ix LIST OF TABLES Table page 1-1 Structural and electr ical properties of CuInSe2 and CuGaSe2 with chalcopyrite structure...................................................................................................................... 8 2-1 Thermodynamic parameters in Cu-Se system..........................................................29 2-2 Parameters for functions used in Ta ble 2-1 in the form of equation (2-1)...............30 2-3 Phase equilibria in the Cu-Se system.......................................................................31 2-4 Experimental and calculated standard formation enthalpies ( Hf298.15K) and entropies ( S298) of Cu-Se compounds.....................................................................32 2-5 The experimental values of the standard formation enthalpy (0 298 K fH ) and energy (0 0 fE ) of -CuInSe2...................................................................................45 2-6 Parameters used to calculate Ef of CuIn3Se5 and CuIn5Se8 ...................................50 2-7. Experimental results of phase rela tionships of Cu-Ga-In ternary system..................66 4-1 The composition of the as-deposited glass/Mo/Cu-In precursor films as determined by EPMA scans along the surface ......................................................107 5-1 Estimated kinetic parameters for the CuGaSe2 formation from glass/GaSe/CuSe bilayer precursor films...........................................................................................130 5-2 Estimated kinetic parameters for the CuGaSe2 formation fr om glass/Mo/Cu-GaSe precursor films...................................................................................................141 5-3 Estimated kinetic parameters for the CuGaSe2 formation from selenization of glass/Mo/Cu-Ga precursor films............................................................................148 6-1 Estimated kinetic parameters for th e CIGS formation from selenization of glass/Mo/Cu-Ga-In precursor films.......................................................................166 6-2 Comparison of reaction pathways an d kinetics for CIS, CGS and CIGS formation from selenization of metallic precursors...............................................167 8-1 Equipment specification of UF-DLTS system.......................................................189

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x 8-2 DLTS scan results of EPV-CIGS cells at a reverse bias (VR) of 0.4 V, a trapfilling pulse of 0.8 V, and a satu ration pulse width of 10 ms.................................191 8-3 Trap density calculation from DL TS analysis of EPV-CIGS cell.........................194 8-4 Summary of DLTS analysis for EPV-CIGS cell....................................................196 8-5 Summary of DLTS analysis for EPV-CIGS cell....................................................197 9-1 Summary of reaction kinetics of Cu(InxGa1-x)Se2 formation from different precursor structures................................................................................................199 A-1 Design parameters of sola r cell for Medici simulation..........................................203 A-2 Basic design parameters of solar cell for Medici simulation.................................206 A-3 Deep defect parameters of so lar cells for Medici simulation.................................207 A-4 Comparison of performance parameters of CIGS cells simulated by Medici........208

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xi LIST OF FIGURES Figure page 1-1 Solar spectrum of AM0 and AM1.5 based on ASTM G173......................................3 1-2 Schematic diagram of light-induced el ectron-hole creation in a p-n junction photodiode..................................................................................................................4 1-3 I-V characteristic of a solar cell under illumination...................................................4 1-4 Efficiency trend of thin film solar cells (CuInSe2, CdTe and a-Si). Taken from Zweibel ......................................................................................................................6 1-5 The schematic structure of a conventional CIGS solar cell.......................................7 1-6 Tetragonal unit cell of a Cu(In,Ga)Se2 chalcopyrite lattice.......................................8 1-7 Schematic diagram of NREL three-st age process for CIGS fabrication....................9 1-8 Schematic diagram of the two-step process for CIGS fabrication...........................10 1-9 Schematic diagram of ISET non-vacu um process for CIGS fabrication.................12 1-10 Schematic diagram of MEE reactor system.............................................................13 1-11 Schematic top view of MEE reactor........................................................................14 1-12 The LabVIEW-based HMI system of MEE reactor.................................................16 2-1 Calculated Cu-Se phase diagram..............................................................................33 2-2 Comparison between the calculated Cu-S e phase diagram and experimental data.34 2-3 Comparison between the calculated chem ical potential of Cu and experimental data in -Cu2-xSe phase............................................................................................35 2-4 Comparison between the calculated chem ical potential of Se and experimental data at 1373 and 1473K............................................................................................36 2-5 Comparison between the calculated Se2 partial pressure and experimental data in Cu-Se system............................................................................................................37

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xii 2-6 Comparison between the calculated heat capacity of each phase and experimental data for Cu2Se.....................................................................................38 2-7 Comparison between calculated heat capacity of each phase and experimental data for CuSe............................................................................................................39 2-8 Geometrical construction of (a ) Kohler and (b) Muggianu model...........................42 2-9 Geometrical constr uction of Toop model.................................................................43 2-10 Pseudo-binary In2Se3-Cu2Se phase diagram............................................................53 2-11 Optimized Gibbs energy -CuInSe2, -CuIn3Se5 and -CuIn5Se8 compared with that estimated from EMF experime nts and ab init io calculation.............................54 2-12. Optimized Gibbs energy of formation of -CuInSe2, -CuIn3Se5 and -CuIn5Se8 compared with that estima ted from EMF experiments a nd ab initio calculation.....55 2-13 Isothermal sections of Cu-In-Se at 500 C. (a) Calculation, (b) Experimental evaluation.................................................................................................................56 2-14 Isothermal sections of Cu-In-Se at 800 C. (a) Calculation, (b) Experimental evaluation.................................................................................................................56 2-15 Isothermal sections of Cu-In-Se at 900 C. (a) Calculation, (b) Experimental evaluation.................................................................................................................57 2-16 Calculated phase diagra m of Cu-In binary system...................................................59 2-17 Calculated phase diagra m of Cu-Ga binary system.................................................60 2-18 Calculated phase diagra m of Ga-In binary system...................................................60 2-19 Isothermal section (500 C, 1atm) of the Cu-Ga-In ternary phase piagram based on the Muggianu’s equation.....................................................................................62 2-20 Isothermal section (500 C, 1atm) of the Cu-Ga-In ternary phase piagram based on the Muggianu’s equation for the range of 0 < x(In) < 0.2 and 0.2 < x(Ga) < 0.4............................................................................................................................ .63 2-21 Isothermal section (350 C, 1atm) of the Cu-Ga-In ternary phase piagram based on the Muggianu’s equation.....................................................................................63 2-22 Isothermal section (800 C, 1atm) of Cu-Ga-In ternary Phase Diagram based on the Muggianu’s equation..........................................................................................64 2-23 Vapor pressure as a function of temper ature in the Cu-Ga-In mixture (Cu:Ga:In = 1:1:1 mole ratio)....................................................................................................64

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xiii 2-24 Vapor pressure as a function of temper ature in the Cu-Ga-In mixture (Cu:Ga:In = 2:1:1 mole ratio)....................................................................................................65 2-25 Modified isothermal section (350 C, 1atm) of the Cu-Ga-In ternary phase diagram with experimental data (symbol)................................................................67 2-26 Modified isothermal section (500 C, 1atm) of the Cu-Ga-In ternary phase diagram.....................................................................................................................67 3-1 Phase diagram of In-Se binary system.....................................................................70 3-2 Phase diagram of Ga-Se binary system....................................................................71 3-3 As-grown precursor structure al ong with overall atomic composition....................72 3-4 Phase evolution of glass/Cu/Se precursor observed by in situ X-ray diffraction.....74 3-5 Phase evolution of glass/Cu-Se precursor observed by in situ X-ray diffraction....77 3-6 Phase evolution of glass/In/Se precursor observed by in situ X-ray diffraction......79 3-7 Phase evolution of glass/In-Se precursor observed by in situ X-ray diffraction......81 3-8 Phase evolution of glass/Ga/Se precursor observed by in situ X-ray diffraction.....82 3-9 Phase evolution of glass/Ga-Se precursor observed by in situ X-ray diffraction....84 4-1 TEM micrographs of as-grown glass/In2Se3/CuSe bilayer precursor films.............89 4-2 Room temperature XRD scans and TEM micrographs of as-grown precursor films.......................................................................................................................... 89 4-3 In situ XRD scans during temperature ramp annealing (10 C/min) of the glass/In2Se3/CuSe sample.........................................................................................90 4-4 In situ time-resolved XRD scans during isot hermal annealing of the glass/ In2Se3/CuSe precursor structure at 250 C...............................................................92 4-5 Avrami model plot for glass/In2Se3/CuSe precursor structure.................................94 4-6 Parabolic model plot for glass/In2Se3/CuSe precursor structure..............................95 4-7 Arrhenius plot of the parabo lic rate constant for glass/In2Se3/CuSe precursor structure....................................................................................................................96 4-8 Room temperature XRD scans of as-grown precursor films...................................97 4-9 In situ XRD scans during temperature ramp annealing (30 C/min) of the glass/InSe/Cu-Se sample..........................................................................................98

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xiv 4-10 Room temperature XRD scans of as -grown glass/CuSe/In-Se precursor................99 4-11 In situ XRD scans during temperature ramp annealing (30 C/min) of the glass/CuSe/In-Se sample........................................................................................100 4-12 Temperature ramp annealing of glass/Mo/Cu-In-Se precursor..............................102 4-13 Isothermal annealing of glass/Mo/Cu-In-Se precursor at selected temperatures in the range 140 to 350 C..........................................................................................103 4-14 CuInSe2 grain sizes estimated by X-ray di ffraction vs. isothermal annealing temperature of glass/Mo/Cu-In-Se precursor.........................................................104 4-15 -2 and grazing incident X-ray diffraction (at = 1.0 and 0.5 ) patterns of an as-deposited glass/Mo/Cu-In precursor film..........................................................105 4-16 Surface and cross-sectiona l SEM images of an as-deposited glass/Mo/Cu-In precursor film and selenized film...........................................................................106 4-17 Selenium chamber design using PANalytical X’Pert system................................107 4-18 In situ X-ray diffraction pattern evolution during the selenization of a glass/Mo/Cu-In precursor films in the 2 range.....................................................109 4-19 In situ X-ray diffraction pattern evolu tion during the isothermal selenization of a glass/Mo/Cu-In precursor film at 280 C...............................................................110 4-20 The Avrami model plot for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films.............................................................................112 4-21 Arrhenius plot for Avrami kinetic constant for -CuInSe2 formation by selenization of glass/Mo/C u-In precursor films.....................................................112 4-22 The parabolic rate model for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films.............................................................................114 4-23 The parabolic rate model for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films.............................................................................114 4-24 Reaction pathway of CIS formation from In2Se3/CuSe precursor projected in ternary Cu-In-Se isothermal phase diagram at 500 C...........................................116 4-25 Reaction pathway of CIS formation fr om intimately mixed Cu-In-Se precursor projected in ternary Cu-In-Se is othermal phase diagram at 500 C.......................117 4-26 Comparison of reaction rates for CI S formation from different precursors estimated by the parabolic and Avrami model.......................................................119

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xv 5-1 Room temperature XRD scans and TEM micrograph of as-grown precursor films........................................................................................................................12 1 5-2 In situ XRD scans during temperatur e ramp annealing (30 C/min) of the glass/GaSe/CuSe sample........................................................................................123 5-3 In situ time-resolved XRD scans during isothermal annealing of the glass/GaSe/CuSe precursor struct ure at selected temperatures..............................125 5-4 Fractional reaction () with respect to time ( t ) at selected isothermal temperatures...........................................................................................................126 5-5 Parabolic rate model plot for gl ass/GaSe/CuSe precursor structure......................127 5-6 Arrhenius plot of the Parabolic rate constant for glass/GaSe/CuSe precursor structure..................................................................................................................127 5-7 Fractional reaction () with respect to time ( t + t *) and Avrami model plot at selected isothermal temperatures...........................................................................130 5-8 Modified Avrami model plot for glass/GaSe/CuSe precursor structure................131 5-9 Arrhenius plot of the Avrami model ra te constant for glass/GaSe/CuSe precursor structure..................................................................................................................132 5-10 TEM-EDS analysis on (a) as-grown glass/GaSe/CuSe precursor, (b) sample annealed at 300 C, for 30 min...............................................................................134 5-11 Room temperature X-ray diffraction of (a) as-grown glass/Mo/Cu-Ga-Se precursor, and (b) thermally annealed CuGaSe2....................................................135 5-12 In situ XRD scans during temperatur e ramp annealing (30 C/min) of the glass/Mo/Cu-Ga-Se sample....................................................................................137 5-13 In situ time-resolved XRD scans during isothermal annealing of the glass/Mo/Cu-Ga-Se precursor struct ure at selected temperatures..........................139 5-14 Comparison of fractional reaction for isothermal experiments and modified Avrami model prediction.......................................................................................140 5-15 Modified Avrami model plot for gl ass/Mo/Cu-Ga-Se precu rsor structure............141 5-16 Arrhenius plot of the Avrami mode l rate constant for glass/Mo/Cu-Ga-Se precursor structure..................................................................................................142 5-17 Room-temperature XRD scans of Cu -Ga as-grown precursor and selenized CuGaSe2 film..........................................................................................................144

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xvi 5-18 X-ray sample holder with a graphite dome for selenization of Cu-Ga precursor films........................................................................................................................14 4 5-19 In situ XRD scans during temperatur e ramp selenization of Cu-Ga/Mo/glass precursor.................................................................................................................146 5-20 In situ XRD scans during isothermal selenization of Cu-Ga/Mo/glass precursor at four different temperatures.................................................................................147 5-21 Comparison of fractional reaction for isothermal experiments and modified Avrami model prediction.......................................................................................149 5-22 Modified Avrami model for the CuGaSe2 formation by selenization of glass/Mo/Cu-Ga precursor.....................................................................................150 5-23 Arrhenius plot of the Avrami model rate constant for the CuGaSe2 formation by selenization of glass/ Mo/Cu-Ga precursor.............................................................150 5-24 Comparison of reaction rates for CI S and CGS formation from different precursors estimated by the parabolic model.........................................................154 5-25 Comparison of reaction rates for CI S and CGS formation from different precursors estimated by the Avrami model............................................................154 6-1 Room-temperature XRD scans of gl ass/Mo/Cu-Ga-In as-grown precursor..........157 6-2 Surface (top) and cross-sectional (bottom) SEM images of (a) an as-deposited glass/Mo/Cu-Ga-In precursor f ilm and (b) selenized film.....................................158 6-3 Temperature ramp HT-XRD scans with a bare glass substrate.............................159 6-4 In situ XRD scans during temperature ramp selenization of Cu-Ga-In/Mo/glass precursor.................................................................................................................160 6-5 Cell refinement for room temperature X -ray diffraction data of a selenized CIGS sample using the tetragonal, I-42d (122) cell type.................................................162 6-6 Lattice constants (a, c) vs. Ga composition of CIGS.............................................162 6-7 In situ XRD scans during isotherm al selenization of glass/Mo/Cu-Ga-In precursor at four di fferent temperatures.................................................................164 6-8 Avrami model and corresponding Arrheniu s plot (inset) for CIGS formation by selenization of glass/Mo /Cu-Ga-In precursor........................................................165 6-9 Arrhenius plot for Avrami rate consta nt for CIGS formation by selenization of glass/Mo/Cu-Ga-In precursor.................................................................................165

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xvii 6-10 Comparison of fractional reaction for is othermal experiments and Avrami model prediction................................................................................................................166 6-11 Comparison of reaction rates for seleni zation of different metallic precursors estimated by the Avrami model.............................................................................168 7-1 The CIS thickness vs. time obtained from kinetic experiment..............................176 7-2 The schematic diagram of th e simplified reaction of CuInSe2 formation from selenization of Cu-In precursor..............................................................................177 7-3 The modified Cu-In phase diagram including metastable CuIn phase..................179 7-4 The comparison of CIS growth rate s between the DICTRA prediction and experiments............................................................................................................180 8-1 Schematic diagram of UF-DLTS system...............................................................186 8-2 Schematic top view of LN2 cryostat in the DLTS system.....................................186 8-3 Simplified wiring diagram of UF-DLTS system....................................................187 8-4 UF-DLTS system...................................................................................................188 8-5 DLTS scans for the EPV-CIGS cell at different delay times (0.02 to 1.0 ms)......190 8-6 Arrhenius plot of DLTS scans for EPV-CIGS cells...............................................192 8-7 Capacitance-temperature scan for a EP V-CIGS cell at a reverse bias of 0.4 V.....193 8-8 Capacitance-voltage (C-V) measur ement for EPV-CIGS at different temperatures...........................................................................................................194 A-1. A bandgap and doping profile for CIS-graded solar cell......................................204 A-2 Absorption coefficient profiles for the materials used in Medici simulation.........205 A-3 Medici simulation results on C-V prof ile for the uniform doping and graded doping CIS cells.....................................................................................................205 A-4 CurrentVoltage (C-V) plots for CIGS cells predicted by Medici simulation......208

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xviii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STUDY OF REACTION PATHWA YS AND KINETICS IN Cu(InxGa1-x)Se2 THIN FILM GROWTH By Woo Kyoung Kim August 2006 Chair: Timothy James Anderson Major Department: Chemical Engineering Assessment of the thermochemistry and phase equilibrium data of the Cu-Se binary and Cu-In-Se ternary systems was performed to suggest the phase di agrams. Sub-lattice models were used to describe the Gibbs ener gy of the condensed solutions. Coupled with previously reported assessments, the Cu -Ga-In phase diagram was predicted by extrapolation of the Cu-Ga, Cu-In and Ga-In binary systems. Ternary interaction parameters were and subsequently added to achieve consistency with recent ternary experimental data. In situ high-temperature X-ray diffraction tec hnique was used to investigate the reaction pathways and phase evolution of binary Cu-Se, In-Se and Ga-Se compounds prepared as an intimate mixture or bi-layer The results revealed that the overall phase transformation of binary metal (Cu, In a nd Ga)-Se compounds qualitatively follows the sequence predicted by the phase diagram, but the detailed reaction pa th of each binary

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xix compound depends on the as-deposited precurs or structure and pha ses produced during the deposition process. Reaction pathways and kinetics of polycrystalline -CuInSe2 (CIS), CuGaSe2 (CGS), and Cu(In,Ga)Se2 (CIGS) formation were also sy stematically investigated using in situ high-temperature X-ray di ffraction during thermal anne aling of stacked bilayer and intimately mixed monolayer precursors, and selenization of elementally mixed metal precursors. The lowest temperature to form CIS was identified as ~140 C, which was achieved by thermal annealing of intimate ly mixed Cu-In-Se precursor. Formation temperatures of CGS (i.e. 260 to 300 C) were relatively higher than those of CIS (i.e. 140 to 250 C) and CIGS (i.e. 260 C). MoSe2 formation was always clearly observed during selenization and for CIS, only after co mplete formation of CIS. Quantitative analysis of time-resolved X-ray diffraction data by adopting the Avrami and parabolic rate models provided reaction order, ra te constant, and activation energy. DICTRA simulation of CIS formation by selenization of a Cu-In precursor was performed using the kinetic resu lts obtained by time-resolved, in situ HTXRD experiments along with the thermodynamic desc ription of the CIS system. The target reaction system was simplified as a pseudo-binary reaction, CuIn + 2Se CuInSe2, for which the reliable mobility parameters fo r Se transport in CIS were obtained.

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1 CHAPTER 1 INTRODUCTION 1.1 Photovoltaic Devices Semiconductor photonic devices generall y fall into one of three functional categories. One group of photoni c devices converts electric al energy into photo-energy such as light emitting diodes (LEDs) and la ser diodes, while the other two groups of photonic devices convert photo-ener gy into electrical energy. If the purpose of photo-toelectrical energy conversion is to detect or determine information about the photon energy, the device is called a photodetector. If the purpose of energy conversion is to produce electrical power, the device is called a photovoltaic device or solar cell [Pie96]. A solar cell converts sunlight into electr icity through the photovoltaic effect which was first observed by nineteen-year-old Ed mund Becquerel, a French experimental physicist, in 1839 while experimenting with an electrolytic cell com posed of two metal electrodes. He found that certain materi als would produce small amounts of electric current when exposed to light [Bec39, Ml93]. Solar cell technology and its application have been enormously developed during the last four decades. Silicon was the first co mmercial solar cell material and is still most widely used in solar cell a pplication. The potential com pound semiconductors such as GaAs, CdTe, InP, CdS and Cu(In,Ga)Se2 cell have been activel y developed [Ml93]. Photovoltaics as one of the renewable ener gy technologies is a lot friendlier to the environment than conventional energy technolog ies, which mainly rely on fossil fuels. Fossil fuels contribute significantly to ma ny environmental problems, e.g., greenhouse

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2 gases, air pollution, and water and soil contamin ation. The performance of a solar cell is measured in terms of its efficiency converti ng sunlight into electricity. Only sunlight with certain energies (or wavelengths) will wo rk efficiently to create electricity, and much of it is reflected or absorbed by the ma terials that make up the cell. Because of this, a typical commercial solar cell has an efficiency of 15%—about only one-sixth of the sunlight striking the cell generates electric ity. Low efficiencies mean that larger arrays are needed and thus high manufacturi ng costs are required. Therefore, improving solar cell efficiencies while holding down th e manufacturing cost is an important goal of the solar cell industry and unive rsity research support [Nre06]. 1.2 Fundamental Physics of Solar Cells For the photovoltaic conversi on, it is necessary to se parate the light-induced electrons and holes, and collect them at extern al contacts. This re quires an internal electric field, which can be generated by homojunctions and heterojunctions of semiconductors, e.g., p-n junction, Schott ky barrier, and MIS (metal-insulatorsemiconductor) structure. Currently, p-n junc tion solar cells are the most widely used devices for photovoltaic energy conversion. The solar radiation reaching the earth has a spectral distribution due to partial reflection by atmosphere and partial transmitta nce to surface of the earth. The radiation distribution outside the atmos phere is similar to that of a “black body” radiation at ~5800K, while the atmosphere at the surface of the earth selectively absorbs the radiation at certain wavelengths. As shown in Figure 1-1, the sta ndard solar spectra (e.g., AM0 and AM1.5) defined by air mass (AM) are im portant in photovoltaic application. The AM0 represents solar spectrum outside of the atmosphere and AM1.5 corresponds the spectrum at sea level. More generally, the AMx is expressed by x = 1/cos( z), where z is

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3 the zenith angle of the sun. When the sun is located at the zenith of the receiving area (i.e., z=0 and thus x=1), AM1 would be spectru m received at sea level on a clear day with the sun at its zenith. Generally, the AM 1.5 spectrum, which is e quivalent to a zenith angle of 48.19 is accepted as a reference spectrum in PV application. Figure 1-1. Solar spectrum of AM0 and AM1.5 based on ASTM G173. Electron-hole pairs in a p-n junction diode are created by absorption of light and then minority carriers of each side move to a junction, as shown in Figure 1-2. At thermodynamic equilibrium with no current flow s, minority carriers reaching the edges of the depletion region are immediately swept out by the electric field (i.e., built-in bias) to the opposite side of the junction, which conseque ntly yields a current flow in the reverse direction of built-in bias.

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4 Figure 1-2. Schematic diagram of light-induced electron-hole creati on in a p-n junction photodiode. Figure 1-3. I-V characteristic of a solar cell under illumination. Several solar cell parameters under illu mination are graphically defined in I-V characteristics, as shown in Figure 1-3. First, Voc (open circuit voltage) and Isc (short circuit current) are the maximum voltage and cu rrent that can be s upplied or derived by the cell for applied illumination conditions, respectively. Next, the Im and Vm are the Ec Ev EFp Ec Ev EFn Recombination Recombination h

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5 current and voltage to yield the maximum power rectangle, i.e., Pmax = ImVm < IscVoc. Finally, the fill factor ( F.F .) and power conversion efficiency () are often used to represent the solar cell perfor mance and are determined by oc sc m m oc scV I V I V I P FF max (1-1) in oc sc in m m inP V I FF P V I P P max (1-2) where Pin is the incident photon energy per secon d. The above relationships, equation (11) and (1-2), demonstrate th at solar cell efficiency () is proportional to Isc, Voc and fill factor. However, considering the general expressions for Voc and Isc, the fundamental material parameters that determine the effi ciency of the solar cell are the lifetime and mobility of the minority carriers, and the interface recombination velocities. These parameters are not independent from each othe r, and are controlled by the structural and electrical propertie s of the solar cell. 1.3 Why CIGS ? Silicon was the first commercial solar cell ma terial and is still most generally used in solar cell applications. However, silic on is not the ideal material for solar cells because it has low light absorption efficiency as well as an indirect band gap. A large number of binary, ternary, and quatern ary compound semiconductors have been investigated for their potential as high perf ormance and inexpensive solar cells that can serve as an alternative to silicon-based solar cells such as single-crystalline, polycrystalline, and amorphous silicon. One of the most promising strategies to lower solar cell manufacturing costs will be the th in-film photovoltaic technology in which thin absorber films (typically < 5 m) are deposited on inexpensive substrates such as

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6 polymer. Chalcopyrite -CuInSe2 (CIS) and its alloys with Ga or S are the most promising candidates as an absorber for high e fficiency thin film solar cells. Recently, the development of CIGS has made rapid pr ogress, and conversion efficiency of 19.5% (AM 1.5G) has been achieved on a laboratory scale [Con05]. Th e efficiencies of three conventional thin film solar cells (i.e., CuInSe2, CdTe and a-Si) are compared in Figure 1-4, which suggests that CIS-based cell is th e most suitable for high performance thin film solar cells. Furthermore, CuInSe2 compound has many advantages as a solar cell absorber, for instance, a high absorption coefficient (~ 105 cm-1), excellent radiation resistance, direct band gap and wi de range of stoichiometry. Figure 1-4. Efficiency trend of thin film solar cells (CuInSe2, CdTe and a-Si). Taken from Zweibel [Zwe05]. The schematic structure of a typical CIGS-b ased thin film solar cell is shown in Figure 1-5. In this structure, a soda-lime glass (SLG) is widely used as a substrate. In a soda-lime glass, the out-diffused Na ion is believed to increase th e electrical conductivity and to reduce the grain boundary en ergy barrier by either forming NaIn defects or

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7 removing mid-gap traps [Wei99]. However, Na2Se is believed to cause a poor adhesion between CIGS and Mo [Hua03]. The recent tr end includes flexible substrates such as polymer and metal foils because the flexibility of substrates allows a potential application to portable solar cells, and a roll-to-roll manufacturing, whic h promises substantial cost reduction. The Mo is a back contact electrode which is generally de posited by sputtering. Polycrystalline CIGS acts as a p-type light absorber, and more importantly forms a p-n junction with an n-type CdS buffer layer. The ZnO (or ZnO:Al) transparent conducting film serves as a window layer, and anti-reflection (AR) coating (e.g., MgF2) improves the light absorption efficiency. As a front contact material, a bilayer Ni/Al grid is used. Figure 1-5. The schematic structure of a conventional CIGS solar cell. CuInSe2 crystallizes in a diamond-like lat tice structure with a face-centered tetragonal unit cell that is referred to a chalc opyrite structure as pi ctured in Figure 1-6. Each selenium atom serves as the center of a tetrahedron of two Cu and two In atoms, and each metallic atom is surrounded by a tetrahedron of selenium atoms. In this structure, each anion (selenium) has two Cu and two In (or Ga) cations as nearest neighbors, whereas each anion has four cations nearly rando mly as nearest neighbors in zinc-blende structure. While the two lattice c onstants of the chalcopyr ite structure (i.e., xNi/Al Ni/Al AR coatin g Substrate (SLG) p -Pol y -CIGS n-CdS n-ZnO Mo

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8 and y-direction) are the same as the lattice constant of the zinc blende structure, the lattice constant of z-direc tion is a double of that of zinc blende structure. Figure 1-6. Tetragonal un it cell of a Cu(In,Ga)Se2 chalcopyrite lattice. Typical lattice constants and el ectrical properties for CuInSe2 and CuGaSe2 with a chalcopyrite structure are summarized in Table 1-1. Table 1-1. Structural and elec trical properties of CuInSe2 and CuGaSe2 with chalcopyrite structure. Lattice constants a (nm) c (nm) Bandgap energy Eg (eV) Absorption coefficient (cm-1) CuInSe2 0.5784 1.1614 1.04 ~ 1 105 CuGaSe2 0.5596 1.1002 1.68 > 3 104 1.4 CIGS Deposition Processes Almost every method of semiconductor proces sing has been tried to synthesize CIGS compound, but only a few of them were suc cessful in producing a high quality CIGS absorber for thin film photovoltaic cell. In this chapter, the widely employed techniques to fabricate high quality CIGS films and the recent efforts to develop low-cost nonvacuum processes are summarized. c a a Cu In or Ga Se

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9 A sophisticated vacuum co-evaporation pr ocess is characterized by simultaneous exposure of high-temperature substrate to C u, Ga, In and Se vapor fluxes, and known to provide the best control of composition thr ough precise control of the temperature and thus each elemental flux. Even though severa l co-evaporation methods including simple single-layer and bilayer processes are availa ble, an NREL 3-stage process using physical vapor deposition (PVD) system currently holds the best CIGS cell efficiency of 19.5 % [Con05]. Figure 1-7. Schematic diagram of NREL th ree-stage process for CIGS fabrication. (Provided by Dr. Noufi in NREL) The schematic diagram of the NREL three-stag e process is illustrated in Figure 1-7. During the first stage, the In, Ga and Se are deposited to form the sesquiselenide, (In,Ga)2Se3. After the second stage of only Cu +Se flux, a Cu-rich CIGS is produced along with a secondary Cu-Se bi nary compound (e.g., conducting Cu2Se), which is known to facilitate the CIGS grain growth. Finally, a slig htly Cu-poor CIGS forms by

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10 adding more indium and gallium at third stag e. The three-stage PVD process, however, has not been successfully implemented in i ndustrial large-area module production mainly due to high production cost caused by hi gh-vacuum and high-temperature operation conditions. Furthermore, co-deposition technique has a limitation in achieving uniformity in large scale deposition. Another conventional process to produce a de vice-quality CIGS absorber is called the two-step method, which has been successfu lly employed in a commercial line of Shell Solar and Showa Shell. The commercialized two-step process cons ists of the deposition of a metallic precursor (e.g., Cu/In/Ga) followe d by subsequent selenization, as shown in Figure 1-8. Traditionally, the metal precurs ors are prepared by sputtering and then selenized at high temperature (~600 C) in a reactive H2Se or Se vapor ambient. However, since H2Se gas and Se vapor are extremely t oxic, a safer selenization method is required. Figure 1-8. Schematic diagram of the tw o-step process for CIGS fabrication. Palm et al. suggested the deposition of a se lenium layer on metal precursor by evaporation followed by a rapid thermal ann ealing [Pal03]. As a novel CIS process, Bindu et al. deposited selenium films on glass subs trate using chemical bath deposition (CBD) at room temperature, totally avoiding use of H2Se or Se vapor [Bin03]. Indium and copper were then deposited on the seleni um layer to yield glass/Se/In/Cu or glass/Se/Cu/In precursor by se quential vacuum evaporation. Finally, the stacked layer

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11 precursors were thermally a nnealed in high vacuum (10-5 mbar) at the temperature range 423 to 673K. As stated in the previous s ection, CIGS is similar in its performance and stability to currently dominant crystalline silicon devices but their market share is still quite low (<1%) mainly due to high production cost. Therefore, the development of more cost effective process, preferably based on lo w temperature and non-vacuum technique, is essential to successful commercialization of CIGS-based thin film solar cells. Example approaches include electrodeposition and scre en printing. Precursor layers obtained by these techniques, however, have not exhi bited electronic properties suitable for commercial solar cells, and also require additional thermal treatments to optimize cell performance parameters [Gan06]. Electrodeposition has been considered as a suitable process for large-scale industrial processes, requiring low ener gy consumption and low capital investment [Zwe99, Bha00]. Two basic methods of elect rodeposition to form CIS or CIGS have been explored with appreciable results. One method represents the co-deposition all elements, i.e., Cu, In, Ga and Se [Cal 98, Bha98, Tau05] and the other includes the deposition of metallic precursors followed by subsequent selenization [Pro96, Gan06]. Basically, electrodeposition of Cu-In-Ga-Se al loys is carried out potentiostatically on Mo-coated substrates from aqueous soluti ons containing complex agents, e.g., CuCl, InCl3, Ga(NO3)3 7H2O, H2SeO3 and KSCN [Tau05, Gan06]. A small area efficiency of over 10% was obtained by electrodeposition of quaternary CIGS followed by subsequent thermal annealing [Gui03]. By adding addi tional indium and gallium, and applying hightemperature annealing in vacuum, an effi ciency of 15.4% was reported [Bha00]. The

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12 stability of the chemical solution, large area non-uniformity and high deposition rate remain a significant challenge [Kae04]. International Solar Electric Technology, Inc. (ISET) employed an interesting nonvacuum process for low cost mass production fo r CIGS solar cells. ISET uses a coating technology of water based precursor inks made of nano-particles of mixed oxides of Cu, In and Ga that are converted to yield CI GS absorber layers of desired electronic properties. The schematic process diagram is shown in Figure 1-9. Figure 1-9. Schematic diagram of ISET nonvacuum process for CIGS fabrication. A water based precursor ink is coated on Mo-coated glass substrate using a ‘knife blade’ coating technique [Kap01, Kap03]. Af ter drying, a layer of mixed oxides with a typical thickness of around 2.5~3.0 m is left on the glass/Mo s ubstrate. This oxide layer is then reduced under a forming gas mixture of H2 and N2 at temperatures in the range 475 to 525 C to obtain a compact coating of metal alloys of Cu-Ga-In. Finally, this alloy coating is selenized in H2Se gas ambient at a temperat ure in the range 440 to 475 C to yield CIGS layer. They reported that sma ll area solar cells with efficiency of ~ 13% have been fabricated by this process. The main advantages of this non-vacuum process include high compositional control of the abso rber layer, high material utilization and low cost.

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13 Spray deposition has also been taken in to account as a possible non-vacuum technique that is amenable to the manufact ure of large area films with low processing costs. Schulz et al. has employed nanoparticle-based pr ecursors for spray deposition of CIGS materials [Sch98]. In their approac h, nanoparticle colloids were prepared by reacting a mixture of CuI and/or [Cu(CH3CN)4](BF4)2 and/or InI3 and/or GaI3 in pyridine with Na2Se in methanol at reduced temperature under inert atmosphere. Colloids with the compositions CuInSe2.5, CuSe, In2Se3 and Cu1.10In0.68Ga0.23Sex were prepared by each corresponding reaction. 1.5 MEE System Description The solar cell research group in the Universi ty of Florida has been using a Plasma Migration Enhanced Epitaxy (PMEE) reactor system to produce Cu(In,Ga)Se2-based absorber layers. Figure 1-10. Schematic diagram of MEE reactor system. The MEE system is essentially a modified Molecular Beam Epitaxy (MBE) system under an ultra high vacuum environment, as schematically shown in Figure 1-10. The BELL JAR Load lock Sorption pump Ventury pump Mechanical pump Mechanical pump Diffusion pump Fore line Rou g h line Fore line TMP

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14 pumping unit is composed of three mechanic al pumps, a large capacity diffusion pump, a turbo molecular pump (TMP), and a liquid-ni trogen cryogenic pump inside the system. To obtain sufficiently low pressure for opening the TMP gate valve in the load lock, the combination of a Venturi pump and a sorpti on pump are employed. Using the ultra high vacuum pumping system, the normal operation pr essure during deposition is in the range 10-8 to 10-7 Torr, depending on the source fluxes and the temperature of the substrates. In comparison with a traditional MBE system, which typically has a drawback of low productivity, one of outstanding advantages of the PMEE system is that it is able to process nine substrates simultaneously by empl oying a large rotating platen. The various types of substrates, such as 2 x2 1cmx1cm square substrates, or 2 diameter round wafers of Si or GaAs, can be loaded on the rotating platen. Figure 1-11. Schematic top view of MEE reactor. The inside of the system consists of four different zones, as shown in Figure 1-11, a heater zone, a metal deposition zone, a load lo ck zone, and a chalcogen zone. The system Ga Cu In Heater Zone Metal Deposition Zone Load Lock Zone Chalcogen Zone Plasma cracker Thermal cracker Na

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15 uses a rotating platen so that every substrat e experiences four zones sequentially and also periodically. In the heater zone there is a radiation heat er to heat the substrates that pass through this zone. The substrates continuously c ool while they pass through the other zones because they do not encounter any othe r heat sources in these zones. In the metal deposition zone three different of metals, such as copper (Cu), indium (In) and gallium (Ga), can be deposited. E ach metal source is evaporated from an effusion cell fitted with a single or dual fila ment heater. The fluxes produced by the Cu and In source are monitored on a real time basis by Electron Impact Emission Spectroscopy (EIES) sensors, which are ca librated using Quartz Crystal Monitors (QCM). In the case of Ga, the flux is monitored by QCM. The loadlock zone is connected to a load -lock system, which is used to load and unload substrates. Therefore, during the deposition, it acts as a cooling zone where neither deposition nor heating occurs. Finally, selenium (Se) is deposited in the chalcogen zone. Selenium vapor is known to be a mixture of low mol ecular weight polymers Se through Se8. Among them, high molecular weight species may not easily react with other species, even in high temperature conditions, so they are traditi onally cracked thermally or exposed to a plasma. Unfortunately, there is no flow sensor instrumented in the system to measure a Se flux and thus the flux is estimated by meas uring the film thickness after deposition. In the case of counter-clock wise rotational de position, each substrate experiences the four steps of heating metal deposition cooling selenium deposition repeatedly and each atomic layer (~ 0.5 nm CIGS/cycle) is deposited sequentially on the substrate.

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16 To achieve the real time control of th e PMEE reactor, a LabVIEW based human machine interface (HMI) system is configured as shown in Figure 1-12 [Kin02]. By using this system, one can monitor and cont rol the important operation parameters such as the substrate heater temp erature, and each source temper ature, the flux of each source and even the sequence of film deposition in a central computer. Figure 1-12. The LabVIEW-based HMI system of MEE reactor. 1.6 Statement of Thesis Work Chalcopyrite Cu(In,Ga)Se2 based cells have clearly dem onstrated their potential as high efficiency thin film solar cells. In a ddition to their high cell efficiency, CIGS thinfilm solar cells exhibit outstanding longterm outdoor stability, excellent radiation hardness, and the potential fo r use in a high performance CIGS/CGS tandem arrangement. The route used to synthesize the CIGS absorber material is critical to achieving high cell efficiency as well as high processing th roughput. As summarized in Chapter 1.4, a variety of processing sequences lead to the form ation of CIGS. This flexibility is partly

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17 due to an inherent stability of -CIGS and a rich phase diagram ( -CuInSe2 is in equilibrium with 8 different solid phases a nd a Se-rich liquid) [Gd00a-c]. The complex chemistry of the quaternary CIGS system, however, has forced absorber synthesis optimization to primarily traverse an empi rical path and discouraged exploration of substantially different appro aches. In particular, very little is known about the fundamental thermochemistry and reaction pathways in the system. Therefore, in this thesis, the equilibrium pathways and reaction kinetics for the formation of Cu(InxGa1-x)Se2 (CIGS), its sub-ternaries (i.e., CuInSe2 and CuGaSe2) and sub-binaries are systematically investigated to assist the development of a cost-effective and high performance CIGS growth process. First, the thermodynamic description of Cu-Se binary, Cu-In-Se and Cu-Ga-In ternary systems are evaluated using the so ftware package ThermoCalc along with available experimental information, as de scribed in Chapter 2. This thermodynamic description is essential to the reliable calcula tion of chemical potentials and identification of equilibrium phases, which are combined with species diffusivities to estimate the diffusion controlled reaction rate. Before digging into the reaction of comp licated ternary (e.g., CIS and CGS) and quaternary (CIGS) compounds, the phase evoluti on of binary metal-selenides (e.g., Cu-Se, In-Se and Ga-Se) is qualita tively investigated using in situ high temperature X-ray diffraction (HTXRD) and compared with the prediction by equilibrium phase diagrams in Chapter 3. Understanding the phase transforma tion of metal-selenide binaries is very important in designing binary bior multi-la yer precursors for rapid thermal processing, which is a promising low-cost approach of CIGS film fabrication.

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18 In Chapter 4, the reaction pathways and kinetics of -CIS formation from different precursors (e.g., glass/In2Se3/CuSe, glass/InSe/Cu-Se, glass/CuSe/In-Se and glass/Mo/Cu-In-Se) and selenization of metallic glass/Mo/Cu-In precursor are systematically investigated using a time-resolved, in situ HTXRD equipped with a customized selenium chamber. Quantitative kinetic analysis using selected solid-state growth models provides kinetic parameters including reaction order, rate constant, and activation energy as well. In Chapter 5, the successful implementation of in situ HTXRD technique in -CIS system (Chapter 4) is extended to explori ng the CGS formation from thermal annealing of stacked precursors (e.g., glass/GaSe/CuSe and glass/Mo/Cu-Ga-Se) and selenization of glass/Mo/Cu-Ga precursor. Subsequentl y, the reaction pathwa ys and kinetics for quaternary CIGS formation by the selenizati on of metallic glass/Mo/Cu-Ga-In precursors are investigated in Chapter 6. Since most solid-state reactions follow a diffusion limited process, it is expected that the diffusion-limited reaction rate woul d be predicted by thermodynamic chemical potentials and diffusivities (or mobilities) of species. Therefore, for a given set of thermodynamic descriptions, (e.g., results obta ined in Chapter 2), the reaction rates experimentally obtained in Chapter 4 through 6 can be used to establish the mobility database of each element (e.g., Cu, In, Ga and Se) in various compounds by employing the companion software to ThermoCalc, DICTRA (DIffusion-Controlled TRAnsformation) program. In Chapter 7, kinetic data for -CIS formation by selenization of glass/Mo/Cu-In precursor ar e used to obtain a mobility expression of selenium.

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19 CHAPTER 2 BINARY AND TERNARY PHAS E DIAGRAM ASSESSMENT 2.1 Cu-Se Binary Phase Diagram Assessment 2.1.1 Introduction The Cu-Se system is an important constitutional binary of the chalcopyrite Cu(Inx,Ga1-x)Se2, which is one of the most promising absorber materials for highefficiency thin film solar cells. Phase equi libria and thermodynamic properties of the CuSe system have been studied by many resear ch groups using differential thermal analysis (DTA), X-ray diffraction, microscopy, calor imetry, electromotive force (EMF), and vapor pressure measurement. More recentl y, an excellent review paper on the phase equilibria of the Cu-In system based on the evaluation of the abundant experimental data was published by Glazov et al. [Gla00], who have been study ing this system for many years and have carried out precise measurements. A thermodynamic description, established w ith the computer-based CALculation of PHAse Diagram (CALPHAD) method [Sau98], is represented as a set of models to express the Gibbs energy of each phase as a function of temperature, pressure and composition. The parameters used in the models of different phases are optimized using the available phase equilibrium and thermo-che mical data. This optimization is expected to make the thermodynamic description self-c onsistent and able to provide complete information about phase equilibria, thermo-che mical properties as well as driving forces of phase transformation and mass transport.

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20 The reliable description for binary Cu-Se system is also a crucial part of the thermodynamic databases for the higher order systems such as the ternary Cu-In-Se and Cu-Ga-Se, and quaternary Cu-In-Ga-Se system s. Thermodynamic optimization for the Cu-Se system was first performed by Cha ng [Cha99] using the previously reported experimental data and ThermoCalc program which is one of most popular CALPHAD software. In his work, an association mode l and a three-sub-lattice model were employed for liquid and Cu2-xSe phases, respectively. The other intermediate phases, Cu3Se2, CuSe and CuSe2, were modeled as line compounds. In this work, the efforts to improve th e previous optimization results by Chang were incorporated to make the models for different phases in th e Cu-Se system more compatible with higher order systems, and the calculated phase diagram and thermodynamic properties more coincident with the recently evaluated results, especially the values suggested by Glazov [Gla00]. 2.1.2 Experimental Information The liquid phase of this system exhibits two miscibility gaps. One in the Cu-rich region was reported by several resear ch groups [Gla91, Gd00b, Ber72, Hey66, Bab75, Bur74, Mur75], and the other in Se-ric h region was tentatively mapped by Glazov [Gla00] and Gdecke [Gd00b] based on very few experimental data. As to the terminal phases, a small solubility of Se in Cu was measured by Smart [Sma46] and Taylor [Tay76], while negligible sol ubility of Cu in Se was pr oposed by Chakrabarti [Cha81]. Four intermediate compounds were e xperimentally iden tified including Cu2-xSe, Cu3Se2, CuSe and CuSe2. Among them, only Cu2-xSe melts congruently. The Cu2-xSe has two polymorphs of -Cu2-xSe (low temperature phase) and -Cu2-xSe (high temperature

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21 phase). The CuSe has three polymorphs including -CuSe, -CuSe and -CuSe. Their crystal structures were summarized by Glazov [Gla00] and Chang [Cha99]. The equilibrium reactions of th e Cu-Se system were reporte d in many papers [Gd00b, Hey66, Ber68, Ogo69, Ogo72, Ber72, Aza76, Abr84]. Th e key equilibrium points have been more recently evaluated and presented with the different accuracy according to the experimental conditions by Gl azov [Gla00]. Some phase tr ansformation temperatures were confirmed to an accuracy of one tenth degree of Kelvin. The standard enthalpies of formation a nd entropies of the intermediate compounds have been determined by various te chniques [Hey66, Gat56, Val68, Rau70,Ask76, Mil74] and summarized by Chang [Cha99]. The heat capacities of two polymorphs of Cu2Se were measured using an adiabatic calor imetry in the range 193 to 773 K [Kub73] and in the range 300 to 1390 K [Bla78]. As pointed out by Kubaschewski [Kub73], the measured heat capacities of the -Cu2-xSe phase are not reliab le above 325 K on account of the transformation. The heat capacities of three polymorphs of CuSe were measured in the range 5.7 to 652.7 K [Sto96] using the same method as used by Kubaschewski [Kub73]. The chemical potential of Cu in Cu2-xSe, as a function of temperature, was measured using coulometric titrations with a solid state galvanic cell, Pt/Cu/CuBr/Cu2xSe/graphite [Mos89]. The act ivities of Se in molten mi xture of Cu and Se were measured by a modified dew-point method at 1373 K [Bla78], and by the transportation method at 1437 K [Aza76]. Several gaseous species have been detected including Sen (n = 1 to 8), Cu, Cu2, CuSe, and Cu2Se. The vapor pressure of Se2 over different condensed phases in the Cu-Se system was reported by Rau [Rau70].

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22 2.1.3 Thermodynamic Optimization The CALPHAD method was applied to obtain a consistent thermodynamic description of the entire Cu-Se system by employing the PARROT module of the ThermoCalc program package [Din91]. Th e CALPHAD method is based on two basic principles: the total Gibbs energy of a system will be at a minimum at thermodynamic equilibrium and the chemical potential of ever y element in different equilibrium phases is the same. Thermodynamic optimization by CALPHAD method can provide the following advantages; Predicts phase diagrams and therm odynamic properties of a system under conditions where no experimental information is available. Calculates phase diagrams and thermodyna mic properties for a higher order system based on the models of its lower order sub-systems. Calculates meta-stable phase diagram. Determine the driving force of phase transformation. The standard Gibbs energy function 0Gi (T) for the element i in phase is described by an equation suggested by SGTE [Din91]: 1 3 2 0ln ) ( ) ( T f T e T d T T c T b a H T G T GSER i i i (2-1) where Hi SER is the molar enthalpy of element i at 298.15 K and 1 bar in its standard element reference (SER) state, and represents any possible pha se. The parameters for 0GCu(T) and 0GSe(T) functions were taken from the SGTE compilation [Din91] and the evaluation results by Chang [Cha99], respectively. To allow the established database to be easily extended to higher order systems and to be compatible with the general CALPHAD database, the sub-lattice models with the

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23 different constitutions according to their structures as presented by Saunders [Sau98] were employed for all the stable phases of the Cu-Se system. The liquid phase is described by an i onic two-sub-lattice model that can be schematically represented as (Cu+1)p(Se-2,Va-q,Se)q. This model is able to describe the short range ordering effectively and is straightforwardly exte nded to higher order systems as compared to the associated soluti on model used by Chang [Cha99]. The Cu+1 state is considered as the only species in the catio nic sub-lattice. Another oxidation state Cu+2 is neglected due to its very small amount. Neutral selenium and hypothetically charged vacancy are introduced in an anion sub-latti ce to maintain the charge neutrality by adjusting the values of p and q The Cu-rich solid solution phase is described by a two-sub-lattice model in terms of (Cu, Se)(Va), which is generally used for the alloy fcc phase in CALPHAD solution database such as SSOL [Din91]. The line compounds Cu3Se2, CuSe, and CuSe2 are described by a two-sub-latt ice model in terms of (Cu)p(Se)q where p and q are the stoichiometric coefficien ts of the compounds. The two polymorphs of the non-stoichiometric Cu2-xSe compound are described by a three-sub-lattice model based on the struct ural study [Cha99]. In this work, the sublattice constitutions (Cu,Va)1(Se,Va)1(Cu)1 used by Chang [Cha99] is simplified to (Cu,Va)1(Se)1(Cu)1 since the measured compositions of Cu2-xSe always show a deficit of Cu. The simplification is intended to keep th e number of parameters to be optimized as low as possible while still perm itting the results to be matched with the apparent data. It does not mean no vacancy exists in the other two sub-lattices. For any phase in the Cu-Se system, the Gibbs energy is represented by

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24 G G G Gxs id ref (2-2) The Gibbs energies, refG, idG and xsG for different phases are described by the following equations: for the liquid phase, liq Se Se liq V Cu V Cu liq Se Cu Se Cu liq refG y q G y y G y y Gq a q a0 : 0 : 0 '1 1 2 1 2 1 (2-3) ) ln ln ln (" " " "2 2Se Se V V Se Se liq idy y y y y y q RT Gq a q a (2-4) liq Se Se Cu Se Se liq V Se Cu Va Se liq xsL y y L y y Gq a q, : " : "2 1 2 2 1 2 (2-5) for the Cu-rich solid solution phase, fcc Cu V Se Se fcc Cu V Cu Cu fcc Cu refa aG y G y G_ : 0 : 0 (2-6) ) ln ln (' ' Se Se Cu Cu fcc Cu idy y y y RT G (2-7) aV Se Cu Se Cu fcc Cu xsL y y G: ' (2-8) for the line compound phases in terms of CupSeq q p q pSe Cu Se Cu Se Cu refG G: 0 (2-9) 0 q pSe Cu idG (2-10) 0 q pSe Cu xsG (2-11) and for the non-stoichiometric compound phases such as -Cu2-xSe and -Cu2-xSe represented as phase a a aV Se V V Cu Se Cu Cu refG y G y G: : 0 : : 0 (2-12) ) ln ln (' ' 'a aV V Cu Cu idy y y y RT G (2-13) Cu Se V Cu V Cu xsa aL y y G: : 0 ' (2-14)

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25 In equation (2-3)-(2-14), 0GA:B and 0GA:B:C represent the Gibbs energy of the socalled end-member compounds AB and ABC, respectively, where A, B, and C is a species such as Cu, In, Se, Va, Cu+1, Se-2 and Va-q ; 0LA,B:B:C is the interaction parameter for the species A and B in the first sub-lattice, while the second and third sub-lattices are occupied by B and C, respectively; yA and yA represent the site fraction of A in the first and second sub-lattice, respectiv ely. An end-member comp ound could be a real or a hypothetical compound. The Gibbs energy for the end-member is represented by the same expression as that for the elements: 1 3 2 : : 0ln ) ( T f T e T d T T c T b a T GC B A (2-15) Each interaction parameter can be expressed by the expa nsion of site fraction and the temperature dependence as the following: n y j iy y L L0) ( (2-16) T L L LB A (2-17) For the compounds like Cu2-xSe and CuSe for which the heat capacities have been measured at different temperatures [Mos89, Bla78, Aza76], the latter four terms ( c, d, e and f ) of equation (2-15) were obt ained from the heat capacity data using the following expression: 2 2) ( T D T C T B A T Cp (2-18) In comparison of equations (15) and (18), the following relations can be derived by using the fundamental relati onships of thermodynamics c = -A ; d = B/2 ; e = -C/6 ; f = -D/2 (2-19)

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26 Before the optimization, the evaluated heat capacity data are directly put into the Gibbs energy expressions in terms of c, d, e and f It can reduce the arbitrary optimization due to too many unknown parameters. For the compound -Cu2-xSe, only the experimental heat capacity data at low te mperature were used in optimization for the reason that transformation would ra ise the heat effect. Thermodynamic optimization was then performed by using the selected experimental data presented in Figure 2-2 and Tables 2-3 and 2-4. A set of selfconsistent model parameters were obtained as the optimization result, with which the calculated phase diagram and thermo-chemical properties of the system agree well with the evaluated experimental results. 2.1.4 Results and Discussion The optimized parameters for describing the Gibbs energy of each phase in the CuSe system are listed in Tables 2-1 and 2-2. The calculated Cu-Se phase diagram is presented in Figure 2-1 and is compared with th e literature data in Fi gure 2-2. Calculated key equilibrium points are compared with the ev aluated values [Gla00] in Table 2-3. The comparison of the calculated standard en thalpy of formation and entropy of the compounds is shown in Table 2-4. The calcula ted chemical potential of Cu is compared with the experimental data in Figure 2-3. The calculated chemical potential of Se is compared with the values converted from the experimental activity data [Mos89] in Figure 2-4. The comparison of the calculat ed vapor pressures of Se over different condensed phases with the experiments is shown in Figure 2-5. The comparison of calculated heat capacities of the Cu2-xSe and CuSe compounds with those of different polymorphs is presented in Figure 2-6 and 2-7.

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27 It can be seen that the overall calculated phase diagram and most of the key phase equilibrium points agree well w ith the experimentally evaluated results [Gla00]. The calculated standard en thalpy of formation, absolute entropy, heat capacity of the compounds, and the vapor pressure of Se2 also agree well with the experimental data. The calculated chemical potentials of Cu and Se agree with most of the experimental data. The calculated eutectoid temperature of -Cu2-xSe/ -Cu2-xSe/Cu3Se2 (334.9K), however, is much higher than that ( 253 K) suggested by Glazov [Gla00] based on the experiments [Ogo69, Ogo72]. If the lower value of the eutectoid temperature is used as constant and other model parameters ar e adjusted, the vapor pressure of Se2 will not agree with the experimental data [Rau70]. The inconsistence can not be solved by adjusting any model parameters of the three phases. Since it is believed that achieving equilibrium between the gas-solid is more likely than between the solid-solid at low temperature, a large weight factor was used for Se vapor pressure data during optimization. The calculated Cu chemical potential of the Cu2-xSe compound agrees well with EMF measurements [Mos89] for x < 0.04, while it decreases more steeply than experimental values for x > 0.04. The difference may be caused by the fact that the rate of Cu diffusion is not sufficiently high to maintain the sample homogeneous during coulometric titration. Another possibility is the presence of electric current that when combined with the ionic compone nt causes the apparent Cu titr ation amount to be greater than the actual value. The calculated Se chemical potentials are compared with experimental values for liqui d phases measured by two di fferent methods, a modified

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28 dew point method at 1373K [Bla78] and a tr ansportation method at 1473K [Aza76]. The results reveal that the calculated values li e well between the two experimental results. 2.1.5 Summary A thermodynamic description for the Cu-S e system has been established based on the abundant experimental data, the recen t evaluation [Gla00], and the previous optimization work [Cha99]. Sub-lattice models with various constitutions were applied for different phases of the system. The models used in this work allow easy extension of the database to higher order systems. The calculated phase diagram and thermo-chemical properties agree well with expe rimental results and thus de monstrate the self-consistency of the established therm odynamic description.

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29 Table 2-1. Thermodynamic parameters in Cu-Se system Phase/model Function Reference G(LIQ,CU+1:SE-2;0) = GCU2SE_B + 17762.5-12.5*T This work G(LIQ,CU+1:VA;0) = GCU_S + 13263.3 9.76894748*T This work G(LIQ,SE;0) = GSE_L [Din91] G(LIQ,CU+1:SE-2,VA;0) = 159272.8 87.93*T This work G(LIQ,CU+1:SE-2,VA;1) = 63335 48.1634*T This work G(LIQ,CU+1:SE-2,SE;0) = -1235-5*T This work Liquid / (Cu+1)p(Se-2,Va-q,Se)q G(LIQ,CU+1:SE-2,SE;1) = -22612.66 This work G(CU2SE_A,CU:SE:CU;0) = GCU2SE_A This work G(CU2SE_A,VA:SE:CU;0) = 50000 + GCU_S + GSE_S This work G(CU2SE_A,CU,VA:*:CU;0) = 50000 This work -Cu2Se / (Cu,Va)(Se)(Cu) G(CU2SE_A,CU,VA:*:CU;1) = -43000 This work G(CU2SE_B,CU:SE:CU;0) = GCU2SE_B This work G(CU2SE_B,VA:SE:CU;0) = 46000 + 18.7*T + GCU2SE_B GCU_S This work G(CU2SE_B,CU,VA:*:CU;0) = -28998 + 14.002*T This work -Cu2Se / (Cu,Va)(Se)(Cu) G(CU2SE_B,CU,VA:*:CU;1) = -8.803*T This work Cu3Se2 /(Cu)0.6(Se)0.4 G(CU3SE2,CU:SE;0) = GCU3SE2 This work -CuSe /(Cu) 0.5(Se) 0.5 G(CUSE_A,CU:SE;0) = GCUSE_A This work -CuSe /(Cu) 0.5(Se) 0.5 G(CUSE_B,CU:SE;0) = GCUSE_B This work -CuSe /(Cu) 0.5(Se) 0.5 G(CUSE_G,CU:SE;0) = GCUSE_G This work CuSe2 /(Cu) 0.33(Se) 0.67 G(CUSE2,CU:SE;0) = GCUSE2 This work G(CU_FCC,CU:VA;0) = GCU_S [Din91] G(CU_FCC,SE:VA;0) = GSE_S + 5000 This work -Cu /(Cu,Se)(Va) G(CU_FCC,CU,SE:VA;0) = -14500 This work -Se G(SE_S,SE;0) = GSE_S [Din91]

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30 Table 2-2. Parameters for functions used in Table 2-1 in the form of equation (2-1) a b c d102 e106 f10-2 T(K) range -7770.4580 130.4852 -24.1124 -0.2657 0.1292 524.7780 2981358 GCU_S -13309.7200 183.6498 -31.3800 0 0 0 13583200 -6657.6530 92.5397 -19.1400 -1.2295 2.6767 0 298760 GSE_S -9059.1660 150.3342 -28.5520 0 0 0 7601500 -9809.1960 288.8134 -52.4000 2.4925 -5.4550 0 2981000 8433.1372 -78.4769 5.3990 -3.5945 5.2017 0 10001150 GSE_L -7460.6200 192.6463 -36.0000 0 0 0 11501500 GCU2SE_A -86772.3609 285.8666 -58.6000 -3.8700 0 0 2986000 GCU2SE_B -85571.9722 454.3173 -90.4176 0.8600 -1.5000 516.6747 2986000 GCU3SE2 -31329.6700 172.9600 -32.0000 0.0319 0 0 2986000 GCUSE_A -28151.0213 110.6613 -21.5224 -0.9115 2.0400 281.4303 2986000 GCUSE_B -27103.8019 111.0630 -22.3684 -0.3715 -2.1800 251.0000 2986000 GCUSE_G -31321.3585 284.3542 -53.3380 6.2458 -24.0000 0 2986000 GCUSE2 -28485.6977 265.0188 -45.3806 0.4484 0 0 2986000

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31 Table 2-3. Phase equilibria in the Cu-Se system Equilibrium Phase composition(at.% Se) T (K) Type Ref. L2 L1 + -Cu2-xSe 31.5 32.6 4 3 33.3 33.5 1380 1380.0 Monotectic [Gla00] This work L1 Cu + -Cu2-xSe 1.8 2.16 0.021 8 10-5 33.3 33.5 13365 1334.2 Eutectic [Gla00] This work L2 L3 + -Cu2-xSe 52.5 50.4 36.5 36.3 99.6 96.7 7961 795.8 Monotectic [Gla00] This work -Cu2-xSe + L3 -CuSe 36.5 36.4 100 99.2 50.0 50.0 652.7 652.7 Peritectic [Gla00] This work -CuSe + L3 CuSe2 50.0 50.0 100 99.7 66.7 66.7 605 604.9 Peritectic [Gla00] This work L3 CuSe2 +Se 100 100 66.7 66.7 100 100 4941 494.0 Eutectic [Gla00] This work -Cu2-xSe; -CuSe; CuSe 36.5 35.5 50.0 50.0 50.0 50.0 410 410.1 Peritectoid or Eutectoid [Gla00] This work -CuSe; -CuSe; CuSe2 50.0 50.0 50.0 50.0 66.7 66.7 410 410.1 Peritectoid or Eutectoid [Gla00] This work Cu + -Cu2-xSe -Cu2-xSe 4 10-8 5.24 10-9 33.3 33.3 33.3 33.3 39615 395.8 Peritectoid [Gla00] This work -Cu2-xSe + -CuSe Cu3Se2 36.3 35.4 50.0 50.0 40.0 40.0 386 385.6 Peritectoid [Gla00] This work Cu3Se2; -CuSe; -CuSe 40.0 40.0 50.0 50.0 50.0 50.0 326.8 326.4 Peritectoid or Eutectoid [Gla00] This work -CuSe; -CuSe; CuSe2 50.0 50.0 50.0 50.0 66.7 66.7 326.8 326.4 Peritectoid or Eutectoid [Gla00] This work -Cu2-xSe -Cu2-xSe + Cu3Se2 35.4 35.0 34 33.3 40.0 40.0 253 334.9 Eutectoid [Gla00] This work L L1 + L2 18 16.3 1699 1698.7 Critical point [Gla00] This work L1 -Cu2-xSe 33.4 33.8 1421 1421.2 Congruent melting point [Gla00] This work

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32 Table 2-4. Experimental and calculat ed standard formation enthalpies ( Hf298.15K) and entropies ( S298) of Cu-Se compounds. Compound Hf,298.15K (kJ/mole) S298 (J/mole.K) Method Reference -Cu2Se 59.3 69.9 62.8 65.7 65.3 59.3 65.86 (0.53) 65.9 157.4 113.9 129.7 129.7 129.7 (4.2) 129.7 Calorimetry EMF Vapor pressure EMF Evaluation Assessment Evaluation Assessment [Gat56] [Val68] [Rau70] [Ask76] [Mil74] [Cha99] [Gla00] This work Cu3Se2 98.9 124.5 94.6 104.6 104.6 98.91 (0.54) 108.8 185 207.2 210.7 207.11 (21) 207.8 Calorimetry DTA EMF Evaluation Assessment Evaluation Assessment [Gat56] [Hey66] [Ask76] [Mil74] [Cha99] [Gla00] This work -CuSe 39.6 46.0 44.0 32.6 41.8 40.8 39.54 (0.42) 41.7 86.2 74.1 78.2 78.2 79.36 (0.06) 79.4 Calorimetry EMF Vapor pressure EMF Evaluation Assessment Evaluation Assessment [Gat56] [Val68] [Rau70] [Ask76] [Mil74] [Cha99] [Gla00] This work CuSe2 43.1 49.0 39.3 48.1 48.1 43.10 (7.1) 46.0 120.6 98.8 107.4 115.4 107.5 (10.5) 108.7 Calorimetry Vapor pressure EMF Evaluation Assessment Evaluation Assessment [Gat56] [rau70] [Ask76] [Mil74] [Cha99] [Gla00] This work

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33 Figure 2-1. Calculated Cu-Se phase diagram

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34 Figure 2-2. Comparison between the calcula ted Cu-Se phase diagram and experimental data

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35 Figure 2-3. Comparison between the cal culated chemical potential of Cu and experimental data in -Cu2-xSe phase

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36 Figure 2-4. Comparison between the cal culated chemical potential of Se and experimental data at 1373 and 1473K

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37 Figure 2-5. Comparison between the calculated Se2 partial pressure and experimental data in Cu-Se system

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38 Figure 2-6. Comparison between the calcu lated heat capacity of each phase and experimental data for Cu2Se

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39 Figure 2-7. Comparison between calcul ated heat capacity of each phase and experimental data for CuSe

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40 2.2 Thermodynamic Description of Tern ary Compounds in Cu-In-Se System 2.2.1 Introduction Since the chalcopyrite CuInSe2 (CIS) was first synthesized in 1953, the Cu-In-Se ternary system has attracted considerable atte ntion due to its application as an absorber material in solar cells. CIS-based ce lls currently hold the world-record energy conversion efficiency (1 9.5%, AM1.5G, 100mW/cm2) for thin film technologies [Con05]. This compound has a large homogene ity range of composition and complicated phase relationships with the other phases. A small deviation in composition about the stoichiometry (Cu:In:Se = 1:1:2) or the ex istence of secondary phases produces large changes in CIS material propertie s and thus its device characteri stics. There is a lack of reliable thermodynamic data for the tern ary compounds in the Cu-In-Se system. Unfortunately these properties are essential to understanding reaction pathways to synthesize CIS and development of novel pr ocesses to fabricate cost-effective highquality CIS films. Common experimental techniques to meas ure thermodynamic properties can not be directly used to estimate the Gibbs energy of these ternary compounds as it is not easy to know their exact corresponding compositions du e to large homogeneity range of the ternary compounds, e.g., -CuInSe2 and -CuIn3Se5 in pseudo-binary In2Se3-Cu2Se phase diagram shown in Figure 2-10. In this work [She06], a set of thermodynamic descriptions for the dominant ternary compounds in the Cu-In-Se system is established by integrating the relevant information, which includes: Experimental measurements of the th ermodynamic properties of the Cu-In-Se ternary compounds. Experimental measurements of phase equilibria including Cu-In-Se ternary compounds.

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41 Established thermodynamic model of the thr ee sub-binaries, i.e., Cu-Se, Cu-In and In-Se. Ab initio calculation on the defect formation energy in the Cu-In-Se ternary compounds. 2.2.2 Extrapolation of Binary Gibbs Energy to Ternary In the CALPHAD method, the excess Gibbs energy expression of a higher-order system is usually predicted from that of the lower-order systems if insufficient experimental data are available for the higher-order system. The basic formulae for doing this are based on various geometrical weig htings of the mole fractions [Hil80] and expressed for ternary system by the general expression: 123 3 2 1 3 1 3 1 ) ( ) (L x x x X X G x x Gij ij j ij i xs ij j i xs mix (2-20) and 3 ) (x w x Xij i ij i ; 3 12 1 ) 12 ( 1x w x X (2-21) 1) ( ) ( ij j ij iX X (2-22) where xs mixG is the contribution of non-ideal in teractions between the components of ternary system, also known as th e excess Gibbs energy of mixing, xi is a mole fraction of i component in ternary compound, Xi(ij) is a mole fraction of i component in binary i-j compound, xs ijG is the excess Gibbs energy of mixing for binary i-j compound, L123 is an excess ternary interaction parameter, and wij is a weighting factor. By adopting different weighting factors, the three commonly used methods such as Kohler, Muggianu and Toop models are easily generated. In the Kohler model, a weighting factor is defined as 2 1 1 12x x x w (2-23)

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42 2 1 2 ) 12 ( 2 2 1 1 3 2 1 1 1 ) 12 ( 1;x x x X x x x x x x x x X (2-24) and can be described geomet rically as Figure 2-8 (a). The Muggianu model adopts a simple weighting factor defined as 5 021 12 w w (2-25) 1 2 ) 12 ( 2 2 1 3 1 ) 12 ( 11 2 1 ; 1 2 1 5 0 x x X x x x x X (2-26) and is geometrically represented by Figure 2-8 (b). In the Maggianu extrapolation it can be seen that the line from the ternary alloy composition to the edge binaries forms a rightangle to the binary. This leads to the c onsequence that, when the alloy composition is dilute in two of the components, the intera ction parameter of these two components will approach regular behavior because the term (xi-xj) becomes small. Figure 2-8. Geometrical construction of (a) Kohler and (b) Muggianu model Both the Kohler and Muggianu models can be considered symmetrical as they treat all three components in the same way. Anothe r method called the Toop model is different in that it considers one of the binary systems doe s not behave in the same as the others, and thus its weighting f actor is defined as 12 3 (b) 1 2 3 (a)

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43 1 ; 021 12 w w (2-27) 3 2 1 ) 12 ( 2 1 ) 12 ( 11 ; x x x X x X (2-28) and geometrically described as Figure 2-9. Practically, the phase boundaries calcula ted by either the Muggianu and Kohler extrapolations seem to provide similar resu lts [Ans78], but it was also noted that the choice of extrapolation method should receiv e more attention when exact knowledge of partial quantities such as activity coefficients is more critical It is known that the Toop model is not suitable for metallic systems but may be appropriate for some ionic liquid systems. It should, however, be used caref ully in all cases as the extrapolation is dependent on which binary is chosen to be have differently, and it is possible to obtain three different answers depe nding on this choice [Sau98]. Figure 2-9. Geometrical construction of Toop model The ThermoCalc program used for optimiza tion of the Cu-In-Se ternary system is adopting a Muggianu model. By plugging equati ons (2-25) and (2-26) into equation (220) with Redlich-Kister equation for the binary excess Gibbs energy, xs ijG, as expressed by 1 2 3

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44 ) ( ) ( ) (3 1 1 13 0 13 3 1 3 2 1 23 0 23 3 2 2 1 1 12 0 12 2 1x x L L x x x x L L x x x x L L x x Gxs mix (2-29) where L0 is the binary interaction parame ter of regular solution model and L1 is the binary interaction parameter of sub-regular solution model. It is generally called the RedlichKister-Muggianu equation. 2.2.3 Experimental Information 2.2.3.1 Ternary compounds Four ternary compounds Cu13In3Se11, CuInSe2, CuIn3Se5, and CuIn5Se8, located on the Cu2Se-In2Se3 pseudo-binary section (Figure 2-10), were identified as stable phases, though several other compounds have been reported [Gd00a-c]. The CuInSe2, CuIn3Se5 and CuIn5Se8 phases have large homogeneity rang es. Under atmospheric pressure, CuInSe2 has two polymorphs separated by a first order transition between chalcopyrite ( ) and sphalerite ( ) structures. The CuIn3Se5 has a tetragonal chalcopyrite-like structure and the CuIn5Se8 has a hexagonal structure. In terestingly, it was found that another phase often co-exi sts with a hexagonal CuIn5Se8. This co-existing phase could be a trigonal [Mer00] or tetragonal [Koh00] structure. The Cu13In3Se11 is reported as a line compound [Gd00b], which is stable within the narrow temperature range 923 to 947 C. 2.2.3.2 Thermodynamic properties Only few thermodynamic data are available for CuInSe2 compounds. The heat capacity of CuInSe2 was measured by Boehnke et al. using both pulsed and semiadiabatic calorimetric techniques, but onl y at low temperature (<300K) [Boe87]. The experimental values of the en thalpy of formation of CuInSe2 at 298K are summarized in

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45 Table 2-5. No thermodynamic information, however, has been reported concerning the CuIn3Se5 and CuIn5Se8 compounds. Table 2-5. The experimental values of the standard formation enthalpy (0 298 ,K fH ) and energy (0 0 ,fE ) of -CuInSe2 0 298 ,K fH (kJ/mol) Method Reference 267.4 260.2 280.0 189.8 204.4 Mass Spectrometry Calculation Calculation Calculation Calculation [Ber73] [Gla79] [Gom84] [Red48] [Moo99] 0 0 ,fE (kJ/mol) 190.30 ab initio [Zha98] Electro-motive force (EMF) measurements were performed by Ider [Ide03], to extract Gibbs energy information of ternary compounds (e.g., CuInSe2, CuIn3Se5, CuIn5Se8) from the appropriate galvanic cell reacti ons. It is noted th at since the exact composition of the participating ternary co mpounds is generally unknown or may be far from the stoichiometry, the resulting therm odynamic properties directly calculated from cell reactions may not be quite reliable. 2.2.3.3 Phase diagrams The Cu2Se-In2Se3 pseudo-binary section [Kon82, F ea86, Haa98] and projection of liquidus surface [Mer00, Kon82, Fea86, Boe87, Bac88] have been reported by several authors. These phase diagrams, however, are quite divergent and thus very difficult to assess. Gdecke et al. reported a series of phase diagra ms of the Cu-In-Se system based on thorough experiments using more than 240 alloys [Gd00a-c], where the phase diagrams, including a projection of liquidus su rfaces, a projection of four-phase plane, three isothermal sections and ten isopleths, are self-consistent.

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46 2.2.4 Ab initio Calculation on the Ternary Cu-In-Se Compounds The formation energies of different poi nt defects in various Cu-In-Se ternary compounds were calculated by Zhang using an ab initio method. The existence of a series of unusual ordered def ect compounds (ODC) along the CuSe2-In2Se3 section and their large off-stoichiometry are explained by the particularly low formation energy of the (2VCu+InCu) defect pair in these compounds [Zha98]. The CuIn3Se5 and CuIn5Se8 are considered as ODC’s of CuinSe2 and form by the reaction of n(CuInSe2) + m(In) Cu(n-3m)In(m+n)Se2n + 3m(Cu) (2-30) where n=2.5, m=0.5 for CuIn3Se5 and n=4 m=1 for CuIn5Se8. The energy change of the reaction is calculated by Er = Eneu + Eint + Eord (2-31) where Eneu is the formation energy of non-interacting neutral defects, Eint is the intrapair interaction energy, and Eord is the pair-pair ordering energy. The formation energies of CuIn3Se5 and CuIn5Se8 compounds can then be calculated by ) ( 5 1 5 0 5 25 32 5 3Se CuIn E E E E Er Cu In f CuInSe f Se CuIn (2-32) ) ( 3 48 52 8 5Se CuIn E E E E Er Cu In f CuInSe f Se CuIn (2-33) As the defect compounds are related to th e end-members in the sub-lattice model, their formation energies are used to estimate the Gibbs energy of the end-members. It can largely reduce the arbitrar y aspects of the model parameters. For example, the formation energy of VCu is defined as the energy change of the reaction CuInSe2( )=InInSe2( )+Cu (2-34)

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47 InInSe2( ) is regarded as a end-member in the sub-lattice model of CuInSe2( ) and its Gibbs energy can be estimated from the formation energy of VCu. 2.2.5 Establishment of Thermodynamic Descriptions In this work, sub-lattice models [Sa u98] are used to describe thermodynamic properties of the ternary compounds. Unlik e conventional thermodynamic optimization evaluating model parameters from abunda nt sources of phase diagrams and thermodynamic experiments, only one set of data were selected for this work to avoid the possible confusion caused by randomly mixing th e divergent data for such a complicated system. 2.2.5.1 Sub-lattice model for diff erent ternary compounds The -CuInSe2 belongs to the family of I-III-VI2 chalcopyrite semiconductors whose structure is similar to the zinc-blende structure where each of the two cations (Cu and In) are coordinated by four anions (Se), but the Se is coordinate d by (2Cu + 2In) with different nearest-neighbors. The Se deficiency is mainly caused by Cu occupying an interstitial position [Zha98], the sub-lattice structure of -CuInSe2 is thus considered as (Cu, In, Va)1 (Cu, In, Va)1 (Se)2 (Cu, Va)1 Formula (5.37) in [Sau98] is used to calcu late Gibbs energy of this phase where the Gibbs energy of the 18 end-members including Cu1In1Se2Va1, Cu1Cu1Se2Va1, and Va1Cu1Se2Va1, needs to be estimated. In the same manner, the sub-lattice structures of CuIn3Se5 and CuIn5Se8 are expressed by (Cu, In, Va)1 (Cu, In, Va)3 (Se)5 (Cu, Va)1 (Cu, In, Va)1 (Cu, In, Va)5 (Se)8 (Cu, Va)1 The -CuInSe2 is a disordered phase of -CuInSe2 with a sphalerite structure where the two metals (Cu and In) can be replaced by each other much more easily than in -

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48 CuInSe2 to achieve almost random mixing. The sub-lattice structure of the -CuInSe2 is considered as (Cu,In,Va)2(Se)1(Se,Va)2 to keep its composition close to the section of Cu2Se-In2Se3, as observed experimentally. 2.2.5.2 Evaluation of Gibbs energies of e nd-members in the sub-lattice model Gibbs energy of formation of CuInSe 2 ( ) To estimate the Gibbs energy of formation of CuInSe2( ), the EMF results reported by Ider [Ide03] were utilized. Three different kinds of galvanic cells were designed: Cell I: W, In(l), In2O3(s) // YSZ // In2O3(s), Cu2Se( ), Cu(s), CuInSe2( or ), C, W Cell II: W, In(l), In2O3(s) // YSZ // In2O3(s), Cu1In3Se5(s), CuInSe2( or ), C, W Cell III: W, In(l), In2O3(s) // YSZ // In2O3(s), Cu1In5Se8(s), Cu1In3Se5(s), C, W The overall reaction of cell I is expressed as 2Cu2Se( ) + In(l) CuInSe2( or ) + 3 Cu(s) (2-35) In this work, the composition of CuInSe2 is assumed to be in stochiometry because the CuInSe2 phase has a relatively narrow compositi on range when it is in equilibrium with Cu2Se( ). Thus if the solubility of In in Cu2Se( ) phase is negligible, the Gibbs energy of formation of CuInSe2( ) can be directly calculated by f Se Cu R f CuInSeG I cell G G) ( ) (2 22 ) ( (2-36) and GR was reported by Ider [Ide03] as GR = -99520 + 54.50 T [J/mol] (949 to 1044K) (2-37) From assessment of the Cu-Se system, the f Se CuG) (2 is expressed by f Se CuG) (2 = 60221.86 95.47 T + 10.21 Tln(T) 0.01 T2 + 3.70 10-6 T3 53288.13/T [J/mol] (2-38) Plugging equations (2-37) and (2-38) into equation (2-36) yields

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49 f CuInSeG) (2 = -209963.72 36.43 T + 20.41 Tln(T) – 0.02 T2 + 7.40 10-6 T3 106576.26/T [J/mol] (2-39) The standard enthalpy of formation of CuInSe2( ) at 298.15K calculated from f CuInSeG) (2 obtained by equation (2-39) is around 218.50 kJ/mol, which is similar to the literature values listed in Table 2-5. Estimation of Gibbs energy of CuInSe 2 ( ), CuIn 3 Se 5 and CuIn 5 Se 8 As mentioned before, EMF experiment al results can pr ovide only a rough estimation of the Gibbs energy of formation of CuInSe2( ), CuIn3Se5 and CuIn5Se8 mainly because of their non-stoichiometric co mposition during cell reaction. Ider [Ide03] reported the Gibbs energy change of r eaction for cell I through III such as GR (Cell I) = -89520 + 45.10 T [J/mol] (1055 to 1150K) (2-40) GR (Cell II) = 90160 – 110.77 T [J/mol] (868 to 1045K) (2-41) GR (Cell III) = 109180 – 125.90 T [J/mol] (1054 to 1179K) (2-42) In the exactly same manner as for CuInSe2( ), the Gibbs energies of formation of other ternary compounds (i.e., CuInSe2( ), CuIn3Se5 and CuIn5Se8) were estimated as f CuInSeG) (2 = -209963.72 145.83 T + 20.41 Tln(T) – 0.02 T2 + 7.40 10-6 T3 106576.26/T [J/mol] (2-43) f Se CuInG5 3 = -438646.71 1794.61 T + 259.98 Tln(T) – 9.84 10-2 T2 + 2.40 10-5 T3 528546.24/T [J/mol] (2-44) f Se CuInG8 5 = -717569.69 3404.57 T + 499.55 Tln(T) – 1.48 10-1 T2 + 4.07 10-5 T3 – 1163668.00/T [J/mol] (2-45)

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50 On the other hand, the Gibbs energy of formation of CuIn3Se5 and CuIn5Se8 at their stoichiometric composition can also be estimated by ab initio calculation where they are considered as ordered defect compounds of CuInSe2. In the same pattern as equations (232) and (2-33), the Gibbs en ergy of formation of CuIn3Se5 and CuIn5Se8 are expressed by ) ( 5 1 5 0 5 25 32 5 3Se CuIn G G G G Gr Cu In f CuInSe f Se CuIn (2-46) ) ( 3 48 52 8 5Se CuIn G G G G Gr Cu In f CuInSe f Se CuIn (2-47) In this work, the volume and entropy change fo r the defect formation reaction is assumed to be negligible and thus the values of Gr(CuIn3Se5) and Gr(CuIn5Se8,) are identical to Er(CuIn3Se5) and Er(CuIn5Se8) calculated by equation (2-31) where the values of Eneu, Eint, and Eord are taken from [Zha98] as show n in Table 2-6. The value of f CuInSeG) (2 is directly calculated from equation (2-39). In summary, the estimated Gibbs energies of formation from the ab initio study are f Se CuInG5 3 = -557341.00 337.26 T + 51.04 Tln(T) – 5.51 10-2 T2 + 1.85 10-5 T3 266441.00/T [J/mol] (2-48) f Se CuInG8 5 = -892788.00 538.09 T + 81.66 Tln(T) – 8.81 10-2 T2 + 2.96 10-5 T3 426305.00/T [J/mol] (2-49) Table 2-6. Parameters used to calculate Ef of CuIn3Se5 and CuIn5Se8 [Zha98]. Eneu(eV) Eint(eV) Eord(eV) Er(eV) CuIn3Se5 2.27 -2.105 -0.225 -0.06 CuIn5Se8 4.54 -4.21 -0.43 -0.10

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51 Estimation of the Gibbs energy of other end-members The Gibbs energy of the other end-members in the -CuInSe2, -CuIn3Se5, CuIn5Se8 compounds is estimated using the defe ct formation energies calculated by Zhang [Zha98] according the defect formati on reactions such as equation (2-34). For example, 0 ) ( 0 ) ( 0 Va Se Cu Va2 1 2 1 1Cu Cu Va CuInSeG E G G (2-50) 11212000 CuInSeCu()() CuInSeCuiCuGGEG (2-51) Optimization of parameters in the Gibbs energy expressions The Gibbs energy expressions of the ternar y compounds are adjusted to satisfy the relevant experimental phase relationships [G d00a-c]. The results are compared with the available data. It is believed that the complicated phase relationships may play an important role in controlling the chemi cal potentials of these compounds within a reasonable range. Finally, the Gibbs energy parameters are optimized as 0 ) (2CuInSeG = -251102.38 688.51 T 135.95 Tln(T) + 0.03 T2 3.47 10-6 T3 – 265806.00/T [J/mol] (2-52) 0 ) (2CuInSeG = -186607.34 + 505.39 T -114.87 Tln(T) [J/mol] (2-53) 05 3Se CuInG = -550466.88 + 1175.69 T 249.24 Tln(T) – 1.02 10-3 T2 1.22 10-7 T3 – 582645.00/T [J/mol] (2-54) 08 5Se CuInG = -940623.58 + 1916.46 T 389.81 Tln(T) + 7.32 10-6 T2 2.90 10-7 T3 – 1006060.00/T [J/mol] (2-55)

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52 The optimized Gibbs energy ( G0) and Gibbs energy of formation ( Gf) are compared with the results of EMF experiment and Ab initio calculation, as represented in Figures 2-11 and 12. 2.2.6 Summary The EMF experimental results, ab initio calculation, and phase equilibrium data were successfully combined to establish relia ble descriptions of Gibbs energy for ternary compounds in the Cu-In-Se system. The EM F result was directly adopted only for the Gibbs energy of CuInSe2( ) by assuming the stochiometric composition. The influence of the solubility of indium in Cu2Se( ) on the electronic transf er and thus the Gibbs energy of formation was also considered The reaction was considered as 2Cu2-3yInySe( ) + (1-y)In(l) CuInSe2( or ) + (3-6y)Cu(s) The number of electrons to be transfe rred is (3-6y) to form one mole of CuInSe2( ). The difference of Gibbs energy of formation between Cu2-3yInySe( ) and Cu2Se is calculated using the formation energy of the defect pair (2VCu+InCu) [Zha98]. This approach, however, yields an unreas onable value of enthalpy of formation for CuInSe2 at 298.15K, whereas the calculation using f Se CuG) (2 expression in equation (238) shows reasonable results, which is in a good agreement with most of literature values. The comparison of the optimized Gibbs energy of the CuInSe2( ), CuIn3Se5 and CuIn5Se8 with that estimated by EMF experiment and ab initio calculation demonstrates reasonable agreement. The phase relati onships concerning th ese ternary compounds follow the experimental isothermal sec tion of the Cu-In-Se system at 500, 800and 900 C shown in Figures 2-13 to 15, respectively. It can be concluded th at a set of reliable

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53 Gibbs energy expression was obtained, alt hough its precision would be further improved with additional experimental and theoretical study. Figure 2-10. Pseudo-binary In2Se3-Cu2Se phase diagram [Gd00a]

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54 Figure 2-11. Optimized Gibbs energy -CuInSe2, -CuIn3Se5 and -CuIn5Se8 compared with that estimated from EMF experiments and ab initio calculation

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55 Figure 2-12. Optimized Gibbs energy of formation of -CuInSe2, -CuIn3Se5 and CuIn5Se8 compared with that estimated from EMF experiments and ab initio calculation

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56 (a) (b) Figure 2-13. Isothermal s ections of Cu-In-Se at 500 C. (a) Calculation [She06], (b) Experimental evaluation [Gd00c] (a) (b) Figure 2-14. Isothermal s ections of Cu-In-Se at 800 C. (a) Calculation [She06], (b) Experimental evaluation [Gd00c]

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57 (a) (b) Figure 2-15. Isothermal s ections of Cu-In-Se at 900 C. (a) Calculation [She06], (b) Experimental evaluation [Gd00c]

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58 2.3 Cu-Ga-In Ternary Phase Diagram Calculation 2.3.1 Introduction The selenization of metallic Cu/Ga/In precursors is one of the most promising industrial processes for CIGS cell fabrication, which is generally called the “two-step process” and has been commercially employe d by Shell Solar and Showa Shell. The commercialized two-step process consists of the deposition of metallic precursors (i.e., Cu/Ga/In) followed by subsequent selenization, as shown in Figure 1-8. Traditionally, the metal precursors are prep ared by sputter deposition a nd then selenized at high temperature (~600 C) in a reactive H2Se or Se vapor ambient. Therefore, understanding the equilibrium phase relationships in the Cu -Ga-In ternary system is essential to the optimization of the two-step process. 2.3.2 Review of Sub-binary Phase Diagrams The phase diagrams of the three sub-bina ry systems, e.g., Cu-In, Cu-Ga and Ga-In, were well assessed by Liu [Liu02], Subram anian [Sub88], and Anderson and Ansara [And91], respectively. Thermodynamic assessm ent of the Cu-In bi nary phase diagram was first performed by Kao et al. [Kao93], based on the review [Bol93] of thermodynamic and phase equilibrium data availabl e in the literature. In their assessment, a Redlich-Kister expression was used to repres ent the Gibbs energies of the liquid and Cu phase, and a Wagner-Schottky model was employed for the Gibbs energy of -Cu2In phase. All other intermetallic phases we re then approximated as line compounds. Recently, Liu et al. [Liu02] reassessed the Cu-In bi nary phase diagram by including additional experimental data [Bah99, Dic00] and adopting a three-sublattice models for and phases, while assuming stoichiometric compounds for other intermetallic phases,

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59 as shown in Figure 2-16. Most recently, Bahari et al. reported new experimental data using DSC, XRD, and EPMA analysis [Bah03] The results indicat e the existence of a solubility region of indium in copper with the limit of the solid solution at 5.20 at.% In at 400 C and of six intermediate phases, i. e., the three low-temperature phases and Cu11In9( ), and the three high-temperature phases and The boundaries of each phase were defined with respect to temperature and composition. Figure 2-16. Calculated phase diagram of Cu-In binary system [Liu02] The general features of the Cu-Ga phase relationships have be en well established by Hansen [Han58] and subsequently re vised by Kittl [Kit64]. Subramanian et al. [Sub88] used these accurately establis hed phase boundaries and some additional thermodynamic data to optimize the thermodynamic parameters for the various intermediate phases. The calculated phase diagram containing three binary phases and is shown in Figure 2-17.

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60 Figure 2-17. Calculated phase diagram of Cu-Ga binary system [Ide03] Figure 2-18. Calculated phase diag ram of Ga-In binary system [And91]

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61 The Ga-In binary system is known to be a simple eutectic type with negligible solubility of indium in solid -Ga. The Ga-In binary phase diagram assessed by Anderson and Ansara [And91] showed a retr ograde tetragonal indium solidus with solubilities of 2.3 at.% gallium in indi um at the eutectic temperature of 15.3 C and of 14.2 at.% indium in the liquid, as evidenced by Figure 2-18. 2.3.3 Prediction of Cu-Ga-In Ternary Phase Diagrams Unfortunately, there are no experimental data available about the interaction between ternary Cu-Ga-In components. Th erefore, Muggianu’s equation based on the summation of the binary inter action parameters was employed to extrapolate the excess Gibbs energy of mixing into ternary system [Sau98], as described in section 2.2.2. To use the ThermoCalc program to estimat e the CGI ternary phase diagram, it is necessary to prepare the TDB (Thermodynamic DataBase) module containing the Gibbs energy information of pure Cu, Ga and In elements as well as the interaction parameters of three sub-binary Cu-Ga, Cu-In and Ga-In systems. The TDB module of ternary CuGa-In system was composed by combining thr ee binary data descri bed in the previous section 2.3.1. For the simplification, the Cu-Ga binary compounds (i.e., and ) were modeled by solid-solution models, while the Cu-In binary compounds (i.e., , and ) except phase modeled by solid-solution model were modeled by sub-lattice models. The Cu-Ga-In ternary phase diagram was then predicted using ThermoCalc program, as shown in Figures 2-19 to 22. Five diffe rent solid solution phases (i.e., Cu-fcc, -Cu7In3, -Cu2In, -Cu7Ga2 and -Cu9Ga4) and a liquid phase region we re included in the 500 C isothermal section of Cu-Ga-In ternary phase diagram shown in Figure 2-19. It is noted that the ternary phase diagrams presented in Figures 2-19 to 22 were estimated on the

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62 basis of binary information only and thus the models do not contain any ternary interaction parameters. To obtain a more re liable ternary phase diagram, one needs to investigate the existence of any new ternary pha ses and the solubility of the third element in binary compounds, and optim ize the ternary interaction parameters in a form of G123 = x1x2x3( L1x1 + L2x2 + L3x3). Furthemore, the vapor pressures for Cu-Ga-In mixtures at several compositions were calculated using the ThermoCalc program in combination with the Cu-Ga-In ternary TDB module. Selected results shown in Figur es 2-23 and 2-24 reve aled that six vapor phase species (i.e., Cu, Cu2, Ga, Ga2, In and In2) dominate the gas phase and the atomic indium is the most volatile among them. Figure 2-19. Isothermal section (500 C, 1atm) of the Cu-Ga-In ternary phase piagram based on the Muggianu’s equation

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63 Figure 2-20. Isothermal section (500 C, 1atm) of the Cu-Ga-In ternary phase piagram based on the Muggianu’s equation for the range of 0 < x(In) < 0.2 and 0.2 < x(Ga) < 0.4 Figure 2-21. Isothermal section (350 C, 1atm) of the Cu-Ga-In ternary phase piagram based on the Muggianu’s equation

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64 Figure 2-22. Isothermal section (800 C, 1atm) of Cu-Ga-In ternary Phase Diagram based on the Muggianu’s equation 1.E-15 1.E-13 1.E-11 1.E-09 1.E-07 1.E-05 1.E-03 1.E-01 1.E+01 500700900110013001500 T (K)Vapor Pressure (Pa) total pressure Cu In2Ga2Cu2Ga In Figure 2-23. Vapor pressure as a function of temperature in the Cu-Ga-In mixture (Cu:Ga:In = 1:1:1 mole ratio)

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65 1.E-15 1.E-13 1.E-11 1.E-09 1.E-07 1.E-05 1.E-03 1.E-01 1.E+01 500700900110013001500 T (K)Vapor Pressure (Pa) Total pressure Cu In2Ga2Cu2Ga In Figure 2-24. Vapor pressure as a function of temperature in the Cu-Ga-In mixture (Cu:Ga:In = 2:1:1 mole ratio) 2.3.4 Modification of Cu-GaIn Ternary Phase Diagrams Recently, an experimental result concerni ng the ternary phase relationship of the Cu-Ga-In system was reported [Pur06b]. In their study, samples were prepared by sequential DC-magnetron sputtering of 8 triple layers of the sequence Cu/CuGa2/In on Mo-coated glass substrates to ensure a good mixing of the components. The samples were annealed in H2 ambient to reduce any oxides at 350 C for 2 min and then cooled to room temperature for subsequent X-ray diffraction analysis. Cu16(In,Ga)9, Cu9(Ga,In)4 alloys, and elemental indium were identified as the equilibrium phases in the Cu-Ga-In composition studied. This was arrived at by assuming that the shifts of Cu16In9 and Cu9Ga4 reflection peaks resulted from the substitution of indium by gallium and gallium by indium, respectively. Consid ering their results as summarized in Table 2-7, the CuGa-In ternary phase diagram predicted by the Muggianu’s equation was modified.

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66 Table 2-7. Experimental results of phase relationships of Cu-G a-In ternary system Atomic fraction No. Cu In Ga Equilibrium phases at 350 C 1 0.479 0.458 0.063 Cu16(In,Ga)9, In 2 0.550 0.365 0.086 Cu16(In,Ga)9, In 3 0.479 0.417 0.104 Cu16(In,Ga)9, Cu9(Ga,In)4, In 4 0.479 0.391 0.130 Cu16(In,Ga)9, Cu9(Ga,In)4, In 5 0.479 0.359 0.161 Cu16(In,Ga)9, Cu9(Ga,In)4, In 6 0.479 0.328 0.193 Cu9(Ga,In)4, In 7 0.640 0.230 0.129 Cu16(In,Ga)9, Cu9(Ga,In)4 8 0.659 0.123 0.218 Cu9(Ga,In)4 Based on experimental data at 350 C, the thermodynamic parameters were manually adjusted to account for the extended so lid solutions as reporte d. To describe the solubility of indium into Cu9Ga4, which is expressed as Cu9(Ga,In)4, the two-sublattice model described by (Cu,Va) (Ga,In) was employ ed. The resulting isothermal section of Cu-Ga-In ternary phase diagram at 350 C and 1 atm along with experimental data is shown in Figure 2-25.

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67 Figure 2-25. Modified isothermal section (350 C, 1atm) of the Cu-Ga-In ternary phase diagram with experimental data (symbol) Figure 2-26. Modified isothermal section (500 C, 1atm) of the Cu-Ga-In ternary phase diagram Furthermore, the optimized thermodynamic parameters are used to predict the isothermal section of Cu-Ga-In phase diagram at 500 C and 1 atm, as displayed in Figure 2-26. It should be noted, however, th at the experimental data used here were based on thin film Cu-Ga-In samples which may have a different equilibrium from bulk material. 2.3.5 Summary and Future Work The Cu-Ga-In ternary phase diagram was predicted by ThermoCalc program employing a Maggianu’s equation based on the sub-binary phase diagrams. Subsequently, the predicted ternary phas e diagrams were modified using recent

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68 experimental data. In the future, the further optimization can be achieved by the followings: Modify the thermodynamic descriptions fo r the sub-binary systems to make the models extendable to higher-order syst ems (sub-lattice model is preferred). Perform the thermal analysis along with X -ray measurements to identify the phase transformation temperatures. Measure the solubility of the third el ements in binary phases (e.g., Ga in -Cu7In3) to estimate the interaction parameters between elements in a sub-lattice. Perform the EMF experiments to obtain the ternary interaction parameters for the liquid and Cu-fcc phases.

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69 CHAPTER 3 METAL (CU, IN, GA)-SE REACTION PATHWAYS 3.1 Introduction The phase equilibria of the binary Cu-Se system have been reviewed by Glazov et al [Gla00] and a thermodynamic assessment using the ThermoCalc software was discussed in chapter 2. Four intermediate binary compounds Cu2-xSe, Cu3Se2, CuSe, and CuSe2 were experimentally identified. The Cu2-xSe compound is known to melt congruently and have two polymorph s: the low-temperature stable -Cu2-xSe phase and the high-temperature modification (i.e., -Cu2-xSe) having a transition temperature of around 396K. Three CuSe polymorphs -CuSe, -CuSe, and -CuSe were also reported. A thermodynamic assessment of the binary In-Se system was performed based on the evaluation of literature by Li et al. [Li04]. Multiple intermediate compounds (In4Se3, InSe, In6Se7, In9Se11, In5Se7 and polymorphic In2Se3 ( , and )) were identified as shown in the phase diagram in Figure 3-1. Phase diagram evaluation and thermodynamic assessment of the binary Ga-Se syst em have been reported by Dieleman et al. [Die82] and by Ider [Ide03], respectively. According to their reports, only two binary compounds (i.e., GaSe and Ga2Se3) are stable in the Ga-Se system, as shown in Figure 3-2. Furthermore, Ga2Se3 has two polymorphisms: a low-temperature stable -Ga2Se3 phase and its high-temperatur e modification (i.e., -Ga2Se3) with a transition temperature of around 967K.

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70 In this thesis (Chapter 4), a systematic study of the reaction pa thways and kinetics of formation of CuInSe2 using in situ high-temperature XRD is presented. In these studies, the reaction pa thway and kinetics of -CuInSe2 formation from different precursors ( e.g., InSe/CuSe [Kim05a] and In2Se3/CuSe [Kim05b, Chapter4]) and selenization of metallic Cu-In precursor have be en presented [Kim06a, Chapter4]. In this chapter, the reaction pathways for binary me tal (i.e., Cu, In and Ga)-Se formation from various precursor structur es were investigated by in situ high-temperature X-ray diffraction. Figure 3-1. Phase diagram of In-Se binary system [Li04]

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71 Figure 3-2. Phase diagram of Ga-Se binary system [Ide03] 3.2 Experimental 3.2.1 Precursor Preparation Precursor films used in this study were grown using a migration enhanced epitaxy (MEE) system described in Chapter 1.5. As in traditional molecular beam epitaxy, an ultra high vacuum environment and effusion cells are employed to generate molecular beam fluxes of elemental sources. In M EE, however, the substrate is sequentially exposed to each source through revolution of a platen containing the su bstrate, rather than a simultaneous co-deposition from all the sour ces. The fluxes of Cu and In sources are controlled by electron impact emission spectroscopy (EIES) sensors while those of Ga and Se sources are controlled by the source temper ature. The base pressure of the system

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72 was established at 8 10 9 Torr, and the pressure during de position was maintained in the range of 10 7 to 10 8 Torr depending on the operating conditions. Further details of the deposition technique and experimental ap paratus are given elsewhere [Kim05b]. As shown in Figure 3-3, si ngle-layer and bilayer metal(i.e., Cu, In and Ga)-Se precursor films were deposited on extremely smooth and sodium-free (alkali level < 0.3%) thin glass substrates (Corning #7059). Glass substrates with a thickness of 0.4 ( 0.127) mm were employed to minimize the te mperature difference and response time between the Pt/Rh heater strip (width ~ 0.5 ) and the precursor film (0.5 0.5 ) in the HTXRD furnace used for subsequent characterization. Figure 3-3. As-grown precursor struct ure along with overall atomic composition The elementally mixed single-layer precursors (i.e., Figure 3-3(a)-(c)) were fabricated by co-depositing metal and Se w ithout heating the substrate to minimize the potential reaction between meta l and Se. Bilayer precursors (i.e., Figure 3-3(d)-(f)) were prepared by depositing a metal film followe d by subsequent deposition of a Se film without heating the substrate. Selenium deposition was controlled to maintain a Se-

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73 excess atomic composition, i.e. [Se]/[Metal] > 2.0, to compensate for the selenium volatilization losses during thermal anneali ng in the HTXRD furnace. The atomic composition of as-grown precursors was measur ed by inductively coupled plasma optical emission spectroscopy (ICP-OES), as inserted in Figure 3-3. 3.2.2 In situ high-temperature X-ray diffraction Two types of high-temperature X-ray di ffractometers (HTXRD), i.e., ScintagHTXRD and PANalytical-HTXRD, were used in this study. The Scintag-HTXRD consists of a Scintag PAD X vertical / goniometer, a Buehler HDK 2.3 furnace, and an mBraun linear position sensitive detector (LPSD ). In contrast to conventional X-ray point scanning detectors that perform the s canning step-by-step from lower to higher angles, the LPSD collects the XRD data simultaneously over the 10 2 window, dramatically shortening the data collection time. This permits in situ time-resolved studies of phase transformations, crystal lization, and grain growth. A type-S thermocouple is welded onto the bottom of a Pt/Rh strip heater to measure the heater temperature directly and give s feedback to the temperatur e controller. Precursors are mounted on the heater strip using carbon or silv er paints to improve the thermal contact between the precursor and heater strip. Th e PANalytical-HTXRD syst em is composed of a PANalytical X’Pert Pro MPD / X-ray diffractometer equi pped with an Anton Paar XRK-900 furnace and an X’Celerator solid stat e detector. A surrounding heater is used in a PANalytical-HTXRD, while a strip heater is used in the Scintag-HTXRD. Both HTXRD furnaces were purged by flowing He and the precursor surface temperature in the furnace was calibrated from measurement of the lattice expansi on of silver powder dispersed on an identical substrate and comp aring the results to the equation suggested by

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74 Touloukian [Tou77]. Since a PANalytical-H TXRD provides better resolution than a Scintag-HTXRD, it was used for the samp les having a poor signal to noise ratio. 3.3 Cu-Se Binary Formation 3.3.1 Glass/Cu/Se Precursor Phase evolution in the glass/Cu/Se precu rsor with an atomic composition of [Se]/[Cu]~2.0 was investigated during temp erature ramp annealing using a PANalyticalHTXRD purged by flowing He. The as-gro wn precursor was first scanned at 25 C for 10 min and then heated to 60 C at a rate of 20 C/min. The X-ray diffraction data were collected for 10 min at every 10 C during subsequent ramp heating to 470 C at a rate of 20 C/min, as shown in Figure 3-4. Figure 3-4. Phase evolution of glass/Cu/Se precursor observed by in situ X-ray diffraction. (JCPDF) Se: 06-0362, CuSe: 20-1020, CuSe2: 26-1115, Cu2-xSe: 06-0680.

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75 The diffraction data at 25 C show the scattering by elemental Se and CuSe, which demonstrates the crystalline CuSe forms dur ing the precursor prep aration even without heating substrate (Tsubstrate = 40 ~ 60 C). The transformation of CuSe into CuSe2 was initiated at approximately 160 C, at which temperature the crystalline Se phase suddenly disappeared, presumably by rapid formation of CuSe2 through reaction of CuSe with the excess Se. It is noted that rapid disappearan ce of Se-related peaks occurs well below the Se melting temperature (~221 C). The Se is likely to be released from CuSe2 as evidenced by the decrease of reflection intensities of CuSe2, which is then followed by the subsequent transformation of CuSe2 into -CuSe at around 250 C. Further heating above 300 C leads to the release of more Se to yield -Cu2-xSe, which is the most stable compound of the Cu-Se binary system at high temperature (Figure 21). A series of temperature-dependent phase evolutions of glass/Cu/Se precursor qualitatively follow the same sequence (i.e., CuSe2 CuSe Cu2-xSe) as predicted equilibrium phase diagram [Gla00, She06], even though the actual phase transition temperatures are different from the equilibrium values. The temperaturedependent phase transformation of this precursor can be summarized as -CuSe + Se CuSe2 T 160 C CuSe2 -CuSe + Se (evaporated) T 250 C 2 -CuSe Cu2-xSe + Se (evaporated) T 300 C 3.3.2 Glass/Cu-Se Precursor Temperature-dependent phase evolution of glass/Cu-Se pr ecursor with an atomic composition of [Se]/[Cu]~2.4 was investigat ed using the Scintag-HTXRD system. The glass/Cu-Se precursor was first scanned at 25 C and then heated to 50 C at a rate of 20

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76 C/min. Four sequential scans (1min acquisition/scan) over the range 22 to 54 (2 ) were taken at 10 C increments while the sample was heated from 50 to 300 C at a rate of 30 C/min in a flowing He atmosphere. After scans at 300 C, the samp les were heated to 400 C at a rate of 60 C/min and then sca nned twice. As shown in Figure 3-5, only a weak CuSe (006) peak is detected at 25 C and unlike Figure 3-4, there are no broad background peaks. Since this peak is so weak, it is not detect ed in every part of sample. The metastable Cu7Se4 phase begins to form at ~80 C as evidenced by Cu7Se4 (320, 321).

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77 Figure 3-5. Phase evolution of glass/Cu-Se precursor observed by in situ X-ray diffraction.(Bottom: 25 to 34 2 magnified). (JCPDF) CuSe: 20-1020, Cu7Se4: 26-0557, Cu2Se: 46-1129. As this metastable phase forms, the CuSe (006) reflection begins to increase and then decrease as more Cu7Se3 forms to return to a weak peak. It is possible that CuSe formation begins to increase and se rves as the seed for nucleating Cu7Se4, which grows encloses the CuSe seed to reduce the peak inte nsity. The subsequent CuSe peak intensity at higher temperature indicates that only a small portion of the Cu is now found in the CuSe phase. The metastable Cu7Se4 phase reacts with amorphous Se (no evidence of Se recrystallization) to fo rm the CuSe at ~170 C, and the coexisting CuSe is partially further selenized to yield the CuSe2 at ~160 C, as evidenced by CuSe2 (111, 120) peaks, which then disappear by decomposing to CuSe at ~210 C. Interestingly, the phase evolution (i.e., CuSe CuSe2 CuSe Cu2Se) of as-grown CuSe is very similar to that (i.e., CuSe CuSe2 CuSe Cu2-xSe + Cu2Se) of glass/Cu/Se described in the

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78 previous section. Finally, the deve lopment of CuSe is maximized at ~220 C followed by peritectic decomposition to the -Cu2Se by releasing Se at above 240 C. Therefore, the dominant phase evolution of glass/ Cu-Se precursor is summarized as 7Cu + 4Se Cu7Se4 T 80 C Cu7Se4 + 3Se 7CuSe T 170 C 2CuSe Cu2Se + Se (evaporated) T 240 C It is expected that the intermediate mi xtures of Cu-Se phase s reduce Se loss as compared to the bilayer structure exposing the surface of the Se top layer to the gas flow. Furthermore this sample had a larger atomic Se/Cu ratio (2.4 vs. 2.0) than the Se/Cu structure. 3.4. In-Se Binary Formation 3.4.1 Glass/In/Se precursor The phase evolution of gla ss/In/Se bi-layer precursor with an overall atomic composition of [Se]/[In]~4.2 was investig ated using the Scintag-HTXRD. The glass/In/Se precursor was first scanned at 25 C and then heated to 60 C at a rate of 20 C/min. Then four sequential scans (1min acquisition/scan) over a range of 22 to 54 (2 ) were taken at 10 C increments while the sample was heated from 60 to 400 C at a rate of 30 C/min in a flowing He atmosphe re. As shown in Figure 3-6, the reflection peaks of pure In, Se and In4Se3 phase were detected at 25 C. The most In-rich compound, In4Se3, is expected to form at the interface of indium and selenium during the deposition of selenium on pre-deposited In/g lass (i.e., the second de position stage), which provides selenium with an extremely indium -rich environment, thus favoring formation of In4Se3. The reflection intensity of pure In begins to decrease at ~120 C and then

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79 completely disappears at ~150 C, which nearly coincides with its melting temperature (Tm~151 C). The peaks of selenium and In4Se3 suddenly disappear to gether at the same temperature of around 170 C. Since the thermodynamic melting temperature of selenium is around 221 C, the abrupt disappearance of selenium peak at 170 C is likely explained by the reactio n of selenium with In4Se3 and liquid indium rather than by melting of selenium. Furthermore, the simultaneous disappearance of In4Se3 and Se peaks strongly supports this explanation. No crystalline phases, how ever, were identified until the appearance of In2Se3 at around 330 C, which is attributed to the formation of a glassy InxSey phase. Figure 3-6. Phase evolution of glass/In/Se precursor observed by in situ X-ray diffraction (JCPDF) Se: 06-0362, In: 05-0642, In4Se3: 83-0039, In2Se3: 65-2447 According to phase diagram of the In-Se bi nary system shown in Figure 3-1 [Li04], there exist 4 intermediate InxSey line compounds between In4Se3 and In2Se3 (InSe, In6Se7, In5Se7 and In9Se11). It is reported that the crystallin e phase of InSe is very difficult to

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80 form at low temperature [Gla00]. Viswanathan et al. reported they could successfully deposit polycrystalline InSe on well-cleaned glas s substrate at a subs trate temperature of 400 C using a vacuum coating method, while they only obtained the amorphous InSe at room temperature deposition [Vis05]. In Ch apter 4, deposition of the glass/InSe/CuSe precursor [Kim05a] gave an amorphous InSe film with deposition at a substrate temperature of 250 C using the MBE system. Finally, the crystalline In2Se3, which is the most stable In-Se compound at high te mperature, is obtained at around 330 C and continues to grow until the completion of annealing (400 C). The ICP compositional analysis (i.e., x(Se) ~ 0.59) on an complete ly annealed sample supports the single phase In2Se3 stoichiometry. The overall phase tran sformation of glass/In/Se precursor is summarized as In (solid) In (liq.) T = 120~150 C In (liq.) + In4Se3 + Se (solid) InxSey (amorphous) T 170 C InxSey (amorphous) + Se (liq.) In2Se3 + Se (evaporated) T 330 C 3.4.2 Glass/In-Se Precursor The glass/In-Se mixed precursor was prepared to have a similar overall composition to glass/In/Se precursor, as confirmed by ICP anal ysis ([Se]/[In] ~ 4.1). Furthermore, an identical annealing procedure as used for gla ss/In/Se precursor was a pplied to glass/In-Se precursor. As shown in Figure 3-7, unlike the bi-layer precur sor, no crystalline phase is detected from the as-deposited precursor. Ra ther a broad intensity is observed in the 2 range 22 to 38 Since, in general, the as-depos ited pure indium has the crystalline structure as shown in glass/ In/Se precursor, indium likely exists as a glassy InxSey phases rather than as elemental In, and thus the seleni um is partially bound in its glassy state.

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81 Interestingly, selenium begins to crystallize at around 120 C as evidenced by growing Se (100) peak, and then gr ows until temperature reaches around 200 C, at which point the Se reflections disappear due to Se melting and/or reacting with glassy InxSey. Subsequent heating leads to the formation of crystalline In2Se3 by further selenization of InxSey, just like in the phase evolution of glass/In/Se precursor. It is interesting to note that the formation temperature of In2Se3 in glass/In-Se precursor is much lower than in glass/In/Se. One expl anation is the shorter diffusion lengths in intimately mixed glass/In-S e precursor as compared to the bi-layer films. Figure 3-7. Phase evolution of glass/In-Se precursor observed by in situ X-ray diffraction. (JCPDF) Se: 06-0362, In2Se3: 65-2447. Again, the ICP analysis (i.e., x(Se ) ~ 0.59) on an annealed sample strongly supports the complete transformation into In2Se3 without any residual phases. The overall phase evolution of glass/In-Se pr ecursor is thus summarized as

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82 In + Se InxSey (glassy) (Deposition) Se (amorphous) Se (crystalline) T 120 C Se (crystalline) Se (liquid) T 200 C Se (liquid) + InxSey (amorphous) In2Se3 + Se (evaporated) T > 200 C 3.5 Ga-Se Binary Formation 3.5.1 Glass/Ga/Se Precursor The PANalytical-HTXRD system was used again for in situ investigation of the phase evolution of the glass/Ga/Se precursor The same characterization scheme (i.e., temperature ramp profile and X-ray scan seque nce) as used for glass/Cu/Se precursor was applied to this sample. First, the precursor was heated to 60 C at a rate of 20 C/min after scanned at 25 C for 30 sec, and then the subsequent X-ray scans were executed at every 10 C for 30 sec during heating to 500 C, as shown in Figure 3-8. Figure 3-8. Phase evolution of glass/Ga/Se precursor observed by in situ X-ray diffraction (JCPDF) Se: 06-0362, GaSe: 29-0628

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83 The room temperature X-ray diffraction on glass/Ga/Se stacked precursor with a selenium excess atomic composition of [Se]/[ Ga]~3.9 shows there is no reflection except a weak Se (102) peak. There is a broa d but low intensity peak centered at 2 25 As temperature increases, however, selenium begi ns to crystallize until temperature reaches the Se melting temperature (~221 C), at which temperature the selenium peaks abruptly disappear. Melted selenium s ubsequently reacts with Ga to form GaSe as evidenced by the appearance of the GaSe reflection peaks. The binary Ga-Se phase diagram shown in Figure 3-2 [Ide03] shows that Ga2Se3 is slightly more stable than GaSe. The excess Se used in this experiment was transformed into GaSe rather than Ga2Se3 as a hightemperature stable phase at 500 C, which is mainly attributed to the high vapor-pressure of Se and stacked structure of glass/Ga/Se, a nd thus preferable Se evaporation to reaction with Ga. Finally, the temperature-dependent phase evolution of gla ss/Ga/Se precursor is summarized as Se (amorphous) Se (crystalline) 25 C < T < 220 C Se (crystalline) Se (liquid) T 220 C Se (liquid) + Ga GaSe + Se (evaporated) T > 220 C 3.5.2 Glass/Ga-Se Precursor The PANalytical-HTXRD system with the sa me characterization procedure as used for the glass/Ga/Se sample was applied to th e glass/Ga-Se mixture sample. As shown in Figure 3-9, X-ray diffraction at room temperature demonstrates no crystalline compounds are produced by the precursor deposition pro cess. The broad reflection between 20 and 35 may be attributed to the scattering by amorphous Se or a glassy Ga-Se phase.

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84 The crystallization of amorphous seleni um is initiated at approximately 120 C and then continues until the temperature reaches around 210 C at which temperature all selenium reflection peaks disappear due to the melting of Se. It is worthwhile to recall the crystallization of Se at the same temperature (~120 C) and subsequent melting at around ~200 C, which are observed during the phase evolution of glass/In-Se precursor, as described in section 3.4. Subsequen tly, the melted Se reacts with Ga and/or amorphous Ga-Se compound to form the Ga2Se3 compound, which is the most stable GaSe compound. Further heating to 500 C causes no more phase transformation. While the glass/Ga/Se precursor form s the GaSe compound at high te mperature as described in the previous section, the gla ss/Ga-Se precursor forms the Ga2Se3 compound because the intermixing of Se with Ga at the molecular level during the precursor MBE deposition makes the reaction of Se with Ga prefer able to the evaporation of Se. Figure 3-9. Phase evolution of glass/Ga-Se precursor observed by in situ X-ray diffraction. (JCPDF) Se: 06-0362, Ga2Se3: 44-0931.

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85 Therefore, the temperature-dependent phase evolution of glass/Ga-Se precursor is summarized as Se (amorphous) Se (crystalline) T 120 C Se (crystalline) Se (liquid) T 210 C Se (liquid) + Ga (liqui d) or GaSe(amorphous) Ga2Se3 + Se (evaporated) T > 210 C 3.6 Summary The reaction pathways and phase evoluti on of binary Cu-Se, In-Se, and Ga-Se precursor structures we re investigated using in situ high-temperature Xray diffraction. The results show the overall phase transfor mation of binary metal (Cu, In and Ga)-Se precursors qualitatively follow the seque nce predicted by the thermodynamic phase diagram. The intermediate reaction of each binary com pound, however, depends on the as-deposited precursor structure and starti ng compounds. For instance, the intimately mixed glass/Cu-Se precursor takes the sequence of Cu7Se4 CuSe Cu2Se while the glass/Cu/Se bi-layer precursor beginning with the CuSe, presumably as an intermediate layer, follows the reaction path of CuSe CuSe2 CuSe Cu2-xSe/Cu2Se. The glass/In-Se and glass/In/Se precursors have a different initial consti tution, i.e., amorphous InxSey and In4Se3 respectively, but ultimately reac h the high-temperature stable In2Se3. It is also found that the excess amorphous se lenium in both glass/ In-Se and glass/Ga-Se precursors begin to crystallize at ~120 C, while the crystallization of selenium is not observed in glass/Cu-Se precursor pa rtly due to the formation of Cu7Se4 at ~80 C. In the future, the isothermal soaking experiments w ill be performed to give the quantitative kinetic information.

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86 CHAPTER 4 CUINSE2 FORMATION PATHWAYS AND KINETICS 4.1 Introduction Chalcopyrite -CuInSe2 (CIS) and its alloys with Ga or S are proven absorber materials for high efficiency thin film solar ce lls. Interestingly, a variety of processing sequences have been demonstrated to form -CuInSe2 (e.g., co-deposition of elements, annealing of stacked elemental layers, dire ct compound formation, and selenization of metal particles). Furthermore, the processes are robust to small fluctuations in process conditions. This versatility is made possi ble, in part, by the complex Cu-In-Se phase diagram, which exhibits equilibria between -CuInSe2 and 8 different solid phases as well as a Se-rich liquid at 773 K [Gd00a-c]. Furthermore the -CuInSe2 phase field has a rather large range of solid solution, sugge sting a point defect ch emistry that includes significant compensation of electronic defects. An examination of equilibrium pathways for the formation of CIS, however, is unable to fully explain this versatility, and thus kinetic limitations are also important. While there have been several studies on the mechanism for forming CIS, the detailed reactio n pathways and kineti cs are not yet fully understood. To date, most studies on the mechanism of CIS formation have been performed using ex-situ methods [Zwe95, Adu95], which gi ve limited kinetic information. Recently, various in situ techniques have been used to investigate the reaction mechanism of CIS. Based on in situ high-temperature X-ray diffrac tion (HTXRD) analysis, Katsui

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87 and Iwata [Kat99] suggested the following reaction pathway for CIS formation from glass/Cu/In/Se stacked elemental layers: 2Cu + 2In +4Se Cu2Se +In2Se + 2Se 2CuInSe2 (4-1) Wolf et al. [Wol00] used thin film calorimetry for the in situ monitoring of reaction kinetics of CIS formation from Cu/In/Se precursor. Using a Kissinger analysis, they suggested an activation energy of 160 kJ/m ol with around 15% st atistical error. Brummer et al. [Bru03] employed in situ high-energy powder diffr action to investigate the phase transformation of three binary syst ems (Cu-Se, In-Se, Cu-In), ternary CIS and quaternary CIGS system using the stack ed elemental film precursors (e.g., glass/Cu/In/Se, glass/Cu/Se, glass/In/Se and glass/Cu/In). They reported several intermediate phase transformations with temperature and the tetragonal CuInSe2 formation temperature of 375~385 C. The same research group identified the several CIS formation reactions during rapid thermal processing of st acked elemental layers: (1) CuSe + InSe CuInSe2, (2) Cu2Se + 2InSe + Se 2CuInSe2, (3) Cu2Se + In2Se3 2CuInSe2 [Her05]. Most recently, they then report ed that the kinetics of the formation of CuInSe2 depends on the binary selenides present in the precursors and the formation of CuInSe2 from a bilayer InSe/CuSe precursor follows the typical diffusion-controlled reaction along with an average activation energy of 128 kJ/mol [Pur06]. As part of this dissertation, a systematic study of the reaction pa thways and kinetics of the formation of CIGS and its subsyste ms from various types of precursors was conducted using time-resolved, in situ high temperature X-ray diffr action technique. In a previous study [Kim05a] using the same system, the formation of CuInSe2 from the bilayer structure InSe/CuSe show ed that a non-crystalline interm ediate phase, most likely

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88 amorphous CuInSe2, appeared during the initial stage of the isothermal heating in air in the temperature range 220 to 270 C. Data analysis based on the Avrami and parabolic rate law models supported a one-dimensional diffusion controlled reaction mode. The combined amorphous and crystalline CuInSe2 interfacial layer functions as a diffusion barrier as well as a nucleation barrier. In this chapter, the results of studies on the reaction pathway and kinetics of -CIS formation from different precursors (e.g., In2Se3/CuSe, CuSe/In-Se and InSe/Cu-Se) and selenization of metallic Cu-In precursor are reported. 4.2 Glass/In2Se3/CuSe Precursor 4.2.1 Precursor Preparation Bilayer glass/In2Se3/CuSe precursor films were deposit ed on sodium-free thin glass substrates (Corning #7059) in the MEE reactor The details of the deposition technique and experimental apparatus are gi ven in chapter 1.5. Glass substrates with a thickness of 0.4 mm were employed to minimize the te mperature difference and response time between the strip heater a nd the precursor film in the HTXRD furnace used for subsequent characterization. The samples were fabricated by first depositing a crystalline In2Se3 film at a substrate temperature of ~360 C under ultra high vacuum conditions (10-7 ~ 10-8 Torr). This was followed by deposition of a crystalline CuSe film on the asgrown In2Se3 layer at a lower substrate temperature (~150 C) to minimize the potential reaction between the In2Se3 and CuSe layers. The total bilayer film thickness (~800 nm) was measured by TEM as shown in Figure 4-1, and the atomic composition of each monolayer (bottom In2Se3: [Se]/[In]~1.4; top CuSe: [Se]/[ Cu]~0.93 ) and overall bilayer ( [Cu]/[In]~0.94; [Se]/[Metal]~1.2 ) film was measured by inductively coupled plasma

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89 optical emission spectroscopy (ICP-OES) The stable structure of both In2Se3 and CuSe at the growth temperature is hexagonal. XRD characterization of the precursor films revealed a highly textured (001) crystalline-In2Se3/crystalline-CuSe bilayer structure as shown in Figure 4-2. Figure 4-1. TEM microgra phs of as-grown glass/In2Se3/CuSe bilayer precursor films 1020304050607080 2 (degree)a.u.In2Se3 (006) CuSe (006) (b) Top layer : CuSe (a) Bottom layer : In2Se3(c) Bilayer : In2Se3 / CuSeIn2Se3 (0 0 12) In2Se3 (111) Figure 4-2. Room temperature XRD scans a nd TEM micrographs of as-grown precursor films: (a) glass/In2Se3 monolayer, (b) glass/CuSe monolayer, (c) glass/In2Se3/CuSe bilayer

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90 4.2.2 Temperature Ramp Annealing Temperature ramp annealing by the Scin tag-HTXRD described in chapter 3.2.2 was used to investigate the phase evolution of the samples and to establish a suitable isothermal annealing temper ature range. The glass/In2Se3/CuSe bilayer sample was first heated to 150 C at a rate of 10 C/min and then X-ray diffraction data were collected during subsequent ramp heating (5 C/min). Scans requiring ~ 1 min were taken at every 5 C increment while the sample was heat ed from 150 to 350 C in a flowing He atmosphere. Figure 4-3. In situ XRD scans during temperature ramp annealing (10 C/min) of the glass/In2Se3/CuSe sample Figure 4-3 demonstrates that the initial In2Se3 and CuSe phases are directly transformed to -CuInSe2 without any intermediate phases. CuInSe2 begins to be detected at a temperature ~ 250 C and the re action is almost complete at 310 C as

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91 evidenced by the lack of detection of In2Se3 and CuSe. The expect ed interfacial reaction pathway is In2Se3 + 2CuSe 2CuInSe2 + Se (evaporated) (4-2) 4.2.3 Isothermal Annealing Time-resolved, high temper ature X-ray diffraction data were collected using a linear position sensitive detector (LPSD), while the bilayer glass/In2Se3/CuSe precursor films were maintained at a constant temperature in a He (flow rate ~100 sccm) atmosphere. The O2 content of the outlet He gas was measured by an O2 analyzer to be less than 0.1 ppm. In the isothermal experiment, the three step temperature ramping was used to minimize heating time without temperature overshooting. Firstly, the temperature was rapidly ramped at rate of 300 C/min to a value of 20 C below the set point temperature, and then at rate of 200 C/min to a value of 10 C below the set point temperature. Finally, the temperature was ramped to a set point at rate of 100 C/min and then held to monitor the isot hermal reaction. A set of experiments was performed with a range of set point temperature determined from the temperat ure ramp scan results shown in Figure 4-3. The set point temperature was set so that the total isothermal holding time was much longer (i.e., several hours) than an in dividual scan but sufficiently fast that an experiment could be completed in one day. Scans were taken approximately every 35 sec. It is noted that an i ndividual scan time for the isothe rmal annealing experiment was much shorter (i.e., scan time of 30 to 120 sec) than for the temperature ramp annealing (i.e., scan time of 5 to 10 min) to obtain ac ceptable time resolution. To complete the reaction, the temperatur e was elevated to 350 C and then maintained for about 12 min until only the -CuInSe2 phase remained and the peak intensity remained constant (see

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92 for example the discontinuity in peak height after 1 hr in Figure 4-4). The temperature range for the isothermal experiments was from 230 to 290 C. The 2 scan range (24 to 34 ) for the isothermal experiments was selected to focus on the major peaks of the reactants and product, i.e., In2Se3 (006), CuSe (006) and -CuInSe2 (112). Figure 4-3 displays the time-resolved XRD da ta collected for the film isothermally reacted at 250 C. To obtain the fractional reaction (), the integrated areas of the In2Se3 (006), CuSe (006), and CuInSe2 (112) peaks were obtained from the diffraction data using the JADE software. These values were normalized assuming that the reactants were completely transformed to crystalline CuInSe2 after each run, and that the texture of the CuInSe2 does not appreciably change thr ough the entire heating process. Figure 4-4. In situ time-resolved XRD scans during isot hermal annealing of the glass/ In2Se3/CuSe precursor structure at 250 C

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93 The reaction kinetics in terms of activa tion energy and reaction order have been investigated using two solid-state reaction models, the “Avrami” and “parabolic rate” models. Analysis of solid state reaction da ta using the Avrami model is commonly used for preliminary identification of the growth rate law. It has been shown that the method yields satisfactory fits to re levant experimental data [Kim 05a, Bam80, Lu99]. Since this model is based on the nuclei growth and an isotropic growth is assumed, the product regions are spherical. The transformati on kinetics under isothermal reaction are described by nkt ) ( exp 1 (4-3) or equivalently, by k n t nln ln 1 ln ln (4-4) where the fractional reaction represents the fraction of reaction completed at time t k is the kinetic rate constant, and n is the Avrami exponent. This analysis has been advocated by Hulbert [Hul69], who showed that the Avra mi exponent can vary between 0.5 and 1.5 in the case of one-dimensional (i.e., radial di rection), diffusion-contro lled reactions. The value of n is close to 0.5 if the nucleation is instantaneous, and close to 1.5 if the nucleation rate is constant throughout the reac tion. Figure 4-5 displays the Avrami plots for the isothermal reaction of the precursor f ilms at different temper atures. Even though data were taken only for 0.1 < < 0.95 to minimize experimental error, the Avrami model expressed by eq. (4-4) di d not yield a satisfactory ( i.e linear) fit.

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94 -2 -1.5 -1 -0.5 0 0.5 1 024681012ln(t) 290C 280C 270C 265C 260C 255C 250C 240C 230Cln[-ln(1)] Figure 4-5. Avrami model plot for glass/In2Se3/CuSe precursor structure The simple parabolic kinetic model [H ul69] was developed based on a reaction between two solid materials with plan ar surfaces, and identical to the In2Se3/CuSe precursor structure. This m odel is consistent with a phys ical process that requires a limiting reactant to diffuse across the product layer that initially formed at the interface of the two reactants. The produc t layer thickness incr eases with time to further decrease the diffusive flux of the limiting reactant. Assu ming a uni-directional pr ocess, the reaction kinetics of parabolic model are described by 2 = kpt (4-5) where is the fractional reaction, kp is the parabolic rate cons tant including the diffusion coefficient of the migrating species, and t is the time. Figure 4-6 shows the plot of 2 vs. t for the same data set previously analyzed by the Avrami model.

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95 0 0.2 0.4 0.6 0.8 1 1.2 050100150200250300350400t (min) 2 290C 280C 270C 265C 260C 255C 250C 240C 230C240C 250C 260C 270C 230C Figure 4-6. Parabolic model plot for glass/In2Se3/CuSe precursor structure It is evident that the parabolic reactio n model provides a much better fit to the data than the Avrami model over the entire set of isothe rmal temperatures (230 to 290 C). It is thus conclude d that the formation of -CuInSe2 in glass/In2Se3/CuSe bilayer precursor films is consistent with a one-dime nsional diffusion contro lled reaction pattern. The Arrhenius equation RT E A ka pexp (4-6) was used to estimate the apparent activation energy Ea for the -CuInSe2 formation process in glass/In2Se3/CuSe bilayer precursor films. An activation energy of 162 ( 5) kJ/mol was estimated from the Arrhenius pl ot shown in Figure 4-7. The estimated activation energy is very close to th e value (~160 kJ/mol) suggested by Wolf et al.

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96 [Wol00] for CIS formation from Cu/In/Se stack s using a Kissinger anal ysis for thin film calorimetry. -11 -9 -7 -5 1.71.81.92 1000/T (1/K) ln k Ea ~ 162 (5) kJ/mol Figure 4-7. Arrhenius plot of the parabolic rate constant for glass/In2Se3/CuSe precursor structure 4.3 Glass/InSe/Cu-Se Precursor 4.3.1 Precursor Preparation For the glass/InSe/Cu-Se bila yer structure, an indium se lenide layer was first grown on to a thin (~0.4 mm) sodium-free glass subs trate in the MEE system with a substrate temperature of approximately 250 C. Subsequently, elemental copper and selenium were co-deposited on the as-grown InSe laye r without heating the substrate to minimize potential reactions between th e InSe, copper and selenium. Considering the possible loss of indium and selenium during temperature ra mp annealing, extra indium and selenium were introduced, which was confirmed by induc tively coupled plasma optical emission spectroscopy (ICP-OES) analys is (i.e., overall [Cu]/[In]~0.89 and [Se]/[Cu+In] ~1.67).

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97 Figure 4-8. Room temperature XRD scans of as-grown precursor films: (a) glass/InSe monolayer, (b) glass/InSe/Cu-Se bilayer The room temperature XRD data on as-d eposited precursors shown in Figure 4-8 demonstrate that the as-grown InSe phase is amorphous, and that the Cu7Se4 phase forms during co-deposition of Cu and Se, even without heating the substrate. 4.3.2 Temperature Ramp Annealing Temperature ramp annealing by the Scin tag-HTXRD described in chapter 3.2.2 was used to investigate the phase evolution of the samples. The glass/InSe/Cu-Se bilayer sample was first heated to 50 C at a rate of 20 C/min and then X-ray diffraction data were collected during subsequent ramp heati ng (30 C/min). Four sequential scans over a range of 20 to 54 (2 ) were taken at 10 C increments while the sample was heated from 50 to 350 C in a flowing He atmosphere, as shown in Figure 4-9.

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98 Figure 4-9. In situ XRD scans during temperature ramp annealing (30 C/min) of the glass/InSe/Cu-Se sample. The results demonstrates that the initial Cu7Se4 phase begins to transform to CuSe by further reaction with Se at around 190 C, and CuInSe2 formation then is initiated with the decrease of CuSe peak at around 230 C. No crystalline InxSey compound, however, was detected, which demonstr ates most of the indium is contained in amorphous InxSey glass. The expected interf acial reaction pathway is Cu7Se4 + 3Se 7CuSe T 190 C CuSe + (InSe) CuInSe2 T 230 C Interestingly, as shown in chapte r 3.3.2, the transformation of Cu7Se4 into CuSe also was detected at around 170 C in the phase evoluti on of glass/Cu-Se precursor, just slightly lower than the temperature observed in this system.

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99 4.4 Glass/CuSe/In-Se Precursor 4.4.1 Precursor Preparation In the same manner as the glass/InSe/Cu-S e precursor, CuSe layer was first grown on to a thin (~0.4 mm) sodium-free glass subs trate in the MEE system with a substrate temperature of approximately 150 C. Elemental indium and selenium were then codeposited on the as-grown CuSe layer without heating substrat e. To compensate for the possible loss of indium and selenium duri ng temperature ramp annealing, the overall atomic composition was controlled as In-rich and Se-rich, which was later confirmed by ICP results of [Cu]/[In ]~0.89 and [Se]/[Cu+In] ~1.78. The room temperature X-ray scan of as-deposited glass/CuSe/InSe precursors, as shown in Fi gure 4-10, clearly shows that the crystalline CuSe forms, but no In-containing compound. Figure 4-10. Room temperature XRD scans of as-grown glass/CuSe/In-Se precursor

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100 4.4.2 Temperature Ramp Annealing Temperature ramp annealing was performed using the identical procedure as used on the structure in chapter 4.3.2. The sample was first heated to 50 C at a rate of 20 C/min and then X-ray diffraction data were collected during subs equent ramp heating (30 C/min) to 350 C. Four sequentia l scans over a range of 20 to 54 (2 ) were taken at 10 C increments while the sample was heated from 50 to 350 C in a flowing He atmosphere. Figure 4-11. In situ XRD scans during temperature ramp annealing (30 C/min) of the glass/CuSe/In-Se sample. As shown in Figure 4-11, initial CuSe ( 006) peak intensity begins to decrease at around 130 C. Part of the initial CuSe phase (not entire amount of CuSe) is first transformed to CuSe2 at around 170 C by reacting with sele nium available in top layer. Once the CuSe2 reaches its maximum intensity at round 190 C, it starts to release selenium, as evidenced by the observation that the CuSe (006) peak intensity increases

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101 again at ~200 C. At the same temperatur e, the other portion of initial CuSe phase, which is not transformed to CuSe2, also releases selenium and yields Cu2-xSe. Finally, the disappearance of CuSe and Cu2-xSe lead to the formation of CuInSe2. Detailed investigation of X-ray diffracti on data revealed the formation of CuInSe2 from glass/CuSe/In-Se precursor is initiated at around 220 C, whic h is similar to that of CuInSe2 formation (~230 C) from glass/InSe/Cu-Se. It is noted that no crystalline In-Se phase was observed. The expected interfacial reaction pathway is CuSe + mSe mCuSe2 + (1-m)CuSe T 170 C mCuSe2 + (1-m)CuSe mCuSe + 0.5(1-m)Cu2-xSe + 0.5(1+m)Se T 190 C mCuSe + nCu2-xSe + InxSey (m+2n)CuInSe2 T 220 C The phase evolution of CuSe phase, i.e., CuSe CuSe2 CuSe and CuSeCu2xSe, follows the general sequence of phase e volution of Cu-Se compound as predicted by Cu-Se binary phase diagram [She06] and expe rimentally demonstrat ed in chapter 3.3. 4.5 Glass/Mo/Cu-In-Se Precursor 4.5.1 Precursor Preparation The glass/Mo/Cu-In-Se precursor was prep ared by co-deposition of elemental Cu, In, and Se onto Mo-coated thin glass substr ate in the MEE system without heating the substrate. The Inand Se-rich composition wa s intended to compensate for the possible volatilization loss of indium and selenium during temperature ramp annealing. The overall atomic composition of [Cu]/[In]~0. 88 and [Se]/[Cu+In] ~1.79 was measured by ICP. The room temperature XRD, which is not shown here, demonstrates that no crystalline phase forms during co-deposition of the precursor.

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102 4.5.2 Temperature Ramp Annealing During temperature ramp annealing from 25 through 350 C, XRD data were continuously collected. Figur e 4-12 demonstrates that -CuInSe2 formation is initiated at around 140 C and the initial amorphous Cu-In-Se elemental mixture is directly transformed to crystalline -CuInSe2 phase without any intermediate phases. It is also noted that the formation reaction was not co mplete by the end of the experiment (350 C). Figure 4-12. Temperature ramp annea ling of glass/Mo/Cu -In-Se precursor 4.5.3 Isothermal Annealing Based on the temperature ramp anneali ng results, isothermal annealing was performed over a wide range of temperature (140 to 350 C). After isothermal annealing for an hour, the temperature was intentionally in creased to 500 C to complete the reaction, as shown in Figure 4-13.

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103 Figure 4-13. Isothermal annealing of glass/Mo/Cu-In-Se precursor at selected temperatures in the range 140 to 350 C The results, as shown in Figur e 4-13, demonstrate that the -CuInSe2 formation from Cu-In-Se elemental mixture is relatively rapid at these temperatures, and thus the

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104 time dependence is not evident in these figures. Increasing the isothermal soaking temperature causes the equilibrium fractional reaction of -CuInSe2 to increase, but its FWHM (Full width at half maximum) to decr ease. The total integrated areas, however, did not change. This is interpreted as the higher isothermal soaking temperature producing the larger -CuInSe2 vertical grain size and thus larger and higher peaks. The estimated grain sizes with resp ect to isothermal temperature are compared in Figure 4-15. The grain sizes were estimated from the peak shape of the CuInSe2 (112) shown in Figure 4-14. The average values of data calculated from 40 to 60 min were taken. However, it is noted that the crystal grain size estimated by X-ray diffraction pe ak is the vertical thickness of grain, but not the lateral diameter. Figure 4-14. CuInSe2 grain sizes estimated by X-ray di ffraction vs. isothermal annealing temperature of glass/Mo/Cu-In-Se precursor

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105 4.6 Selenization of Glass/Mo/Cu-In Precursor 4.6.1 Precursor Preparation The glass/Mo/Cu-In precursor was prepar ed in a migration-enhanced molecular beam epitaxial (MEE) deposition system under ultra high vacuum conditions (10-7 to 10-8 Torr). Since molybdenum is widely used as a back-contact material in CIS-based solar cells, elemental Cu and In were co-deposited on the Mo-coated, sodium-free thin glass (Corning 7059: 0.4 mm thickness) without hea ting the substrate to minimize the reaction between Cu and In. The overall atomic com position ([Cu]/[In] ~ 1.0) of glass/Mo/Cu-In as-deposited precursor film was determin ed by inductively coupled plasma optical emission spectroscopy (ICP-OES) a nd its phase constitution (Cu2In, CuIn, and In) was identified by both -2 and grazing incident X-ray di ffraction (GIXD), as shown in Figure 4-15. Figure 4-15. -2 and grazing incident X-ray diffraction (at = 1.0 and 0.5 ) patterns of an as-deposited glass/Mo/Cu-In precursor film

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106 The thicknesses of the Mo layer (~0.3 m), Cu-In film (~0.6 m), and selenized CuInSe2 film (~2 m) were measured by SEM images of cleaved samples, as shown in Figure 4-16 (b) and (d). The matrix-isla nd structure on the surface of the as-grown precursor is apparent in the SEM surface imag es and the islands were identified as an indium-rich or nearly pure indium phas e by GIXD and electron probe microanalysis (EPMA), as presented in Table 4-1. It is noted that the electron beam used in EPMA analysis can penetrate into the sample (at l east 0.5 micron) and thus the EPMA result for island is the sum of the values for island (e .g., ~0.2 micron thickness) and matrix beneath (e.g., ~0.3 micron for the pene tration depth of 0.5 micron). Figure 4-16. Surface and cross-sectional SEM images of an as-deposited glass/Mo/Cu-In precursor film (a: surface; b: cross-sec tion) and selenized film (c: surface; d: cross-section)

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107 Table 4-1. The composition of the as-de posited glass/Mo/Cu-In precursor films as determined by EPMA scans along the surface (Va = 6 keV) Matrix Island Cu (at.%) 59.4 (1.2) 36.0 (1.0) In (at.%) 40.6 (1.2) 64.0 (1.0) 4.6.2 Selenization Chamber Design A selenization chamber was designed for use in the PANalytical X’pert system to allow in situ observation of CuInSe2 formation from Cu+In elemental mixtures as shown in Figure 4-17. Selenium powder was placed on the XRD sample holder as a selenium source with the precursor sample. The sample holder containing a selenium and precursor was covered with an aluminum foil with a thickness of 18( 2) micron and tied with a Ni wire to minimize the Se vapor loss. Figure 4-17. Selenium chamber design using PANalytical X’Pert system The sample temperature was calibrated from a determination of the lattice expansion of silver powder dispersed on an identical Mo-coated gl ass substrate covered with an aluminum foil. Precursor sample Selenium powder Aluminum foil Sample holder (Macor) X-ray tube PSDChamber In Out (He) Capton/Be window CW in out Surrounding Heater Ni wire

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108 4.6.3 Temperature Ramp Selenization During the selenization of glass/Mo/Cu-In by temperature ramp annealing (~20 C /min), the formation of CuSe and its transformation to CuSe2, and then CuSe2 to CuInSe2 were observed from ~230 to 300 C as shown in Figure 4-18(a) and (b). The formation of CuInSe2 was initiated at a temperature between 250 and 300 C. Additionally, the production of MoSe2, accompanied by a rapid decrease of Mo (110) reflection intensity, was clearly detected at temperatures above 440 C, and only after the production of CuInSe2 was complete. In another experiment in which an insufficient amount of Se powder was placed in the well, the intensity of the CuInSe2 reflection kept increasing without producing MoSe2 even after 440 C, which demonstrates the formation of CuInSe2 is preferred to that of MoSe2. These results are consistent with a simple equilibrium analysis of po ssible reaction pathways. Using values for the Gibbs energy of the components [Din91, Ide03, Kna91], the Gibbs energy changes for standard reactions for Mo reduction of CuInSe2 to produce either the elements or Cu2Se, given below, are all positiv e and thus consistent with preferred formation of CuInSe2. CuInSe2(s) + Mo(s) MoSe2(s) + Cu(s) + In(l) Gf 300 C = 89.8 and, Gf 500 C = 104 kJ/mol (4-7) 2CuInSe2(s) + Mo(s) MoSe2(s) + Cu2Se(s) + 2In(l) + Se(l) Gf 300 C = 236 and, Gf 500 C = 249 kJ/mol (4-8)

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109 Figure 4-18. In situ X-ray diffraction patte rn evolution during the selenization of a glass/Mo/Cu-In precursor films in the 2 range (a) 23 to 58 and (b) 25 to 35 This result suggests that m onitoring the presence of MoSe2 can be used for detecting complete formation of an absorber layer and perhaps a simple I-V characteristic

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110 can be used. There have been a few reports about MoSe2 formation and its contribution to the performance of CI GS solar cells. Wada et al reported that the (100) and (110) reflections of MoSe2 in Mo/CIGS absorbers deposited by a typical three stage process were detected by XRD and the Mo/CIGS hetero-contact including the MoSe2 layer would be a favorable ohmic-type wh ile the Mo/CIGS without MoSe2 layer exhib its a Schottkytype contact [Wad01]. 4.6.4 Isothermal Selenization Isothermal annealing at selected temperatures between 260 and 330 C was then performed for kinetic analysis using selected reaction models. A sample scan (scan time 1 min) is shown in Figur e 4-19 for annealing at 280 C. The 2 scan range (20 to 30) for the isothermal experiments was selected since the major reflection for the product CuInSe2 (112) lies within this range. Figure 4-19. In situ X-ray diffraction pattern evolution during the isothermal selenization of a glass/Mo/Cu-In precursor film at 280 C

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111 To complete the reaction, the te mperature was elevated to 500 C after each run and then maintained for about 12 min until only the -CuInSe2 phase remained as evident by a constant peak intensity. The fractional reactions of product CuInSe2 phase were estimated using the normalized -CuInSe2 (112) peak area assuming that the maximum peak area represents complete reaction. Th e reaction kinetics in terms of an activation energy and reaction order were estimated us ing two solid-state reaction models, the “Avrami” and “parabolic rate” models [Kim 05a, Kim05b, Hul69], which were introduced in chapter 4.2. In the Avrami model the transformation kinetics under isothermal reaction are described by equations (4-3) and (4-4). For ex perimental data of thes e particular samples, the n values over the entire temperature ra nge, except at the highest temperature 330 C (n=0.3) studied, are between 0.6 and 0.8, s uggesting the Avrami model is appropriate for this reacting system below 330 C as shown in Figure 4-20.

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112 -1.2 -0.8 -0.4 0 0.4 0.8 456789ln (t)ln(-ln(1))260C 270C 290C 300C 330C Figure 4-20. The Avrami model plot for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films -9 -8 -7 -6 -5 -4 -3 1.651.71.751.81.851.9 1000/T, K-1ln kEa = 124 (19) kJ/mol Figure 4-21. Arrhenius plot fo r Avrami kinetic constant for -CuInSe2 formation by selenization of glass/Mo /Cu-In precursor films

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113 The low value of the estimated Avrami e xponents also suggests that the nucleation of -CuInSe2 occurs so rapidly that the nucleatio n time is nearly zero. The Arrhenius equation (4-4) was used to estima te the apparent activation energy Ea for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films. An activation energy of 124 (19) kJ/mol was estimated from the Arrh enius plot shown in Figure 4-21, where the data for 330 C anneal was not used since it was considered as an outlier. The simple parabolic rate model [Kim05a, Kim05b, Hul69] is another widely used one that was successfully employed for the CuInSe2 formation from In2Se3/CuSe bilayer precursor in chapter 4.2. As the reaction pr oceeds, further reaction is limited by diffusion across the product layer to form more product layer at one of the interfaces of the two reactants. Assuming a uni-directional proces s (i.e., planar growth front), the reaction kinetics of the parabolic model is described by 2 ~ kpt (4-12) where is the fractional reaction, kp is the parabolic rate constant incorporating the diffusion coefficient of the migrating species, and t is time. Figure 4-22 shows the plot of 2 vs. t for the same data set as used previous ly for the Avrami model analysis. The parabolic rate model also provides a good fit to the data over the entire isothermal experiment range (260 to 330 C). An activation energy of 100 (14) kJ/mol estimated from the Arrhenius plot excluding the data for 330 C is similar to the value estimated by Avrami model.

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114 0 0.2 0.4 0.6 0.8 1 020406080100 time (min) 260C 270C 290C 300C 330C2 Figure 4-22. The parabolic rate model for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films -9.5 -9 -8.5 -8 -7.5 -7 -6.5 -6 1.651.71.751.81.851.9 1000/T, K-1ln kEa ~ 100 (14) kJ/mol Figure 4-23. The parabolic rate model for -CuInSe2 formation by selenization of glass/Mo/Cu-In precursor films

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115 Based on the results of these two models, the formation of -CuInSe2 from selenization of Cu-In/Mo/gla ss precursor films apparently follows a one-dimensional diffusion controlled reaction w ith a nucleation and subsequent growth sequence. The process likely involves the rapid nucleation of CIS at the inte rface and formation of a thin and planar -CuInSe2 layer on top of the Cu-In films, which serves to limit reactant diffusion and thus formation of -CuInSe2. 4.7 Summary Time-resolved, in situ high-temperature X-ray diffraction was successfully applied to investigate the reaction pathway and kinetics of polycrystalline -CuInSe2 formation from several different precursor structures, such as glass/In2Se3/CuSe, glass/InSe/Cu-Se, glass/CuSe/In-Se, glass/Mo/Cu-In-Se and glass/Mo/Cu-In. The qualitative reaction pathway obs ervation during the temperature ramp annealing of the glass/ In2Se3/CuSe bilayer precursor dem onstrated that the stacked bilayer In2Se3/CuSe phases directly transform to -CuInSe2, as shown in Figure 4-24. Quantitative kinetic analysis of X-ray diffraction data obtained during isothermal annealing fits the parabolic rate reaction model, which suggests that -CuInSe2 formation in a bilayer glass/In2Se3/CuSe precursor follows a one-d imensional diffusion controlled reaction pattern with an activation energy of 162 ( 5) kJ/mol. The process likely involves the fo rmation of a thin and planar -CuInSe2 layer at the In2Se3-CuSe interface. The reaction layer forms sufficiently rapidly that no nucleation incubation time is apparent. This layer serves to limit reactant diffusion and thus the rate of further reaction. Gi ven the rapid diffusivity of Cu in -CuInSe2, it seems reasonable that continued growth of -CuInSe2 occurs by Cu diffusion across the barrier

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116 to the In2Se3-CuInSe2 interface to react with In2Se3, which also requires transport of Se in the same direction. Of course it is likely that some of the excess Se is also lost on the top side due to volatilizati on, as evidenced by the comparison of ICP results between precursor ([Se]/[Metal] ~ 1.2) and annealed CuInSe2 ([Se]/[Metal] ~ 0.94). Figure 4-24. Reaction pathway of CIS formation from In2Se3/CuSe precursor projected in ternary Cu-In-Se isotherm al phase diagram at 500 C For glass/InSe/Cu-Se precursor, the re sults of temperature ramp annealing demonstrates that the initial Cu7Se4 phase begins to be transformed to CuSe by further reaction with Se at around 190 C, and CuInSe2 formation then is initiated with the decrease of CuSe peak at around 230 C. For glass/CuSe/In-Se precursor, part of initial CuSe phase is first transformed to CuSe2 at around 170 C by reacting with selenium available in the top layer, then starts to release selenium at 190 C. At the same temperature, the other portion of initial CuSe phase also re leases selenium to yield the Cu2-xSe. Finally, the disappearance of CuSe and Cu2-xSe lead to the formation of

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117 CuInSe2. On the other hand, intimately mixe d glass/Mo/Cu-In-Se precursor directly forms CuInSe2 at low temperature (200 C). The -CuInSe2 formation from glass/Mo/Cu-In-Se precursor is initiated at around 140 C, and the initial amorphous Cu-In-Se elemen tal mixtures are di rectly transformed to crystalline -CuInSe2 phase without any intermediate phases, as illustrated in Figure 425. Isothermal soaking experiments at selected temperature (140 to 400 C) revealed that the -CuInSe2 formation occurs so rapidly (less th an 1 min) at given temperature, and both the saturated fractional reaction and product grain size increase with isothermal soaking temperature. Figure 4-25. Reaction pathway of CIS formation from intimately mixed Cu-In-Se precursor projected in ternary Cu-In-S e isothermal phase diagram at 500 C During the selenization of glass/Mo/Cu-In precursor structure by temperature ramp annealing, the formation of CuSe and its transformation to CuSe2, and then CuSe2 to

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118 CuInSe2 were observed in the te mperature range ~230 to 300 C. The production of MoSe2 accompanied by a rapid decrease of Mo (110) peak height, occurred at temperatures above 440 C only after the production of CuInSe2 was complete. The -CuInSe2 formation by the selenization of glass/Mo/Cu-In precursors could be described by a one-dimensional diffusion c ontrolled reaction process. For this reaction, the activation energi es of 124 (19) and 100 (14) kJ/mol were estimated with the Avrami and parabolic rate models, respectively. Both of these values for the activation energy are betw een the value for CuInSe2 formation from a glass/InSe/CuSe bilayer precursor (66 kJ/mol) and the value for CuInSe2 formation from a glass/In2Se3/CuSe bilayer precursor (162 5 kJ/mol ) estimated from similar hot-stage XRD studies [Kim05a-b]. In summary, the reaction rates in terms of kinetic constants were compared for CIS formation from different precursor structur es as shown in Figure 4-26. The kinetic analysis using both parabolic and Avrami m odels suggests that the CIS formation from InSe/CuSe precursor is faster than that from In2Se3/CuSe and Cu-In precursor structures at low temperature. Interestingly, in the pl ots of parabolic rate constants, the crossover between In2Se3/CuSe and InSe/CuSe precu rsors was observed at 265 C, which concludes that In2Se3/CuSe precursor may lead to the CIS phase faster than InSe/CuSe precursor at the temperature higher than 265 C.

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119 Figure 4-26. Comparison of reaction rates fo r CIS formation from different precursors estimated by the parabolic and Avrami model.

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120 CHAPTER 5 CUGASE2 FORMATION PATHWAYS AND KINETICS 5.1 Introduction One approach to obtain an even higher effi ciency CIGS based-solar cell is a tandem cell structure that uses the high-efficiency In-rich CIGS device as the bottom cell and a wider band-gap absorber for the top cell. CuGaSe2 has a band-gap energy of 1.68 eV, and thus is a promising absorber material for the top cell in a CIGS tandem solar cell structure [Sch00, Fis01, Rus04]. Recently, a record-efficiency of 10.23% for a surfacemodified single junction CuGaSe2 cell was reported by NREL [Abu05]. While there have been several studies regarding the equilibrium phase diagram [Gd00a-c] and reaction mechanism [Zwe 95, Adu95, Kat99, Bru03, Wol00] of CuInSe2, only a few fundamental investigations of the CGS system have been reported. Purwins et al. reported the formation of CuGaSe2 from a stacked bilayer Ga2Se3/Cu2Se followed a nucleation and growth model w ith an activation energy of 129 kJ/mol, which is extracted from a Kissinger analysis of differential scanning calorimetric data [Pur06]. In previous studies, in situ time-resolved, high-temper ature X-ray diffraction was successfully employed to investigate th e reaction pathway and kinetics of -CuInSe2 formation from different precursors (e.g., InSe/CuSe [Kim05a], In2Se3/CuSe [Kim05b], CuSe/In-Se, InSe/Cu-Se and Cu-In-Se) and selenization of metallic Cu-In precursor [Kim06a]. In this chapter, the reaction pa thways and kinetics for CuGaSe2 formation from thermal annealing of glass/GaSe/CuSe and glass/Mo/Cu-Ga-Se, and selenization of

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121 glass/Mo/Cu-Ga precursor we re investigated using in situ time-resolved, hightemperature X-ray diffraction. 5.2 Glass/GaSe/CuSe Precursor 5.2.1 Precursor Preparation Bilayer GaSe/CuSe precursor films were deposited on extremely smooth and sodium-free (alkali level < 0.3% ) thin glass substr ates (Corning #7059). Glass substrates with a thickness of 0.4 ( 0.127) mm were employed to minimize the temperature difference and response time betw een the Pt/Rh heater strip a nd the precursor film in the HTXRD furnace used for subsequent characteri zation. The precursors were fabricated by depositing a GaSe film at a substrate temperature of ~250 C, followed by deposition of a crystalline CuSe film on the as-grown GaSe layer at a lower substrate temperature of ~150 C to minimize the potential reaction between the GaSe and CuSe precursor layers. Figure 5-1. Room temperature XRD scans and TEM micrograph of as-grown precursor films: (a) glass/GaSe monolayer (b) glass/GaSe/CuSe bilayer. 10203040506070 2 a.u.CuSe (102) CuSe (006) CuSe (110) CuSe (101) CuSe (108) CuSe (116) GaSe Glass CuSe GaSe GlassCuSe: JCPDS #34-0171 (a) (b)

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122 The bilayer structure and its total film thickness (~700 nm) were identified by TEM as shown in Figure 5-1, and the atomic composition was measured by inductively coupled plasma optical emission spectro scopy (ICP-OES), yiel ding the ratios of [Cu]/[Ga]~1.02 and [Se]/[Metal]~0.97. The XRD and TEM characterization of the precursor films revealed an amorphous-GaSe / polycrystalline-CuSe bilayer structure as shown in Figure 5-1. 5.2.2 Temperature Ramp Annealing Temperature ramp annealing using Scintag HT-XRD system was first performed to investigate the phase evoluti on of the samples and to esta blish a suitable isothermal annealing temperature range. The glass/GaSe /CuSe bilayer sample was first heated to 150 C at a rate of 30 C/min and then X-ra y diffraction data were collected for 1 min during subsequent ramp heating (30 C/min). Four sequential scans ove r a range of 20 to 54 (2 ) were taken for 1 min at 10 C increments while the sample was heated from 150 to 350 C in a flowing He atmosphere. Figur e 5-2 demonstrates that the initial CuSe phase begins to be transformed to -Cu2-xSe at around 230 C, and CuGaSe2 formation is initiated with the decrease of -Cu2-xSe peak at around 260 C. The expected interfacial reaction pathway is 2CuSe Cu2-xSe + Se at ~230C Cu2-xSe + Se + 2GaSe 2CuGaSe2 at ~260C 5.2.3 Isothermal Annealing Time-resolved, high temperature X-ray di ffraction data were collected using a linear position sensitive detector (LPSD), wh ile the bilayer glass/GaSe/CuSe precursor

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123 films were maintained at a constant te mperature in a He (flow rate ~100 sccm) atmosphere. Figure 5-2. In situ XRD scans during temp erature ramp annealing (30 C/min) of the glass/GaSe/CuSe sample. A set of isothermal experiments were performed with a range of set point temperature selected from the temperature ra mp scan results shown in Figure 5-2. The set point temperature was selected so that the total isothermal holding time was much longer (i.e. several hours) than an in dividual scan time (~ 35 sec). A three-step heating protocol was used to minimize heating time w ithout temperature overs hooting. Initially, the temperature was rapidly ramped at a rate of 300 C/min to a value 20 C below the set-point temperature, a nd then at a rate of 200 C/min to a value 10 C below the setpoint temperature. Finally, the temperature was ramped to a set point at a rate of 100 C/min, and then held at the set-point te mperature to monitor the evolution of the

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124 isothermal reaction. To complete the r eaction, the temperature was elevated to 500 C and maintained for about 12 min until only the CuGaSe2 phase remained and the corresponding peak intensity remained c onstant. The temperature range for the isothermal experiments was from 280 to 370 C. The 2 scan range (24 to 34 ) for the isothermal experiments was selected to focus on the major peaks of the reactant, intermediate and product, i.e., CuSe (006), Cu2-xSe (111), and CuGaSe2 (112). Figure 5-3 displays the time-resolved XRD da ta collected for the film isothermally reacted at different temperatures. The comp arison between the isothermal plots at four different temperatures clearly illustrates that the reaction rate increases with temperature and follows a deceleratory reaction pattern To obtain the fractional reaction (), which is defined as the fraction of reaction completed at time t the integrated intensities of the product CuGaSe2 (112) peaks were obtained by peak f itting the diffraction data using the software package JADE, and were norma lized assuming that the reactants were completely transformed to crystalline CuGaSe2 after each run, and that the texture of the CuGaSe2 did not appreciably change through the en tire heating process. As shown in Figure 5-4, an analysis of the fractional reaction () with respect to time at different isothermal temperatures demonstrates that CuGaSe2 formation follows the deceleratory reaction trend, which is consistent with diffusion-controlled re action kinetics. The reaction kinetics in terms of activation energy ( Ea), kinetic constant ( k ) and reaction order ( n ) were investigated employing two conventional diffusion-controlled reaction models, i.e. parabolic rate and Avrami models In chapter 4, it has been shown that these methods yield satisfactory fits to relevant experimental data such as CuInSe2

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125 formation from glass/InSe/CuSe and glass/In2Se3/CuSe bilayer precursors, and selenization of Cu-In metallic precursor. Figure 5-3. In situ time-resolved XRD scans during isothermal annealing of the glass/GaSe/CuSe precursor structure at selected temperatures (i.e. 280, 300, 330 and 370 C) As mentioned in chapter 4, the simple pa rabolic rate model [Hul69] was developed based on a reaction between two solid materials with planar surfaces, a case identical to the GaSe/CuSe precursor structure considered here. This model is consistent with a physical process that requires a limiting reacta nt to diffuse across the product layer that initially formed at the interface of the two reactants. The product layer thickness increases with time to further decrease the diffusive flux of the limiting reactant.

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126 0 0.2 0.4 0.6 0.8 1 1.2 0102030405060 time (t), minFractional reaction ( 280 C 300 C 340 C 370 C Figure 5-4. Fractional reaction () with respect to time ( t ) at selected isothermal temperatures Assuming a uni-directional proce ss with a boundary condition of = 0 at time t = 0, the reaction kinetics of the parabolic mode l are described by equa tion 4-4. Figure 5-5 shows the plot of 2 vs. t for the isothermal reaction of the precursor films at different temperatures, including the corr esponding Arrhenius plot as s hown in Figure 5-6. It is evident that the parabolic reaction model prov ides a satisfactory fit to the data over the entire set of isothermal temperatures (280 to 370 C).

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127 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0102030405060 time (min)2280 C 300 C 370 C 340 C Figure 5-5. Parabolic rate model plot for glass/GaSe/CuSe precursor structure -8 -6 -4 -2 0 1.51.61.71.81.9 1000/T (1/K)ln k(Ea ~ 11516 kJ/mol) Figure 5-6. Arrhenius plot of the Parabolic rate constant for glass/GaSe/CuSe precursor structure

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128 The extracted parabolic kinetic constants ( kp) are summarized in Table 5-1. It is concluded that the formation of CuGaSe2 in a glass/GaSe/CuSe bilayer precursor films is consistent with a one-dimensional diffusion controlled reaction pattern. The implied process involves the forma tion and growth of a CuGaSe2 layer at the GaSe-CuSe interface, which limits the reactant diffusi on and thus the rate of further reaction. Finally, the data in the Arrhenius plot of Figure 5-6 along with the Arrhenius equation 4-6 is used to estimate the apparent activation energy Ea for the CuGaSe2 formation reaction in glass/GaSe/CuSe bilayer precursor films, yielding a value of Ea = 115 ( 16) kJ/mol. As a more sophisticated growth model, th e Avrami model was applied to the data. The Avrami model considers a reaction of the additive type between two reactants, where the product phase is growing from randomly di stributed nuclei within a reactant phase. Analysis of solid-state reaction data us ing the Avrami model, which has more sophisticated form than parabolic rate model, is commonly used for preliminary identification of growth rate laws. Since an isotropic growth is assumed in the Avrami model, the product regions should be spherical. As a consequence, when the growth of the nuclei is diffusion-controll ed, the parabolic growth law introduced in the previous section is also applicable, i.e ., the growth rate in any direction is proportional to t0.5. The isothermal Avrami transformation kinetics with an initial condition of ( t =0) = 0 are given by equation 4-3. If an induction period exists before crystallizatio n starts, the Avrami expression can be modified as ) )) ( ( exp( 10nt t k (5-1) where t0 is the time before crystallization starts [Nor69].

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129 According to the results of our isothermal experiments shown in Figure 5-3 and 54, the CuGaSe2 formation was already initiated befo re the temperatur e reached the setpoint, i.e ., ( t =0) 0. A model that substitutes o, where o is the fractional conversion at t=0, was evaluated initially, but did not represent the data well. Thus a second approach was taken. Considering th is initial condition, a modified Avrami expression is suggested as below, a lthough a physical basis is not evident: ) *)) ( ( exp( 1nt t k (5-2) or equivalently, as k n t t nln *) ln( ) 1 ln ln( (5-3) where t* is the time constant which satis fies the initial condition (i.e., ( t = 0) = 0) at given temperature. Also, this time constant represents the starting time of reaction that is extrapolated from the Avrami model plot (i.e., ( t = -t* ) = 0). To find the kinetic parameters, n, k and t* the following iteration steps are employed. Guess the time constant t* Find n and k by a linear fitting of ln(-ln(1-)) vs. ln( t + t* ) Apply the initial condition, ( t =0) = 0 to Equation (5-3) k n t n ln *) ln( ) 1 ln ln(0 (5-4) The steps and are repeated until an acceptable error ( ) is obtained. The resulting Avrami model plot was comp ared with the experimental data in Figure 5-7. The Avrami model expressed by Equation (5-3) yields a satisfactory (i.e., linear) fit with the estimated kinetic parameters summarized in Table 5-1.

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130 Table 5-1. Estimated kinetic parameters for the CuGaSe2 formation from glass/GaSe/CuSe bilayer precursor films ( kp and k : apparent kinetic constants n : Avrami exponents and t : time constant for modified Avrami model) Parabolic model Modified Avrami model Temperature [ C] kp 103 [s-1] n k 103 [s-1] t* [s] 280 0.050 ( 8.02 10-4) 0.70 ( 7.4 10-3) 0.129 ( 1.20 10-4) 0 # 300 0.237 ( 2.92 10-3) 0.69 ( 9.1 10-3) 0.693 ( 8.71 10-4) 75.0 340 0.623 ( 2.38 10-2) 0.73 ( 1.3 10-2) 1.74 ( 3.47 10-3) 49.2 370 2.22 ( 2.32 10-1) 0.68 ( 2.2 10-2) 7.97 ( 4.53 10-2) 24.6 #: Experimentally determined since no pre-reaction was observed for this run. 0 0.2 0.4 0.6 0.8 1 1.2 0102030405060 time (t+t*), minFractional reaction ( 280 C 300 C 340 C 370 C Figure 5-7. Fractional reaction () with respect to time ( t + t *) and Avrami model plot at selected isothermal temperatures (Sym bols: experiments, solid line: Avrami model prediction)

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131 In the case of one-dimensional, diffusioncontrolled reactions with first-order nucleation processes, the Avrami exponent can vary between 0.5 and 1.5 depending on the nucleation frequency. The value of n is close to 0.5 if the nucleation is instantaneous, and close to 1.5 if the nucl eation rate is constant thr oughout the reaction [Hul69]. As shown in the Table 5-1, the values of th e Avrami exponents lie between 0.68 and 0.73, which are close to the lower limiting value of 0.5. Figures 5-8 and 5-9 displays the Avrami model and corresponding Arrhenius pl ots for the same data set previously analyzed by the parabolic rate model. -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 345678910 ln(t+t*)ln[-ln(1-)]280 C 300 C 370 C 340 C (n = 0.68~0.73) Figure 5-8. Modified Avrami model plot for glass/GaSe/CuSe precursor structure The resulting Avrami exponents thus suggest that nucleation occurs so rapidly that the nucleation time may be negl ected. This is consistent with the suggestion that nucleation and subsequent growth have occu rred before the start of the isothermal experiment, i.e., t=0. Formation of nuclei and their growth either in the deposition

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132 process or during the heating st ep is consistent with rapi d nucleation as estimated by n 0.5. Using an Arrhenius model of the form given in Equation (5-2), it is readily established that the appare nt activation energy is 124 ( 19) kJ/mol, which is in agreement with the value of 115 ( 16) kJ/mol obtained via the parabo lic rate-model analysis. These activation energies for CGS formation are larger than the value of 65~66 kJ/mol [Kim05a] obtained by parabolic and Avrami model analysis for -CIS formation from glass/InSe/CuSe stacked bilayer precursor having a structur e analogous to the glass/GaSe/CuSe used in this study. -10 -8 -6 -4 1.51.61.71.81.9 1000/T (1/K)ln k(Ea ~ 12419 kJ/mol) Figure 5-9. Arrhenius plot of the Avrami model rate constant for glass/GaSe/CuSe precursor structure

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133 5.2.4 TEM-EDS Analysis To support the high temperature X-ray di ffraction results on reaction pathway and kinetics of CGS formation, a TEM-EDS (ener gy dispersive X-ray spectrometry) analysis was performed using a JEOL JEM 2010 F S canning Transmission Electron Microscope. First, the glass/GaSe/CuSe precursor was isothe rmally soaked on the Pt/Rh strip heater of 300 C for 30 min in a flowing He, and then quenched by turning off the heater power and increasing the He flow rate. A strip h eater system directly heating the bottom of sample is much more feasible for quenching experiment than an environmental heater system heating the entire volume of ambient gas inside furnace. Both the as-grown precursor and 300 C -annealed sample were coated by carbon to ge t better electrical conductivity and thus better image resolution during TEM analysis. The TEM samples were prepared using a FEI Strata DB 235 focused ion beam (FIB). It is noted that an Augrid instead of conventional Cu-grid was us ed to hold TEM samples to prevent Cu-grid from interfering with the EDS analysis for Cu concentration profile. The TEM images along with EDS line scan re sults were compared in Figure 5-10. A bilayer structure of as-grown glass/GaSe/C uSe precursor is clearly illustrated by the TEM image and EDS scan results in Figure 5-10(a). Interestingly, the EDS gallium concentration profile shows a small tail on the top side of the CuSe layer, which is attributed to the diffraction by gallium accu mulated during the bombardment of gallium ion used by the FIB system. The TEM imag e and EDS line scan results of 300 C – annealed sample shown in Figure 5-10(b) demonstr ate that CuGaSe2 forms at the interface between GaSe and CuSe layers, which explicitly supports the primary assumption of the parabolic growth model. A ccording to the plot of fractional reactions with respect to time at 300 C shown in Figure 5-4, the glass/GaSe/CuSe film

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134 isothermally annealed at 300 C for 30 min is expected to yield around 0.7 of fractional reaction, which is pictorially evidenced by TEM image in Figure 5-10(b). Figure 5-10. TEM-EDS analysis on (a) as-grown glass/GaSe/CuSe precursor, (b) sample annealed at 300 C, for 30 min

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135 There is no evidence for the Cu diffusion into GaSe and Ga diffusion into CuSe layer. There is, however, a non-uniformity in the Ga concentration within the CGS layer, while the concentration of Cu and Se is consistent over the entire CGS region. It may be qualitatively explained by a lower value of diffusi vity of Ga than that of Cu into CGS that yields a Cu-rich CGS at the top part of CGS and a Ga-rich CGS at the bottom part of CGS layer. 5.3 Glass/Mo/Cu-Ga-Se Precursor 5.3.1 Precursor Preparation The glass/Mo/Cu-Ga-Se precursors were prepared by co-deposition of elemental Cu, Ga, and Se on Mo-coated thin glass substr ate in the MEE system without heating the substrate. Figure 5-11. Room temperature X-ray diffr action of (a) as-grown glass/Mo/Cu-Ga-Se precursor, and (b) thermally annealed CuGaSe2

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136 ICP analysis revealed a Cu-rich ([Cu]/ [Ga]~1.08) and Se-rich ([Se]/[Cu+Ga] ~1.73) overall atomic composition. As show n in Figure 5-11, the room temperature XRD pattern for the as-grown precursor and comple tely annealed samples demonstrate that no crystalline phase forms during co-deposition of the elements (i.e., Cu, Ga, and Se), and polycrystalline CuGaSe2 can be produced by thermal treatment of the Cu-Ga-Se elemental mixture. 5.3.2 Temperature Ramp Annealing Temperature ramp annealing with Scintag HT-XRD system was used to investigate the phase evolution of the samples and to establish a suitable isothermal annealing temperature range. The glass/Mo/ Cu-Ga-Se precursor was first heated to 100 C at a rate of 30 C/min, and then four sequential X-ray scans (scan time: 1min) over a 2 range of 20 to 54 were taken at 10 C increments dur ing subsequent ramp heating up to 400 C at a rate of 30 C/min in a flowing He atmosphere. The O2 content of the outlet He gas was measured by an O2 analyzer to be less than 0.1 ppm. The results shown in Figure 5-12 reveal that CuSe2 forms at around 160 C followed by its transformation to CuSe at around 200 C, and CuGaSe2 formation then is initiated with the decrease of CuSe p eak at around 280 C. No crystalline GaxSey compound, however, was detected, which suggests most of the gallium is contained in the amorphous state (GaxSey compound or liquid Ga) before participating in the CuGaSe2 formation reaction. Figure 5-10(b) demonstrates the 2 location of CGS (112) peak is relatively stable with respect to temperat ure while the CuSe (102) peak significantly shifts to lower values of 2 as the temperature increases, which qualitatively indicates that the thermal expansion coefficient of CGS is considerably smaller than that of CuSe.

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137 Figure 5-12. In situ XRD scans during temp erature ramp annealing (30 C/min) of the glass/Mo/Cu-Ga-Se sample

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138 5.3.3 Isothermal Annealing Time-resolved, high temperature X-ray di ffraction data were collected using a linear position sensitive detector (LPSD), wh ile the glass/Mo/Cu-Ga-Se precursor films were maintained at a constant temperature in a He (flow rate ~100 sccm) atmosphere. In the isothermal experiment, the three-step temperature ramping protocol was used to minimize heating time without temperature ove rshooting, as previously mentioned at section 5.2.3. Once the temperature reached the set point value, it was held at the setpoint temperature to monitor the evolution of the isothermal reaction. To complete the reaction, the temperature was elevated to 600 C and maintained for about 12 min until only the CuGaSe2 phase remained and the corresponding peak intensity remained constant. It is noted that, considering th e formation temperature of CIS and CGS, the final elevation temperature of 500 C instead of 600 C was used for isothermal annealing experiments for CIS formation as described in chapter 4. The temperature range for the isothermal experiments was 300 to 400 C and X-ray scan time was 30 sec. Figure 5-13 displays the time-resolved XR D data collected for the glass/Mo/ CuGa-Se film isothermally reac ted at selected temperatures. The comparison between the isothermal plots at four different temperatur es clearly illustrates that the reaction rate increases with temperature. To obtain the fract ional reaction (), which is defined as the fraction of reaction completed at time t the peak heights of the product CuGaSe2 (112) were obtained by peak fitting the diffracti on data using JADE, and were normalized assuming that the reactants were completely transformed to crystalline CuGaSe2 after each run, and that the texture of the CuGaSe2 did not appreciably change through the entire heating process.

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139 Figure 5-13. In situ time-resolved XRD scans during isothermal annealing of the glass/Mo/Cu-Ga-Se precursor structur e at selected temperatures (i.e. 300, 325, 350 and 375 C) It should be pointed out that the peak height was used inst ead of the integrated peak intensity, because it was difficult to obtain a c onsistent profile of peak intensity by fitting the broad diffraction pattern, especially for the 300 and 325 C anneals. According to the results of the previous X-ray experiments (C hapter 4 and 5) on isot hermal annealing of various precursor structures, however, it is accep table to use the peak height in place of the peak intensity within an allowable erro r range. Estimated fractional reaction values with respect to isothermal soaking time at di fferent isothermal temperatures are shown in Figure 5-14.

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140 Figure 5-14. Comparison of fractional reacti on for isothermal experiments and modified Avrami model prediction (Solid line: model predictions, symbol: experimental data). The reaction kinetics in terms of activation energy ( Ea), kinetic constant ( k ), and reaction order ( n ) are modeled using a modified Avra mi model, which is suggested in chapter 5.2.3. According to the results of the isothermal experiments shown in Figure 515, part of CuGaSe2 formation has already occurred before the sample reached the setpoint temperature, i.e., ( t =0) 0. Considering this initia l condition, a modified Avrami model is expressed by equation 5-3. By using the iteration procedure explained in chapter 5.2.3, Avrami exponent (n), kine tic constant (k), and time constant ( t* ) are obtained, as summarized in Table 5-2. It is seen for the results in the Table that the values of t* are shorter for the larger isothermal soak temperature that represents more extent of pre-reaction. This is replaced by the experimental measure in absolute rate of reaction with temperature that causes

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141 much more growth to cause and the equivalent amount of growth at time, t*, at the higher soak temperature, will react at a higher rate. Table 5-2. Estimated kinetic parameters for the CuGaSe2 forma tion from glass/Mo/CuGa-Se precursor films (k: apparent kine tic constants, n: Avrami exponents and t*: time constant for modified Avrami model) Modified Avrami model Temperature [ C] n k 103 [s-1] t* [s] 300 0.22 ( 5.0 10-3) 0.0181 ( 7.23 10-5) 30.0 325 0.19 ( 6.6 10-3) 0.0265 ( 2.40 10-4) 18.8 350 0.15 ( 9.6 10-3) 0.722 ( 1.79 10-2) 5.5 375 0.11 ( 1.8 10-2) 1.25 ( 1.76 10-1) 2.8 -1.6 -1.2 -0.8 -0.4 0 246810 ln(t+t*)ln(-ln(1))n = 0.11 ~ 0.22 300 C 325 C 350 C 375 C Figure 5-15. Modified Avrami model plot for glass/Mo/C u-Ga-Se precursor structure As shown in Figure 5-14, the fractional react ions with respect to isothermal soaking time predicted by modified Avrami model in a very good agreement with experimentally

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142 determined values. From the Arrhenius plot for kinetic constants, as inserted in Figure 5-16, the apparent activation energy was estimated as 197 50 kJ/mol. -10 -8 -6 -4 -2 0 1.51.61.71.8 1000/Tlnk(Ea = 19750 kJ/mol) Figure 5-16. Arrhenius plot of the Avrami model rate constant for glass/Mo/Cu-Ga-Se precursor structure It is noticeable that the time constant (t *) decreases with temperature, which was also observed in isothermal annealing of gl ass/GaSe/CuSe precursor. Interestingly, the estimated values of Avarmi exponents lie in th e range 0.11 to 0.22, which is quite out of validity range of conventional Avrami mode l. Theoretically, the range of Avrami exponents should be 0.5~1.5 for one-dimensi onal, 1.5~2.5 for two-dimensional and 2.5~3.5 for three-dimensional diffusion cont rolled reaction. Alt hough the experimental data are well fitted mathematically by a modi fied Avrami model, the isothermal reaction of CGS formation from glass/Mo/Cu-Ga-Se th us may not be described meaningfully by the Avrami growth model. Therefore, it is concluded that the CGS formation from intimately mixed Cu-Ga-Se precursor does not follow the diffusion controlled reaction

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143 pattern, which is not surprisi ng because there is no substan tial diffusion barrier between intimately mixed reacting elements. 5.4 Selenization of Glass/Mo/Cu-Ga Precursor 5.4.1 Precursor Preparation The glass/Mo/Cu-Ga precursor was prepared in a migration enhanced molecular beam epitaxial (MEE) reactor under ultra high vacuum conditions (10-7 to 10-8 Torr). Since molybdenum is a widely used back-contact material in CIGS-based solar cells, the elemental Cu and Ga were deposited on the Mo-coated, sodium-free thin glass (Corning 7059: alkali level < 0.3%, 0.4 mm thickness) without heating the substrate to minimize the unintended reaction between Cu and Ga. The overall atomic composition of the CuGa film as-deposited on the Mo/glass subs trate was measured as [Cu]/[Ga] = 1.01 by inductively coupled plasma op tical emission spectroscopy (ICP-O ES). The result is that the atomic ratio of the film, [Cu]/[Ga] = 1.01. The crystalline phases present in the asgrown precursor (mainly CuGa2) and selenized film (mainly CuGaSe2 and MoSe2) were identified by room-temperature XRD (R T-XRD), as shown in Figure 5-17. The thicknesses of the Mo (~0.4 m), Cu-Ga (~0.7 m), and selenized CuGaSe2 (~1.2 m) films were measured by SEM images of cl eaved samples, which are not shown here. 5.4.2 Selenization Chamber Design The phase evolution and reaction kinetic s during selenization of glass/Mo/Cu-Ga precursors were investigat ed using time-resolved, in situ high-temperature X-ray diffraction (HT-XRD), whic h consists of the PANa lytical X’Pert Pro MPD /X-ray diffractometer equipped with an Anton P aar XRK-900 furnace and an X’Celerator solid state detector.

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144 Figure 5-17. Room-temperature XRD scans of Cu-Ga as-grown precursor and selenized CuGaSe2 film. Figure 5-18. X-ray sample holder with a graphite dome for selenization of Cu-Ga precursor films. Selenium powder was placed in wells on the HT-XRD sample holder adjacent to the precursor film. As shown in Figure 518, the HT-XRD sample holder containing the

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145 precursor film and selenium powder was cove red with an X-ray transparent graphite dome, which is customized to minimize Se vapor loss. 5.4.3 Temperature Ramp Selenization The selenization reaction was thermally pr omoted via temperature-ramp annealing at a rate of around 20 C/min under in situ XRD observation to identify the possible intermediate phases and the temperature range for formation of the CuGaSe2. As shown in Figure 5-19, the results reveal that CuSe forms in the temperature range of approximately 260 to 370 C, and that the onset of formation of CuGaSe2 occurs at approximately 300 C. A strong carbon (002) peak from the graphite dome was consistently observed at around a 2 value of 27. Fortunately, this peak did not overlap with any peaks of the anticipated phases. It is also noted that the peak intensities are attenuated over the entire 2 range in the temperature range 370 and 600 C, which is attributed to the scattering of the incoming X-ray by Se vapor within the chamber. Thus the almost full recovery of peak intensiti es at 600 C demonstrates the complete consumption of Se powder at this temperature. The formation of MoSe2 identified in the RT-XRD scan for the selenized film, as shown in Figure 5-17(b), was not detected under in situ HT-XRD observation during temperature-ramp annealing, which is attributed to the relatively low resolution at the higher scan rate of HT-XRD (~8 /min) than that of RT-XRD (~1 /min). There are several reports on MoSe2 formation at the interface of CIGS and Mo layers and its positive contribution to the efficiency of CIGS solar cells [Wad01, Sha96, Abo05].

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146 Figure 5-19. In situ XRD scans during temp erature ramp selenization of Cu-Ga/Mo/glass precursor. Wada et al reported that the (100) an d (110) reflections of MoSe2 in Mo/CIGS absorbers deposited by a typica l three-stage process were detected by XRD. They suggested that the Mo/CIGS hetero-contact with the MoSe2 layer makes a favorable ohmic contact, while Mo/CIGS without a MoSe2 layer exhibits a Sc hottky-type contact [Wad01]. In Chapter 3, it was shown that selenization of Cu-In/Mo/glass precursor [Kim06a] produced MoSe2, but was only detected after complete formation of CuInSe2. MoSe2 detection was also accompanied by a rapid decrease of the Mo (110) reflection intensity, which was clearly detected at a temperature above 440 oC. The greater thermodynamic stability of CIS over MoSe2 is consistent with this observation. Since MoSe2 was not detected during thermal anneal because of the low sensitivity of the detection in this specific set of experiments, it is not clear if MoSe2 only forms after complete CGS formation.

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147 5.4.4 Isothermal Selenization Isothermal annealing at selected temperatures between 330 and 400 oC was then performed for estimating kinetic parameters us ing an appropriate reaction model. The 2 scan range (22 to 30o) for the isothermal experiment s was selected since the major reflection for the product CuGaSe2 (112) lies within this range To complete the reaction, the temperature was elevated to 550 oC after each run and then maintained at this temperature for about 12 mi n or until only the CuGaSe2 phase remained as evidenced by constant peak intensity. Figure 5-20 displays the time-reso lved XRD data collected for the film isothermally annealed at different temperatures. The comparison between the isothermal plots at four different temperatur es clearly illustrates that the reaction rate increases with temperature. Figure 5-20. In situ XRD scans during is othermal selenizati on of Cu-Ga/Mo/glass precursor at four di fferent temperatures.

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148 To obtain the fractional reaction (), which is defined as the fraction of reaction completed at time t the integrated intensit ies of the product CuGaSe2 (112) peaks were obtained by fitting the diffraction data. The in tegrated intensities were then normalized assuming that the Cu-Ga precursors were co mpletely selenized to crystalline CuGaSe2 after the high temperature anneal at the e nd of the run, and that the texture of the CuGaSe2 did not appreciably change th rough the entire heating process According to the results of the isothermal experiments shown in Figure 5-20, nucleati on and partial growth of the CuGaSe2 phase occurred during the heating pe riod before the sample temperature reached the set-point value, i.e ., (t=0) 0. The reaction kinetics in terms of an activation energy and reaction or der was investigated using the modified Avrami model which is suggested in the previous chapter 5.2. Detailed procedure to find kinetic parameters using the modified Avrami model wa s described in the previous chapter 5.2.3. For these experimental data, the estimated Avrami exponents ( n ), kinetic constants ( k ), and time constants ( t* ), are summarized in Table 5-3. Table 5-3. Estimated kinetic parameters for the CuGaSe2 formation from selenization of glass/Mo/Cu-Ga precursor films. ( k : apparent kinetic constants, n : Avrami exponent and t *: time constant of the modified Avrami model) Modified Avrami Model Parameters Temperature [ C] n k 103 [s-1] t* [s] 330 0.57 ( 1.5 10-2) 0.302 ( 1.63 10-3) 0 # 350 0.55 ( 1.1 10-2) 0.703 ( 2.27 10-3) 38.6 370 0.61 ( 1.7 10-2) 1.38 ( 7.71 10-3) 62.0 400 0.61 ( 2.8 10-2) 2.92 ( 4.26 10-2) 54.3 #: Experimentally determined since no pre-reaction was observed for this run.

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149 Figure 5-21. Comparison of fractional reacti on for isothermal experiments and modified Avrami model prediction (Solid line: model predictions, symbol: experimental data) As shown in Figure 5-21, the compar ison between the fr actional reaction by experiments and the prediction by a modifi ed Avrami model demonstrates that a modified Avrami model fits the expe rimental data set very well. The n values over the entire temperature range (330 to 400 oC) lie in the relatively na rrow range 0.55 and 0.61. These values are close to the lower limiting va lue of 0.5 thus suggesting rapid nucleation. The low value of the estimated Avrami exponents suggests that the nucleation of CuGaSe2 occurs so rapidly (e.g., during the ra mping time) that the nucleation time is nearly negligible. The Arrhenius equation wa s used to estimate the apparent activation energy, Ea, for CuGaSe2 formation by selenization of gla ss/Mo/Cu-Ga precursor films. An activation energy of 109 (7) kJ/mol was estimated from the Arrhenius plot shown in Figure 5-23.

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150 -2 -1.5 -1 -0.5 0 0.5 1 1.5 456789 ln (t+t*)ln[ -ln(1)]n = 0.55 ~ 0.61 330 C 350 C 370 C 400 C Figure 5-22. Modified Avrami model for the CuGaSe2 formation by selenization of glass/Mo/Cu-Ga precursor -9 -8 -7 -6 -5 1.451.51.551.61.651.7 1000/T, K-1ln (k)(Ea = 109 7 kJ/mol) Figure 5-23. Arrhenius plot of the Avrami m odel rate constant for the CuGaSe2 formation by selenization of glass/Mo/Cu-Ga precursor

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151 The value of 109 (7) kJ/mol is simila r to the activation energy of 124 (19) kJ/mol estimated for selenization of glass/ Mo/Cu-In precursor using the Avrami model and Arrhenius plot [Kim06a]. Also, this value is reasonably cl ose to the activation energies of 124 (19) kJ/mol estimated for CGS formation from bilayer glass/GaSe/CuSe in chapter 5.2 and 129 kJ/mol estimated fo r CGS formation from the stacked bilayer Ga2Se3/Cu2Se by Purwins et al. [Pur06]. It is interesting to compare the results for formation of CGS to those for CuInSe2. Similar experiments using a Cu-In precursor showed a different reaction sequence (CuSe formation followed by CuSe2 and then CuInSe2). Analysis of the rate data by both the Avrami and parabolic rate models provided estimated activa tion energies of 124 ( 19) and 100 ( 14) kJ/mol, respectively, which are similar to the values determined here for CGS, suggesting the CuSe diffusioncontrolled formation step may be rate limiting. It is also noted that from comparison of the standard errors of activation energies for CuGaSe2 and CuInSe2 formation by selenization of metallic precursors, it is concluded that the graphite dome used for selenization of Cu-Ga provides more reliable experimental results than the aluminum foil cover used for selenization of Cu-In. The experimental reliability of a graphite dome could be attrib uted to its superior X-ray transparency and operability to an aluminum foil. The X-ray transparency of the graphite dome is clearly evidenced by the negligible loss in reflection intensity, while employing an aluminum foil cover sacrifices the reflection intensity and thus the accuracy of experiments. Based on the results of the Avrami model analysis, the formation of CuGaSe2 from selenization of glass/Mo/Cu -Ga precursor films apparently

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152 follows a one-dimensional diffusion controlled reaction with a nucleation and subsequent growth sequence. 5.5 Summary Time-resolved, in situ high-temperature X-ray diffraction was successfully applied to investigate the reaction pathway and kinetics of polycrystalline CuGaSe2 formation from thermal annealing of glass/GaSe/CuSe bilayer and glass/Mo/Cu-Ga-Se elementally mixed precursor, and selenization of glass/Mo/Cu-Ga metallic precursors. The qualitative reaction pathway obser vation during the temperature ramp annealing of glass/GaSe/CuSe bilayer precursor demonstrated that the initial CuSe phase begins to be transformed to -Cu2-xSe at approximately 230 C, followed by CuGaSe2 formation initiated at around 260 C, whic h may be described as the reaction Cu2-xSe + 2GaSe + Se 2CuGaSe2. Quantitative kinetic analys is of X-ray diffraction data obtained during isothermal anne aling fits both the parabolic rate and Avrami growth models, which suggests that CuGaSe2 formation in a bilayer glass/GaSe/CuSe precursor follows a one-dimensional diffusion controlled reaction pattern. The activation energy of this reaction, 115 ( 16) kJ/mol (parabolic rate model) or 124 ( 19) kJ/mol (Avrami model), is much higher than that found for -CIS obtained by the same type of experiments, i.e., glass/InSe/CuSe [Kim05a ]. The TEM-EDS analysis on 300 C – annealed sample demonstrates that CuGaSe2 forms at the interface between GaSe and CuSe layers, which explicitly supports th e primary assumption of parabolic growth model. The results of temperature ramp ann ealing of glass/Mo/Cu-Ga-Se precursor revealed that the CuSe2 forms at around 160 C followed by its transformation to CuSe at

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153 around 200 C, and CuGaSe2 formation then is initiated with the decrease of CuSe peak at around 280 C. The kinetic analysis usi ng a modified Avrami model for isothermal soaking experiments suggest that this reaction should not follow the diffusion controlled reaction pattern since there is no substantial diffusion barrier between intimately mixed reactants. The reaction pathways and chemical kinetics of CuGaSe2 formation from glass/Mo/Cu-Ga precursor st ructures were investigated using time-resolved in situ hightemperature X-ray diffraction equipped with a graphite dome. The results show that the selenization process of Cu-Ga films produces a CuSe phase at temperatures ranging from 260 to 370 C, and that CuGaSe2 phase first starts to appe ar at approximately 300 C. The kinetic analysis on the selenization of Cu-Ga films shows that a modified Avrami model for chemical reaction fits the experime ntal data set well, yielding an activation energy of Ea = 109 (7) kJ/mol. This value of ac tivation energy is very close to that estimated for the CuGaSe2 formation from glass/GaSe/CuSe bilayer (i.e., 124 19 kJ/mol estimated with the modified Avrami model) and from selenization of Cu-In/Mo/glass precursor (i.e., 124 19 kJ/mol estimated with the Avrami model). It is concluded that the Cu-Ga selenization also follows a pathway along a one-dimensional diffusioncontrolled reaction that takes place in concert with a nucleation and growth mechanism. As summary, the reaction rates of CIS and CGS formation are compared using kinetic constants for different precursor structures displaye d in Figures 5-24 and 5-25. The kinetic analysis using both parabolic and Avrami models suggests that the CGS formation from GaSe/CuSe precursor or from selenization of Cu-Ga precursor is much slower than that CIS formation from similar precursor structures. Furthermore, the CGS

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154 formation using a GaSe/CuSe precursor is even faster than using the selenization of CuGa precursor. In the near future, the CGS fabrication using the ra pid thermal processing of a GaSe/CuSe precursor structure will be performed in our research group. -12 -10 -8 -6 -4 1.41.51.61.71.81.922.1 1000/T (1/K) ln k InSe/CuSe In2Se3/CuSe CuIn selenization GaSe/CuSe 265 C Parabolic growth model Figure 5-24. Comparison of reaction rates for CIS and CGS formation from different precursors estimated by the parabolic model. -12 -10 -8 -6 -4 1.41.51.61.71.81.922.1 1000/T (1/K) ln k InSe/CuSe GaSe/CuSe CuIn selenization CuGa selenization Avrami model Figure 5-25. Comparison of reaction rates for CIS and CGS formation from different precursors estimated by the Avrami model

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155 CHAPTER 6 CU(IN,GA)SE2 FORMATION FROM SELEN IZATION OF METALLIC CU-GA-IN 6.1 Introduction Recent advances in the development of high efficiency (19. 5 % AM1.5G [Con05]) polycrystalline thin film Cu(InxGa1-x)Se2 (CIGS) solar cells are extremely promising. In addition to its high cell efficiency, CIGS th in-film solar cells e xhibit outstanding longterm outdoor stability, excellent radiation hardness, and the potential for use in a CIGS/CGS tandem arrangement. The route us ed to synthesize the CIGS absorber material is critical to achi eving high cell efficiency as we ll as high processing throughput. Interestingly, a variety of processing seque nces lead to the formation of CIGS, for instance, co-deposition of elements, rapid th ermal processing of stacked elemental layer, and selenization of metallic precursor. This flexibility is partly due to an inherent stability of -CIGS and a rich phase diagram ( -CuInSe2 is in equilibrium with 8 different solid phases and a Se-rich liquid) [Gd00a-c]. The complex chemistry of the 4component CIGS system, however, has for ced absorber synthesis optimization to primarily traverse an empirical path and discouraged explorat ion of substantially different approaches. In particular, very little is known about the fundamental thermochemistry and reaction pathways in the system. In ch apters 4 and 5, the reaction pathways and kinetics of -CIS formation from different pr ecursors (e.g., InSe/CuSe [Kim05a], In2Se3/CuSe [Kim05b], Cu-In-Se) and selenizati on of metallic Cu-In precursor [Kim06a], and CGS formation from thermal annealing of GaSe/CuSe and se lenization of Cu-Ga

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156 precursor [Kim06b] were investigated. In th is chapter, the reaction kinetics for CIGS formation by the selenization of co-deposited me tallic Cu-Ga-In precursors is reported. 6.2 Experimental The glass/Mo/Cu-Ga-In precursors were grown using Migration Enhanced Epitaxy (MEE) deposition system under ultra high vacuum conditions (10-7 ~ 10-8 Torr). Since molybdenum is widely used as a back-contact material in CIGS-based solar cells, elemental Cu, Ga, and In were co-deposited on the Mo-coated, sodium-free thin glass (Corning 7059: alkali le vel < 0.3%, 0.4 mm thickness) w ithout heating the substrate to minimize the reaction between elements. Th e overall atomic composition of the asdeposited precursor film is determined by inductively coupled plas ma optical emission spectroscopy (ICP-OES). Further descripti on of MEE reactor and deposition technique was given in chapter 1.5. The phase evolution and reaction kinetic s during selenization of glass/Mo/Cu-GaIn precursors were investig ated using time-resolved, in situ high-temperature X-ray diffraction (HT-XRD), whic h consists of a PANalytical X’Pert Pro MPD /X-ray diffractometer equipped with an Anton P aar XRK-900 furnace and an X’Celerator solid state detector. Selenium powder was placed in wells on the HT-XRD sample holder adjacent to the precursor film The HT-XRD sample holder containing the precursor film and selenium pellet was then covered with an X-ray transparent graphite dome to minimize Se vapor loss, as used for the selenization of glass/Mo/Cu-Ga precursor described in chapter 5.

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157 6.3 Results and Discussion 6.3.1 Precursor Characterization The overall composition of as-deposited glass/Mo/Cu-Ga-In pr ecursor film was close to that known to produce high efficiency CIGS cells, i.e ., Cu-rich (Cu/Ga+In ~ 1.3) and Ga/Ga+In ~ 0.3. The room-temperature XRD pattern shown in Figure 6-1 suggests that Cu11In9, CuIn, and pure In formed during de position of the precursor layer. Figure 6-1. Room-temperature XRD scans of glass/Mo/Cu-Ga-In as-grown precursor In the Cu-In binary phase diagram (F igure 2-16) suggested by Liu [Liu02], however, the compound CuIn is not consid ered to be stable while the compound Cu11In9 is well known to be stable. There are many reports concerning the observation of the apparently meta-stable CuIn phase during Cu -In or Cu-Ga-In film preparation [Che96, Mat97, Pis03, Son03]. In particular, Song et al. [Son03] reported that the CuIn phase was identified along with Cu11In9 in the multilayer Cu-Ga-In precursor film deposited on

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158 glass by DC magnetron sputtering. It is also noted that no phase containing Ga was detected, which suggests Ga present in an amor phous state perhaps as a glass or slightly super-cooled liquid (Ga melting te mperature is 29.78 C). The thicknesses of Mo (~0.4 m), Cu-Ga-In film (~0.6 m), and selenized CIGS film (~1.1 m) were measured by SEM images of cleaved samples, as shown in Figure 6-2. Figure 6-2. Surface (top) and cross-sectional (bottom) SEM images of (a) an asdeposited glass/Mo/Cu-Ga -In precursor film a nd (b) selenized film. The matrix-island structure on the surface of the as-grown precursor is apparent in the SEM surface images of Figure 6-2(a). The islands were identified as an indium-rich or nearly pure indium phase by SEM-EDS (energ y dispersive x-ray spectrometer). It is interesting that the same matrix-island stru cture containing In-rich islands was observed on the surface of the glass/Mo/Cu-In precursor films as shown in Chapter 4.5. 6.3.2 Temperature Ramp Annealing As a preliminary experiment, a backgr ound scan was taken using a bare glass substrate covered by the graphite dome under a flowing He. The temperature ramp rate

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159 and X-ray scan conditions matched those us ed in the runs with the Mo and metal precursors in place during selenization. As shown in Figure 6-3, a strong carbon (002) peak from the graphite dome was detected at 2 ~27, which is very close to the position of the preferred CIGS (112) peak (2 =26.9). Thus the height of sample inside the XRD chamber was intentionally shifted away from the normal to cause the sample reflection peaks to shift sufficiently to separate the CIGS (112) peak from the carbon (002) peak with only a slight decrease in the sample reflection intensities. Figure 6-3. Temperature ramp HT-XRD scans with a bare glass substrate. The selenization reactions were followed during temperature-ramp annealing under in situ XRD observation to identify the temperatur e range for formation of CIGS, as well as any intermediate and by-product phases. Th e precursor was first scanned at 25 C and then heated to 100 C at a rate of 20 C/min. The X-ray diffraction da ta were collected at Glass H

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160 every 10 C interval during subseque nt ramp heating to 600 C. A 2 scan in the range 20 to 60 could be taken in 5 min. Finally, the selenized sample was scanned again at room temperature. Figure 6-4. In situ XRD scans during temperature ramp selenization of Cu-GaIn/Mo/glass precursor.

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161 The background scan data shown in Figure 6-3 were carefully subtracted from the original scans using the JADE software to make the resultant sample peaks more visible, as shown in Figure 6-4. The results revealed that the In (110) p eak disappears above its melting temperature (~151 C), followed by the melting of Cu11In9 at around 250 C, which is slightly lower than the Cu11In9 equilibrium melting temperature of ~307 C [Liu02]. The disappearance of the CuIn ( 34 1) peak along with the s ubsequent appearance of CIGS (220/204) peak is consistent with the formation of CIGS by reaction of Cu-In with amorphous Ga containing material (e.g., Cu-Ga solid solu tions) and Se at around 260 C. The CuSe begin to form approximately 260 C but disa ppeared at 370 C. The onset of formation of CIGS also occurred at approximatel y 260 C. Additionally, the production of MoSe2, accompanied by a decrease of Mo (110) reflectio n intensity, was explicitly detected at temperature above approximately 400 C. The MoSe2 formation is known not only to improve the adhesion but also to produ ce a good quality ohmic-type contact at the CIGS/Mo interface, which improves the effi ciency of CIGS cells [Wad01, Sha96, Abo05]. The Ga composition in the resulting CIGS was estimated by the unit cell refinement method using X-ray diffraction data, as shown in Figure 65. The tetragonal I-42d (122) Cu(In0.7Ga0.3)Se2 structure was used as an initial cell for the refinement, and the 6 peaks of CIGS (i.e., 112, 103, 211, 220, 312 and 400) evident in the XRD pattern of selenized CIGS were taken into account, calibrating their 2 location internally by the strong Mo (110) peak.

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162 Figure 6-5. Cell refinement for room temper ature X-ray diffraction data of a selenized CIGS sample using the tetragonal, I-42d (122) cell type Figure 6-6. Lattice constants (a, c) vs. Ga composition of CIGS y = -0.0169x + 0.5784 R2 = 0.9969 y = -0.0588x + 1.1624 R2 = 0.9988 0.56 0.57 0.58 0.59 0.6 00.10.20.30.40.50.60.70.80.91x(Ga)Lattice constant (a), nm1.05 1.07 1.09 1.11 1.13 1.15 1.17Lattice constant (c), nm a (PDF# 40-1488) a (PDF# 35-1101) a (PDF# 35-1102) c (PDF# 40-1488) c (PDF# 35-1101) c (PDF# 35-1102)

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163 Using the refined CIGS cell lattice constants a~0.571 ( 1.08 10-4) and c~1.14 ( 9.08 10-4) nm along with the relationship between composition and lattice constants for Cu(In,Ga)Se2 shown in Figure 6-6, the Ga com position was estimated as x(Ga) = 0.35 to 0.39. This result suggests partial evapor ation of indium occurred during the temperature ramp annealing. This is not su rprising since the vapor pressure of In is relatively high (1.0 x 10-10 Torr at 400 C) 6.3.3 Isothermal Annealing Isothermal annealing at selected temperatures between 250 and 320 oC was then performed for kinetic analysis using a selected reaction model. The 2 scan range (22 to 30o) for the isothermal experiments was used since the major reflection for the product CIGS (112) lays within this range. To complete the reaction, the temperature was elevated to 550 oC after each run and then maintained at this temperature for about 12 min or until the peak intensity of CIGS phase remained constant. Figure 6-7 displays the time-resolved XRD da ta collected for the film isothermally soaked at selected different temperatures The background scan data (Figure 6-3) corresponding with isothermal soak temperatur es were subtracted from isothermal X-ray pattern. The comparison between the isothe rmal transformations at four different temperatures explicitly illustrates that th e reaction rate increase s with temperature. To obtain the fractional reaction ( ), which is defined as the fraction of reaction completed at time t the intensities of th e product CIGS (112) peak s were integrated by precisely fitting the diffraction da ta using JADE program. The integrated intensities then were normalized assuming that the Cu-Ga-In precursors were completely selenized to crystalline CIGS (i.e., = 1) after the high temperature (550 oC) anneal at the end of the

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164 run, and that the texture of the CIGS di d not appreciably chan ge through the entire heating process. Figure 6-7. In situ XRD scans during isot hermal selenization of glass/Mo/Cu-Ga-In precursor at four di fferent temperatures The reaction kinetics in terms of a rate c onstant, reaction order, and activation energy were quantitatively investigated using th e Avrami model [Kim05a, Kim06a-b, Hul69], which is commonly used in Chapters 4 and 5. For our experimental data, the kinetic constants ( k ) and Avrami exponents ( n ) were estimated by linear regression using equation (4-4) as shown in Figure 6-8, a nd the resulting kinetic parameters were summarized in Table 6-1. The compar ison between the fractional reaction by experiments and the prediction by an Avrami model demonstrates that an Avrami model fits the experimental data set ve ry well, as shown in Figure 6-9.

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165 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 456789 ln(t)ln[ -ln(1)]300 C280 C 260 C 250 C n = 0.45~0.58 Figure 6-8. Avrami model and corresponding Ar rhenius plot (inset) for CIGS formation by selenization of glass/ Mo/Cu-Ga-In precursor. -10 -9 -8 -7 -6 -5 1.71.751.81.851.91.95 1000/T, K-1ln (k)(Ea = 109 7 kJ/mol) Figure 6-9. Arrhenius plot for Avrami rate constant for CIGS formation by selenization of glass/Mo/Cu-Ga-In precursor

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166 The n values over the entire temperature range (250 to 300 oC) lie in between 0.45 and 0.58, which are close to the lower li miting value of 0.5 for one-dimensional, diffusion-controlled reactions. The low value of the estimated Avrami exponents suggests that the CIGS formation by selenizat ion of glass/Mo/Cu-Ga -In precursor films follows one-dimensional, diffusion-controlled reaction pattern, where the nucleation of CIGS occurs so rapidly that the nuc leation time is nearly negligible. Table 6-1. Estimated kinetic parameters fo r the CIGS formation from selenization of glass/Mo/Cu-Ga-In precursor films ( k : apparent kinetic constants and n : Avrami exponents) Figure 6-10. Comparison of fractional reacti on for isothermal experiments and Avrami model prediction (Solid lines: model pr edictions, symbols: experiments). Temperature [C] n k 103 [s-1] 250 0.58 ( 0.022) 0.138 ( 1.5010-3) 260 0.50 ( 0.036) 0.430 ( 1.5410-2) 280 0.52 ( 0.034) 0.951 ( 2.6110-2) 300 0.45 ( 0.044) 2.99 ( 1.5510-1)

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167 The Arrhenius equation (4-6) was used to estimate the apparent activation energy Ea for CIGS formation by selenization of gl ass/Mo/Cu-Ga-In precursor films. The Arrhenius plot inserted in Figure 6-10 yiel ds an activation ener gy of 144 (17) kJ/mol. 6.3.4 Comparison Between CIS, CGS, and CIGS Formation It is interesting to compare the formati on of CIGS from selenization of Cu-Ga-In precursor with that of CIS [Kim06a] and CG S [Kim06b] from selenization of Cu-In and Cu-Ga precursors, respectively. Their experiment al results are summarized in Table 6-2. Table 6-2. Comparison of reaction pathways and kineti cs for CIS, CGS and CIGS formation from selenization of metallic precursors. Avrami model analysis Precursors (glass/Mo/ Metal) Selenization pathways CIGS Fo rm ati on Temp. n Ea (kJ/mol) Ref. Cu-In CuSe CuSe2 CIS ~250 C 0.61~0.84 124 (19) Kim06a Cu(Ga0. 3,In0. 7) CuSe CIGS ~260 C 0.45~0.58 144 (17) This w o r k Cu-Ga CuSe CGS ~300 C 0.55~0.61 109 (7) Kim06b Each precursor film (i.e., Cu-In, Cu-Ga and Cu-Ga0.3-In0.7) was prepared on a Mo-coated thin glass substrate by co-depos ition of elements without heat ing the substrate. During the selenization of Cu-Ga and Cu-Ga-In prec ursors, the formation of CuSe followed by CGS and CIGS formation was detected, while the selenization of Cu-In precursor showed a different reaction sequence, i.e ., CuSe formation followed by CuSe2 and then CuInSe2. Additionally, the production of MoSe2, accompanied by a decrease of Mo (110)

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168 reflection intensity, was obser ved in experimental results with three precursors. The formation temperature of CGS (~300 oC), as estimated by temperature ramp anneal at a rate of 20 oC/min, was relatively higher than that of CIS (~250 oC) and CIGS (~260 oC). The Avrami model analysis suggested the formation of CIS, CGS and CIGS from selenization of their metallic precursors follo ws one-dimensional, diffusion-controlled reaction pattern along with an activation energy range of 110 to 140 kJ/mol. The formation of CGS, which has the highest formation temperature (~300 oC), showed the lowest apparent activation en ergy of 109 (7) kJ/mol. The reaction rates for selenization of Cu-In, Cu-Ga, and Cu-Ga-In metallic prec ursors were compared using Avrami kinetic constants, as shown in Figure 6-11. The co mparison revealed that the selenization rates of Cu-In and Cu-Ga-In ([Ga]:[In]~30:70) are similar to each other, but considerably higher than that of Cu-Ga precursor. Figure 6-11. Comparison of reaction rates for selenization of different metallic precursors estimated by the Avrami model.

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169 6.4 Summary The reaction pathways and chemical kine tics of Cu(In,Ga)Se2 formation from glass/Mo/Cu-Ga-In precursor were investigated using time-resolved, in situ hightemperature X-ray diffraction equipped with a graphite dome. The results show that the selenization of glass/Mo/Cu-Ga-In produces an intermediate CuSe phase in the temperature range 260 to 370 C. The formati on of CIGS is initiated at approximately 260 C, which is close to the temperature of the initial appearance of CuSe. The MoSe2 formation was detected at a temperature a bove approximately 400 C. The estimated Ga composition of the CIGS suggested the partia l loss of indium duri ng temperature ramp selenization. The Avrami model analysis suggested that the Cu(In,Ga)Se2 formation by the selenization of glass/Mo/Cu-Ga-In precursors could be described by a onedimensional diffusion controlled reaction pro cess yielding an apparent activation energy of 144 (17) kJ/mol. This value of activa tion energy is higher than that (i.e., 109 7 kJ/mol) estimated for the CuGaSe2 forma tion from selenization of glass/Mo/Cu-Ga precursor. It is concluded that the Cu-Ga -In selenization follows a pathway along a onedimensional diffusion-controlled reaction that takes place in concert with a nucleation and growth mechanism.

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170 CHAPTER 7 DIFFUSION MODELING OF CU-IN SELENIZATION 7.1 Introduction In the previous Chapters 4 through 6, it wa s experimentally demonstrated that the Cu(In,Ga)Se2 formation by annealing bilayer bi nary precursors (i.e., InSe/CuSe [Kim05a], In2Se3/CuSe [Kim05b] and GaSe/CuSe) a nd selenizing metallic precursors (i.e., Cu-In [Kim06a], Cu-Ga [Kim06b] and Cu-In-Ga [Kim06c]) follow a onedimensional diffusion controlled reaction patte rn. To simulate these diffusion-controlled transformations, both thermodynamic and kinetic descriptions are essential. Thus the results of simulations and their accuracy cr itically depend on the quality of these descriptions. A complete thermodynamic description consists of Gibbs energy expressions for every phase in the system and kinetic descriptions pr ovide expressions for the mobility of every species in each phase and the rate constants for chemical reaction of all phases and species. The software Ther moCalc and DICTRA (DIffusion-Controlled TRAnsformation) [Bor00] considers the ther modynamic and diffusion information, and execute two main functions. One is to evaluate the model parameters of the thermodynamic and kinetic parameters. The other is to perform simulation of the thermodynamic and kinetic behavior of a system. The Main features of ThermoCalc and DICTRA are (1) capability to predict thermodynamic and kinetic behavior of a highe r order system based on the information of its sub-systems, (2) capability to predict th ermodynamic and kinetic behavior of a system

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171 under conditions where no experimental data ar e available, and (3) reduction of storage of data. Our research group has been working on establishing the ther modynamic database of subternary (i.e., Cu-In-Se [S he06]), pseudo-binaries (i.e., Cu2Se-In2Se3 and Cu2SeGa2Se3) and sub-binaries (e.g., Cu-Se, In-Se, Ga-Se [Ide03]) of the quaternary Cu-In-GaSe system using ThermoCalc pr ogram and EMF measurements. The DICTRA package is a flexible system for simulation of diffusion-controlled transformations in multi-component alloys and has been employed successfully to simulate complex systems, e.g., heat treat ments of multi-component alloys [Hg97]. The DICTRA program, however, can only handle simple geometries such as planar, cylindrical and spherical, of which all can be reduced into one space variable. Also, unfortunately the mobility or diffusivity information on Cu-In-Ga-Se and its subsystems is not well established. In this work, an at tempt was made to estimate mobility in the CuIn-Se system by analysis of the in situ HT-XRD measurements using the DICTRA program. 7.2 Multi-component Diffusion Theory In the presence of a concentration gradie nt, a net flux of the corresponding species follows Fick’s first law, which, in the isothermal and isobaric one-phase binary alloy with diffusion of species k in only the z direction, is expressed as z c D Jk k k (7-1) where Jk is the interdiffusion flux defined with respect to the fixed-volume, ck is the concentration of k and Dk is the diffusivity or the interdiffusion coefficient of species k [Bor00].

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172 Fick’s first law is not very useful by itsel f, but its combination with the continuity equation leads to the fundamental diffusion equation, which is usually called Fick’s second law. k kJ z t c (7-2) z c D z t ck k k (7-3) In multi-component systems, it is noted that the diffusivity (Dk) in equation (7-1) not only depend on concentration but also on the concentration gradients. The multicomponent extension to Fick’s first law was first expressed by Onsager [Ons31a, b], who postulated that each thermodynamic flux was linearly related to every thermodynamic force. Thus, in the same cas e of equation (7-1), we have z L Ji n i ki k 1 (7-4) where i is the chemical potential for each species which may be assumed to be a unique function of the composition, i.e., i = f ( c1, c2, ….., cn) and 'kiL can be considered as a proportional factor which depends on the mobility of the individual species. The flux, Jk, is defined as 01 n i k kJ V (7-5) where Vk is the volume of each species. Generall y, however, it is much more convenient to express the fluxes as functions of gradient in concentration rather than gradient in chemical potential, which can be obtained by ap plying the chain rule fo r derivation, i.e.,

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173 z c c L Jj n j j i n i ki k 1 1 (7-6) or equivalently, z c D Jj n j kj k 1 (7-7) and j i n i ki kjc L D 1 (7-8) where i/cj values are purely thermodynamic quant ities, sometimes referred to as thermodynamic factors. It is thus evident th at the diffusivities can be composed of two separate terms, purely thermodynamic part and kinetic part, which will be described later. The n concentration gradients in equation (7-7) are not independent and, for practical calculations, one usually eliminates one of them. The reduced diffusivities in a fixed volume frame of reference, where it is assumed that all the substitutional species have the same partial molar volumes and fu rthermore only the substitutional species contributes to the volume, are expressed as kn kj n kjD D D (when j is substitutional) (7-9) kj n kjD D (when j is interstitial) (7-10) where the concentration gradient of n has been eliminated. By applying this simplification, equation (7-7) becomes z c D Jj n j n kj k 1 1 (7-11) This equation suggests the possibility that the concentration grad ient of one species may cause another species to diffuse, whic h was proposed [Dar42] and experimentally verified [Dar49] by Darken. In his experime nt, two Fe-Si-C steels with similar carbon

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174 content, but with different si licon content, were welded t ogether and annealed. It was observed that carbon diffused from low carbon co ncentration to high concentrations, socalled up-hill diffusion. By combining equation (7-11) with equati on (7-2), the coupled partial differential equations (PDE’s), which are suitable for practical calculations in multi-component system, are obtained. If all n kjD are constant, it is possible to obtain analytical solutions [Gup71], but generally numerical met hods must be used as in DICTRA. 7.3 Thermodynamic and Kinetic Basis for DICTRA As described in the previous section, it is evident that the simulation using the DICTRA program requires both thermodynamic a nd kinetic information. The calculation of phase diagram (CALPHAD) method, estab lished by the pioneering work of Kaufman and Bernstein [Kau70], is one of most power ful techniques to calcu late phase diagrams using thermodynamic data. In the CALPHAD me thod, the Gibbs energy of an individual phase is modeled as a function of temperat ure, composition, and sometimes pressure. The equilibrium at given conditions is simp ly calculated by a Gibbs energy minimization procedure. The thermodynamic parameters in the Gibbs energy models are evaluated from the available thermodynamic information by an optimization program, e.g., PARROT [Jan84] in ThermoCalc. Inspired by the CALPHAD method, Ande rsson and gren [And92] suggested a similar method to calculate kinetic data, wh ich represents the atomic mobility of the individual species in a multi-component phase as a function of temperature, pressure, and composition. From absolute-reaction rate th eory arguments, they expressed the mobility

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175 coefficient for element B (BM) in terms of a frequency factor (0 BM) and an activation enthalpy (BQ) such as RT Q RT M MB B Bexp0 (7-12) where R is the ideal gas constant and T is the absolute temperature. In general, both 0 BM and BQ depend on temperature, pressure and com position. In the same manner as the CALPHAD approach, they represente d the composition dependency of 0 BM and BQ as a linear combination of the values at each end-point of the composition space and a Redlich-Kister expansion, i.e., r j i j i B r ij j i i i B i Bx x x x x ) (, 1 (7-13) where B represents 0lnBM or BQ. The i B and j i B r terms are the B values for pure i element and the binary interaction parameter between i and j elements, respectively. The xi and xj are the mole fractions for i and j elements. Each individual model parameter (i.e., i B and i B r ) is stored in the DICTRA database and may be expressed as a polynomial in temperature and pressure, if necessary. In the CALPHAD method, the model parameters (i.e., i B and j i B r ) are determined by an optimization procedure using experimental information. The reason to store the individual mobilities in the DICTRA database instead of the interdiffusion coefficients is to reduce the data storage requirement. The interdiffusion coeffi cients can be calculated from the element mobilities and thermodynamic factors using equation (7-8). Further information on DICTRA is available in the DICTRA manual and review paper [Bor00].

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176 7.4 Diffusion Modeling of Seleni zation of Cu-In Precursor 7.4.1 Kinetic Experiments Reaction kinetics of -CuInSe2 (CIS) formation from Cu-In/Mo/glass precursor during selenization was investigated using in situ high-temperature X-ray diffraction [Kim06a], as described in chapter 3. Since the kinetic data obtained from XRD analysis were well fitted with the parabolic rate mode l, it was concluded that the reaction follows one-dimensional diffusion controlled reaction pa ttern. By assuming that the total film thickness is 2 micron and the fr actional reaction of CIS is directly proportional to the thickness of CIS layer via one-dimensional gr owth model, the CIS thickness profile is obtained with respect to time, as shown in Fi gure 7-1. This kinetic result was used as input data for DICTRA modeling. Figure 7-1. The CIS thickness vs. tim e obtained from kinetic experiment.

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177 In the kinetics experiment, the overall atom ic composition ([Cu]/[In] = 1.0) of the as-deposited Cu-In/Mo/glass precursor film was determined by inductively coupled plasma optical emission sp ectroscopy (ICP-OES) and it s phase constitution (Cu2In, CuIn and In) was identified by both -2 and grazing incident Xray diffraction (GIXD). Therefore, the overall selenization of Cu-In precursor to yield -CuInSe2 is expressed as mCu2In + nCuIn + mIn + (4m+2n)Se (2m+n)CuInSe2 (7-14) Unfortunately, the current version of DI CTRA program can not handle external boundary conditions in conjunction with stochi ometric phases and this problem becomes more evident in ternary or higher order syst em. Although the system of interest is nonstoichiometric, it will be simplified as a stoichiometric one. Thus reacting system is a pseudo-binary system by considering the Cu-In precursor as a single element. Since the atomic composition of Cu-In precursor wa s determined as [Cu]/[In]~1.0, the stoichiometric Cu1In1 compound was assumed as a single reacting element. Therefore, the simplified pseudo-binary reaction is expressed as CuIn + 2Se CuInSe2 (7-15) and schematically shown in Figure 7-2. Figure 7-2. The schematic diagram of the simplified reaction of CuInSe2 formation from selenization of Cu-In precursor. CuIn CuIn Se vapor Se vapor CuInSe2

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178 7.4.2 Diffusion Modeling Using DICTRA As mentioned in section 7.3, the diffusion coefficient of each element is calculated by the product of a thermodynamic factor and a kinetic factor. Thermodynamic database of Cu-In-Se ternary system was recently esta blished by the assessment of experimental phase diagrams [Gd00a, Gd00b, Gd00a], EMF measurement of ternary compounds [Ide03] and thermodynamic models of sub-bina ries (i.e., Cu-Se, In-Se and Cu-In), as described in chapter 3. Therefore, th e thermodynamic information for the ternary CuInSe2 and elemental Se is available. The thermodynamic information of CuIn compound, however, is not obvious because th e CuIn compound is not included in the assessed Cu-In binary phase diagram [Liu02] and thus in the Cu-In-Se ternary phase diagram either. The identification of the Cu In compound was reported in several papers [Pis03, Son03, Mat97]. Pisarkiewicz et al. observed the CuIn phase along with Cu2In, Cu11In9 and CuIn2 in the multilayer metallic Cu/In precursor film fabricated by magnetron sputtering [Pis03]. Similarly, Song et al. reported that the CuIn phase was identified in the multilayer Cu-Ga-In precu rsor film deposited on glass by DC magnetron sputtering [Son03]. Thus, it is evident that the CuIn compound forms, but is likely to be a metastable phase. In this work, the metastable CuIn phase was intentionally added to the Cu-In thermodynamic database by optimizing thermodynamic parameters while retaining the existing Cu-In phase diagram and equilibrium phase relationships, as shown in Figure 7-3. Thus, the thermodynamic inform ation for the CuIn phase can be calculated.

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179 Figure 7-3. The modified Cu-In phase diagram including metastable CuIn phase In the current DICTRA simulation, only three phases (i.e., -CuInSe2 (CIS), CuIn and Se) are considered, as shown in Figure 72. It is also assumed that Se diffuses through CIS layer to reach the interface of CIS-CuIn and then reacts with CuIn to form additional CIS. Therefore, the driving force for the growth of -CuInSe2 would be the difference of Se chemical potential between the top (i.e., Se-CIS interface) and bottom (i.e., CIS-CuIn interface) part of CIS layer. The mobility parameters of Se in CIS phase are evaluated by DICTRA optimization to fit th e kinetic experimental data. In DICTRA database, the mobility parameter, MQ, is expressed as a function of temperature such as 0lnB BM RT Q MQ (7-13)

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180 where the 0 BM is a frequency factor and the BQ is an activation enthalpy as described in equation (7-12). The numerical optimization using the given experimental data yielded these mobility parameters as ) 01406 0 ln( 725 136 ln0RT M RT Q MQB B [J/mol] (7-14) and thus, 725 136BQ [J/mol] (7-15) 0.014060BM (7-16) Figure 7-4. The comparison of CIS growth rates between the DICTRA prediction (solid lines) and experiments (symbols). It is interesting to note that the va lue of resultant activation enthalpy (BQ~137 kJ/mol) is close to the activation energy (Ea = 100 14 kJ/mol) estimated by parabolic growth model using experimental data [K im06a]. The growth rates of CIS layer

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181 predicted by DICTRA simulation agree well wi th the experimental results as shown in Figure 7-4. 7.5 Summary Based on the kinetic data obtained by in situ time-resolved, high-temperature X-ray diffraction, the DICTRA simulation on the CIS formation by selenization of Cu-In precursor was performed. Due to the limita tion of current versi on of DICTRA program, the target reaction system was simplified as CuIn + 2Se CuInSe2. For this simple reaction, the reliable mobility parameters of Se were obtained by the optimization using experimental data. Accordingly, it is evident that the predicted growth rates of CIS agree very well with the experimental results. In terestingly, the calculated activation enthalpy (BQ~137 kJ/mol) is similar to the activation energy (Ea = 100 14 kJ/mol) estimated by parabolic growth model using experimental data.

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182 CHAPTER 8 DEFECT CHARACTERIZATION BY DEEP LEVEL TRANSIENT SPECTROSCOPY (DLTS) TECHNIQUE 8.1 Introduction The large composition homogeneity range a nd the deviation from stoichiometry in compound semiconductors such as Cu(In,Ga)Se2 (CIGS) are attributed to defects in material such as anti-site defects, vacancies, interstitials, and defect clusters. It is well known that CIGS films can be produced in both pand n-type conductivities by introducing native defects with or without extrinsic impurities. The doping mechanism and point defect chemistry of CIGS, however are not well understood at the fundamental level. Deep-level defects are known to play an important role in determining the recombination mechanisms, which directly cont rol minority carrier lifetimes and thus cell efficiency in p-n junction solar cells. Ther efore, it is extremely important to understand defect properties to further improve th e cell efficiency of solar cells. The deep level transient spectroscopy (DLTS) technique is a powerful tool for determining the defect energy level, capture cross-section, and trap density [Lan74]. Several DLTS results on CIGS-based solar cells have been reported by Igalson [Iga00, Iga01, Iga02, Iga03]. They have employe d conventional DLTS, reverse-bias DLTS, and Laplace transform analysis of cap acitance transients to inves tigate the defect spectra in the bulk and at the interface of standard Zn O/CdS/ Cu(In,Ga)Se2 devices. They also used a modified DLTS that combines junc tion spectroscopy with il lumination in a double pulse approach to identify the minority carrier traps acting as recombination centers in

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183 the CIGS absorber layer. Bhattacharya et al. at NREL reported DLTS results for CdS/CIGS-based cells prepared from solu tion-based electroplated and auto-plated precursors, and by physical vapor deposition [B ha01]. In a previous study that included this author, DLTS analysis was performed on CIS and CIGS-based solar cells produced by NREL, EPV and UF [Ker04]. In this chap ter, the experimental setup and operation procedures for the DLTS system are describe d, and DLTS measurem ents were conducted on several CISand CIGSsolar cells. 8.2 Operation Principle of DLTS Technique The DLTS technique is base d on the transient capacitance change associated with the thermal emission of charge carriers from a trap level to thermal equilibrium after an initial non-equilibrium condition in the space-charge region of a Schottky barrier or a p-n junction diode. The polarity of the DLTS peak depends on the capacitance change after trapping the minority or majority carriers. In general, a minority ca rrier trap produces a positive DLTS peak, while a majority carrier trap yields a negative DLTS peak. If an abrupt junction with Nt << Nd is assumed in a p-n junction diode, the change of transient capacitance can be simplified to /) 0 ( ) (te C t C (8-1) where Nt is the trap density, Nd is the background doping density, and is the reciprocal emission time constant. The DLTS scan along the temperature axis is obtained by taking the difference of equation (8-1) at preset t1 and t2 rate windows, as expressed by / / 2 12 1) 0 ( ) ( ) ( ) (t te e C t C t C S (8-2) The maximum emission rate, 1/ max, can be obtained by setting dS( )/d =0, which yields

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184 ) / ln(2 1 2 1 maxt t t t (8-3) It is noted that the DLTS signal, S( ), reaches its maximum at max corresponding to the characteristic temperature, Tm. In the DLTS operation, max is controlled by a manipulated variable called “delay time”, a nd a set of characteristic temperatures (Tm) are obtained at different delay time variables (~ max) For an electron trap in a p-n juncti on diode, the electron emission rate ( en) can be expressed by kT E g N v ec th n n exp 1 1 (8-4) where n is the electron capture cross-section, < vth> is the average thermal velocity, Nc is the effective density of conduction band states, g is the degeneracy factor, and E is the activation energy of the electron trap. Since Nc and < vth> are varied with temperature to T1.5 and T0.5 respectively, equation (8-4 ) can be expressed as kT E A T T en n exp 12 2 (8-5) where A is a proportionality constant. The DLTS thermal scans provide information about characteristic temperatures (Tm) corresponding to the maxi mum DLTS signal at the pre-set delay time (~ max). Therefore, the capture cross-section ( n) and trap activation energy ( E) can be estimated from the Arrhenius plot as expressed by m n m m nT k E A T T e 1 ln 1 ln ln2 max 2 (8-6) Finally, assuming that the trap density is much smaller than the doping concentration, i.e ., Nt<
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185 d tN C C N 0) 0 ( 2, (8-7) where C(0) = C0-C(0) is the net capacitance change due to thermal emission of electrons from the trap level, C0 = C(VR) is the junction capacitance measured at a quiescent reverse bias voltage (VR), C(0) is the capacitance measured at t=0 and Nd is the background doping density. Further detailed de scription about the principles of DLTS can be found in other references [Li93]. Th e standard procedure to perform DLTS scan and data analysis to obtain the trap in formation is described in section 8.4. 8.3 Equipment Description of UF-DLTS System The UF Deep Level Transient Spec troscopy (DLTS) system, which was commercially developed by Sula Technologies, consists of a deep level spectrometer, a Lake Shore 331S temperature controller, a roughing pump, and a liquid nitrogen cryostat, which allows the temperature as low as 77K by combination with a variable speed circulation pump, is shown in Figures 8-1 a nd 8-2. The control unit of the deep level spectrometer is composed of five functional groups as shown in Figure 8-1. A pulse generator applies repetitive bias pulses to sample, and also provides 1 MHz test signal for capacitance measurements. The capacitance meter consists of an innovative selfbalancing bridge circuit that detects small, rapid change in capacitance following junction bias pulse. It can also be used for static capacitance-voltage (C-V) measurements. The correlator automatically re moves DC background from capacitance meter output and amplifies the resultant signal change. The transient is then analyzed using the rate window algorithm reported by Lang [Lan74]. Correlation is based on a modified double boxcar signal averaging technique.

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186 Figure 8-1. Schematic diagram of UF-DLTS system. Figure 8-2. Schematic top view of LN2 cryostat in the DLTS system. Cable to temperature controller Cable to DLTS unit Exhaust valve Rough p um p Circulation p um p

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187 Finally, an additional pulse generator and a correlator are used for spatial profiling of deep levels using Double Correlation D eep Level Spectroscopy (DDLTS). The second correlator can also be used to record simultaneously two DLTS spectra at different rate windows. The temperature controller is ope rated directly by computer and the control unit of the deep level spectrometer is connect ed to the computer via a BNC adaptor and NI-DAQ card. Figure 8-3. Simplified wiring diagram of UF-DLTS system.

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188 The Sula Technologies operating software developed using National Instruments LabVIEW (ver.5.1) is available both as a s ource code and as an executable program. Currently, a stand-alone executable program is installed in the DLTS system. The simplified wiring diagram is shown in Figure 8-3. The DLTS system was originally purchased from Sula Technologies in 1990, and recently (in 2003) some components were upgraded including operation software and temperature cont roller. The actual picture of upgraded UF-DLTS system is shown in Figure 8-4, and equipment specifications are summarized in Table 8-1. Figure 8-4. UF-DLTS system (Picture taken in 2004).

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189 Table 8-1. Equipment speci fication of UF-DLTS system. No. Components Vendor (Model) 1 DLS (Deep Level Spectrometer) Sula technologies 2 Operation software (executabl e version) Sula technologies 3 Temperature controller Lakeshore (331S) 4 LN2 cryostat Sula technologies 5 2-channel Oscilloscope (20MHz) Tequipment.net (Leader LS8022) 6 BNC adapter module National Instruments (BNC 2090) 7 Probe tips for electrodes Micromanipulator Co. (7B-100) 8 Circulation pump Walchem 406G 8.4 DLTS Measurement of CIGS Cells In this section, the detailed procedures to perform the DLTS scans, analyze the scan data, and then obtain the defect informa tion (defect activation en ergy, defect density and capture cross-section) are described us ing the DLTS results of CIGS solar cells provided by Energy Photovoltaic (EPV) Inc. 8.4.1 DLTS Scan First, a series of DLTS scans was taken at selected operation conditions with the different rate windows ( ). For the EPV-CIGS cells, a reverse bias (VR) of 0.4 V, a trapfilling pulse of 0.8 V, and a saturation pulse width of 10 ms were employed. During the DLTS thermal scans, the temperature ramping rate was limited at 0.1 K/sec or less for the precise temperature control.

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190 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0100200300400500 Temperature (K) C (pF) 1 ms 0.5 ms 0.2 ms 0.1 ms 0.05 ms 0.02 msReverse bias = 0.4 V Pulse height = 0.8 V Pulse width = 10 msDelay time Figure 8-5. DLTS scans for the EPV-CIGS cell at different delay times (0.02 to 1.0 ms). Since the sensitivity of the DLTS signal is generally proportional to C/C0, a smaller junction capacitance (C0) would provide a better sensitiv ity. It is also known that the junction capacitance is dir ectly proportional to the junctio n area for a given device. Therefore, the CIGS cell with a small area of 1 mm 0.8 mm was used to maximize the sensitivity of the DLTS signal. As shown in Figure 8-5, a majority carrier (i.e., hole) trap was observed from the DLTS scans. Based on Figure 8-5, characteristic temperatures (Tm) were obtained at different rate windows ( ), as summarized in Table 8-2. In the UF DLTS system, a rate window ( ) is calculated by multiplying the preset delay time by a proportional factor (=4.3), e.g., = 4.3 delay time. It is also noted that the characteristic temperatures (Tm) can be estimated from both the heating and cooling cycles of the DLTS scans for given delay times. For the reasonably low temperature

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191 ramp rate, both heating and cooling scans are expected to provide similar results. As shown in Table 8-2, the Tm values obtained by heating scan s are much higher than those by cooling scans for delay time 0.05 ms, while both results are almost identical for delay time 0.1 ms. Therefore, the average values of Tm were used for the subsequent analysis. Table 8-2. DLTS scan results of EPV-CIGS cells at a reverse bias (VR) of 0.4 V, a trapfilling pulse of 0.8 V, and a satu ration pulse width of 10 ms. Delay time (ms) Rate window, (sec) Tm by cooling (K) Tm by heating (K) Ave. Tm (K) 0.02 0.000086 238.5 257.5 248.0 0.05 0.000215 232.5 241.5 237.0 0.1 0.00043 224.7 224.5 224.6 0.2 0.00086 213.7 214.5 214.1 0.5 0.00215 198.5 198.5 198.5 1.0 0.0043 187.4 187.5 187.5 8.4.2 Estimation of Trap Activation Energy and Capture Cross-section To estimate the trap activation energy and capture cross-section, Arrhenius plot is used as expressed by m n m m nT k E A T T e 1 ln 1 ln ln2 max 2 (8-6) and is graphically shown in Figure 8-6. The results represent the hole trap activation energy ( E=Et-Ev) of 0.20 0.0076 eV which is similar to that of VIn (0.17 eV) calculated by Zhang [Zha98], and capture cross-section ( p) of 3.1 10-24 cm2. In these DLTS measurements, it was assumed that the capture cross-section ( p) is independent of temperature. However, more generally, the capture cross-section ( p) can be expressed by kT E pbe/ 0 (8-8)

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192 where 0 is the capture cross-section when temperature approaches infinity, and Eb is the activation energy of capture cross-section. -6 -5 -4 -3 -2 44.555.5 1000/T, (K-1) ln(en/T2) E ~ 0.20 ( 0.0076) eV Figure 8-6. Arrhenius plot of DLTS scans for EPV-CIGS cells. 8.4.3 Estimation of Trap Density In DLTS analysis, a trap density is calculated approximately by a tN C C N 0) 0 ( 2 (8-9) The variables in equation (8-9), howev er, have different values depending on characteristic temperatures (Tm) listed in Table 8-2. First, in the DLTS system, C(0) is obtained directly from DLTS signal correspond ing to the characteris tic temperature at different delay time. The C0 is the junction capacitance m easured at a quiescent reverse bias voltage (VR), which also depends on temperature.

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193 30 35 40 45 50 55 60 50100150200250300350 Temperature (K)Capacitance (pf)Reverse bias = 0.4 V Figure 8-7. Capacitance-temperat ure scan for a EPV-CIGS cell at a reverse bias of 0.4 V. To get C0(T, VR), an additional capacitance-temperature (C-T) scan should be performed at given reverse bias, e.g., VR = 0.4 V in this case, as shown in Figure 8-7. Finally, the background doping density, Na, can be estimated by capacitance-voltage (CV) measurements at different temperature. For an asymmetrically doped abrupt junction, junction capacitance is simplified to a bi s aV V A qN C 2 0 22 1 (8-10) where C is the junction capacitance, q is the electronic charge (~1.610-19 C), s is the dielectric constant, 0 is the permittivity of free space (~8.8510-12 F/m), A is the area of diode, Vbi is the built-in voltage of device and Va is the applied voltage. Equation (8-10) shows that Na can be extracted from the slope for a linear plot of 1/C2 vs. Va, and Vbi is estimated from the intercept of plot..

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194 30 40 50 60 70 80 -2-1.5-1-0.500.5 Applied voltage (V)Capacitance (pf)100 200 300 400 5001/C2 *106248K 237K 224K 214K 198K 187K 248K Figure 8-8. Capacitance-vol tage (C-V) measurement fo r EPV-CIGS at different temperatures. For different temperatures, capacitancevoltage (C-V) measurement results are shown in Figure 8-8. As shown in Figure 8-8, the 1/C2 vs. Va plot for CIGS cell does not show a straight line, which suggests a non-uni formity of doping concentration. Therefore, average doping density is used to estimate a trap density. Finally, the calculated trap densities are summarized in Table 8-3. Table 8-3. Trap density calculation fro m DLTS analysis of EPV-CIGS cell. Delay time (ms) Ave. Tm (K) C(0) (pF) C0 (pF) Na (cm-3) NT (cm-3) 0.05 237.0 0.5296 45.80 1.31 1015 3.03 1013 0.1 224.6 0.4628 44.00 1.34 1015 2.82 1013 0.2 214.1 0.3949 42.54 1.35 1015 2.51 1013 0.5 198.5 0.3128 40.31 1.38 1015 2.14 1013 1.0 187.5 0.2772 38.94 1.40 1015 1.99 1013

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195 The DLTS analysis for the NREL-CIGS cell was also performed by following the same procedure. The results revealed a minority carrier trap with an activation energy of E = 0.069 eV. Interestingly, this value is identical to our previous result ( E = 0.07 eV) [Ker04] estimated for another NREL-CIGS ce ll by using the NREL DLTS system, which clearly demonstrates the reliability of our DLTS system. The DLTS results of both EPVCIGS and NREL-CIGS cell are summarized in Table 8-4 and 8-5, respectively. 8.5 Summary The UF-DLTS system was successfully upgraded and its parameters were reasonably optimized. The detailed system description including an equipment specification was summarized, and the sta ndard operation procedure (SOP) was illustrated using the DLTS results of EPV-CIGS cell. A comparison of the trap activation energy estimated by our DLTS system with that by NREL DLTS system demonstrates a good reliability of our system.

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196 Table 8-4. Summary of DLTS analysis for EPV-CIGS cell. Delay time (sec) Tm (K) CoolingTm (K) HeatingTm(H)-Tm(C)Ave. Tm1000/TLn(T2/En) 0.020.000086238.5257.5192484.0323-1.6657 0.050.000215232.5241.592374.2194-2.4912 0.10.00043224.7224.5-0.2224.64.4524-3.0769 0.20.00086213.7214.50.8214.14.6707-3.6743 0.50.00215198.5198.50198.55.0378-4.4393 10.0043187.4187.50.1187.455.3348-5.0179 slope-2264.45 Y-intercept7.000 kB8.62E-05eV/K E -0.195eV 3.12E-24 cm 2 .Delay time Ave. Tm C(0) C0(Tm)Na(Tm) 0.052370.529645.81.31E+15 0.1224.60.4628441.34E+15 0.2214.10.394942.541.35E+15 0.5198.50.312840.311.38E+15 1187.450.277238.941.40E+15DLTS Analysis EPV (VR/Pulse = 0.4/0.8)NT3.03E+13 2.82E+13 2.51E+13 2.14E+13 1.99E+13 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0100200300400500600700800 Temperature (K) C (pF) 1 ms 0.5 ms 0.2 ms 0.1 ms 0.05 ms 0.02 msReverse bias = 0.4 V Pulse height = 0.8 V Pulse width = 10 msDelay time -6 -5 -4 -3 -2 44.555.5 1000/T, (K-1) ln(en/T2) E ~ 0.20 ( 0.0076) eV

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197 Table 8-5. Summary of DLTS analysis for EPV-CIGS cell. Delay time (sec) Tm (K) CoolingTm (K) HeatingTm(H)-Tm(C)Ave. Tm1000/TLn(T2/En) 0.020.000086 0.050.0002151201208.333333-1.13011 0.10.000431121128.928571-1.68527 0.20.000861041049.615385-2.23020 0.50.00215979710.30928-3.00713 10.0043888811.36364-3.50553 slope-805.00 Y-intercept5.505 kB8.62E-05eV/K E -0.069eV 1.39E-23 cm2Delay time Ave. Tm C(0) C0(Tm)Na(Tm) 0.051200.85688.073.72E+15 0.11120.732586.1653.64E+15 0.21040.637183.43.57E+15 0.5970.499481.53.56E+15 1880.422879.6854.45E+15 5.45E+13 4.36E+13 4.72E+13DLTS Analysis NREL-CIGS (VR/Pulse = 0.5/0.7)NT7.23E+13 6.19E+13 -4 -3 -2 -1 89101112 1000/T, K-1ln(en/T2) 0 0.2 0.4 0.6 0.8 1 0100200300400500 Temperature (K) C (pF) 0.05 ms 0.1 ms 0.2 ms 0.5 ms 1 msReverse bias = 0.5 V Pulse height = 0.7 V Pulse width = 10 ms

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198 CHAPTER 9 CONCLUSIONS AND FUTURE WORK A thermodynamic description for the Cu -Se binary system was successfully established using the abundant experimental data, recent evaluation by Glazov [Gla00], and previous optimization work by Chang [C ha99]. Sub-lattice models with various constitutions were reasonably applied to desc ribe the Gibbs energy of different phases of the system. Furthermore, these Cu-Se optim ization results were utilized to obtain a reliable set of expressions for Gibbs energy for solution in the ternary Cu-In-Se system. The EMF experimental results, defect formation energy by ab initio calculation, and phase equilibrium data were integrated to ob tain a reliable set of expressions of Gibbs energy for ternary solution in the Cu-In-Se system. The Cu-Ga-In ternary phase diagram was predicted by a Maggianu’s equation base d on the sub-binary phase diagrams. Subsequently, the predicted ternary phas e diagrams were modified using recent experimental data. Since the assessment of the Cu-In-Se and Cu-Ga-In ternary systems was performed by now, it is proposed to conti nue the research on Cu-Ga-Se and Ga-In-Se phase diagrams to predict the complete thermochemistry of the quaternary Cu-In-Ga-Se system. In situ high-temperature X-ray diffraction tec hnique was successfully employed to investigate the reaction pathwa ys and phase evolution of bi nary Cu-Se, In-Se and Ga-Se compounds. It is concluded that the overall phase transformati on of binary metal (Cu, In and Ga)-Se compounds qualitatively fo llows the sequence predicted by the thermodynamic phase diagram, but the detaile d reaction path of each binary compound

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199 depends on the as-deposited precursor struct ure and starting compounds. As future work, the isothermal soaking experiments charac terized by TEM-EDS as well as HTXRD are suggested to estimate the kinetic parameters (e .g., rate constants and activation energies) and species diffusivities, which are essential to the development of robust process model. Reaction pathways and kinetics of polycrystalline -CIS, CGS, and CIGS formation were systematically investigated using thermal annealing of stacked bilayer and intimately mixed monolayer precursor, and selenization of elementally mixed metal precursors. Generally, ann ealing of precursors having di fferent structures follows different reaction routes and thus yields slightly differe nt initiation temperature of Cu(InxGa1-x)Se2 formation. The selenization chamber using selenium powders (or small pellets) was successfully employed, and the MoSe2 formation was always clearly observed during selenization. The results of reaction kinetic s using Avrami and parabolic growth models are summarized in Table 9-1. Table 9-1. Summary of reaction kinetics of Cu(InxGa1-x)Se2 formation from different precursor structures Avrami model Parabolic Precursor Ambient Product Tf (product) [ C]* n Ea (kJ/mol) Ea (kJ/mol) **InSe/CuSe Air CIS 220 0.6-0.866 65 In2Se3/CuSe He CIS 250 N/A N/A 162 5 InSe/Cu-Se He CIS 230 CuSe/In-Se He CIS 220 Cu-In-Se He CIS 140 N/A N/A N/A Cu-In He/Se CIS 270 0.6-0.8 124 19 100 14 GaSe/CuSe He CGS 260 0.7 124 19 115 16 Cu-Ga-Se He CGS 280 0.1-0.2 197 50 N/A Cu-Ga He/Se CGS 300 0.6 109 7 N/A Cu-Ga-In He/Se CIGS 260 0.5-0.6 144 17 N/A Tf(product): Temperature of product formation ** InSe/CuSe: Data cited from our previous publication [Kim05a]. The results summarized in the Table 91 lead to the following conclusions:

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200 1. Formation temperatures of CGS (i.e., 260 to 300 C) are relatively higher than those of CIS (i.e., 140 to 250 C) and CIGS (i.e., 260 C). 2. The Cu(InxGa1-x)Se2 formation from thermal anneali ng of binary bilayer precursors and selenization of metallic precursors follows one-dimensional diffusion controlled reaction, while Cu(InxGa1-x)Se2 formation from intimately mixed precursors (e.g, Cu-In-Se and Cu-Ga-Se) does not. 3. The lowest temperature to form CIS is identified as ~140 C, which is achieved by thermal annealing of intimately mixed Cu-In-Se precursor. 4. The Cu(InxGa1-x)Se2 formation by thermal annealing of binary bilayer precursors follows both a simple parabolic rate and Avrami growth model, except for crystalline/crystalline bilayer precursor (e.g., In2Se3/CuSe), which is only explained by a parabolic rate model. 5. The Cu(InxGa1-x)Se2 formation by selenization of elemental metal mixtures (e.g, Cu-In, Cu-Ga, Cu-In-Ga) follows a one-d imensional diffusion controlled reaction with a nucleation and growth sequence. DICTRA simulation of CIS formation by selenization of a Cu-In precursor was performed using the kinetic resu lts obtained by time-resolved, in situ HTXRD along with thermodynamic descriptions achieved in chapte r 2 and already available in literature. Due to the limitation of current version of DICTRA program, however, the target reaction system was simplified as a pseudo-binary reaction, CuIn + 2Se CuInSe2, for which the reliable mobility parameters of Se were obtained.

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201 APPENDIX A EXPLORATION OF MEDICI SIMULA TION OF CIGS SOLAR CELLS A.1 Overview of Medici Medici is a commercial device simulation program that can be used to simulate the behavior of semiconductor devices such as MOS and bipolar transistors [Med]. It models the two-dimensional distributions of potential and carrier concentrations in a device, and predicts electrical character istics for arbitrary bias c onditions. The program solves Poisson’s equation and both the electron and hole current-continuity equations to analyze devices such as diodes and bipolar transistors as well as effects in which the current flow involves both carriers, such as CMOS and latc h-up. It simulates the behavior of deep submicron devices by providing the ability to solve the electron a nd hole energy balance equations self-consistently with other devi ce equations. Basically, Medici uses a nonuniform triangular simulation grid, and can m odel arbitrary device ge ometries with both planar and non-planar surface topographies. The simulation grid can also be refined automatically during the solution process. This flexibility makes modeling of complicated devices and structures possib le. A number of physical models are incorporated into this program for accurate simulations, including models for recombination, photo-generation, impact io nization, band-gap na rrowing, band-to-band tunneling, and carrier mobility and lifetime. Medici also incorporates the Boltzmann and Fermi-Dirac statistics, including the in complete ionization of impurities. Due to the high cost and complexity, howev er, Medici has not been used for solar cell simulation as often as AMPS-1D (Ana lysis of Microelectronic and Photonic

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202 Structures) and SCAPS-1D (Sol ar cell CAPacitance Simulator in 1 Dimension). In a previous study, the effects of grain boundari es in the CIS absorber layer on the device performance of ZnO/CdS/CIS/Mo-glass sola r cells were successfully modeled using Medici [Yoo05]. A.2 Non-uniformity of Doping Concentration In chapter 8.4.3, the results of capacit ance-voltage (C-V) measurements on CIGS cell showed the non-linear plot of 1/C2 vs. V, which suggests a non-uniformity of doping concentration. A possible cause of the vari ation in doping concentr ation is Gagrading within CIGS layer, which is generate d unintentionally duri ng the CIGS deposition process (e.g., 3 stage process) or inten tionally by controlling th e composition of CIGS absorber. Unintentional proces s-related Ga grading is known to be a consequence of the Cu depleted absorber surface in high-effici ency CIGS cell [Dul01]. Dullweber et al. [Dul01] reported that the graded band gap re duces recombination in solar cell, and hence improve the open-circuit voltage. Furthermor e, appropriate band gap grading increases the short-circuit current by increasing light ab sorption and carrier collection, and thus the cell efficiencies. Song et al. [Son04] studied a variety of graded band-gap structures including space charge region (SCR) gradi ng, back surface region grading, and double grading of the CIGS absorber layer using AMPS-1D simulation program. They reported that an optimal band-gap profile, adopting a double grading consisting of the front spacecharge region (SCR) grading and back surf ace grading, improves significantly the cell efficiency up to 19.83% (AM1.5G) while the uniform band gap cell shows 15.42% efficiency. In this chapter, the simulation of C-V profile for band gap graded CIGS cell was carried out using Medici (Avant!) software with a band gap profile as input parameters.

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203 A.3 Medici Simulation of C-V Profile To verify the feasibility of Medici simulation for non-linear 1/C2 vs. V, two simplified CIS/CdS/ZnO solar cell structur es were used. One structure (e.g., CISuniform) has a uniform band-gap and doping co ncentration while the other (e.g., CISgrading) has a grading band gap and doping concentration pr ofile. The front and back contact electrodes, i.e., ZnO and Mo, were assumed to be Ohmic type. Most of the physical and electrical parameters of each la yer for both structures were cited in the previous Medici [Yoo05] and AMPS-1D [Son04] simulations, as shown in Table A-1 and Figure A-1. A band gap grad ing and doping profile for CIS-grading cell was used for this preliminary simulation. Table A-1. Design parameters of solar cell for Medici simulation. Layers Thickness (nm) Band gap Eg (eV) Electron affinity (eV) Doping (cm-3) Dielectric constant, CIS-uniform ZnO 50 3.3 4.00 5 1017 9 CdS 100 2.4 3.75 6 1016 10 CIS 2000 1.04 3.80 8 1016 13.6 CIS-grading ZnO 50 3.3 4.0 5 1017 9 CdS 100 2.4 3.75 6 1016 10 CIS-1 400 1.04 3.80 1 1015 13.6 CIS-2 400 1.1 3.78 5 1015 13.6 CIS-3 400 1.2 3.73 1 1016 13.6 CIS-4 400 1.3 3.69 5 1016 13.6 CIS-5 400 1.4 3.65 1 1017 13.6 The variation of Ga compositi on in CIGS films is expect ed to change the physical and electrical properties of the CIS films such as band gaps, hole concentrations [Sch99], bulk defect densities [Han01], absorption coe fficients and electron affinities. It is reported that the addition of Ga to CIS films increases the band gap by mainly lowering

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204 the position of the conduction-band minimum [W ei95], but makes a negligible change in mobility at room temperature [Sch99]. 0 20 40 60 80 100 120 140 00.511.52 Distance from junction (micron)Carrier concentration / 1015 (cm-3)0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Band gap (eV)Doping concentration Band gap grading Figure A-1. A bandgap and doping pr ofile for CIS-graded solar cell. As shown in Table A-1, different para meters (e.g., electron affinities and doping density) for the band gap graded CIS layers were applied in this Medici simulation. The light absorption coefficient profiles for the CI S layers with different band gaps and other layers were summarized in Figure A-2. In this preliminary simulation, defect densities were not considered. To obtain the C-V profile, an AC small signal analysis with a 1MHz frequency was performed for the applied reve rse bias range of -2 to 0V. The C-V simulation results for CIS-uniform and CIS-gr ading cells are shown in Figure A-3. As revealed in Figure 8-11, a uniform band gap CIS cell shows a linear 1/C2 vs. V relationship which is a conventional behavior for a one-side abrupt p-n junction diode, while a band gap graded CIS cell follows a non-linear 1/C2 vs. V relationship which is similar to the behavior of a traditional CIGS cell measured in Figure 8-8.

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205 Figure A-2. Absorption coefficient profiles for the materials used in Medici simulation. Figure A-3. Medici simulati on results on C-V profile for th e uniform doping and graded doping CIS cells.

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206 A.4 Medici Simulation on Gr ading Band Gap CIGS Cell Based on the preliminary results, more deta iled CIGS cells with a graded band gap were designed for the performance simulati on. Basic design parameters of each layer were determined with reference to our AM PS-1D simulation work [Son04] on the CIGS cells with various band gap profiles. It is note d that, in this simulation, two layers with a high recombination interface layer (HRL in Table A-2) and an inverted surface layer (OVC in Table A-2) were added to the model with an effective recombination center. An inverted surface layer, which is referred to as an ordered vacancy compound (OVC), is considered as a thin In-r ich n-type layer (e.g., CuIn2Se3.5 or CuIn3Se5) [Sch93] or a general surface defect layer [H er99, Gui98]. This layer can improve the cell performance since the electrical juncti on is shifted away from the high-recombination interface between the CdS and CIGS layers, and thus the recombination rate decreases [Son04]. Table A-2. Basic design parameters of solar cell for Medici simulation Layers Thickness (nm) Band gap Eg (eV) Affinity (eV) Doping (cm-3) Remark CIGS-uni n-ZnO 50 3.3 4.00 5 1017 n-CdS 30 2.4 3.75 6 1016 n-HRL 5 1.5 3.8 5 1014 n-OVC 30 1.3 3.95 3 1012 p-CIGS 1965 1.2 3.85 8 1016 Ea=40, 90 meV Ed=70 meV CIGS-grade n-ZnO 50 3.3 4.0 5 1017 n-CdS 100 2.4 3.75 6 1016 n-HRL 5 1.5 3.8 5 1014 n-OVC 30 1.3 3.95 3 1012 p-CIGS-1 865 1.16 3.87 8 1016 p-CIGS-2 220 1.2 3.85 8 1016 p-CIGS-3 220 1.24 3.83 8 1016 p-CIGS-4 220 1.3 3.80 8 1016 p-CIGS-5 220 1.35 3.77 8 1016 p-CIGS-6 220 1.4 3.75 8 1016 Ea=40, 90 meV Ed=70 meV

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207 As summarized in Table A-2 and A-3, it is assumed that the doping concentration, deep-level defect density and carrier life times ( n or p) are constant in the CIGS layers. Deep-level defect parameters of each laye r are summarized in Table A-3. In this simulation, an AM1.5 spectrum [ASTM G173] wh ich is used as a standard spectrum for solar cell application was adopted to improve the reliability of simulation results. Table A-3. Deep defect parameters of solar cells for Medici simulation Donor defects Acceptor defects Layers Ed (eV) Nd (cm-3) n (sec) p (sec) Ea (eV) Na (cm-3) n (sec) p (sec) CIGS-uni n-ZnO 1.7 1.5 1017 3.3 10-9 3.3 10-8 1.7 1.5 1017 3.3 10-8 3.3 10-9 n-CdS 1.2 1.0 1016 1.0 10-8 1.0 10-7 1.2 1.0 1016 1.0 10-7 1.0 10-8 n-HRL 0.8 1.0 1017 5.0 10-9 5.0 10-8 0.8 1.0 1017 1.7 10-7 1.7 10-8 n-OVC 0.7 8.0 1015 1.1 10-7 1.1 10-6 0.7 8.0 1015 1.1 10-6 1.1 10-7 p-CIGS 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 CIGS-grade n-ZnO 1.7 1.5 1017 3.3 10-9 3.3 10-8 1.7 1.5 1017 3.3 10-8 3.3 10-9 n-CdS 1.2 1.0 1016 1.0 10-8 1.0 10-7 1.2 1.0 1016 1.0 10-7 1.0 10-8 n-HRL 0.8 1.0 1017 5.0 10-9 5.0 10-8 0.8 1.0 1017 1.7 10-7 1.7 10-8 n-OVC 0.7 8.0 1015 1.1 10-7 1.1 10-6 0.7 8.0 1015 1.1 10-6 1.1 10-7 p-CIGS-1 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 p-CIGS-2 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 p-CIGS-3 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 p-CIGS-4 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 p-CIGS-5 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 p-CIGS-6 1.07 1.0 1015 9.1 10-7 9.1 10-6 0.87 1.0 1015 9.1 10-6 9.1 10-7 The current density-voltage (J-V) plots of uniform band gap and grading band gap CIGS cells predicted by Medici simulation ar e shown in Figure A-4. The performance parameters (e.g., Jsc, Voc, FF and ) obtained by Medici simulation were compared with the results of AMPS-1D simula tion [Son04] for the CIGS cells with the similar structure and device parameters in Table A-4. The comparison between the Medici and AMPS-1D

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208 simulations demonstrates that the simula tion results by Medici are acceptable even though further optimization of device parameters is necessary to achieve better reliability. Table A-4. Comparison of performance para meters of CIGS cells simulated by Medici Cell Jsc (mA/cm2) Voc (mV) FF (%) (%) CIGS-uni 28.4 710 79.3 16.0 Medici CIGS-grade 30.1 700 80.7 17.0 CIGS-uni 32.3 655 74.6 15.7 AMPS-1D [Son04] CIGS-grade 34.3 675 79.4 18.4 -35 -25 -15 -5 5 0200400600800 Voltage (mV)Current density (mA/cm2) CIGS-uni CIGS-grade Figure A-4. CurrentVoltage (C-V) plots for CIGS cells pr edicted by Medici simulation.

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PAGE 237

218 BIOGRAPHICAL SKETCH Woo Kyoung Kim was born at a small town, DongHae in South Korea, on 24 December 1971. He entered Sung Kyun Kwan University in 1990, where he studied chemical engineering and gradua ted at the top of engineering college. Then he joined the polymer and colloid engineering laboratory at chemical engi neering department of Seoul National University for his master’s research in 1994. His master’s research covered the thermally induced phase separation in NylonPEG blends. After receiving his master’s degree in 1994, he started hi s industrial research at Sams ung General Chemicals, Co., in South Korea, where he mainly has worked on the process development and scale-up of polyethylene and polypropylene polymerizati on process. Duri ng the industrial experience at petrochemical company for more five years, he was encouraged to study the environmentally friendly future energy. Finally, he joined the electronic material processing group at chemical engi neering department in University of Florida, where he stepped into new field, thin film solar cells.


Permanent Link: http://ufdc.ufl.edu/UFE0015717/00001

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Title: Study of Reaction Pathways and Kinetics in Cu(InxGa1-x)Se2 Thin Film Growth
Physical Description: Mixed Material
Copyright Date: 2008

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Permanent Link: http://ufdc.ufl.edu/UFE0015717/00001

Material Information

Title: Study of Reaction Pathways and Kinetics in Cu(InxGa1-x)Se2 Thin Film Growth
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

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Holding Location: University of Florida
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STUDY OF REACTION PATHWAYS AND KINETICS
IN Cu(InxGal-x)Se2 THIN FILM GROWTH















By

WOO YOUNG KIM


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006


































Copyright 2006

by

Woo Kyoung Kim

































To my wife Eun Mi, lovely son Jin Woo and my parents.















ACKNOWLEDGMENTS

First of all, I would like to express my sincere appreciation to my research advisor,

Dr. Timothy J. Anderson. His academic encouragement and considerate support have

inspired me to establish the capability to perform independent research, which will be an

invaluable asset to my future career. I also want to show my gratitude to my supervisory

committee, Dr. Sheng S. Li, Dr. Oscar D. Crisalle and Dr. Valentin Craciun, for kind

advice and helpful discussion. I also want to give my special thanks to Dr. E. Andrew

Payzant in Oak Ridge National Laboratory for his generous assistance in high

temperature X-ray diffraction experiments, and Dr. Jianyun Shen for her help in

thermodynamic calculation.

Many thanks should be returned to former members of the UF solar cell research

team, Dr. Suku Kim, Dr. Serkan Kincal and Dr. Seokhyun Yoon, who instructed me how

to operate the MEE system and how to conduct my research. It was also a great pleasure

to work with Jiyon Song, Ryan Kaczynski, Ryan Acher, Xuege Wang, Andre Baran, Wei

Liu and Matt Monroe in the UF solar cell research team, and many other graduate

students in electronic material processing group. Finally, I would like to thank Gerald R.

Bourne for teaching me how to use FIB, and Kerry Siebein for TEM-EDS analysis at

Major Analytical Instrumentation Center.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ...................................... .... ..................... ix

LIST OF FIGURES ......... ......................... ...... ........ ............ xi

A B ST R A C T ................................................................................................................... xviii

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 Photovoltaic D devices ................................................ .. .. ............ ............... 1
1.2 Fundam mental Physics of Solar C ells ............................................ .....................2
1 .3 W h y C IG S ? ............................................................................................................ 5
1.4 C IG S D position P rocesses ........................................................................ ...... 8
1.5 M EE System D description .................................. .....................................13
1.6 Statement of Thesis Work ................... ................................. 16

2 BINARY AND TERNARY PHASE DIAGRAM ASSESSMENT...........................19

2.1 Cu-Se Binary Phase Diagram Assessment ...................................... ...............19
2 .1.1 Introdu action ................................................................... 19
2.1.2 Experim ental Inform ation ........................................ ....... ............... 20
2.1.3 Therm odynam ic Optim ization......................................... ............... 22
2.1.4 Results and D discussion ......... ........................................... ........... .... 26
2.1.5 Sum m ary................................. ... ....... .....................28
2.2 Thermodynamic Description of Ternary Compounds in Cu-In-Se System .........40
2.2.1 Introduction ................................... .... ................... ............ 40
2.2.2 Extrapolation of Binary Gibbs Energy to Ternary ...................................41
2.2.3 Experim ental Inform ation ............................................... .....................44
2.2.3.1 Ternary com pounds.............. ......... ........................ .............. 44
2.2.3.2 Therm odynam ic properties ................................... ............... ..44
2.2.3.3 Phase diagram s ......... .... ..... ......... .......... ...............45
2.2.4 Ab initio Calculation on the Ternary Cu-In-Se Compounds ....................46
2.2.5 Establishment of Thermodynamic Descriptions .....................................47
2.2.5.1 Sub-lattice model for different ternary compounds .......................47









2.2.5.2 Evaluation of Gibbs energies of end-members in the sub-lattice
m o d e l ...............................................................4 8
2.2.6 Summary..................................52........... ........52
2.3 Cu-Ga-In Ternary Phase Diagram Calculation.........................................58
2 .3 .1 Intro du action ................ .. .......................... ........................ ....................5 8
2.3.2 Review of Sub-binary Phase Diagrams.................................................58
2.3.3 Prediction of Cu-Ga-In Ternary Phase Diagrams ....................................61
2.3.4 Modification of Cu-Ga-In Ternary Phase Diagrams..............................65
2.3.5 Sum m ary and Future W ork ............................................. ............... 67

3 METAL (CU, IN, GA)-SE REACTION PATHWAYS.................. ........ .......69

3 .1 In tro d u ctio n ............. .. ............... ................. .................................................. 6 9
3.2 Experim mental .......... ...... ............................. .. ..... ...... ................. 71
3.2.1 Precursor Preparation ............................... ............... 71
3.2.2 In situ high-temperature X-ray diffraction ...........................................73
3.3 C u-Se B inary F orm ation ............................................................ .....................74
3.3.1 Glass/Cu/Se Precursor .......... ............................... 74
3.3.2 G lass/C u-Se Precursor.......................................... ........... ............... 75
3.4. In-Se Binary Formation ........... ........ ......... ........................... 78
3.4.1 G lass/In/Se precursor........................................... ........................... 78
3.4.2 G lass/In-Se Precursor ........................ ....... ............ ......... ............ ... 80
3.5 G a-Se B inary F orm ation ............................................................ .....................82
3.5.1 G lass/G a/Se Precursor ...................... .. .. ........................... ............... 82
3.5.2 G lass/G a-Se Precursor........................................... .......... ............... 83
3.6 Sum m ary ............... ........ .......................................................................... 85

4 CUINSE2 FORMATION PATHWAYS AND KINETICS ......................................86

4 .1 In tro d u ctio n ............................................................................. 8 6
4.2 Glass/In2Se3/CuSe Precursor ................................................... ............... ... 88
4.2.1 Precursor Preparation ........................................ ........................... 88
4.2.2 Temperature Ramp Annealing ....................................... ............... 90
4.2.3 Isotherm al A nnealing ........................................ ........................... 91
4.3 G lass/InSe/Cu-Se Precursor........................................... ........................... 96
4.3.1 Precursor Preparation ........................................ ........................... 96
4.3.2 Temperature Ramp Annealing ....................................... ............... 97
4.4 G lass/C uSe/In-Se Precursor.................................................................... .. ... ..99
4.4.1 Precursor Preparation ........................................ ........................... 99
4.4.2 Temperature Ramp Annealing ...................................... ............... 100
4.5 Glass/M o/Cu-In-Se Precursor............. ....................................... ............... 101
4.5.1 Precursor Preparation ........................................ .......... ............... 101
4.5.2 Temperature Ramp Annealing ...................................... ............... 102
4.5.3 Isotherm al A nnealing ........................................ .......................... 102
4.6 Selenization of Glass/Mo/Cu-In Precursor ................................................. 105
4.6.1 Precursor Preparation ........................................ .......... ............... 105
4.6.2 Selenization Chamber D design ...................................... ............... 107









4.6.3 Tem perature Ram p Selenization ................................... .................108
4.6.4 Isotherm al Selenization .................................................... ... ............... 110
4 .7 Sum m ary ............................................... ... ............................... 115

5 CUGASE2 FORMATION PATHWAYS AND KINETICS .................................120

5 .1 In tro d u ctio n ................................................................................................... 12 0
5.2 G lass/G aSe/CuSe Precursor........................................................................... 121
5.2.1 Precursor Preparation ........................................ .......... ............... 121
5.2.2 Temperature Ramp Annealing ...................................... ............... 122
5.2.3 Isotherm al A nnealing ........................................ .......................... 122
5.2.4 TE M -ED S A nalysis....................................................... ............... 133
5.3 Glass/M o/Cu-G a-Se Precursor .................................. ............... ............... 135
5.3.1 Precursor Preparation ........................................ .......... ............... 135
5.3.2 Temperature Ramp Annealing ...................................... ............... 136
5.3.3 Isotherm al A nnealing ........................................ .......................... 138
5.4 Selenization of Glass/Mo/Cu-Ga Precursor ................................... 143
5.4.1 Precursor Preparation ........................................ .......... ............... 143
5.4.2 Selenization Chamber D design ...................................... ............... 143
5.4.3 Tem perature Ram p Selenization ................................... .................145
5.4.4 Isotherm al Selenization ...................................................................... 147
5.5 Summary .............................................. ..................... 152

6 CU(IN,GA)SE2 FORMATION FROM SELENIZATION OF METALLIC CU-
G A -IN .......................................................................................................1 5 5

6.1 Introduction ................................................................................................ ..... 155
6.2 Experim mental ............................................................. ........... 156
6.3 R results and D discussion ......................................................... .............. 157
6.3.1 Precursor Characterization ............................................ ............... 157
6.3.2 Temperature Ramp Annealing ...................................... ............... 158
6.3.3 Isotherm al A nnealing ................................ .......... ............... ... 163
6.3.4 Comparison Between CIS, CGS, and CIGS Formation...........................167
6 .4 S u m m ary ................................................... .............. ................ 16 9

7 DIFFUSION MODELING OF Cu-In SELENIZATION .........................................170

7 .1 Intro du action ................... ..................................... ....................... 17 0
7.2 M ulti-component Diffusion Theory ........................................ ...............171
7.3 Thermodynamic and Kinetic Basis for DICTRA..............................................174
7.4 Diffusion Modeling of Selenization of Cu-In Precursor ...............................176
7.4.1 K inetic Experim ents ........................................................................... 176
7.4.2 Diffusion Modeling Using DICTRA................................ ..................1.78
7 .5 S u m m ary .................................. ............................................... 1 8 1









8 DEFECT CHARACTERIZATION BY DEEP LEVEL TRANSIENT
SPECTROSCOPY (DLTS) TECHNIQUE ......................................... ...............182

8 .1 In tro du ctio n ......................................................... ....................... 182
8.2 Operation Principle of DLTS Technique...........................................................183
8.3 Equipment Description of UF-DLTS System ....................................................185
8.4 DLTS Measurement of CIGS Cells ..................................... ...............189
8 .4 .1 D L T S S can ..................... .......... .. ... ...... .. ........................... 18 9
8.4.2 Estimation of Trap Activation Energy and Capture Cross-section ..........191
8.4.3 Estim ation of Trap Density .............. .... ......................................... 192
8.5 Sum m ary .................................. ................................ ......... 195

9 CONCLUSIONS AND FUTURE WORK.................. ........ ................... 198

APPENDIX EXPLORATION OF MEDICI SIMULATION OF CIGS SOLAR
C E L L S ........................................................................... 2 0 1

A 1 O overview of M edici ......... ................. ..................................... ............... 201
A.2 Non-uniformity of Doping Concentration ................................. ... ................ 202
A.3 Medici Simulation of C-V Profile ............................ ..... ............... 203
A.4 Medici Simulation on Grading Band Gap CIGS Cell....................................206

LIST OF REFEREN CE S ................ .......... ........................ ..... .....................209

B IO G R A PH IC A L SK E T C H ........................................ ............................................218















LIST OF TABLES


Table page

1-1 Structural and electrical properties of CuInSe2 and CuGaSe2 with chalcopyrite
structure ..................................................... ........................... 8

2-1 Thermodynamic parameters in Cu-Se system .....................................................29

2-2 Parameters for functions used in Table 2-1 in the form of equation (2-1) ..............30

2-3 Phase equilibria in the Cu-Se system ............................................. .................. 31

2-4 Experimental and calculated standard formation enthalpies (AHfo298.15K) and
entropies (oS298) of Cu-Se compounds. ........................................ ............... 32

2-5 The experimental values of the standard formation enthalpy (AHO, 298) and
energy (AE ) of a-CuInSe2 ......... ................. .............................. .... ........... 45

2-6 Parameters used to calculate AEf of CuIn3Se5 and CuInsSes ................................50

2-7. Experimental results of phase relationships of Cu-Ga-In ternary system ..............66

4-1 The composition of the as-deposited glass/Mo/Cu-In precursor films as
determined by EPMA scans along the surface .............................................107

5-1 Estimated kinetic parameters for the CuGaSe2 formation from glass/GaSe/CuSe
b ilay er precu rsor film s ........................................ ........................................... 130

5-2 Estimated kinetic parameters for the CuGaSe2 formation from glass/Mo/Cu-Ga-
Se precursor film s .................. ...................................... .. ........ .... 141

5-3 Estimated kinetic parameters for the CuGaSe2 formation from selenization of
glass/M o/Cu-Ga precursor film s. ........................................ ....................... 148

6-1 Estimated kinetic parameters for the CIGS formation from selenization of
glass/M o/Cu-Ga-In precursor film s ............................................ ............... 166

6-2 Comparison of reaction pathways and kinetics for CIS, CGS and CIGS
formation from selenization of metallic precursors. ................... ....... ............167

8-1 Equipment specification ofUF-DLTS system. ............................................... 189









8-2 DLTS scan results of EPV-CIGS cells at a reverse bias (VR) of 0.4 V, a trap-
filling pulse of 0.8 V, and a saturation pulse width of 10 ms.............................191

8-3 Trap density calculation from DLTS analysis of EPV-CIGS cell. ......................194

8-4 Summary of DLTS analysis for EPV-CIGS cell.............. ..................196

8-5 Summary of DLTS analysis for EPV-CIGS cell.............. ..................197

9-1 Summary of reaction kinetics of Cu(InxGal-x)Se2 formation from different
precursor structures ........................................ .......................... 199

A-1 Design parameters of solar cell for Medici simulation. .......................................203

A-2 Basic design parameters of solar cell for Medici simulation ..............................206

A-3 Deep defect parameters of solar cells for Medici simulation..............................207

A-4 Comparison of performance parameters of CIGS cells simulated by Medici........208
















LIST OF FIGURES


Figure page

1-1 Solar spectrum of AMO and AM1.5 based on ASTM G173 ....... ............... .3

1-2 Schematic diagram of light-induced electron-hole creation in a p-n junction
photodiode ................................................... ........................... 4

1-3 I-V characteristic of a solar cell under illumination .............................................4

1-4 Efficiency trend of thin film solar cells (CuInSe2, CdTe and a-Si). Taken from
Z w eib el .................... ......... ......... ........ .... ................ ............... 6

1-5 The schematic structure of a conventional CIGS solar cell. .....................................7

1-6 Tetragonal unit cell of a Cu(In,Ga)Se2 chalcopyrite lattice. ......................................8

1-7 Schematic diagram of NREL three-stage process for CIGS fabrication....................9

1-8 Schematic diagram of the two-step process for CIGS fabrication...........................10

1-9 Schematic diagram of ISET non-vacuum process for CIGS fabrication ..............12

1-10 Schematic diagram of MEE reactor system. ....................................................13

1-11 Schem atic top view of M EE reactor. .................................................................... 14

1-12 The LabVIEW-based HMI system of MEE reactor............................ .............16

2-1 Calculated Cu-Se phase diagram .................. ........... ..................... 33

2-2 Comparison between the calculated Cu-Se phase diagram and experimental data .34

2-3 Comparison between the calculated chemical potential of Cu and experimental
data in P-C u2-xSe phase .............................................. ............ .... ..... ...... 35

2-4 Comparison between the calculated chemical potential of Se and experimental
data at 1373 and 1473K ........... .................................... .............. .. .... ...... 36

2-5 Comparison between the calculated Se2 partial pressure and experimental data in
Cu-Se system .................................... ................................ .........37









2-6 Comparison between the calculated heat capacity of each phase and
experim ental data for C u2Se.......................................................... ............... 38

2-7 Comparison between calculated heat capacity of each phase and experimental
data for CuSe .................................... ................................ .........39

2-8 Geometrical construction of (a) Kohler and (b) Muggianu model...........................42

2-9 Geometrical construction of Toop model.............................................. ........... 43

2-10 Pseudo-binary In2Se3-Cu2Se phase diagram ................................. ..................... 53

2-11 Optimized Gibbs energy a-CuInSe2, P-CuIn3Se5 and y-CuInsSe8 compared with
that estimated from EMF experiments and ab initio calculation ...........................54

2-12. Optimized Gibbs energy of formation of a-CuInSe2, P-CuIn3Ses and y-CuInsSes
compared with that estimated from EMF experiments and ab initio calculation.....55

2-13 Isothermal sections of Cu-In-Se at 500 OC. (a) Calculation, (b) Experimental
ev a lu a tio n ......................................................................... 5 6

2-14 Isothermal sections of Cu-In-Se at 800 OC. (a) Calculation, (b) Experimental
ev a lu a tio n ......................................................................... 5 6

2-15 Isothermal sections of Cu-In-Se at 900 OC. (a) Calculation, (b) Experimental
ev a lu a tio n ......................................................................... 5 7

2-16 Calculated phase diagram of Cu-In binary system.............................. ..............59

2-17 Calculated phase diagram of Cu-Ga binary system ...........................................60

2-18 Calculated phase diagram of Ga-In binary system..................... ............... 60

2-19 Isothermal section (500 C, latm) of the Cu-Ga-In ternary phase piagram based
on the M uggianu 's equation ......................................................................... ...... 62

2-20 Isothermal section (500 C, latm) of the Cu-Ga-In ternary phase piagram based
on the Muggianu's equation for the range of 0 < x(In) < 0.2 and 0.2 < x(Ga) <
0.4............... ........................................ ......... 63

2-21 Isothermal section (350 C, latm) of the Cu-Ga-In ternary phase piagram based
on the M uggianu's equation ........................................................ ............... 63

2-22 Isothermal section (800 C, latm) of Cu-Ga-In ternary Phase Diagram based on
the M uggianu's equation .......................................................... ............... 64

2-23 Vapor pressure as a function of temperature in the Cu-Ga-In mixture (Cu:Ga:In
= 1 :1 : 1 m o le ratio ) ............................................... ................ 6 4









2-24 Vapor pressure as a function of temperature in the Cu-Ga-In mixture (Cu:Ga:In
= 2 :1 : 1 m o le ratio ) ............................................... ................ 6 5

2-25 Modified isothermal section (350 C, latm) of the Cu-Ga-In ternary phase
diagram with experimental data (symbol)............... ............................................. 67

2-26 Modified isothermal section (500 C, latm) of the Cu-Ga-In ternary phase
diagram ............... ................................ ................ .. ............... .. 67

3-1 Phase diagram of In-Se binary system .......................................... ............... 70

3-2 Phase diagram of Ga-Se binary system ...................... .......................... ............ 71

3-3 As-grown precursor structure along with overall atomic composition....................72

3-4 Phase evolution of glass/Cu/Se precursor observed by in situ X-ray diffraction.....74

3-5 Phase evolution of glass/Cu-Se precursor observed by in situ X-ray diffraction. ...77

3-6 Phase evolution of glass/In/Se precursor observed by in situ X-ray diffraction......79

3-7 Phase evolution of glass/In-Se precursor observed by in situ X-ray diffraction......81

3-8 Phase evolution of glass/Ga/Se precursor observed by in situ X-ray diffraction.....82

3-9 Phase evolution of glass/Ga-Se precursor observed by in situ X-ray diffraction.. ..84

4-1 TEM micrographs of as-grown glass/In2Se3/CuSe bilayer precursor films.............89

4-2 Room temperature XRD scans and TEM micrographs of as-grown precursor
fi lm s ............................................................................ .8 9

4-3 In situ XRD scans during temperature ramp annealing (10 C/min) of the
glass/In2Se3/C uSe sam ple............................................... .............................. 90

4-4 In situ time-resolved XRD scans during isothermal annealing of the glass/
In2Se3/CuSe precursor structure at 250 C ...................... ............................... 92

4-5 Avrami model plot for glass/In2Se3/CuSe precursor structure.............................94

4-6 Parabolic model plot for glass/In2Se3/CuSe precursor structure.............................95

4-7 Arrhenius plot of the parabolic rate constant for glass/In2Se3/CuSe precursor
structure ............................................................... ..... ..... ......... 96

4-8 Room temperature XRD scans of as-grown precursor films .................................97

4-9 In situ XRD scans during temperature ramp annealing (30 C/min) of the
glass/InSe/Cu-Se sam ple. ...... ........................... .......................................98









4-10 Room temperature XRD scans of as-grown glass/CuSe/In-Se precursor ..............99

4-11 In situ XRD scans during temperature ramp annealing (30 C/min) of the
glass/CuSe/In-Se sample. ..... ........................... .......................................100

4-12 Temperature ramp annealing of glass/Mo/Cu-In-Se precursor..............................102

4-13 Isothermal annealing of glass/Mo/Cu-In-Se precursor at selected temperatures in
the range 140 to 350 C ............................... ............ ................ ............. 103

4-14 CuInSe2 grain sizes estimated by X-ray diffraction vs. isothermal annealing
temperature of glass/M o/Cu-In-Se precursor....................................................... 104

4-15 0-20 and grazing incident X-ray diffraction (at co = 1.0 and 0.50) patterns of an
as-deposited glass/Mo/Cu-In precursor film .................... ............. 105

4-16 Surface and cross-sectional SEM images of an as-deposited glass/Mo/Cu-In
precursor film and selenized film ..................................................................... 106

4-17 Selenium chamber design using PANalytical X'Pert system .............................107

4-18 In situ X-ray diffraction pattern evolution during the selenization of a
glass/Mo/Cu-In precursor films in the 20 range...............................................109

4-19 In situ X-ray diffraction pattern evolution during the isothermal selenization of a
glass/Mo/Cu-In precursor film at 280 C .............. ..... .........................110

4-20 The Avrami model plot for a-CuInSe2 formation by selenization of
glass/Mo/Cu-In precursor films ..................... .. ......... .. ............... 112

4-21 Arrhenius plot for Avrami kinetic constant for a-CuInSe2 formation by
selenization of glass/Mo/Cu-In precursor films ............................................... 112

4-22 The parabolic rate model for a-CuInSe2 formation by selenization of
glass/Mo/Cu-In precursor films ............................................ ............... 114

4-23 The parabolic rate model for a-CuInSe2 formation by selenization of
glass/Mo/Cu-In precursor films ............................................ ............... 114

4-24 Reaction pathway of CIS formation from In2Se3/CuSe precursor projected in
ternary Cu-In-Se isothermal phase diagram at 500 C......................................116

4-25 Reaction pathway of CIS formation from intimately mixed Cu-In-Se precursor
projected in ternary Cu-In-Se isothermal phase diagram at 500 C .......................117

4-26 Comparison of reaction rates for CIS formation from different precursors
estim ated by the parabolic and Avrami m odel......................................................119









5-1 Room temperature XRD scans and TEM micrograph of as-grown precursor
fi lm s ............. ................... ............. ...................... ................ 1 2 1

5-2 In situ XRD scans during temperature ramp annealing (30 C/min) of the
glass/GaSe/CuSe sam ple. ...... ........................... .......................................123

5-3 In situ time-resolved XRD scans during isothermal annealing of the
glass/GaSe/CuSe precursor structure at selected temperatures.............................125

5-4 Fractional reaction (a) with respect to time (t) at selected isothermal
tem peratures ........................................................................ 126

5-5 Parabolic rate model plot for glass/GaSe/CuSe precursor structure ....................127

5-6 Arrhenius plot of the Parabolic rate constant for glass/GaSe/CuSe precursor
structure ..................................... .................. .............. .......... 127

5-7 Fractional reaction (a) with respect to time (t+t*) and Avrami model plot at
selected isotherm al tem peratures ........................................ ....................... 130

5-8 Modified Avrami model plot for glass/GaSe/CuSe precursor structure ..............131

5-9 Arrhenius plot of the Avrami model rate constant for glass/GaSe/CuSe precursor
structure ..................................... .................. .............. .......... 132

5-10 TEM-EDS analysis on (a) as-grown glass/GaSe/CuSe precursor, (b) sample
annealed at 300 OC, for 30 m in........................................ ........................... 134

5-11 Room temperature X-ray diffraction of (a) as-grown glass/Mo/Cu-Ga-Se
precursor, and (b) thermally annealed CuGaSe2 ........................................ 135

5-12 In situ XRD scans during temperature ramp annealing (30 C/min) of the
glass/M o/Cu-G a-Se sam ple......................................................... ............... 137

5-13 In situ time-resolved XRD scans during isothermal annealing of the
glass/Mo/Cu-Ga-Se precursor structure at selected temperatures........................139

5-14 Comparison of fractional reaction for isothermal experiments and modified
A vram i m odel prediction .............................................. ............................. 140

5-15 Modified Avrami model plot for glass/Mo/Cu-Ga-Se precursor structure ..........141

5-16 Arrhenius plot of the Avrami model rate constant for glass/Mo/Cu-Ga-Se
precursor structure .................. ............................................. .... 142

5-17 Room-temperature XRD scans of Cu-Ga as-grown precursor and selenized
C uG aSe2 film .................................................. ................. 144









5-18 X-ray sample holder with a graphite dome for selenization of Cu-Ga precursor
fi lm s ............................................................................................. 14 4

5-19 In situ XRD scans during temperature ramp selenization of Cu-Ga/Mo/glass
precursor................................... ................................. .......... 146

5-20 In situ XRD scans during isothermal selenization of Cu-Ga/Mo/glass precursor
at four different tem peratures. .................................................................... ....... 147

5-21 Comparison of fractional reaction for isothermal experiments and modified
A vram i m odel prediction .............................................. ............................. 149

5-22 Modified Avrami model for the CuGaSe2 formation by selenization of
glass/M o/Cu-G a precursor ............................................. ............................ 150

5-23 Arrhenius plot of the Avrami model rate constant for the CuGaSe2 formation by
selenization of glass/M o/Cu-G a precursor.............................................................150

5-24 Comparison of reaction rates for CIS and CGS formation from different
precursors estimated by the parabolic model. .............................. ......... ...... .154

5-25 Comparison of reaction rates for CIS and CGS formation from different
precursors estimated by the Avrami model ...................................................154

6-1 Room-temperature XRD scans of glass/Mo/Cu-Ga-In as-grown precursor ..........157

6-2 Surface (top) and cross-sectional (bottom) SEM images of (a) an as-deposited
glass/Mo/Cu-Ga-In precursor film and (b) selenized film.............. ................158

6-3 Temperature ramp HT-XRD scans with a bare glass substrate. ..........................159

6-4 In situ XRD scans during temperature ramp selenization of Cu-Ga-In/Mo/glass
p recu rso r............................................................................................ . 16 0

6-5 Cell refinement for room temperature X-ray diffraction data of a selenized CIGS
sample using the tetragonal, I-42d (122) cell type.................................................162

6-6 Lattice constants (a, c) vs. Ga composition of CIGS .................. ............... 162

6-7 In situ XRD scans during isothermal selenization of glass/Mo/Cu-Ga-In
precursor at four different temperatures ......................................... ...........164

6-8 Avrami model and corresponding Arrhenius plot (inset) for CIGS formation by
selenization of glass/Mo/Cu-Ga-In precursor. .....................................................165

6-9 Arrhenius plot for Avrami rate constant for CIGS formation by selenization of
glass/M o/Cu-G a-In precursor.......................................... ........................... 165









6-10 Comparison of fractional reaction for isothermal experiments and Avrami model
prediction ..................................... .......................... .... .... ......... 166

6-11 Comparison of reaction rates for selenization of different metallic precursors
estim ated by the Avram i m odel. ........................................ ........................ 168

7-1 The CIS thickness vs. time obtained from kinetic experiment. ..........................176

7-2 The schematic diagram of the simplified reaction of CuInSe2 formation from
selenization of Cu-In precursor. ................................. 177

7-3 The modified Cu-In phase diagram including metastable Culn phase ................179

7-4 The comparison of CIS growth rates between the DICTRA prediction and
ex p erim en ts ...................................................... ................ 18 0

8-1 Schematic diagram of UF-DLTS system. ................................... ............... 186

8-2 Schematic top view of LN2 cryostat in the DLTS system................................ 186

8-3 Simplified wiring diagram of UF-DLTS system............................................187

8-4 UF-DLTS system. .................... .. ......... ... .. ............ ............... 88

8-5 DLTS scans for the EPV-CIGS cell at different delay times (0.02 to 1.0 ms). .....190

8-6 Arrhenius plot of DLTS scans for EPV-CIGS cells ......................... ...........192

8-7 Capacitance-temperature scan for a EPV-CIGS cell at a reverse bias of 0.4 V.....193

8-8 Capacitance-voltage (C-V) measurement for EPV-CIGS at different
tem peratures. ...................................................................... 194

A-1. A band- gap and doping profile for CIS-graded solar cell. .....................................204

A-2 Absorption coefficient profiles for the materials used in Medici simulation.........205

A-3 Medici simulation results on C-V profile for the uniform doping and graded
doping C IS cells. ................................................................... 205

A-4 Current- Voltage (C-V) plots for CIGS cells predicted by Medici simulation......208















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

STUDY OF REACTION PATHWAYS AND KINETICS IN Cu(InxGal-x)Se2 THIN
FILM GROWTH

By

Woo Kyoung Kim

August 2006

Chair: Timothy James Anderson
Major Department: Chemical Engineering

Assessment of the thermochemistry and phase equilibrium data of the Cu-Se binary

and Cu-In-Se ternary systems was performed to suggest the phase diagrams. Sub-lattice

models were used to describe the Gibbs energy of the condensed solutions. Coupled with

previously reported assessments, the Cu-Ga-In phase diagram was predicted by

extrapolation of the Cu-Ga, Cu-In and Ga-In binary systems. Ternary interaction

parameters were and subsequently added to achieve consistency with recent ternary

experimental data.

In situ high-temperature X-ray diffraction technique was used to investigate the

reaction pathways and phase evolution of binary Cu-Se, In-Se and Ga-Se compounds

prepared as an intimate mixture or bi-layer. The results revealed that the overall phase

transformation of binary metal (Cu, In and Ga)-Se compounds qualitatively follows the

sequence predicted by the phase diagram, but the detailed reaction path of each binary


xviii









compound depends on the as-deposited precursor structure and phases produced during

the deposition process.

Reaction pathways and kinetics of polycrystalline a-CuInSe2 (CIS), CuGaSe2

(CGS), and Cu(In,Ga)Se2 (CIGS) formation were also systematically investigated using

in situ high-temperature X-ray diffraction during thermal annealing of stacked bilayer

and intimately mixed monolayer precursors, and selenization of elementally mixed metal

precursors. The lowest temperature to form CIS was identified as -140 C, which was

achieved by thermal annealing of intimately mixed Cu-In-Se precursor. Formation

temperatures of CGS (i.e. 260 to 300 OC) were relatively higher than those of CIS (i.e.

140 to 250 C) and CIGS (i.e. 260 C). MoSe2 formation was always clearly observed

during selenization and for CIS, only after complete formation of CIS. Quantitative

analysis of time-resolved X-ray diffraction data by adopting the Avrami and parabolic

rate models provided reaction order, rate constant, and activation energy.

DICTRA simulation of CIS formation by selenization of a Cu-In precursor was

performed using the kinetic results obtained by time-resolved, in situ HTXRD

experiments along with the thermodynamic description of the CIS system. The target

reaction system was simplified as a pseudo-binary reaction, Culn + 2Se CuInSe2, for

which the reliable mobility parameters for Se transport in CIS were obtained.














CHAPTER 1
INTRODUCTION

1.1 Photovoltaic Devices

Semiconductor photonic devices generally fall into one of three functional

categories. One group of photonic devices converts electrical energy into photo-energy

such as light emitting diodes (LEDs) and laser diodes, while the other two groups of

photonic devices convert photo-energy into electrical energy. If the purpose of photo-to-

electrical energy conversion is to detect or determine information about the photon

energy, the device is called a photodetector. If the purpose of energy conversion is to

produce electrical power, the device is called a photovoltaic device or solar cell [Pie96].

A solar cell converts sunlight into electricity through the photovoltaic effect which

was first observed by nineteen-year-old Edmund Becquerel, a French experimental

physicist, in 1839 while experimenting with an electrolytic cell composed of two metal

electrodes. He found that certain materials would produce small amounts of electric

current when exposed to light [Bec39, M6193].

Solar cell technology and its application have been enormously developed during

the last four decades. Silicon was the first commercial solar cell material and is still most

widely used in solar cell application. The potential compound semiconductors such as

GaAs, CdTe, InP, CdS and Cu(In,Ga)Se2 cell have been actively developed [M6193].

Photovoltaics as one of the renewable energy technologies is a lot friendlier to the

environment than conventional energy technologies, which mainly rely on fossil fuels.

Fossil fuels contribute significantly to many environmental problems, e.g., greenhouse









gases, air pollution, and water and soil contamination. The performance of a solar cell is

measured in terms of its efficiency converting sunlight into electricity. Only sunlight

with certain energies (or wavelengths) will work efficiently to create electricity, and

much of it is reflected or absorbed by the materials that make up the cell. Because of

this, a typical commercial solar cell has an efficiency of 15%-about only one-sixth of

the sunlight striking the cell generates electricity. Low efficiencies mean that larger

arrays are needed and thus high manufacturing costs are required. Therefore, improving

solar cell efficiencies while holding down the manufacturing cost is an important goal of

the solar cell industry and university research support [Nre06].

1.2 Fundamental Physics of Solar Cells

For the photovoltaic conversion, it is necessary to separate the light-induced

electrons and holes, and collect them at external contacts. This requires an internal

electric field, which can be generated by homojunctions and heterojunctions of

semiconductors, e.g., p-n junction, Schottky barrier, and MIS (metal-insulator-

semiconductor) structure. Currently, p-n junction solar cells are the most widely used

devices for photovoltaic energy conversion.

The solar radiation reaching the earth has a spectral distribution due to partial

reflection by atmosphere and partial transmittance to surface of the earth. The radiation

distribution outside the atmosphere is similar to that of a "black body" radiation at

-5800K, while the atmosphere at the surface of the earth selectively absorbs the radiation

at certain wavelengths. As shown in Figure 1-1, the standard solar spectra (e.g., AMO

and AM1.5) defined by air mass (AM) are important in photovoltaic application. The

AMO represents solar spectrum outside of the atmosphere and AM1.5 corresponds the

spectrum at sea level. More generally, the AMx is expressed by x = 1/cos(Oz), where 0z is










the zenith angle of the sun. When the sun is located at the zenith of the receiving area

(i.e., Oz=0 and thus x=l), AM1 would be spectrum received at sea level on a clear day

with the sun at its zenith. Generally, the AM1.5 spectrum, which is equivalent to a zenith

angle of 48.190, is accepted as a reference spectrum in PV application.


2.5


E AMO
S2.0 AM1.5



1.5


;a
S1.0
Il,





0.0
0 500 1000 1500 2000 2500 3000 3500 4000
Wavelength (nm)

Figure 1-1. Solar spectrum of AMO and AM1.5 based on ASTM G173.

Electron-hole pairs in a p-n junction diode are created by absorption of light and

then minority carriers of each side move to a junction, as shown in Figure 1-2. At

thermodynamic equilibrium with no current flows, minority carriers reaching the edges of

the depletion region are immediately swept out by the electric field (i.e., built-in bias) to

the opposite side of the junction, which consequently yields a current flow in the reverse

direction of built-in bias.









Recombination

6k


/ 4 4$hv


t
Recombination
Figure 1-2. Schematic diagram of light-induced electron-hole creation in a p-n junction
photodiode.



V oc
VV










I


Figure 1-3. I-V characteristic of a solar cell under illumination.

Several solar cell parameters under illumination are graphically defined in I-V

characteristics, as shown in Figure 1-3. First, Vo (open circuit voltage) and Isc (short

circuit current) are the maximum voltage and current that can be supplied or derived by

the cell for applied illumination conditions, respectively. Next, the Im and Vm are the









current and voltage to yield the maximum power rectangle, i.e., Pmax = ImVm < IsVoc.

Finally, the fill factor (F.F.) and power conversion efficiency (7) are often used to

represent the solar cell performance and are determined by

Pmax ImVm
FF ax (1-1)
IVo IoV"
sc oc sc oc

Pmax ImVm FF IsV(1-
]n in in

where P,n is the incident photon energy per second. The above relationships, equation (1-

1) and (1-2), demonstrate that solar cell efficiency (q) is proportional to Is, Vo and fill

factor. However, considering the general expressions for Vo and Is, the fundamental

material parameters that determine the efficiency of the solar cell are the lifetime and

mobility of the minority carriers, and the interface recombination velocities. These

parameters are not independent from each other, and are controlled by the structural and

electrical properties of the solar cell.

1.3 Why CIGS ?

Silicon was the first commercial solar cell material and is still most generally used

in solar cell applications. However, silicon is not the ideal material for solar cells

because it has low light absorption efficiency as well as an indirect band gap. A large

number of binary, ternary, and quaternary compound semiconductors have been

investigated for their potential as high performance and inexpensive solar cells that can

serve as an alternative to silicon-based solar cells such as single-crystalline,

polycrystalline, and amorphous silicon. One of the most promising strategies to lower

solar cell manufacturing costs will be the thin-film photovoltaic technology in which thin

absorber films (typically < 5 [tm) are deposited on inexpensive substrates such as










polymer. Chalcopyrite a-CuInSe2 (CIS) and its alloys with Ga or S are the most

promising candidates as an absorber for high efficiency thin film solar cells. Recently,

the development of CIGS has made rapid progress, and conversion efficiency of 19.5%

(AM 1.5G) has been achieved on a laboratory scale [Con05]. The efficiencies of three

conventional thin film solar cells (i.e., CuInSe2, CdTe and a-Si) are compared in Figure

1-4, which suggests that CIS-based cell is the most suitable for high performance thin

film solar cells. Furthermore, CuInSe2 compound has many advantages as a solar cell

absorber, for instance, a high absorption coefficient (- 105 cm-1), excellent radiation

resistance, direct band gap and wide range of stoichiometry.


20
NREL
CuInSe2 NREL
o CdTe NREL
16- a-Si Univ. ofSo.Flori-- NREL
S BP Solar EuroCIS
C Boeing Boeing
12 Kodak ARCUniv. of So. FL
r Photon Energ
VU L Boein g AMETEK /
C ~ United Solar
Monosolar o k Boeing
K 8 odak
U Matsushita
Im Boeing ECD
t ~ '-- Univ. of Maine
LI 4


RCA
a I a a a I a a a I a a i I I I I I i i I I
1975 1980 1985 1990 1995 2000 2005
Year
Figure 1-4. Efficiency trend of thin film solar cells (CuInSe2, CdTe and a-Si). Taken from
Zweibel [Zwe05].

The schematic structure of a typical CIGS-based thin film solar cell is shown in

Figure 1-5. In this structure, a soda-lime glass (SLG) is widely used as a substrate. In a

soda-lime glass, the out-diffused Na ion is believed to increase the electrical conductivity

and to reduce the grain boundary energy barrier by either forming Nain defects or









removing mid-gap traps [Wei99]. However, Na2Se is believed to cause a poor adhesion

between CIGS and Mo [Hua03]. The recent trend includes flexible substrates such as

polymer and metal foils because the flexibility of substrates allows a potential application

to portable solar cells, and a roll-to-roll manufacturing, which promises substantial cost

reduction. The Mo is a back contact electrode, which is generally deposited by sputtering.

Polycrystalline CIGS acts as a p-type light absorber, and more importantly forms a p-n

junction with an n-type CdS buffer layer. The ZnO (or ZnO:Al) transparent conducting

film serves as a window layer, and anti-reflection (AR) coating (e.g., MgF2) improves the

light absorption efficiency. As a front contact material, a bilayer Ni/Al grid is used.

Ni/AI Ni/AI

F WAR coating 01
n-ZnO
n-CdS
p-Poly-CIGS
Mo
Substrate
(SLG)

Figure 1-5. The schematic structure of a conventional CIGS solar cell.

CuInSe2 crystallizes in a diamond-like lattice structure with a face-centered

tetragonal unit cell that is referred to a chalcopyrite structure as pictured in Figure 1-6.

Each selenium atom serves as the center of a tetrahedron of two Cu and two In atoms,

and each metallic atom is surrounded by a tetrahedron of selenium atoms. In this

structure, each anion (selenium) has two Cu and two In (or Ga) cations as nearest

neighbors, whereas each anion has four cations nearly randomly as nearest neighbors in

zinc-blende structure. While the two lattice constants of the chalcopyrite structure (i.e., x-









and y-direction) are the same as the lattice constant of the zinc blende structure, the

lattice constant of z-direction is a double of that of zinc blende structure.










C


SCu
0 In or Ga
a ISe

Figure 1-6. Tetragonal unit cell of a Cu(In,Ga)Se2 chalcopyrite lattice.

Typical lattice constants and electrical properties for CuInSe2 and CuGaSe2 with a

chalcopyrite structure are summarized in Table 1-1.

Table 1-1. Structural and electrical properties of CuInSe2 and CuGaSe2 with chalcopyrite
structure.
Lattice constants Bandgap energy Absorption coefficient
a (nm) c (nm) Eg (eV) ca (cm-1)
CuInSe2 0.5784 1.1614 1.04 ~ 1x105

CuGaSe2 0.5596 1.1002 1.68 > 3x104


1.4 CIGS Deposition Processes

Almost every method of semiconductor processing has been tried to synthesize CIGS

compound, but only a few of them were successful in producing a high quality CIGS

absorber for thin film photovoltaic cell. In this chapter, the widely employed techniques

to fabricate high quality CIGS films and the recent efforts to develop low-cost non-

vacuum processes are summarized.









A sophisticated vacuum co-evaporation process is characterized by simultaneous

exposure of high-temperature substrate to Cu, Ga, In and Se vapor fluxes, and known to

provide the best control of composition through precise control of the temperature and

thus each elemental flux. Even though several co-evaporation methods including simple

single-layer and bilayer processes are available, an NREL 3-stage process using physical

vapor deposition (PVD) system currently holds the best CIGS cell efficiency of 19.5 %

[Con05].

1st stage 2nd stage 3rd stage

600 C
12 Open 600 oC
shutter
10 -
S8 400 oC
04 8
: Se
6 --K 30 f
S6 .: In
0 20 U
a 4 mCu
m In
10

0 0 I I "

-10 0 10 20 30 40 50 60
Run time (min)
Figure 1-7. Schematic diagram of NREL three-stage process for CIGS fabrication.
(Provided by Dr. Noufi in NREL)

The schematic diagram of the NREL three-stage process is illustrated in Figure 1-7.

During the first stage, the In, Ga and Se are deposited to form the sesquiselenide,

(In,Ga)2Se3. After the second stage of only Cu+Se flux, a Cu-rich CIGS is produced

along with a secondary Cu-Se binary compound (e.g., conducting Cu2Se), which is

known to facilitate the CIGS grain growth. Finally, a slightly Cu-poor CIGS forms by









adding more indium and gallium at third stage. The three-stage PVD process, however,

has not been successfully implemented in industrial large-area module production mainly

due to high production cost caused by high-vacuum and high-temperature operation

conditions. Furthermore, co-deposition technique has a limitation in achieving

uniformity in large scale deposition.

Another conventional process to produce a device-quality CIGS absorber is called the

two-step method, which has been successfully employed in a commercial line of Shell

Solar and Showa Shell. The commercialized two-step process consists of the deposition

of a metallic precursor (e.g., Cu/In/Ga) followed by subsequent selenization, as shown in

Figure 1-8. Traditionally, the metal precursors are prepared by sputtering and then

selenized at high temperature (-600 C) in a reactive H2Se or Se vapor ambient.

However, since H2Se gas and Se vapor are extremely toxic, a safer selenization method is

required.


Step (1) Step (2)
Metal deposition Selenization

H2Se
Cu/In/Ga O CIGS
Tsub> 600 OC

Figure 1-8. Schematic diagram of the two-step process for CIGS fabrication.

Palm et al. suggested the deposition of a selenium layer on metal precursor by

evaporation followed by a rapid thermal annealing [Pal03]. As a novel CIS process,

Bindu et al. deposited selenium films on glass substrate using chemical bath deposition

(CBD) at room temperature, totally avoiding use of H2Se or Se vapor [Bin03]. Indium

and copper were then deposited on the selenium layer to yield glass/Se/In/Cu or

glass/Se/Cu/In precursor by sequential vacuum evaporation. Finally, the stacked layer









precursors were thermally annealed in high vacuum (10-5 mbar) at the temperature range

423 to 673K.

As stated in the previous section, CIGS is similar in its performance and stability to

currently dominant crystalline silicon devices, but their market share is still quite low

(<1%) mainly due to high production cost. Therefore, the development of more cost

effective process, preferably based on low temperature and non-vacuum technique, is

essential to successful commercialization of CIGS-based thin film solar cells. Example

approaches include electrodeposition and screen printing. Precursor layers obtained by

these techniques, however, have not exhibited electronic properties suitable for

commercial solar cells, and also require additional thermal treatments to optimize cell

performance parameters [Gan06].

Electrodeposition has been considered as a suitable process for large-scale

industrial processes, requiring low energy consumption and low capital investment

[Zwe99, BhaOO]. Two basic methods of electrodeposition to form CIS or CIGS have

been explored with appreciable results. One method represents the co-deposition all

elements, i.e., Cu, In, Ga and Se [Cal98, Bha98, Tau05] and the other includes the

deposition of metallic precursors followed by subsequent selenization [Pro96, Gan06].

Basically, electrodeposition of Cu-In-Ga-Se alloys is carried out potentiostatically on

Mo-coated substrates from aqueous solutions containing complex agents, e.g., CuC1,

InC13, Ga(N03)3.7H20, H2SeO3 and KSCN [Tau05, Gan06]. A small area efficiency of

over 10% was obtained by electrodeposition of quaternary CIGS followed by subsequent

thermal annealing [Gui03]. By adding additional indium and gallium, and applying high-

temperature annealing in vacuum, an efficiency of 15.4% was reported [BhaOO]. The









stability of the chemical solution, large area non-uniformity and high deposition rate

remain a significant challenge [Kae04].

International Solar Electric Technology, Inc. (ISET) employed an interesting non-

vacuum process for low cost mass production for CIGS solar cells. ISET uses a coating

technology of water based precursor inks made of nano-particles of mixed oxides of Cu,

In and Ga that are converted to yield CIGS absorber layers of desired electronic

properties. The schematic process diagram is shown in Figure 1-9.


Precursor coating Reduction Selenization

o:. Mixed oxides :: N2 u-a-nH2Se
MO .
Glass 475-5250C Glass 440-475 oc Glass


Figure 1-9. Schematic diagram of ISET non-vacuum process for CIGS fabrication.

A water based precursor ink is coated on Mo-coated glass substrate using a 'knife

blade' coating technique [KapOl, Kap03]. After drying, a layer of mixed oxides with a

typical thickness of around 2.5-3.0 jtm is left on the glass/Mo substrate. This oxide layer

is then reduced under a forming gas mixture of H2 and N2 at temperatures in the range

475 to 525 C to obtain a compact coating of metal alloys of Cu-Ga-In. Finally, this

alloy coating is selenized in H2Se gas ambient at a temperature in the range 440 to 475 C

to yield CIGS layer. They reported that small area solar cells with efficiency of- 13%

have been fabricated by this process. The main advantages of this non-vacuum process

include high compositional control of the absorber layer, high material utilization and

low cost.










Spray deposition has also been taken into account as a possible non-vacuum

technique that is amenable to the manufacture of large area films with low processing

costs. Schulz et al. has employed nanoparticle-based precursors for spray deposition of

CIGS materials [Sch98]. In their approach, nanoparticle colloids were prepared by

reacting a mixture of Cul and/or [Cu(CH3CN)4](BF4)2 and/or InI3 and/or Gal3 in pyridine

with Na2Se in methanol at reduced temperature under inert atmosphere. Colloids with

the compositions CuInSe2.5, CuSe, In2Se3 and Cul.loIno.68Gao.23Sex were prepared by each

corresponding reaction.

1.5 MEE System Description

The solar cell research group in the University of Florida has been using a Plasma

Migration Enhanced Epitaxy (PMEE) reactor system to produce Cu(In,Ga)Se2-based

absorber layers.

Load lock
BELL JAR

Sorption
pump I
TMP
Ventury
pum p Fore
Fore
line
Mechanical

Rough line pump

pump
Fore line


Diffusion
pump
Figure 1-10. Schematic diagram of MEE reactor system.

The MEE system is essentially a modified Molecular Beam Epitaxy (MBE) system

under an ultra high vacuum environment, as schematically shown in Figure 1-10. The









pumping unit is composed of three mechanical pumps, a large capacity diffusion pump, a

turbo molecular pump (TMP), and a liquid-nitrogen cryogenic pump inside the system.

To obtain sufficiently low pressure for opening the TMP gate valve in the load lock, the

combination of a Venturi pump and a sorption pump are employed. Using the ultra high

vacuum pumping system, the normal operation pressure during deposition is in the range

10-8 to 10-7 Torr, depending on the source fluxes and the temperature of the substrates.

In comparison with a traditional MBE system, which typically has a drawback of

low productivity, one of outstanding advantages of the PMEE system is that it is able to

process nine substrates simultaneously by employing a large rotating platen. The various

types of substrates, such as 2"x2", Icmxlcm square substrates, or 2" diameter round

wafers of Si or GaAs, can be loaded on the rotating platen.


Heater Zone



OCU Thermal
cracker
Metal Chalcogen
Deposition Zone
Zone
Plasma
in cracke







Load Lock
Zone
Figure 1-11. Schematic top view of MEE reactor.

The inside of the system consists of four different zones, as shown in Figure 1-11, a

heater zone, a metal deposition zone, a load lock zone, and a chalcogen zone. The system









uses a rotating platen so that every substrate experiences four zones sequentially and also

periodically.

In the heater zone there is a radiation heater to heat the substrates that pass through

this zone. The substrates continuously cool while they pass through the other zones

because they do not encounter any other heat sources in these zones.

In the metal deposition zone three different of metals, such as copper (Cu), indium

(In) and gallium (Ga), can be deposited. Each metal source is evaporated from an

effusion cell fitted with a single or dual filament heater. The fluxes produced by the Cu

and In source are monitored on a real time basis by Electron Impact Emission

Spectroscopy (EIES) sensors, which are calibrated using Quartz Crystal Monitors

(QCM). In the case of Ga, the flux is monitored by QCM.

The loadlock zone is connected to a load-lock system, which is used to load and

unload substrates. Therefore, during the deposition, it acts as a cooling zone where

neither deposition nor heating occurs.

Finally, selenium (Se) is deposited in the chalcogen zone. Selenium vapor is

known to be a mixture of low molecular weight polymers Se through Ses. Among them,

high molecular weight species may not easily react with other species, even in high

temperature conditions, so they are traditionally cracked thermally or exposed to a

plasma. Unfortunately, there is no flow sensor instrumented in the system to measure a

Se flux and thus the flux is estimated by measuring the film thickness after deposition. In

the case of counter-clock wise rotational deposition, each substrate experiences the four

steps of heating -> metal deposition -> cooling -> selenium deposition repeatedly and

each atomic layer (- 0.5 nm CIGS/cycle) is deposited sequentially on the substrate.









To achieve the real time control of the PMEE reactor, a LabVIEW based human

machine interface (HMI) system is configured as shown in Figure 1-12 [Kin02]. By

using this system, one can monitor and control the important operation parameters such

as the substrate heater temperature, and each source temperature, the flux of each source

and even the sequence of film deposition in a central computer.




&--- s I l s"m-















mipl 4.m 4 Ii i


Figure 1-12. The LabVIEW-based HMI system of ME reactor.

1.6 Statement of Thesis Work

Chalcopyrite Cu(In,Ga)Se2 based cells have clearly demonstrated their potential as

high efficiency thin film solar cells. In addition to their high cell efficiency, CIGS thin-

film solar cells exhibit outstanding long-term outdoor stability, excellent radiation

hardness, and the potential for use in a high performance CIGS/CGS tandem arrangement.

The route used to synthesize the CIGS absorber material is critical to achieving high cell

efficiency as well as high processing throughput. As summarized in Chapter 1.4, a

variety of processing sequences lead to the formation of CIGS. This flexibility is partly
Fiue -2.Te aVIWbae MIsstmofXfi eatr









due to an inherent stability of a-CIGS and a rich phase diagram (a-CuInSe2 is in

equilibrium with 8 different solid phases and a Se-rich liquid) [GodOOa-c]. The complex

chemistry of the quaternary CIGS system, however, has forced absorber synthesis

optimization to primarily traverse an empirical path and discouraged exploration of

substantially different approaches. In particular, very little is known about the

fundamental thermochemistry and reaction pathways in the system.

Therefore, in this thesis, the equilibrium pathways and reaction kinetics for the

formation of Cu(InxGal-x)Se2 (CIGS), its sub-ternaries (i.e., CuInSe2 and CuGaSe2) and

sub-binaries are systematically investigated to assist the development of a cost-effective

and high performance CIGS growth process.

First, the thermodynamic description of Cu-Se binary, Cu-In-Se and Cu-Ga-In

ternary systems are evaluated using the software package ThermoCalc along with

available experimental information, as described in Chapter 2. This thermodynamic

description is essential to the reliable calculation of chemical potentials and identification

of equilibrium phases, which are combined with species diffusivities to estimate the

diffusion controlled reaction rate.

Before digging into the reaction of complicated ternary (e.g., CIS and CGS) and

quaternary (CIGS) compounds, the phase evolution of binary metal-selenides (e.g., Cu-Se,

In-Se and Ga-Se) is qualitatively investigated using in situ high temperature X-ray

diffraction (HTXRD) and compared with the prediction by equilibrium phase diagrams in

Chapter 3. Understanding the phase transformation of metal-selenide binaries is very

important in designing binary bi- or multi-layer precursors for rapid thermal processing,

which is a promising low-cost approach of CIGS film fabrication.









In Chapter 4, the reaction pathways and kinetics of a-CIS formation from different

precursors (e.g., glass/In2Se3/CuSe, glass/InSe/Cu-Se, glass/CuSe/In-Se and

glass/Mo/Cu-In-Se) and selenization of metallic glass/Mo/Cu-In precursor are

systematically investigated using a time-resolved, in situ HTXRD equipped with a

customized selenium chamber. Quantitative kinetic analysis using selected solid-state

growth models provides kinetic parameters including reaction order, rate constant, and

activation energy as well.

In Chapter 5, the successful implementation of in situ HTXRD technique in a-CIS

system (Chapter 4) is extended to exploring the CGS formation from thermal annealing

of stacked precursors (e.g., glass/GaSe/CuSe and glass/Mo/Cu-Ga-Se) and selenization of

glass/Mo/Cu-Ga precursor. Subsequently, the reaction pathways and kinetics for

quaternary CIGS formation by the selenization of metallic glass/Mo/Cu-Ga-In precursors

are investigated in Chapter 6.

Since most solid-state reactions follow a diffusion limited process, it is expected

that the diffusion-limited reaction rate would be predicted by thermodynamic chemical

potentials and diffusivities (or mobilities) of species. Therefore, for a given set of

thermodynamic descriptions, (e.g., results obtained in Chapter 2), the reaction rates

experimentally obtained in Chapter 4 through 6 can be used to establish the mobility

database of each element (e.g., Cu, In, Ga and Se) in various compounds by employing

the companion software to ThermoCalc, DICTRA (DIffusion-Controlled

TRAnsformation) program. In Chapter 7, kinetic data for a-CIS formation by

selenization of glass/Mo/Cu-In precursor are used to obtain a mobility expression of

selenium.














CHAPTER 2
BINARY AND TERNARY PHASE DIAGRAM ASSESSMENT

2.1 Cu-Se Binary Phase Diagram Assessment

2.1.1 Introduction

The Cu-Se system is an important constitutional binary of the chalcopyrite

Cu(Inx,Gal-x)Se2, which is one of the most promising absorber materials for high-

efficiency thin film solar cells. Phase equilibria and thermodynamic properties of the Cu-

Se system have been studied by many research groups using differential thermal analysis

(DTA), X-ray diffraction, microscopy, calorimetry, electromotive force (EMF), and

vapor pressure measurement. More recently, an excellent review paper on the phase

equilibria of the Cu-In system based on the evaluation of the abundant experimental data

was published by Glazov et al. [Gla00], who have been studying this system for many

years and have carried out precise measurements.

A thermodynamic description, established with the computer-based CALculation of

PHAse Diagram (CALPHAD) method [Sau98], is represented as a set of models to

express the Gibbs energy of each phase as a function of temperature, pressure and

composition. The parameters used in the models of different phases are optimized using

the available phase equilibrium and thermo-chemical data. This optimization is expected

to make the thermodynamic description self-consistent and able to provide complete

information about phase equilibria, thermo-chemical properties as well as driving forces

of phase transformation and mass transport.









The reliable description for binary Cu-Se system is also a crucial part of the

thermodynamic databases for the higher order systems such as the ternary Cu-In-Se and

Cu-Ga-Se, and quaternary Cu-In-Ga-Se systems. Thermodynamic optimization for the

Cu-Se system was first performed by Chang [Cha99] using the previously reported

experimental data and ThermoCalc program, which is one of most popular CALPHAD

software. In his work, an association model and a three-sub-lattice model were employed

for liquid and Cu2-xSe phases, respectively. The other intermediate phases, Cu3Se2, CuSe

and CuSe2, were modeled as line compounds.

In this work, the efforts to improve the previous optimization results by Chang

were incorporated to make the models for different phases in the Cu-Se system more

compatible with higher order systems, and the calculated phase diagram and

thermodynamic properties more coincident with the recently evaluated results, especially

the values suggested by Glazov [Gla00].

2.1.2 Experimental Information

The liquid phase of this system exhibits two miscibility gaps. One in the Cu-rich

region was reported by several research groups [Gla91, GodOOb, Ber72, Hey66, Bab75,

Bur74, Mur75], and the other in Se-rich region was tentatively mapped by Glazov

[Gla00] and Godecke [GodOOb] based on very few experimental data. As to the terminal

phases, a small solubility of Se in Cu was measured by Smart [Sma46] and Taylor

[Tay76], while negligible solubility of Cu in Se was proposed by Chakrabarti [Cha81].

Four intermediate compounds were experimentally identified including Cu2-xSe, Cu3Se2,

CuSe and CuSe2. Among them, only Cu2-xSe melts congruently. The Cu2-xSe has two

polymorphs of c-Cu2-xSe (low temperature phase) and 3-Cu2-xSe (high temperature









phase). The CuSe has three polymorphs including a-CuSe, P-CuSe and y-CuSe. Their

crystal structures were summarized by Glazov [Gla00] and Chang [Cha99]. The

equilibrium reactions of the Cu-Se system were reported in many papers [GodOOb, Hey66,

Ber68, Ogo69, Ogo72, Ber72, Aza76, Abr84]. The key equilibrium points have been

more recently evaluated and presented with the different accuracy according to the

experimental conditions by Glazov [Gla00]. Some phase transformation temperatures

were confirmed to an accuracy of one tenth degree of Kelvin.

The standard enthalpies of formation and entropies of the intermediate compounds

have been determined by various techniques [Hey66, Gat56, Val68, Rau70,Ask76,

Mil74] and summarized by Chang [Cha99]. The heat capacities of two polymorphs of

Cu2Se were measured using an adiabatic calorimetry in the range 193 to 773 K [Kub73]

and in the range 300 to 1390 K [Bla78]. As pointed out by Kubaschewski [Kub73], the

measured heat capacities of the a-Cu2-xSe phase are not reliable above 325 K on account

of the ca- transformation. The heat capacities of three polymorphs of CuSe were

measured in the range 5.7 to 652.7 K [Sto96] using the same method as used by

Kubaschewski [Kub73].

The chemical potential of Cu in Cu2-xSe, as a function of temperature, was

measured using coulometric titrations with a solid state galvanic cell, Pt/Cu/CuBr/Cu2-

xSe/graphite [Mos89]. The activities of Se in molten mixture of Cu and Se were

measured by a modified dew-point method at 1373 K [Bla78], and by the transportation

method at 1437 K [Aza76]. Several gaseous species have been detected including Sen (n

= 1 to 8), Cu, Cu2, CuSe, and Cu2Se. The vapor pressure of Se2 over different condensed

phases in the Cu-Se system was reported by Rau [Rau70].









2.1.3 Thermodynamic Optimization

The CALPHAD method was applied to obtain a consistent thermodynamic

description of the entire Cu-Se system by employing the PARROT module of the

ThermoCalc program package [Din91]. The CALPHAD method is based on two basic

principles: the total Gibbs energy of a system will be at a minimum at thermodynamic

equilibrium and the chemical potential of every element in different equilibrium phases is

the same. Thermodynamic optimization by CALPHAD method can provide the

following advantages;

* Predicts phase diagrams and thermodynamic properties of a system under
conditions where no experimental information is available.

* Calculates phase diagrams and thermodynamic properties for a higher order system
based on the models of its lower order sub-systems.

* Calculates meta-stable phase diagram.

* Determine the driving force of phase transformation.

The standard Gibbs energy function OG', (T) for the element i in phase (p is described by

an equation suggested by SGTE [Din91]:

OGV(T)=G,"(T)-HSER =a+b.T+c-T-InT+d-T2 +e.T3 +f .T1 (2-1)

where HSER is the molar enthalpy of element i at 298.15 K and 1 bar in its standard

element reference (SER) state, and (p represents any possible phase. The parameters for

OGcu'(T) and OGsej(T) functions were taken from the SGTE compilation [Din91] and the

evaluation results by Chang [Cha99], respectively.

To allow the established database to be easily extended to higher order systems and

to be compatible with the general CALPHAD database, the sub-lattice models with the









different constitutions according to their structures as presented by Saunders [Sau98]

were employed for all the stable phases of the Cu-Se system.

The liquid phase is described by an ionic two-sub-lattice model that can be

schematically represented as (Cu+l)p(Se2,Va', Se)q. This model is able to describe the

short range ordering effectively and is straightforwardly extended to higher order systems

as compared to the associated solution model used by Chang [Cha99]. The Cu+ state is

considered as the only species in the cationic sub-lattice. Another oxidation state Cu+2 is

neglected due to its very small amount. Neutral selenium and hypothetically charged

vacancy are introduced in an anion sub-lattice to maintain the charge neutrality by

adjusting the values ofp and q.

The Cu-rich solid solution phase is described by a two-sub-lattice model in terms of

(Cu, Se)(Va), which is generally used for the alloy fcc phase in CALPHAD solution

database such as SSOL [Din91]. The line compounds Cu3Se2, CuSe, and CuSe2 are

described by a two-sub-lattice model in terms of (Cu)p(Se)q where p and q are the

stoichiometric coefficients of the compounds.

The two polymorphs of the non-stoichiometric Cu2-xSe compound are described by

a three-sub-lattice model based on the structural study [Cha99]. In this work, the sub-

lattice constitutions (Cu,Va)i(Se,Va)i(Cu)i used by Chang [Cha99] is simplified to

(Cu,Va)i(Se)i(Cu)i since the measured compositions of Cu2-xSe always show a deficit of

Cu. The simplification is intended to keep the number of parameters to be optimized as

low as possible while still permitting the results to be matched with the apparent data. It

does not mean no vacancy exists in the other two sub-lattices.

For any phase (p in the Cu-Se system, the Gibbs energy is represented by









G'= refG '+ldG '+x"G (2-2)

The Gibbs energies, refG", dG and X"G for different phases are described by the

following equations:

for the liquid phase,

ref hq i" O lq y u +" yO q 0 G 'iq (2-3)
S Y Cu 1 YSe-2 C+1 Se -2 +1 Y GCu+ V1 Se uSe + )

'dGhq = RT q(yS In ys + YVq "n yq + YSq y lnye) (2-4)
x Ghq q 1(2-4)

XsGlq Y2 y.q LV CI Se-2, V + YSe-2 se s-Se (2-5)


for the Cu-rich solid solution phase,

ef GCu fcc = Yc oGcc + y OG fc (2-6)

dGCu fc = RT(yc~ Ilnycu + -In y') (2-7)


xsGc c = Yc se LCu Se V (2-8)

for the line compound phases in terms of CupSeq

ref CupSeq _=0CuPSeq (2-9)
S GICe u Se (2-9)

idGCupSe = 0 (2-10)

xsGCupSeq =0 (2-11)

and for the non-stoichiometric compound phases such as a-Cu2-xSe and 3-Cu2-xSe

represented as phase (p,

ref = ycu oG's + Yv oG s ( 2-12)
SCu :S Ycu:S.SeCu + Y V V:Se.:V (2-12)

idG = RT(ycu ln yc + y" ln y ) (2-13)

XG( Yc L, o (2-14)
S= "*Y' *LcCu V Se Cu









In equation (2-3)-(2-14), OGA4:B and 0GA:B:-C represent the Gibbs energy of the so-

called end-member compounds AB and ABC, respectively, where A, B, and C is a

species such as Cu, In, Se, Va, Cu+1, Se-2 and Va q; OLA,B:B:C is the interaction parameter

for the species A and B in the first sub-lattice, while the second and third sub-lattices are

occupied by B and C, respectively; y and y'A represent the site fraction of A in the first

and second sub-lattice, respectively. An end-member compound could be a real or a

hypothetical compound. The Gibbs energy for the end-member is represented by the

same expression as that for the elements:

OGBc(T) =a+b.T+c.T.InT+dT2 +eT3 + f T1 (2-15)

Each interaction parameter can be expressed by the expansion of site fraction and

the temperature dependence as the following:


L = L(y y,)V (2-16)
y=O

YL= LA +LB, T (2-17)

For the compounds like Cu2-xSe and CuSe for which the heat capacities have been

measured at different temperatures [Mos89, Bla78, Aza76], the latter four terms (c, d, e

andf) of equation (2-15) were obtained from the heat capacity data using the following

expression:

C,(T) =A+B*T+C T2 +D*T2 (2-18)

In comparison of equations (15) and (18), the following relations can be derived by

using the fundamental relationships of thermodynamics

c -A; d =- B/2; e -C/6; f -D/2 (2-19)









Before the optimization, the evaluated heat capacity data are directly put into the

Gibbs energy expressions in terms of c, d, e andf It can reduce the arbitrary

optimization due to too many unknown parameters. For the compound a-Cu2-xSe, only

the experimental heat capacity data at low temperature were used in optimization for the

reason that ca-3 transformation would raise the heat effect.

Thermodynamic optimization was then performed by using the selected

experimental data presented in Figure 2-2 and Tables 2-3 and 2-4. A set of self-

consistent model parameters were obtained as the optimization result, with which the

calculated phase diagram and thermo-chemical properties of the system agree well with

the evaluated experimental results.

2.1.4 Results and Discussion

The optimized parameters for describing the Gibbs energy of each phase in the Cu-

Se system are listed in Tables 2-1 and 2-2. The calculated Cu-Se phase diagram is

presented in Figure 2-1 and is compared with the literature data in Figure 2-2. Calculated

key equilibrium points are compared with the evaluated values [Gla00] in Table 2-3. The

comparison of the calculated standard enthalpy of formation and entropy of the

compounds is shown in Table 2-4. The calculated chemical potential of Cu is compared

with the experimental data in Figure 2-3. The calculated chemical potential of Se is

compared with the values converted from the experimental activity data [Mos89] in

Figure 2-4. The comparison of the calculated vapor pressures of Se over different

condensed phases with the experiments is shown in Figure 2-5. The comparison of

calculated heat capacities of the Cu2-xSe and CuSe compounds with those of different

polymorphs is presented in Figure 2-6 and 2-7.









It can be seen that the overall calculated phase diagram and most of the key phase

equilibrium points agree well with the experimentally evaluated results [Gla00]. The

calculated standard enthalpy of formation, absolute entropy, heat capacity of the

compounds, and the vapor pressure of Se2 also agree well with the experimental data.

The calculated chemical potentials of Cu and Se agree with most of the experimental data.

The calculated eutectoid temperature of a-Cu2-xSe/3-Cu2-xSe/Cu3Se2 (334.9K),

however, is much higher than that (< 253 K) suggested by Glazov [Gla00] based on the

experiments [Ogo69, Ogo72]. If the lower value of the eutectoid temperature is used as

constant and other model parameters are adjusted, the vapor pressure of Se2 will not

agree with the experimental data [Rau70]. The inconsistence can not be solved by

adjusting any model parameters of the three phases. Since it is believed that achieving

equilibrium between the gas-solid is more likely than between the solid-solid at low

temperature, a large weight factor was used for Se vapor pressure data during

optimization.

The calculated Cu chemical potential of the Cu2-xSe compound agrees well with

EMF measurements [Mos89] for x < 0.04, while it decreases more steeply than

experimental values for x > 0.04. The difference may be caused by the fact that the rate

of Cu diffusion is not sufficiently high to maintain the sample homogeneous during

coulometric titration. Another possibility is the presence of electric current that when

combined with the ionic component causes the apparent Cu titration amount to be greater

than the actual value. The calculated Se chemical potentials are compared with

experimental values for liquid phases measured by two different methods, a modified









dew point method at 1373K [Bla78] and a transportation method at 1473K [Aza76]. The

results reveal that the calculated values lie well between the two experimental results.

2.1.5 Summary

A thermodynamic description for the Cu-Se system has been established based on

the abundant experimental data, the recent evaluation [Gla00], and the previous

optimization work [Cha99]. Sub-lattice models with various constitutions were applied

for different phases of the system. The models used in this work allow easy extension of

the database to higher order systems. The calculated phase diagram and thermo-chemical

properties agree well with experimental results and thus demonstrate the self-consistency

of the established thermodynamic description.










Table 2-1. Thermodynamic parameters in Cu-Se system


Phase/model Function Reference

Liquid / G(LIQ,CU+1:SE-2;0) = GCU2SE B + 17762.5-12.5*T This work
G(LIQ,CU+1:VA;0) = GCU S + 13263.3 9.76894748*T This work
(Cu+'),(Se-2,Va, Se)q G(LIQ,SE;0) = GSE L [Din91]
G(LIQ,CU+1:SE-2,VA;0) = 159272.8 87.93*T This work
G(LIQ,CU+1:SE-2,VA;1) = 63335 48.1634*T This work
G(LIQ,CU+1:SE-2,SE;0) = -1235-5*T This work
G(LIQ,CU+1:SE-2,SE;1) = -22612.66 This work
a-Cu2Se / G(CU2SE A,CU:SE:CU;0) = GCU2SE A This work
(Cu,Va)(Se)(Cu) G(CU2SE A,VA:SE:CU;0) = 50000 + GCU S + GSE S This work
G(CU2SE A,CU,VA:*:CU;0) = 50000 This work
G(CU2SE A,CU,VA:*:CU;1) = -43000 This work
P-Cu2Se / G(CU2SE B,CU:SE:CU;0) = GCU2SE B This work
(Cu,Va)(Se)(Cu) G(CU2SEB,VA:SE:CU;0) = This work
46000 + 18.7*T + GCU2SE B GCU S
G(CU2SE B,CU,VA:*:CU;0) = -28998 + 14.002*T This work
G(CU2SE B,CU,VA:*:CU;1)= -8.803*T This work
Cu3Se2 /(Cu)o 6(Se)o 4 G(CU3SE2,CU:SE;0) = GCU3SE2 This work
a-CuSe /(Cu) 5(Se)o 5 G(CUSEA,CU:SE;0) = GCUSEA This work
P-CuSe /(Cu) o 5(Se) 5 G(CUSEB,CU:SE;0) = GCUSEB This work
y-CuSe /(Cu) o 5(Se) 5 G(CUSEG,CU:SE;0) = GCUSEG This work
CuSe2 /(Cu) 0 33(Se) 0 67 G(CUSE2,CU:SE;0) = GCUSE2 This work
a-Cu /(Cu,Se)(Va) G(CUFCC,CU:VA;0)= GCU_S [Din91]
G(CUFCC,SE:VA;0) = GSES + 5000 This work
G(CUFCC,CU,SE:VA;0) = -14500 This work
y-Se G(SES,SE;0) = GSE_S [Din91]











Table 2-2. Parameters for functions used in Table 2-1 in the form of equation (2-1)



a b c dx102 ex106 fx10-2 T(K)
range
298-
-7770.4580 130.4852 -24.1124 -0.2657 0.1292 524.7780 8
GCUS 1358-
-13309.7200 183.6498 -31.3800 0 0 0 3
3200
298-
-6657.6530 92.5397 -19.1400 -1.2295 2.6767 0 298
GSE S 760
760-
-9059.1660 150.3342 -28.5520 0 0 0
1500
298-
-9809.1960 288.8134 -52.4000 2.4925 -5.4550 0 298
1000
1000-
GSE L 8433.1372 -78.4769 5.3990 -3.5945 5.2017 0 1
1150-
-7460.6200 192.6463 -36.0000 0 0 0 50
1500
298-
GCU2SE A -86772.3609 285.8666 -58.6000 -3.8700 0 0 298
6000
298-
GCU2SE B -85571.9722 454.3173 -90.4176 0.8600 -1.5000 516.6747 2
~- 6000
298-
GCU3SE2 -31329.6700 172.9600 -32.0000 0.0319 0 0 298
6000
298-
GCUSE A -28151.0213 110.6613 -21.5224 -0.9115 2.0400 281.4303 298
6000
298-
GCUSE B -27103.8019 111.0630 -22.3684 -0.3715 -2.1800 251.0000 2
~- 6000
298-
GCUSE G -31321.3585 284.3542 -53.3380 6.2458 -24.0000 0 298
6000
298-
GCUSE2 -28485.6977 265.0188 -45.3806 0.4484 0 0 298
6000










Table 2-3. Phase equilibria in the Cu-Se system


Equilibrium Phase composition(at.% Se) T (K) Type Ref.
+ 31.5 4 33.3 1380 [Gla00]
L L+p-CuSe 32.6 3 33.5 1380.0 Monotectic This work
=1.8 0.021 33.3 13365 [Gla00]
Li -> Cu+ P-Cu2xSe 2.16 8x10-5 33.5 1334.2 Eutectic This work
L 52.5 36.5 -99.6 7961 [Gla00]
L2 L3+ -CUxSe 50.4 36.3 96.7 795.8 Monotectic This work
S+ L Y 36.5 100 50.0 652.7 [Gla00]
-CuSe + L3 -CuSe 36.4 99.2 50.0 652.7 Peritectic This work
50.0 100 66.7 605 [Gla00]
y-CuSe + L3 CuSe2 50.0 99.7 66.7 604.9 Peritectic This work
L3 = 100 66.7 100 4941 E c [Gla00]
L3 CuSe+Se100 66.7 100 494.0 Eutectic This work
P-Cuz2-Se; y-CuSe; P- 36.5 50.0 50.0 410 Peritectoid or [Gla00]
CuSe 35.5 50.0 50.0 410.1 Eutectoid This work
50.0 50.0 66.7 410 Peritectoid or [Gla00]
-CuSe -CuSe; CuSe2 50.0 50.0 66.7 410.1 Eutectoid This work
Cu + P-Cuz2-Se 4-4x10-8 33.3 =-33.3 39615 Perit d [Gla00]
a-Cu2-xSe 5.24x10-9 33.3 33.3 395.8 This work
P-Cuz2xSe + P-CuSe <-> 36.3 50.0 40.0 386 Peritectoid [Gla00]
Cu3Se2 35.4 50.0 40.0 385.6 This work
40.0 50.0 50.0 326.8 Peritectoid or [Gla00]
Cu3Se2; -CuSe;-CuSe 40.0 50.0 50.0 326.4 Eutectoid This work
50.0 50.0 66.7 326.8 Peritectoid or [Gla00]
-Cue; -Cue; CuSe2 50.0 50.0 66.7 326.4 Eutectoid This work
P-Cuz-xSe C a-Cu2-xSe = 35.4 -34 40.0 <253 Eutectoid [Gla00]
+ Cu3Se2 35.0 33.3 40.0 334.9 This work
18 1699 [Gla00]
L L + L1699 Critical point [Gla0
L1 + L 16.3 1698.7 This work
33.4 1421 Congruent [Gla00]
Li <- p-Cuz-xSe 33.8 1421.2 melting point This work










Table 2-4. Experimental and calculated standard formation enthalpies
entropies (oS298) of Cu-Se compounds.


(AHf0298.15K) and


Compound -AHf,298.15K S298 Method Reference
(kJ/mole) (J/mole.K)
a-Cu2Se 59.3 Calorimetry [Gat56]
69.9 EMF [Val68]
62.8 157.4 Vapor pressure [Rau70]
65.7 113.9 EMF [Ask76]
65.3 129.7 Evaluation [Mil74]
59.3 129.7 Assessment [Cha99]
65.86 (+0.53) 129.7 (4.2) Evaluation [Gla00]
65.9 129.7 Assessment This work
Cu3Se2 98.9 Calorimetry [Gat56]
124.5 DTA [Hey66]
94.6 185 EMF [Ask76]
104.6 207.2 Evaluation [Mil74]
104.6 210.7 Assessment [Cha99]
98.91 (+0.54) 207.11 (21) Evaluation [Gla00]
108.8 207.8 Assessment This work
a-CuSe 39.6 Calorimetry [Gat56]
46.0 EMF [Val68]
44.0 86.2 Vapor pressure [Rau70]
32.6 74.1 EMF [Ask76]
41.8 78.2 Evaluation [Mil74]
40.8 78.2 Assessment [Cha99]
39.54 (+0.42) 79.36 (+0.06) Evaluation [Gla00]
41.7 79.4 Assessment This work
CuSe2 43.1 Calorimetry [Gat56]
49.0 120.6 Vapor pressure [rau70]
39.3 98.8 EMF [Ask76]
48.1 107.4 Evaluation [Mil74]
48.1 115.4 Assessment [Cha99]
43.10 (7.1) 107.5 (10.5) Evaluation [Gla00]
46.0 108.7 Assessment This work




















S1200- L -3
fcc(Cu)
S1000- P-cu2-xSe


S800-


600-
y-CuSe

-40pcuse CuSe2 Se
a-Cu2-x Se Cu3Se2 -CuS
200 i 1 --1 ii
A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole fraction of Se

Figure 2-1. Calculated Cu-Se phase diagram


























C)


E
(D
I-


Figure 2-2. Comparison between the calculated Cu-Se phase diagram and experimental
data


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole fraction of Se
















0 Measured [Mos89]
X | A 623 K
0 6 648K
S, 673 K
= -10- X 698 K

0

*" -15-
Calculated
0 --- 6 2 3 K
U -20- 648 K

S.......- 673 K

-25- 698 K



-30
A0.30 0.31 0.32 0.33 0.34 0.35 0.36

Mole fraction of Se
Figure 2-3. Comparison between the calculated chemical potential of Cu and
experimental data in 3-Cu2-xSe phase

















O
6-I
x -4
"5
E
% -



m -


-16



.C
u








A
-14

-14





Figure 2-4


P -Cu2.-Se + L2
Calculated
13731
.----- 14731
-


t-

L1+ p-Cu2 .Se
I: S Measured
0 1373K [Bla78]
AAA A 1473K [Aza76
S- Li+ L2


t-

I


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Mole fraction of Se

Comparison between the calculated chemical potential of Se and
experimental data at 1373 and 1473K


1.9 1.0





















CI ^ CuSe2




J-C u2-x Se
0-





-10-


fcc (Cu)
-15-



-20
S 0.5 1.0 1.5 2.0 2.5
1000/T (1/K)


Figure 2-5. Comparison between the calculated Se2 partial pressure and experimental
data in Cu-Se system























0
E

CL
'a-

C-
a-

(D
Ma






A


1500


Temperature (K)


Figure 2-6. Comparison between the calculated heat capacity of each phase and
experimental data for Cu2Se


0 500 1000






39



80- I I I I I I I I

Measured [Sto96]
75-


70-

0
o
E
65-

o y-CuSe
S60-
C.)

a p -CuSe
o 55

"" a-CuSe
50-


45-


40 -Il l l i I I I

A 200 250 300 350 400 450 500 550 600 650 700

Tem perature (K)


Figure 2-7. Comparison between calculated heat capacity of each phase and
experimental data for CuSe









2.2 Thermodynamic Description of Ternary Compounds in Cu-In-Se System

2.2.1 Introduction

Since the chalcopyrite CuInSe2 (CIS) was first synthesized in 1953, the Cu-In-Se

ternary system has attracted considerable attention due to its application as an absorber

material in solar cells. CIS-based cells currently hold the world-record energy

conversion efficiency (19.5%, AM1.5G, 100mW/cm2) for thin film technologies

[Con05]. This compound has a large homogeneity range of composition and complicated

phase relationships with the other phases. A small deviation in composition about the

stoichiometry (Cu:In:Se = 1:1:2) or the existence of secondary phases produces large

changes in CIS material properties and thus its device characteristics. There is a lack of

reliable thermodynamic data for the ternary compounds in the Cu-In-Se system.

Unfortunately these properties are essential to understanding reaction pathways to

synthesize CIS and development of novel processes to fabricate cost-effective high-

quality CIS films.

Common experimental techniques to measure thermodynamic properties can not be

directly used to estimate the Gibbs energy of these ternary compounds as it is not easy to

know their exact corresponding compositions due to large homogeneity range of the

ternary compounds, e.g., a-CuInSe2 and 3-CuIn3Se5 in pseudo-binary In2Se3-Cu2Se

phase diagram shown in Figure 2-10. In this work [She06], a set of thermodynamic

descriptions for the dominant ternary compounds in the Cu-In-Se system is established by

integrating the relevant information, which includes:

* Experimental measurements of the thermodynamic properties of the Cu-In-Se
ternary compounds.

* Experimental measurements of phase equilibria including Cu-In-Se ternary
compounds.









* Established thermodynamic model of the three sub-binaries, i.e., Cu-Se, Cu-In and
In-Se.

* Ab initio calculation on the defect formation energy in the Cu-In-Se ternary
compounds.

2.2.2 Extrapolation of Binary Gibbs Energy to Ternary

In the CALPHAD method, the excess Gibbs energy expression of a higher-order

system is usually predicted from that of the lower-order systems if insufficient

experimental data are available for the higher-order system. The basic formulae for

doing this are based on various geometrical weightings of the mole fractions [Hil80] and

expressed for ternary system by the general expression:


G =3 3 x G +X XxL (2-20)
Gm x = Yxx X +x x2 3L123
-1 j1 = X (1) (1)

and X() = X, +wmx3 ; X1(12) = x +w12x3 (2-21)


X, (j) + Xj() = 1 (2-22)

where Gx is the contribution of non-ideal interactions between the components of

ternary system, also known as the excess Gibbs energy of mixing, x, is a mole fraction of

i component in ternary compound, X,;) is a mole fraction of i component in binary i-j

compound, GC is the excess Gibbs energy of mixing for binary i-j compound, L123 is an

excess ternary interaction parameter, and w, is a weighting factor. By adopting different

weighting factors, the three commonly used methods such as Kohler, Muggianu and

Toop models are easily generated.

In the Kohler model, a weighting factor is defined as


w12 __ 1 (2-23)
x, + X2









X X X
1(12) = X + 3 = ; X2(12) (2-24)
X, +X2 X, +x2 X + X2

and can be described geometrically as Figure 2-8 (a). The Muggianu model adopts a

simple weighting factor defined as

12 = 21 = 0.5 (2-25)


X1(12) =X1 + 0.5x3 (l + ,1 -2); X2(12) (I +x2 1) (2-26)
2 2

and is geometrically represented by Figure 2-8 (b). In the Maggianu extrapolation it can

be seen that the line from the ternary alloy composition to the edge binaries forms a right-

angle to the binary. This leads to the consequence that, when the alloy composition is

dilute in two of the components, the interaction parameter of these two components will

approach regular behavior because the term (xi-xj) becomes small.

3 3

(a) (b)










1 2 1 2
Figure 2-8. Geometrical construction of (a) Kohler and (b) Muggianu model

Both the Kohler and Muggianu models can be considered symmetrical as they treat all

three components in the same way. Another method called the Toop model is different in

that it considers one of the binary systems does not behave in the same as the others, and

thus its weighting factor is defined as









,12 = 0; 21 = 1 (2-27)

X1(12) = x,; X2(12) = 1 X, = X + X3 (2-28)

and geometrically described as Figure 2-9.

Practically, the phase boundaries calculated by either the Muggianu and Kohler

extrapolations seem to provide similar results [Ans78], but it was also noted that the

choice of extrapolation method should receive more attention when exact knowledge of

partial quantities such as activity coefficients is more critical. It is known that the Toop

model is not suitable for metallic systems but may be appropriate for some ionic liquid

systems. It should, however, be used carefully in all cases as the extrapolation is

dependent on which binary is chosen to behave differently, and it is possible to obtain

three different answers depending on this choice [Sau98].

3












1 2
Figure 2-9. Geometrical construction of Toop model

The ThermoCalc program used for optimization of the Cu-In-Se ternary system is

adopting a Muggianu model. By plugging equations (2-25) and (2-26) into equation (2-

20) with Redlich-Kister equation for the binary excess Gibbs energy, GC", as expressed

by









Gix = xx12 ( +2 -x2)+- ) +x L +L (x-x) +

+x,x, {L+J3(x, -x)+.--) (2-29)

where Lo is the binary interaction parameter of regular solution model and L' is the binary

interaction parameter of sub-regular solution model. It is generally called the Redlich-

Kister-Muggianu equation.

2.2.3 Experimental Information

2.2.3.1 Ternary compounds

Four ternary compounds Cu13In3Se1n, CuInSe2, CuIn3Se5, and CuInsSes, located on

the Cu2Se-In2Se3 pseudo-binary section (Figure 2-10), were identified as stable phases,

though several other compounds have been reported [GodOOa-c]. The CuInSe2, CuIn3Se5

and CulnsSe8 phases have large homogeneity ranges. Under atmospheric pressure,

CuInSe2 has two polymorphs separated by a first order transition between chalcopyrite

(a) and sphalerite (6) structures. The CuIn3Se5 has a tetragonal chalcopyrite-like

structure and the CuIn5Se8 has a hexagonal structure. Interestingly, it was found that

another phase often co-exists with a hexagonal CuInsSes. This co-existing phase could

be a trigonal [MerOO] or tetragonal [KohOO] structure. The Cul31n3Sell is reported as a

line compound [GodOOb], which is stable within the narrow temperature range 923 to 947

oC.

2.2.3.2 Thermodynamic properties

Only few thermodynamic data are available for CuInSe2 compounds. The heat

capacity of CuInSe2 was measured by Boehnke et al. using both pulsed and semi-

adiabatic calorimetric techniques, but only at low temperature (<300K) [Boe87]. The

experimental values of the enthalpy of formation of CuInSe2 at 298K are summarized in









Table 2-5. No thermodynamic information, however, has been reported concerning the

CuIn3Se5 and CulnsSes compounds.

Table 2-5. The experimental values of the standard formation enthalpy (AH0,298K) and
energy (AE,0 ) of a-CulnSe2
AH,298 (kJ/mol) Method Reference
267.4 Mass Spectrometry [Ber73]
260.2 Calculation [Gla79]
280.0 Calculation [Gom84]
189.8 Calculation [Red48]
204.4 Calculation [Moo99]

AEf,0 (kJ/mol)

190.30 ab initio [Zha98]


Electro-motive force (EMF) measurements were performed by Ider [Ide03], to

extract Gibbs energy information of ternary compounds (e.g., CuInSe2, CuIn3Ses,

CuIn5Ses) from the appropriate galvanic cell reactions. It is noted that since the exact

composition of the participating ternary compounds is generally unknown or may be far

from the stoichiometry, the resulting thermodynamic properties directly calculated from

cell reactions may not be quite reliable.

2.2.3.3 Phase diagrams

The Cu2Se-In2Se3 pseudo-binary section [Kon82, Fea86, Haa98] and projection of

liquidus surface [MerOO, Kon82, Fea86, Boe87, Bac88] have been reported by several

authors. These phase diagrams, however, are quite divergent and thus very difficult to

assess. Godecke et al. reported a series of phase diagrams of the Cu-In-Se system based

on thorough experiments using more than 240 alloys [GodOOa-c], where the phase

diagrams, including a projection of liquidus surfaces, a projection of four-phase plane,

three isothermal sections and ten isopleths, are self-consistent.









2.2.4 Ab initio Calculation on the Ternary Cu-In-Se Compounds

The formation energies of different point defects in various Cu-In-Se ternary

compounds were calculated by Zhang using an ab initio method. The existence of a

series of unusual ordered defect compounds (ODC) along the CuSe2-In2Se3 section and

their large off-stoichiometry are explained by the particularly low formation energy of the

(2Vcu+Incu) defect pair in these compounds [Zha98].

The CuIn3Se5 and CulnsSe8 are considered as ODC's of CuinSe2 and form by the

reaction of

n(CulnSe2) + m(In) Cu(n-3m)In(m+n)Se2n + 3m(Cu) (2-30)

where n=2.5, m=0.5 for CuIn3Se5 and n=4 m=l for CulnsSes. The energy change of the

reaction is calculated by

AE, = AEne, + AE,nt AEord (2-31)

where AEne, is the formation energy of non-interacting neutral defects, zAEt, is the intra-

pair interaction energy, and AEod is the pair-pair ordering energy. The formation

energies of CuIn3Se5 and CulnsSes compounds can then be calculated by

AEs = 2.5AEns +0.5E, -1.5Ec, +AE (Culn3Ses) (2-32)
Cu 3n3Se5 Cu 2nSeI

AEn, = 4AEC + E, -3Ecl + AE (CulInSe,) (2-33)

As the defect compounds are related to the end-members in the sub-lattice model,

their formation energies are used to estimate the Gibbs energy of the end-members. It

can largely reduce the arbitrary aspects of the model parameters. For example, the

formation energy of Vcu is defined as the energy change of the reaction

CuInSe2(a)=InInSe2(a)+Cu (2-34)









InInSe2(a) is regarded as a end-member in the sub-lattice model of CuInSe2(a) and

its Gibbs energy can be estimated from the formation energy of Vcu.

2.2.5 Establishment of Thermodynamic Descriptions

In this work, sub-lattice models [Sau98] are used to describe thermodynamic

properties of the ternary compounds. Unlike conventional thermodynamic optimization

evaluating model parameters from abundant sources of phase diagrams and

thermodynamic experiments, only one set of data were selected for this work to avoid the

possible confusion caused by randomly mixing the divergent data for such a complicated

system.

2.2.5.1 Sub-lattice model for different ternary compounds

The a-CuInSe2 belongs to the family of I-III-VI2 chalcopyrite semiconductors

whose structure is similar to the zinc-blende structure where each of the two cations (Cu

and In) are coordinated by four anions (Se), but the Se is coordinated by (2Cu + 2In) with

different nearest-neighbors. The Se deficiency is mainly caused by Cu occupying an

interstitial position [Zha98], the sub-lattice structure of a-CulnSe2 is thus considered as

(Cu, In, Va)1 (Cu, In, Va)1 (Se)2 (Cu, Va)i

Formula (5.37) in [Sau98] is used to calculate Gibbs energy of this phase where the

Gibbs energy of the 18 end-members including CulInlSe2Val, CuiCuiSe2Val, and

VaiCulSe2Val, needs to be estimated. In the same manner, the sub-lattice structures of

CuIn3Se5 and CuInsSes are expressed by

(Cu, In, Va)i (Cu, In, Va)3 (Se)5 (Cu, Va)i

(Cu, In, Va)i (Cu, In, Va)5 (Se)8 (Cu, Va)i

The 6-CuInSe2 is a disordered phase of a-CuInSe2 with a sphalerite structure where

the two metals (Cu and In) can be replaced by each other much more easily than in a-









CuInSe2 to achieve almost random mixing. The sub-lattice structure of the 6-CuInSe2 is

considered as (Cu,In,Va)2(Se)i(Se,Va)2 to keep its composition close to the section of

Cu2Se-In2Se3, as observed experimentally.

2.2.5.2 Evaluation of Gibbs energies of end-members in the sub-lattice model

Gibbs energy of formation of CuInSe2 (a)

To estimate the Gibbs energy of formation of CuInSe2(a), the EMF results reported

by Ider [Ide03] were utilized. Three different kinds of galvanic cells were designed:

Cell I: W, In(l), In203(s) //YSZ // In203(s), Cu2Se(P), Cu(s), CuInSe2(a or 6), C, W

Cell II: W, In(l), In203(s) // YSZ // In203(s), CulIn3Se5(s), CuInSe2(a or 6), C, W

Cell III: W, In(l), In203(s) // YSZ //In203(s), CulIn5Ses(s), CulIn3Ses(s), C, W

The overall reaction of cell I is expressed as

2Cu2Se(P) + In(l) <- CuInSe2(a or 6 ) + 3 Cu(s) (2-35)

In this work, the composition of CuInSe2 is assumed to be in stochiometry because

the CuInSe2 phase has a relatively narrow composition range when it is in equilibrium

with Cu2Se(P). Thus if the solubility of In in Cu2Se(P) phase is negligible, the Gibbs

energy of formation of CuInSe2(c) can be directly calculated by

AGCune2( = AGR (cell I) + 2AG 2 (2-36)

and AGR was reported by Ider [Ide03] as

AGR = -99520 + 54.50xT [J/mol] (949 to 1044K) (2-37)

From assessment of the Cu-Se system, the AGCS2, p is expressed by

AG2 ;~ = 60221.86 95.47xT + 10.21xTln(T) 0.01xT2 + 3.70x10-6xT3

53288.13/T [J/mol] (2-38)

Plugging equations (2-37) and (2-38) into equation (2-36) yields









AGcuinse2 = -209963.72 36.43xT + 20.41xTln(T) 0.02xT2 + 7.40x10-6xT3

106576.26/T [J/mol] (2-39)

The standard enthalpy of formation of CuInSe2(a) at 298.15K calculated from

AGuonse2() obtained by equation (2-39) is around 218.50 kJ/mol, which is similar to the

literature values listed in Table 2-5.

Estimation of Gibbs energy of CuInSe2(6), Culn3Ses and CuIn5Ses

As mentioned before, EMF experimental results can provide only a rough

estimation of the Gibbs energy of formation of CuInSe2(6), CuIn3Se5 and CulnsSes

mainly because of their non-stoichiometric composition during cell reaction. Ider [Ide03]

reported the Gibbs energy change of reaction for cell I through III such as

AGR (Cell I) = -89520 + 45.10xT [J/mol] (1055 to 1150K) (2-40)

AGR (Cell II) = 90160 110.77xT [J/mol] (868 to 1045K) (2-41)

AGR (CellIII) = 109180 125.90xT [J/mol] (1054 to 1179K) (2-42)

In the exactly same manner as for CuInSe2(a), the Gibbs energies of formation of

other ternary compounds (i.e., CuInSe2(6), CuIn3Se5 and CuInsSes) were estimated as

AGcins(s = -209963.72 145.83xT + 20.41xTln(T) 0.02xT2 + 7.40x10-6xT3

106576.26/T [J/mol] (2-43)

AGf;,e =-438646.71 1794.61 xT + 259.98xTln(T) 9.84x10-2xT2

+ 2.40x10-5xT3 528546.24/T [J/mol] (2-44)

AGc,,, = -717569.69 3404.57xT + 499.55xTln(T) 1.48x10-1xT2


+ 4.07x10-5xT3 1163668.00/T [J/mol]


(2-45)









On the other hand, the Gibbs energy of formation of CuIn3Se5 and CuInsSes at their

stoichiometric composition can also be estimated by ab initio calculation where they are

considered as ordered defect compounds of CulnSe2. In the same pattern as equations (2-

32) and (2-33), the Gibbs energy of formation of Culn3Se5 and CulnsSes are expressed by

AGC = 2.5AG +0.5G, -1.5GC, + AG (Culn3Se,) (2-46)
Culn Se5 Cu'nSe2

AG s = 4AG~ + G 3GC, +AG, (Culn Se,) (2-47)
Cu~n5Se. CulnSe2

In this work, the volume and entropy change for the defect formation reaction is assumed

to be negligible and thus the values of AG,(CuIn3Ses) and AG,(CuInsSes) are identical to

AE,(CuInsSes) and AE,(CuInsSe8) calculated by equation (2-31) where the values of AEneu,

AEn,, and AEod are taken from [Zha98] as shown in Table 2-6. The value of AGCnse

is directly calculated from equation (2-39).

In summary, the estimated Gibbs energies of formation from the ab initio study are

AGc ,,S = -557341.00 337.26xT + 51.04xTln(T) 5.51x10-2xT2

+ 1.85x10-5 T3 266441.00/T [J/mol] (2-48)

AG, ,,s = -892788.00 538.09xT + 81.66xTln(T) 8.81x10-2xT2

+ 2.96x10- xT3 426305.00/T [J/mol] (2-49)

Table 2-6. Parameters used to calculate AE'of CuIn3Se5 and CuInsSe8 [Zha98].
AEneu(eV) AEint(eV) AEord(eV) AEr(eV)
CuIn3Se5 2.27 -2.105 -0.225 -0.06
CuIn5Se8 4.54 -4.21 -0.43 -0.10









Estimation of the Gibbs energy of other end-members

The Gibbs energy of the other end-members in the a-CulnSe2, P-CuIn3Ses, y-

CuIn5Se8 compounds is estimated using the defect formation energies calculated by

Zhang [Zha98] according the defect formation reactions such as equation (2-34).

For example,

GVa1Cu1 = GSea+ CunSec c- G VC (2-50)

GCuIise2cu G/ ne2(c) +Ecu()+ Gu (2-51)

Optimization of parameters in the Gibbs energy expressions

The Gibbs energy expressions of the ternary compounds are adjusted to satisfy the

relevant experimental phase relationships [God00a-c]. The results are compared with the

available data. It is believed that the complicated phase relationships may play an

important role in controlling the chemical potentials of these compounds within a

reasonable range. Finally, the Gibbs energy parameters are optimized as

GCinse2(a) = -251102.38 688.51xT 135.95xTln(T) + 0.03xT2

3.47x10-xT3 265806.00/T [J/mol] (2-52)

Guinse2() = -186607.34 + 505.39xT -114.87xTln(T) [J/mol] (2-53)

GC3se, = -550466.88 + 1175.69xT 249.24xTln(T) 1.02x10-3xT2

1.22x107xT3 582645.00/T [J/mol] (2-54)

GCnSse8 = -940623.58 + 1916.46xT 389.81xTln(T) + 7.32x10-6xT2

2.90x107xT3 1006060.00/T [J/mol] (2-55)









The optimized Gibbs energy (Go) and Gibbs energy of formation (AG') are

compared with the results of EMF experiment and Ab initio calculation, as represented in

Figures 2-11 and 12.

2.2.6 Summary

The EMF experimental results, ab initio calculation, and phase equilibrium data

were successfully combined to establish reliable descriptions of Gibbs energy for ternary

compounds in the Cu-In-Se system. The EMF result was directly adopted only for the

Gibbs energy of CuInSe2(u) by assuming the stochiometric composition. The influence

of the solubility of indium in Cu2Se(3) on the electronic transfer and thus the Gibbs

energy of formation was also considered. The reaction was considered as

2Cu2-3yInySe(P) + (1-y)In(l) <- CuInSe2(a or 6 ) + (3-6y)Cu(s)

The number of electrons to be transferred is (3-6y) to form one mole of

CuInSe2(a). The difference of Gibbs energy of formation between Cu2-3yInySe(3) and

Cu2Se is calculated using the formation energy of the defect pair (2Vcu+Incu) [Zha98].

This approach, however, yields an unreasonable value of enthalpy of formation for

CuInSe2 at 298.15K, whereas the calculation using AGCse(pf expression in equation (2-

38) shows reasonable results, which is in a good agreement with most of literature values.

The comparison of the optimized Gibbs energy of the CuInSe2(6), CuIn3Se5 and

CuIn5Ses with that estimated by EMF experiment and ab initio calculation demonstrates

reasonable agreement. The phase relationships concerning these ternary compounds

follow the experimental isothermal section of the Cu-In-Se system at 500, 800 and 900

C shown in Figures 2-13 to 15, respectively. It can be concluded that a set of reliable









Gibbs energy expression was obtained, although its precision would be further improved

with additional experimental and theoretical study.


0 0.1
In2Se3


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cu2Se


Figure 2-10. Pseudo-binary In2Se3-Cu2Se phase diagram [GodOOa]











0



-500 -
G
(kJ/mol)

-1000 -



-1500 -



-2000 -



-2500 -



-3000


p


This work

ab initio


p


500


1000
T (K)


1500


2000


Figure 2-11. Optimized Gibbs energy a-CuInSe2, P-CuIn3Se5 and y-CuInsSes compared
with that estimated from EMF experiments and ab initio calculation










0




-200




-400
AGf
(kJ/mol)

-600




-800




-1000


This work = EMF[Ide03]


EMF[IdeD3J

ab initio


500
T (K)


1000


1500


2000


Figure 2-12. Optimized Gibbs energy of formation of c-CuInSe2, P-CuIn3Se5 and y-
CuIn5Ses compared with that estimated from EMF experiments and ab initio
calculation






























0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 0.9 1.0
Cu In


Figure 2-13. Isothermal sections of Cu-In-Se at 500 OC. (a) Calculation [She06], (b)
Experimental evaluation [GodOOc]


0 0.1 0.2 0,3 0.4 0.5 0.6 0.7 0.8 0.9 1,0
Cu In


0 0.1 0.2 0.3 0.4 0.5 0,6 0.7 0.8 0.9 1.0
Cu


Figure 2-14. Isothermal sections of Cu-In-Se at 800 OC. (a) Calculation [She06], (b)
Experimental evaluation [GodOOc]
















(a) (b)


Se Se
10

0.9 0.9
0.8 0.8
0.7 0.7
0.6 006
0.5 0.5
0.4 0.4
0.3 03
0.20.2
0.1 0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
In Cu In Cu





Figure 2-15. Isothermal sections of Cu-In-Se at 900 OC. (a) Calculation [She06], (b)
Experimental evaluation [GddOOc]









2.3 Cu-Ga-In Ternary Phase Diagram Calculation

2.3.1 Introduction

The selenization of metallic Cu/Ga/In precursors is one of the most promising

industrial processes for CIGS cell fabrication, which is generally called the "two-step

process" and has been commercially employed by Shell Solar and Showa Shell. The

commercialized two-step process consists of the deposition of metallic precursors (i.e.,

Cu/Ga/In) followed by subsequent selenization, as shown in Figure 1-8. Traditionally,

the metal precursors are prepared by sputter deposition and then selenized at high

temperature (-600 C) in a reactive H2Se or Se vapor ambient. Therefore, understanding

the equilibrium phase relationships in the Cu-Ga-In ternary system is essential to the

optimization of the two-step process.

2.3.2 Review of Sub-binary Phase Diagrams

The phase diagrams of the three sub-binary systems, e.g., Cu-In, Cu-Ga and Ga-In,

were well assessed by Liu [Liu02], Subramanian [Sub88], and Anderson and Ansara

[And91], respectively. Thermodynamic assessment of the Cu-In binary phase diagram

was first performed by Kao et al. [Kao93], based on the review [Bol93] of

thermodynamic and phase equilibrium data available in the literature. In their assessment,

a Redlich-Kister expression was used to represent the Gibbs energies of the liquid and Cu

phase, and a Wagner-Schottky model was employed for the Gibbs energy of r-Cu2In

phase. All other intermetallic phases were then approximated as line compounds.

Recently, Liu et al. [Liu02] reassessed the Cu-In binary phase diagram by including

additional experimental data [Bah99, DicOO] and adopting a three-sublattice models for y

and q' phases, while assuming stoichiometric compounds for other intermetallic phases,










as shown in Figure 2-16. Most recently, Bahari et al. reported new experimental data

using DSC, XRD, and EPMA analysis [Bah03]. The results indicate the existence of a

solubility region of indium in copper with the limit of the solid solution at 5.20 at.% In at

400 C and of six intermediate phases, i.e., the three low-temperature phases 6, q and

Culln9(O), and the three high-temperature phases y, r' and P. The boundaries of each

phase were defined with respect to temperature and composition.


1200- I I I I I


1000-

Liquid
y 800-


5 600-
L


400- /


200-



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0,8 0.9 1.0
CU Mole fraction of In In
Figure 2-16. Calculated phase diagram of Cu-In binary system [Liu02]

The general features of the Cu-Ga phase relationships have been well established

by Hansen [Han58] and subsequently revised by Kittl [Kit64]. Subramanian et al.

[Sub88] used these accurately established phase boundaries and some additional

thermodynamic data to optimize the thermodynamic parameters for the various

intermediate phases. The calculated phase diagram containing three binary phases 3, y

and t is shown in Figure 2-17.





















VI 800-
u0


600-
L
0.
E
400-
I-


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

CU Mole fraction of Ga Ga

Figure 2-17. Calculated phase diagram of Cu-Ga binary system [Ide03]


200- I I I I I I




150-


0%
M 100- Liquid


In
I .^-- In--

E 50
0 .


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ga Mole fraction of In In

Figure 2-18. Calculated phase diagram of Ga-In binary system [And91]









The Ga-In binary system is known to be a simple eutectic type with negligible

solubility of indium in solid a-Ga. The Ga-In binary phase diagram assessed by

Anderson and Ansara [And91] showed a retrograde tetragonal indium solidus with

solubilities of 2.3 at.% gallium in indium at the eutectic temperature of 15.3 C and of

14.2 at.% indium in the liquid, as evidenced by Figure 2-18.

2.3.3 Prediction of Cu-Ga-In Ternary Phase Diagrams

Unfortunately, there are no experimental data available about the interaction

between ternary Cu-Ga-In components. Therefore, Muggianu's equation based on the

summation of the binary interaction parameters was employed to extrapolate the excess

Gibbs energy of mixing into ternary system [Sau98], as described in section 2.2.2.

To use the ThermoCalc program to estimate the CGI ternary phase diagram, it is

necessary to prepare the TDB (Thermodynamic DataBase) module containing the Gibbs

energy information of pure Cu, Ga and In elements as well as the interaction parameters

of three sub-binary Cu-Ga, Cu-In and Ga-In systems. The TDB module of ternary Cu-

Ga-In system was composed by combining three binary data described in the previous

section 2.3.1. For the simplification, the Cu-Ga binary compounds (i.e., 3, y and ) were

modeled by solid-solution models, while the Cu-In binary compounds (i.e., 6, y, q and 0)

except P phase modeled by solid-solution model were modeled by sub-lattice models.

The Cu-Ga-In ternary phase diagram was then predicted using ThermoCalc program, as

shown in Figures 2-19 to 22. Five different solid solution phases (i.e., Cu-fcc, 6-Cu7In3,

r-Cu2In, ,-CU7Ga2 and y-Cu9Ga4) and a liquid phase region were included in the 500 C

isothermal section of Cu-Ga-In ternary phase diagram shown in Figure 2-19. It is noted

that the ternary phase diagrams presented in Figures 2-19 to 22 were estimated on the









basis of binary information only and thus the models do not contain any ternary

interaction parameters. To obtain a more reliable ternary phase diagram, one needs to

investigate the existence of any new ternary phases and the solubility of the third element

in binary compounds, and optimize the ternary interaction parameters in a form of G12 =

x]x2X3(L]x] + L2x2 + L3x3).

Furthemore, the vapor pressures for Cu-Ga-In mixtures at several compositions

were calculated using the ThermoCalc program in combination with the Cu-Ga-In ternary

TDB module. Selected results shown in Figures 2-23 and 2-24 revealed that six vapor

phase species (i.e., Cu, Cu2, Ga, Ga2, In and In2) dominate the gas phase and the atomic

indium is the most volatile among them.

Ga


0.9

X(Ga) 0 .
0.7
CugGa4 (7 0.6
Cu7Ga2( ) 0.5 \

Liquid


cu-fcc (a) B0.2
0.,
0 EL L EL ,' --
Cu 0 U. / -(n) 0.6 0.a 1.0 In
Cu X(In) In
Cuyln3(6) Cu2ln(q)
Figure 2-19. Isothermal section (500 C, latm) of the Cu-Ga-In ternary phase piagram
based on the Muggianu's equation









Ga
0, 4R -V-


CugGa4()




I
0.21
Cu7Ga2(-) ,


0 0.05
Cu-fcc (a)


0.10 0.15 0.20


Figure 2-20. Isothermal section (500 C, latm) of the Cu-Ga-In ternary phase piagram
based on the Muggianu's equation for the range of 0 < x(In) < 0.2 and 0.2 <
x(Ga) < 0.4

Ga


D. 8 -

0. &4'


CugGa4(y)


Cu7Ga2()-
0.2Z


Cu-fcc

0 0.2 4 0.6
CU Cu7TIn3() Cu2In(rq)
Figure 2-21. Isothermal section (350 C, latm) of the
based on the Muggianu's equation


0.B 1.0


Cu-Ga-In ternary phase piagram


0.20

Cu












Ga


Cu


0 0.2 0.4 0.6 0.8 1.0


Figure 2-22. Isothermal section (800 C, latm) of Cu-Ga-In ternary Phase Diagram
based on the Muggianu's equation


1.E+01

1.E-01

1.E-03

1.E-05
U)
T 1.E-07
0)

o

1.E-11

1.E-13


1.E-15 --
500


700 900 1100 1300
T (K)


1500


Figure 2-23. Vapor pressure as a function of temperature in the Cu-Ga-In mixture
(Cu:Ga:In = 1:1:1 mole ratio)











1.E+01
.0 In
OTotal pressure ..
1.E-01 Ga

q Cu
1.E-03- Q-

1 .E-05 In

0 Q ." Ga2
u 1.E-07- *
Cu2

& 1.E-09

1.E-11 0

1.E-13

1.E-15i .
500 700 900 1100 1300 1500
T (K)
Figure 2-24. Vapor pressure as a function of temperature in the Cu-Ga-In mixture
(Cu:Ga:In = 2:1:1 mole ratio)

2.3.4 Modification of Cu-Ga-In Ternary Phase Diagrams

Recently, an experimental result concerning the ternary phase relationship of the

Cu-Ga-In system was reported [Pur06b]. In their study, samples were prepared by

sequential DC-magnetron sputtering of 8 triple layers of the sequence Cu/CuGa2/In on

Mo-coated glass substrates to ensure a good mixing of the components. The samples

were annealed in H2 ambient to reduce any oxides at 350 oC for 2 min and then cooled to

room temperature for subsequent X-ray diffraction analysis. Cul6(In,Ga)9, Cu9(Ga,In)4

alloys, and elemental indium were identified as the equilibrium phases in the Cu-Ga-In

composition studied. This was arrived at by assuming that the shifts of Cul61n9 and

Cu9Ga4 reflection peaks resulted from the substitution of indium by gallium and gallium

by indium, respectively. Considering their results as summarized in Table 2-7, the Cu-

Ga-In ternary phase diagram predicted by the Muggianu's equation was modified.










Table 2-7. Experimental results of phase relationships of Cu-Ga-In ternary system
No. Atomic fraction Equilibrium phases at 350 C
Cu In Ga
1 0.479 0.458 0.063 Cui6(In,Ga)9, In
2 0.550 0.365 0.086 Cui6(In,Ga)9, In
3 0.479 0.417 0.104 Cui6(In,Ga)9, Cu9(Ga,In)4, In
4 0.479 0.391 0.130 Cui6(In,Ga)9, Cu9(Ga,In)4, In
5 0.479 0.359 0.161 Cui6(In,Ga)9, Cu9(Ga,In)4, In
6 0.479 0.328 0.193 Cu9(Ga,In)4, In
7 0.640 0.230 0.129 Cui6(In,Ga)9, Cu9(Ga,In)4
8 0.659 0.123 0.218 Cu9(Ga,In)4

Based on experimental data at 350 C, the thermodynamic parameters were

manually adjusted to account for the extended solid solutions as reported. To describe the

solubility of indium into Cu9Ga4, which is expressed as Cu9(Ga,In)4, the two-sublattice

model described by (Cu,Va) (Ga,In) was employed. The resulting isothermal section of

Cu-Ga-In ternary phase diagram at 350 C and 1 atm along with experimental data is

shown in Figure 2-25.


Ga


0.9"
0.8-/


(7) 0.4-
Cug(Ga,ln)4 --


0 0.1 0.2
CU Cu,7


0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cu1,(In,Ga),-(q)










Figure 2-25. Modified isothermal section (350 C, latm) of the Cu-Ga-In ternary phase
diagram with experimental data (symbol)


Ga

1.0

0.9

0.8

0.7

0.6 Liquid

0.5

0.4
Cuo(Ga,In)4 -(y)
0.3
CGa2(M)
0.2

0.1
Cu-fcc
0
0 0.1 0.2 .3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cu Cun3() C(In,a),-I) I


Figure 2-26. Modified isothermal section (500 C, latm) of the Cu-Ga-In ternary phase
diagram

Furthermore, the optimized thermodynamic parameters are used to predict the

isothermal section of Cu-Ga-In phase diagram at 500 OC and 1 atm, as displayed in

Figure 2-26. It should be noted, however, that the experimental data used here were

based on thin film Cu-Ga-In samples which may have a different equilibrium from bulk

material.

2.3.5 Summary and Future Work

The Cu-Ga-In ternary phase diagram was predicted by ThermoCalc program

employing a Maggianu's equation based on the sub-binary phase diagrams.

Subsequently, the predicted ternary phase diagrams were modified using recent






68


experimental data. In the future, the further optimization can be achieved by the

followings:

* Modify the thermodynamic descriptions for the sub-binary systems to make the
models extendable to higher-order systems (sub-lattice model is preferred).

* Perform the thermal analysis along with X-ray measurements to identify the phase
transformation temperatures.

* Measure the solubility of the third elements in binary phases (e.g., Ga in 6-Cu7In3)
to estimate the interaction parameters between elements in a sub-lattice.

* Perform the EMF experiments to obtain the ternary interaction parameters for the
liquid and Cu-fcc phases.














CHAPTER 3
METAL (CU, IN, GA)-SE REACTION PATHWAYS

3.1 Introduction

The phase equilibria of the binary Cu-Se system have been reviewed by Glazov et

al. [Gla00] and a thermodynamic assessment using the ThermoCalc software was

discussed in chapter 2. Four intermediate binary compounds Cu2-xSe, Cu3Se2, CuSe, and

CuSe2 were experimentally identified. The Cu2-xSe compound is known to melt

congruently and have two polymorphs: the low-temperature stable a-Cu2-xSe phase and

the high-temperature modification (i.e., 3-Cu2-xSe) having a transition temperature of

around 396K. Three CuSe polymorphs a-CuSe, P-CuSe, and y-CuSe were also reported.

A thermodynamic assessment of the binary In-Se system was performed based on the

evaluation of literature by Li et al. [Li04]. Multiple intermediate compounds (In4Se3,

InSe, In6Se7, In9Sen1, InsSe7 and polymorphic In2Se3 (c, 3, y and 6)) were identified as

shown in the phase diagram in Figure 3-1. Phase diagram evaluation and thermodynamic

assessment of the binary Ga-Se system have been reported by Dieleman et al. [Die82]

and by Ider [Ide03], respectively. According to their reports, only two binary compounds

(i.e., GaSe and Ga2Se3) are stable in the Ga-Se system, as shown in Figure 3-2.

Furthermore, Ga2Se3 has two polymorphisms: a low-temperature stable 3-Ga2Se3 phase

and its high-temperature modification (i.e., a-Ga2Se3) with a transition temperature of

around 967K.









In this thesis (Chapter 4), a systematic study of the reaction pathways and kinetics

of formation of CuInSe2 using in situ high-temperature XRD is presented. In these

studies, the reaction pathway and kinetics of c-CuInSe2 formation from different

precursors (e.g., InSe/CuSe [Kim05a] and In2Se3/CuSe [Kim05b, Chapter4]) and

selenization of metallic Cu-In precursor have been presented [Kim06a, Chapter4]. In this

chapter, the reaction pathways for binary metal (i.e., Cu, In and Ga)-Se formation from

various precursor structures were investigated by in situ high-temperature X-ray

diffraction.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
In x(se) Se

Figure 3-1. Phase diagram of In-Se binary system [Li04]


































0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ga x(Se) Se
Figure 3-2. Phase diagram of Ga-Se binary system [Ide03]

3.2 Experimental

3.2.1 Precursor Preparation

Precursor films used in this study were grown using a migration enhanced epitaxy

(MEE) system described in Chapter 1.5. As in traditional molecular beam epitaxy, an

ultra high vacuum environment and effusion cells are employed to generate molecular

beam fluxes of elemental sources. In MEE, however, the substrate is sequentially

exposed to each source through revolution of a platen containing the substrate, rather than

a simultaneous co-deposition from all the sources. The fluxes of Cu and In sources are

controlled by electron impact emission spectroscopy (EIES) sensors while those of Ga

and Se sources are controlled by the source temperature. The base pressure of the system









was established at 8x10-9 Torr, and the pressure during deposition was maintained in the

range of 10-7 to 10-8 Torr depending on the operating conditions. Further details of the

deposition technique and experimental apparatus are given elsewhere [Kim05b].

As shown in Figure 3-3, single-layer and bilayer metal(i.e., Cu, In and Ga)-Se

precursor films were deposited on extremely smooth and sodium-free (alkali level <

0.3%) thin glass substrates (Corning #7059). Glass substrates with a thickness of 0.4

(+0.127) mm were employed to minimize the temperature difference and response time

between the Pt/Rh heater strip (width 0.5") and the precursor film (0.5"x0.5") in the

HTXRD furnace used for subsequent characterization.

(a) (b) (c)

Cu+Se In+Se Ga+Se

Glass Glass Glass
[Se]/[Cu] 2.4 [Se]/[In] ~ 4.1 [Se]/[Ga] ~ 6.1

(d) (e) (f)

Se Se Se

Cu In Ga
Glass Glass Glass
[Se]/[Cu] 2.0 [Se]/[In] ~ 4.2 [Se]/[Ga] 3.9

Figure 3-3. As-grown precursor structure along with overall atomic composition

The elementally mixed single-layer precursors (i.e., Figure 3-3(a)-(c)) were

fabricated by co-depositing metal and Se without heating the substrate to minimize the

potential reaction between metal and Se. Bilayer precursors (i.e., Figure 3-3(d)-(f)) were

prepared by depositing a metal film followed by subsequent deposition of a Se film

without heating the substrate. Selenium deposition was controlled to maintain a Se-









excess atomic composition, i.e., [Se]/[Metal] > 2.0, to compensate for the selenium

volatilization losses during thermal annealing in the HTXRD furnace. The atomic

composition of as-grown precursors was measured by inductively coupled plasma optical

emission spectroscopy (ICP-OES), as inserted in Figure 3-3.

3.2.2 In situ high-temperature X-ray diffraction

Two types of high-temperature X-ray diffractometers (HTXRD), i.e., Scintag-

HTXRD and PANalytical-HTXRD, were used in this study. The Scintag-HTXRD

consists of a Scintag PAD X vertical 0/0 goniometer, a Buehler HDK 2.3 furnace, and an

mBraun linear position sensitive detector (LPSD). In contrast to conventional X-ray

point scanning detectors that perform the scanning step-by-step from lower to higher

angles, the LPSD collects the XRD data simultaneously over the 100 20 window,

dramatically shortening the data collection time. This permits in situ time-resolved

studies of phase transformations, crystallization, and grain growth. A type-S

thermocouple is welded onto the bottom of a Pt/Rh strip heater to measure the heater

temperature directly and gives feedback to the temperature controller. Precursors are

mounted on the heater strip using carbon or silver paints to improve the thermal contact

between the precursor and heater strip. The PANalytical-HTXRD system is composed of

a PANalytical X'Pert Pro MPD 0/0 X-ray diffractometer equipped with an Anton Paar

XRK-900 furnace and an X'Celerator solid state detector. A surrounding heater is used

in a PANalytical-HTXRD, while a strip heater is used in the Scintag-HTXRD. Both

HTXRD furnaces were purged by flowing He and the precursor surface temperature in

the furnace was calibrated from measurement of the lattice expansion of silver powder

dispersed on an identical substrate and comparing the results to the equation suggested by










Touloukian [Tou77]. Since a PANalytical-HTXRD provides better resolution than a

Scintag-HTXRD, it was used for the samples having a poor signal to noise ratio.

3.3 Cu-Se Binary Formation

3.3.1 Glass/Cu/Se Precursor

Phase evolution in the glass/Cu/Se precursor with an atomic composition of

[Se]/[Cu]-2.0 was investigated during temperature ramp annealing using a PANalytical-

HTXRD purged by flowing He. The as-grown precursor was first scanned at 25 C for

10 min and then heated to 60 OC at a rate of 20 C/min. The X-ray diffraction data were

collected for 10 min at every 10 C during subsequent ramp heating to 470 C at a rate of

20 C/min, as shown in Figure 3-4.







470

400













s JII- ----------------- 26~----~- -- ------------^-u---la \+5(5
300 2-Phase evolution of glass/Cu/Se precursor observed by in xSe


CuSe




+uSe(o)
60 + Se.
25 .

20 25 30 35 40 45 50 55 60
26

Figure 3-4. Phase evolution of glass/Cu/Se precursor observed by in situ X-ray
diffraction. (JCPDF) Se: 06-0362, CuSe: 20-1020, CuSe2: 26-1115, Cu2-xSe:
06-0680.









The diffraction data at 25 C show the scattering by elemental Se and CuSe, which

demonstrates the crystalline CuSe forms during the precursor preparation even without

heating substrate (Tsubstrate = 40 60 OC). The transformation of CuSe into CuSe2 was

initiated at approximately 160 C, at which temperature the crystalline Se phase suddenly

disappeared, presumably by rapid formation of CuSe2 through reaction of CuSe with the

excess Se. It is noted that rapid disappearance of Se-related peaks occurs well below the

Se melting temperature (-221 C). The Se is likely to be released from CuSe2 as

evidenced by the decrease of reflection intensities of CuSe2, which is then followed by

the subsequent transformation of CuSe2 into y-CuSe at around 250 C. Further heating

above 300 C leads to the release of more Se to yield 3-Cu2-xSe, which is the most stable

compound of the Cu-Se binary system at high temperature (Figure 2-1). A series of

temperature-dependent phase evolutions of glass/Cu/Se precursor qualitatively follow the

same sequence (i.e., CuSe2 CuSe Cu2-xSe) as predicted equilibrium phase diagram

[Gla00, She06], even though the actual phase transition temperatures are different from

the equilibrium values. The temperature-dependent phase transformation of this

precursor can be summarized as y-CuSe + Se CuSe2

T 160 C

CuSe2 y-CuSe + Se (evaporated) T 250 C

2y-CuSe Cu2-xSe + Se (evaporated) T 300 C

3.3.2 Glass/Cu-Se Precursor

Temperature-dependent phase evolution of glass/Cu-Se precursor with an atomic

composition of [Se]/[Cu]-2.4 was investigated using the Scintag-HTXRD system. The

glass/Cu-Se precursor was first scanned at 25 OC and then heated to 50 OC at a rate of 20










C/min. Four sequential scans (Imin acquisition/scan) over the range 22 to 540 (20) were

taken at 10 OC increments while the sample was heated from 50 to 300 OC at a rate of 30

C/min in a flowing He atmosphere. After scans at 300 OC, the samples were heated to

400 C at a rate of 60 C/min and then scanned twice. As shown in Figure 3-5, only a

weak CuSe (006) peak is detected at 25 C and unlike Figure 3-4, there are no broad

background peaks. Since this peak is so weak, it is not detected in every part of sample.

The metastable Cu7Se4 phase begins to form at -80 OC as evidenced by Cu7Se4 (320, 321).


Cu2Se CuSe
(111) (102)


CuSe(006)







k Cu7Se4(320)


30 CuSe(O0b;)
25 ~


























CuSe4: 26-0557, Cu2Se: 46-1129.
(321) _-34
-- ---- ---0 31- 323

27 28 29 30
22527 2--5 --20


Figure 3-5. Phase evolution of glass/Cu-Se precursor observed by in situ X-ray
diffraction.(Bottom: 25 to 340 20 magnified). (JCPDF) CuSe: 20-1020,


As this metastable phase forms, the CuSe (006) reflection begins to increase and then

decrease as more Cu7Se3 forms to return to a weak peak. It is possible that CuSe

formation begins to increase and serves as the seed for nucleating Cu7Se4, which grows

encloses the CuSe seed to reduce the peak intensity. The subsequent CuSe peak intensity

at higher temperature indicates that only a small portion of the Cu is now found in the

CuSe phase.

The metastable Cu7Se4 phase reacts with amorphous Se (no evidence of Se

recrystallization) to form the CuSe at -170 C, and the coexisting CuSe is partially

further selenized to yield the CuSe2 at -160 C, as evidenced by CuSe2 (111, 120) peaks,

which then disappear by decomposing to CuSe at -210 C. Interestingly, the phase

evolution (i.e., CuSe -- CuSe2 CuSe Cu2Se) of as-grown CuSe is very similar to

that (i.e., CuSe -- CuSe2 CuSe Cu2-xSe + Cu2Se) of glass/Cu/Se described in the









previous section. Finally, the development of CuSe is maximized at -220 C followed by

peritectic decomposition to the 3-Cu2Se by releasing Se at above 240 C. Therefore, the

dominant phase evolution of glass/Cu-Se precursor is summarized as

7Cu + 4Se Cu7Se4 T 80 C

Cu7Se4 + 3Se 7CuSe T 170 C

2CuSe Cu2Se + Se (evaporated) T 240 C

It is expected that the intermediate mixtures of Cu-Se phases reduce Se loss as

compared to the bilayer structure exposing the surface of the Se top layer to the gas flow.

Furthermore this sample had a larger atomic Se/Cu ratio (2.4 vs. 2.0) than the Se/Cu

structure.

3.4. In-Se Binary Formation

3.4.1 Glass/In/Se precursor

The phase evolution of glass/In/Se bi-layer precursor with an overall atomic

composition of [Se]/[In]-4.2 was investigated using the Scintag-HTXRD. The

glass/In/Se precursor was first scanned at 25 OC and then heated to 60 OC at a rate of 20

oC/min. Then four sequential scans (Imin acquisition/scan) over a range of 22 to 540

(20) were taken at 10 OC increments while the sample was heated from 60 to 400 OC at a

rate of 30 oC/min in a flowing He atmosphere. As shown in Figure 3-6, the reflection

peaks of pure In, Se and In4Se3 phase were detected at 25 oC. The most In-rich

compound, In4Se3, is expected to form at the interface of indium and selenium during the

deposition of selenium on pre-deposited In/glass (i.e., the second deposition stage), which

provides selenium with an extremely indium-rich environment, thus favoring formation

of In4Se3. The reflection intensity of pure In begins to decrease at -120 OC and then










completely disappears at -150 OC, which nearly coincides with its melting temperature

(Tm-151 C). The peaks of selenium and In4Se3 suddenly disappear together at the same

temperature of around 170 C. Since the thermodynamic melting temperature of

selenium is around 221 C, the abrupt disappearance of selenium peak at 170 OC is likely

explained by the reaction of selenium with In4Se3 and liquid indium rather than by

melting of selenium. Furthermore, the simultaneous disappearance of In4Se3 and Se

peaks strongly supports this explanation. No crystalline phases, however, were identified

until the appearance of In2Se3 at around 330 C, which is attributed to the formation of a

glassy InxSey phase.


In2Se3




300








2200




25 Se25 2-


Figure 3-6. Phase evolution of glass/In/Se precursor observed by in situ X-ray diffraction
(JCPDF) Se: 06-0362, In: 05-0642, In4Se3: 83-0039, In2Se3: 65-2447

According to phase diagram of the In-Se binary system shown in Figure 3-1 [Li04],

there exist 4 intermediate InxSey line compounds between In4Se3 and In2Se3 (InSe, In6Se7,

InsSe7 and In9Senl). It is reported that the crystalline phase of InSe is very difficult to









form at low temperature [Gla00]. Viswanathan et al. reported they could successfully

deposit polycrystalline InSe on well-cleaned glass substrate at a substrate temperature of

400 C using a vacuum coating method, while they only obtained the amorphous InSe at

room temperature deposition [Vis05]. In Chapter 4, deposition of the glass/InSe/CuSe

precursor [Kim05a] gave an amorphous InSe film with deposition at a substrate

temperature of 250 C using the MBE system. Finally, the crystalline In2Se3, which is

the most stable In-Se compound at high temperature, is obtained at around 330 C and

continues to grow until the completion of annealing (400 C). The ICP compositional

analysis (i.e., x(Se) 0.59) on an completely annealed sample supports the single phase

In2Se3 stoichiometry. The overall phase transformation of glass/In/Se precursor is

summarized as

In (solid) In (liq.) T= 120-150 C

In (liq.) + In4Se3 + Se (solid) InxSey (amorphous) T 170 C

InxSey (amorphous) + Se (liq.) In2Se3 + Se (evaporated) T 330 C

3.4.2 Glass/In-Se Precursor

The glass/In-Se mixed precursor was prepared to have a similar overall composition to

glass/In/Se precursor, as confirmed by ICP analysis ([Se]/[In] 4.1). Furthermore, an

identical annealing procedure as used for glass/In/Se precursor was applied to glass/In-Se

precursor. As shown in Figure 3-7, unlike the bi-layer precursor, no crystalline phase is

detected from the as-deposited precursor. Rather a broad intensity is observed in the 20

range 22 to 380. Since, in general, the as-deposited pure indium has the crystalline

structure as shown in glass/In/Se precursor, indium likely exists as a glassy InxSey phases

rather than as elemental In, and thus the selenium is partially bound in its glassy state.







81


Interestingly, selenium begins to crystallize at around 120 C as evidenced by

growing Se (100) peak, and then grows until temperature reaches around 200 C, at

which point the Se reflections disappear due to Se melting and/or reacting with glassy

InxSey. Subsequent heating leads to the formation of crystalline In2Se3 by further

selenization of InxSey, just like in the phase evolution of glass/In/Se precursor. It is

interesting to note that the formation temperature of In2Se3 in glass/In-Se precursor is

much lower than in glass/In/Se. One explanation is the shorter diffusion lengths in

intimately mixed glass/In-Se precursor as compared to the bi-layer films.

*







350

00.












S40o--4- 50
30
25
22


Figure 3-7. Phase evolution of glass/In-Se precursor observed by in situ X-ray diffraction.
(JCPDF) Se: 06-0362, In2Se3: 65-2447.

Again, the ICP analysis (i.e., x(Se) ~ 0.59) on an annealed sample strongly

supports the complete transformation into In2Ses without any residual phases. The overall

phase evolution of glass/In-Se precursor is thus summarized as
phase evolution of glass/In-Se precursor is thus summarized as