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Diffusion in thin films Johnson, Dale Bernard 1968

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DIFFUSION IN THIN FILMS by DALE BERNARD JOHNSON B„Se,(Hons), The University of B r i t i s h Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of METALLURGY We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 196 8 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o lumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n -t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Dale Bernard Johnson Department o f Metallurgy The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 10, I 9 6 8 1 ABSTRACT The nature of di f f u s i o n along thin evaporated films has been studied by o p t i c a l and transmission electron micro-scopy,, The thicknesses of the films were measured by multiple-beam interferometryo A preliminary survey of some 2 2 binary metal systems showed that only four - Ag-Se, Cu-Se, Cu-Te, and Ag-Te - diffused measurably at room temperature, -In these four systems i t was found possible to study only the d i f -fusion of Cu or Ag into Se and Te; the reverse d i f f u s i o n experiments f a i l e d , presumably because of extensive Kirkendall porosity which developed on the Se or Te side of the d i f f u s i o n couples, impeding the motion of these atoms c The room temperature growth rates in each system were observed to be higher when the structure of the Se or Te consisted of i s o l a t e d islands with a highly disordered i n t e r - i s l a n d network. This e f f e c t was attributed to a short c i r c u i t d i f f u s i o n process analogous to grain bound-ary d i f f u s i o n which took place i n the i n t e r - i s l a n d channels. The e f f e c t was more pronounced i n Cu-Te and Ag-Te where electron microscopy observations of the phase boundary interfaces showed a marked tendency for grain i i boundary d i f f u s i o n to occur at a l l Se and Te thicknesses. For continuous films of Se and Te, the growth rates were found to be independent of the absolute thickness. Because of the evaporation geometry used i n de-pos i t i n g the couples, there was a c r i t i c a l thickness r a t i o of Ag or Cu to Se or Te that had to be exceeded i n order for d i f f u s i o n to proceed. Theoretical treatment of the problem, based on the stoichiometry of the phases formed during d i f f u s i o n , gave predictions of the c r i t i c a l r a t i o that were generally i n good agreement with the experi-mental values obtainedo In each system the c r i t i c a l r a t i o was found to be independent of the absolute Se or Te thickness. It was also possible to predict the composit-ion of the phase formed during d i f f u s i o n using the c r i t i c a l r a t i o . In every system but Cu-Te, the composition de-termined i n thi s way was i n agreement with that given by electron d i f f r a c t i o n analysis of the d i f f u s i o n zone. The activation energies for d i f f u s i o n in Ag-Se, Cu-Te, and Ag-Te were f a i r l y low suggesting that short c i r c u i t d i f f u s i o n was the predominant mechanism i n these systems. The acti v a t i o n energy i n Cu-Se was quite large (2 3 kcal/mole), and i t appears that the d i f f u s i o n mechanism i n t h i s case i s not consistent with that i n the other systems. An i n t e r e s t i n g observation made during electron microscopy studies i n Cu-Se was the formation of a second phase when high electron beam i n t e n s i t i e s were used. This phase (CUgSe2), not observed i n normal d i f f u s i o n experi-ments up to 5 0°C, grew d e n d r i t i c a l l y in the presence of the electron beam. i v TABLE OF CONTENTS Page CHAPTER 1 INTRODUCTION . . . . . . . . , . . . . . 1 1.1 Previous Work, » . . » » - . . . . . . . 1 1.2 Object of the Present Investigation. . , 4 1, 3 Diffusion Theory . . . . . . . . . . . . 5 1.3.1 Atomic Models for. Diffusion , . . 5 1.3.2 Mathematics of Diffusion. . . . . 10 1,4 The Structure of Evaporated Thin Films . 18 1.4.1 Thin Film Nucleation, . . . . . . 18 1.4.2 The Growth of Thin Films. . . . . 21 1.4.3 The Properties of Thin Films. , . 25 CHAPTER 2 EXPERIMENTAL PROCEDURE . . . . . . . . . 28 2.1 Vacuum Equipment . . . . . . . . . . . . 28 2.2 Film Deposition, , , , , . . . . . . . . 29 2.2.1 Sample Preparation. . . . . . . . 29 2.2.2 Film Thicknesses. . . . . . . . . 31 2.2.3 Temperature Tests . . . . . . . . 32 2.2.4 Measurement of Diffusion Rate Constant . . . . . . . . . 32 2.2.5 Electron Microscopy . . . . . . . 34 2.3 Different Evaporation Configurations . » 3 5 2.4 Other Systems, . . . . . . . . . . . . . 37 CHAPTER 3 LATERAL DIFFUSION IN Ag-Se . . . . . . . 41 3.1 Introduction , „ . . , . . , , . . . . » 41 3.2 Diffusion V Table of Contents (Cont'd) Page 3 . 2 . 1 Growth Rate, , . . . . . . . . . 4 1 4 3 . 2 . 2 E f f e c t of Se Thickness on Rate Constant. . . . . . . . . 4 8 3 . 2 . 3 The Structure of Se Films. . . . 5 1 3 . 2 . 4 E f f e c t of Thickness Ratio 6n the Rate Constant . . . . . 5 5 3 . 2 . 5 Theoretical Determination of the C r i t i c a l Ratio. . , , . 6 0 3 . 2 . 6 Temperature Dependence of the Rate Constant . . . . . 6 4 3 , 3 Electron Microscopy . . . . . . . . . . 6 7 CHAPTER 4 LATERAL DIFFUSION IN Cu-Te, . . . . . . 7 4 4 . 1 Introduction . . . . . . . . . . . . . 7 4 4 . 2 Diffusion Kinetics, . , 0 , 0 0 . , . . 7 6 4 . 2 . 1 Growth R a t e . . . . . . . . . . . 7 6 4 . 2 . 2 E f f e c t of Te Thickness on 4 . 2 . 3 The Structure of Te Films. . . . 8 1 4 . 2 . 4 C r i t i c a l Ratio . , , . , . . „ . 8 3 4 . 2 . 5 Temperature Dependence of the Rate Constant . . . . . 8 6 4 . 3 Electron Microscopy 0 . . . . . . . . . 9 0 CHAPTER 5 LATERAL DIFFUSION IN Ag-Te. . . . . . . 9 9 5 , 1 Introduction, . . . . . . . . . . . . . 9 9 5 o 2 Kinetics. 0 , 0 , 0 0 0 0 0 0 0 . , 0 , 9 9 5 , 3 Electron Microscopy , , . „ . . 0 . . . 1 0 6 CHAPTER 6 LATERAL DIFFUSION IN Cu-Se, . . . . . . 1 1 4 6 . 1 Introduction, . . . . . 0 . . . . . . . 1 1 4 G & 2 r \ i r i G " t l C S o 0 o 0 0 o 0 0 o 0 o o o 0 o o 115 6 0 2 . 1 Growth Rate. . . . . . . . . . . 1 1 5 6 . 2 . 2 Dependence of the Rate Constant on Se Thickness . . . 1 1 8 v i Table of Contents (Cont'd) 6.2.3 C r i t i c a l Ratio, , . . 6.2.4 Temperature Dependence 0 0 0 0 0 0 6,3 Electron Microscopy 0 0 0 0 0 0 9 0 0 0 0 6.3.1 Normal Growth . 6.3.2 Dendritic Growth 0 0 0 0 0 0 0 0 0 0 0 0 0 Page 120 123 126 126 133 CHAPTER 7 SUMMARY AND CONCLUSIONS 7,1 Discussion and Summary 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7.1.1 Growth Kinetics . . . . 7.1.2 Rate Constant Dependence on Film Thickness . . 7.1.3 C r i t i c a l Ratio, . . . . 7.1.4 Temperature Dependence. 7.1.5 Electron Microscopy . . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 145 145 14 5 146 147 147 14 9 lik Estimation of Diffusion Coefficients . . 150 7,D The Mechanism of Rapid Diffusion . . . . 154 7,4 Conclusions, , . . , . , . . . » . » . . 158 APPENDIX , 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 161 BIBLIOGRAPHY 0 0 0 " '0 0 0 0 0 0 0 o 0 o o 0 0 0 0 0 167 v i i LIST OF FIGURES Page 1.1 Models f o r Diffusion, . 0 . » . » . . o . . . . . . 6 1.2 S e l f - d i f f u s i o n i n Single Crystal and Poly c r y s t a l l i n e S i l v e r , . . „ » . , . . . . . . 8 1.3 Concentration P r o f i l e s with Increasing Time i n a Single-Phase Binary System . . . . . . 11 1.4 Diffusion Couple i n an Intermediate Phase System with No Terminal S o l i d S o l u b i l i t y . . . . 13 1.5 Concentration P r o f i l e of an Intermediate Phase System i n X-Space. . . . . . . . . . . . . 14 1.6 The Free Energy of Formation of an Aggregate of Film Material as a Function of Size . . . . . 20 1.7 Growth of an Ag Film, 22 1.8 Manner of Coalescence of Two Small Rounded N l i C X S l o o o o o o o o o o o o o o o o o o o o o 23 1.9 The Density of Dislocations i n a Gold D 6 p O S X ~ t o o o o o o o o o o o o o o O O O O O O O 25 * i^ J O "U. 2.1 Vacuum Equipment. , 0 , . . , , , » . . . . . . . . -JD 2.2 Main Evaporation Configuration. . . . . . . . . . . 30 2.3 Measurement of Film Thicknesses 33 2.4 Evaporation Configuration for Electron Microscopy Specimen, . . . . . . . . . . . . . . 34 2.5 Alternative Evaporation Geometries, . . . . . . . . 36 3.1 Equilibrium Phase Diagram for Ag-Se . . . . . . . . 42 3.2 Ag-Se Diffusion Couple, , 0 . . . . . . . . . . . . 43 3.3 Typical Plot of x versus t at Room Tsinpsx s^'tviiir's o o o a o o o o o o o o o o o o o o o 45 3.4 Plot of x versus -ft 46 v i i i L i s t of Figures (Cont'd) Page 3.5 Growth of a Diffusion Zone i n Ag-Se. . . . . . . . 47 3.6 Eff e c t of Se Thickness on Growth Rate, 49 3.7 Rate Constant as a Function of Se Thickness. . . . 50 3.8 Structure of Se Films. . . . . . . . . . . . . . . 52 3.9 Appearance of Phase Boundary at Varying S 6 Tin x c Jen 6 S S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 3.10 Stages i n the Formation of a Continuous Amorphous Se Film . . . . . . . . . . . . . . . 56 3.11 Fischer's Model f o r Grain Boundary Diffusion . . . 57 3.12 E f f e c t of Thickness Ratio on Growth Rate . . . . . 58 3.13 Growth Rate as a Function of Thickness Rcl"tlO o o o o o o o o o o o o o o o o o o o o o 5 9 3.14 Theoretical Diffusion Couple M-Y 61 3.15 Temperature Dependence of the Rate C O I'l S "t clXl "t X Tl " S S o o o o o o o o o o o o o o o 6 5 3.16 Arrhenius Plot f o r Ag-Se . . . o o . . . . . . . . 66 3.17 Comparison of Thin Film to Bulk Temperature JOS p 6J"1 d S I l C S O O O O O O O O O O O O O O O O O O Q 6 8 3.18 Advance of the Phase Boundary in Ag-Se . . . . . . 69 3.19 Diffusion Zone in Ag-Se, . . . . . . . . . . . . . 71 3.20 Selected Area D i f f r a c t i o n Pattern of Diffusion Zons o o o o o o o o o o o o o o o o o "73 4.1 Equilibrium Phase Diagram of Cu-Te . . . . . . . . 75 4.2 Selected Area D i f f r a c t i o n Pattern of Pure Te „ . . 77 4.3 Typical Plot of x versus -ft i n Cu-Te . . . . . . . 78 4.4 E f f e c t of Te Thickness on Kinetics . . . . . . . . 79 4.5 Rate Constant as a Function of Te 'Pi*lXClCri6 S S o o o o o o o o o o o o o o o o o o o 8 0 ix L i s t of Figures (Cont'd) Page 4.6 The Growth of a Te Thin Film, . . . . . . . . . . , 82 4.7 Growth Rate as a Function of Thickness Rc^ *t l O o o o o o o o o o o o o o o o o o o o o o o 84 4.8 Arrhenius Plot for Cu-Te, . . . . . . . . . . . . . . 87 4.9 Comparison of Bulk to Thin Film Temperature Dependence . . . . . . . . . . . . . 88 4.10 Motion of the Cu„ Te Phase Boun d c L r y o o o o o o o o 31 O 4.11 Diffusion Into a 200 A Te Film, . . . . . . . . . . 92 4.12 Phase Boundary Interfaces at High Magnifi C3. "tXOn o o o o o o o o o o Q o o o o o o o 34 4.13 The Surrounding of a Grain of Te by the Diffusion Zone Interface . . . . . . . . . . . . 95 4.14 Schematic Sketch of the Surrounding of a Te Grain by the Phase Boundary Interface Shown i n Figure 4„13 . . . . . . . , . 96 4.15 Selected Area D i f f r a c t i o n Pattern of the Diffusio n Zone of a Cu-Te Thin Film Couple . . . 97 5.1 Equilibrium Phase Diagram of Ag-Te. . . . . . . . . 100 5.2 Growth Rate as a Function of Te Thickness . , . „ „ 102 5.3 Growth Rate as a Function of Thickness Ratio, , . . 103 5.4 Arrhenius Plot for Ag-Te, . . . . . . . . . . . . . 105 o 5.5 Phase Boundary Interface in a 210 A Te Film . . . . 107 5.6 Evidence of Grain Boundary Diffusion in a 1000 ft Te Film . „ » . . . . . . . . . . . . . 109 5.7 Selected Area D i f f r a c t i o n Pattern of the Diffusion Zone i n Ag-Te, . . . . . . . . . . . . I l l 5.8 Electron Beam Heat-Induced Second Phase 11*1 ^§ T S o 0 0 O 0 o o o o O O 0 0 O 0 O O O 0 o 112 6.1 Typical Kinetics Plots in Cu-Se . . . . . . . . . . 116 6.2 General Form of the Majority of Growth Plots. . . . 117 X L i s t of Figures (Cont'd) Page 6.3 Rate Constant as a Function of Se Th 1 C J^CrXG S S O O 0 0 0 0 O O O O O O O O O O O 9 O 9 119 o 6.4 Phase Boundary Interface i n a 125 A Se Film . . . . 121 6.5 Rate Constant as a Function of Thickness R<3."tXO o o 0 0 o o o o o o o o e o o o o o o o a o 12 2 6.6 Arrhenius Plot for Cu-Se, . . . . . . . . . . . . . 124 6.7 Motion of the Phase Boundary Interface XXI C\i*"" SS O O O O O O O Q 0 0 0 0 9 0 Q O O O O O 127 6.8 Columnar Grains i n Diffusion Zone . . . . . . . . . 128 6.9 Selected-Area D i f f r a c t i o n Pattern of the D x f f vis xon Zon6 o o o o o o o o o o o o o o <> <> o 12 9 6.10 Growth Tip at High Magnification, . . . . . . . . . 131 6.11 Selected Area D i f f r a c t i o n Patterns of Single Growth Tips 132 6.12 Schematic Indexing of D i f f r a c t i o n Patterns. . „ . , 134 6.13 Motion of Dendritic Phase Interface . . . . . . . . 136 6.14 Nature of the Dendritic Phase . . . . . . . . . . . 137 6.15 Boundary Between Dendritic and Non-DGndi^xizic Phciss o o o o o o o o o o © o o o o o © 138 6.16 Selected Area D i f f r a c t i o n Pattern of the Dendritic Phase i n Cu-Se . . . . . . . . . . 139 6.17 Dendrite Analysis . . . . . 0 . . . . . . . . . . . 141 6.18 Dendrite Analysis . . . . . . . . . 142 A . l Plot of x against >[t i n Ag-Te . . . . . . . . . . . 162 A,2 Effect of Non-Ideal Masking on Resulting F X l l T l S " t S p 0 O 0 0 0 O O O O 0 0 O Q 0 O O 0 o o o 163 A.3 Evaporation of Se Across an Actual Ag S"tep fl o o o o o o o o o o o o o o o o o o o o o 165 x i LIST OF TABLES Page 2 o l Other Systems i n which the P o s s i b i l i t y of Lateral Diffusion was Investigated, . . . . . 3 8 2 „ 2 Expected Diffusion Coefficients i n Some Possible Thin Film Diffusion Systems , , . , . . 39 3.1 C r i t i c a l Ratio Dependence on the Absolute S 6 T h l C l C T l G S S o o o o o o o o o o o o o o o o o o S O 4.1 R for Intermetallic Phases i n Cu-Te. . . . . . . . 85 c 4.2 C r i t i c a l Ratio as a Function of Absolute T © T i l l ClCI"!© S S o o o o o o o o o o o o o o o o o o 8 5 6,1 Theoretical C r i t i c a l Ratios i n Cu-Se, 123 7.1 Activation Energies for Thin Film Couples . . . . . 148 7.2 Summary of Lateral Diffusion in the Four Systems Investigated, . . . . . . . . . . . 151 7.3 Calculation of Diffusion Coefficients . . . . . . . 153 ACKNOWLEDGEMENT The author would l i k e to express his gratitude to his research d i r e c t o r , Dr, L,.C, Brown, for his advice and en-couragement during the course of t h i s research project. He also wishes to thank other faculty members and fellow graduate students for many useful and stimulating discussions. The assistance of the technical s t a f f i s g r a t e f u l l y acknowledged. This research was financed in part by a National Research Council Studentship, a Cominco Fellowship, and a Defense Research Board Research Assistantship. 1 CHAPTER 1 INTRODUCTION In recent years thin films have acquired a wide range of applications i n the f i e l d s of optics and electronics » , The development of the technology of t h i n f i l m electronics devices, in p a r t i c u l a r , has led to a q [I c great deal of i n t e r e s t in t h e i r structure and properties ' 9 » Therefore, many investigations have been centered around t h e i r fundamental properties and how they compare with 7 those of bulk material.„ Comparatively l i t t l e work has been car r i e d out, however, on thin f i l m d i f f u s i o n . Such studies are of considerable potential interest since evaporated thin films are of high purity, can be grown in both s i n g l e - c r y s t a l and p o i y e r y s t a l l i n e form, and can be observed by transmission electron microscopy, 1,1 Previous Work The methods used to investigate d i f f u s i o n in bulk couples are generally inapplicable to evaporated films because any method of sectioning i s impossible and the quantity of material available i s inadequate for chemical 2 analysis. Radioactive tracer techniques cannot be used since the absorption of the films i s ne g l i g i b l e even f o r low energy B-rays. Consequently no changes in emission can be detected as radioactive p a r t i c l e s diffuse through the films. In the past, most measurements of d i f f u s i o n i n q thin films have involved the use of o p t i c a l methods , One technique employed to study d i f f u s i o n i n two superimposed thin films uses variations in r e f l e c t i v i t y as the d i f -fusion zone reaches the metal surface, 9 . . Weaver and Brown have investigated d i f f u s i o n i n superimposed Au-Al films by t h i s method. They found that changes i n r e f l e c t i v i t y at the metal surface were due to a sharply defined phase boundary and that the compound formed during d i f f u s i o n was A ^ A l . The growth of the d i f f u s i o n layer obeyed the parabolic law x = kt where k i s the d i f f u s i o n rate constant. The d i f f u s i o n rate constant and activation energy for d i f f u s i o n of Al into a Au f i l m were independent of the Au f i l m thickness in the range 70 ft. to 3000 8 i n d i c a t i n g that the d i f f u s i o n mechanism f o r the very thin films was the same as f o r thicker ones. R e f l e c t i v i t y measurements were also used by 10 9 Schopper and Weaver and Brown to investigate thin f i l m d i f f u s i o n i n the Au-Pb system where, i n contrast to Au-Al, r e f l e c t i v i t y changes r e s u l t from the growth of a diffuse phase boundary. The growth rate, however, was s t i l l 3 parabolic with time. Measurements showed that variations i n r e f l e c t i v i t y were due to the formation of AuPb2 during d i f f u s i o n , The p o s s i b i l i t y of investigating d i f f u s i o n along a f i l m p a r a l l e l to the surface was f i r s t demonstrated by Monch"^,, The work apparently started with attempts to produce radiation detectors, A f i l m of Te was evaporat-ed so as to form a bridge between two thick Ag electrodes which had themselves been evaporated onto a collodion f i l m . On ageing, the Ag diffused into the Te, forming a yellowish-brown band of Ag2Te spreading outwards from the 12 13 sxlver. Mohr • measured the coeffxcient of dxffusxon of the Ag by determining the widths of the di f f u s i o n zone as a function of time, A variation with the thickness of Te was attributed to a folding or c r i n k l i n g of the thicker films which became detached from t h e i r underlying sub-strates. Measurements over a range of temperature gave D = D Q expC-B/T) where D Q = 5xl0 7 cm2/day and B = 6010 deg""1. Similar experiments were carried out using Se instead of Te by Kienel'^ and Zorll"'"^ but the films were deposited on substrates at l i q u i d nitrogen temperatures because of the r e l a t i v e v o l a t i l i t y of the Se. Measure-ments of d i f f u s i o n rate were again made by determining the width of the d i f f u s i o n zone as a function of time and the r e s u l t s , although approximate, were in general agree-ment with the e a r l i e r results f o r Ag-Te. 16 In 1963 Parkinson studied l a t e r a l d i f f u s i o n i n 4 the Cu-Te system by electron microscopy. Observations were made on the moving d i f f u s i o n zone interface and no evidence of grain boundary d i f f u s i o n was seen. Volume d i f -fusion was the proposed mechanism for d i f f u s i o n in the f i l m couples with K = K Q expC-E/RT] where K Q = 7,55xl0~ 2 cm /sec and E = 10.0 kcal/mole. 1.2 Object of the Present Investigation The main purpose of th i s study was to carry out a thorough investigation of l a t e r a l d i f f u s i o n - that i s , d i f f u s i o n along a f i l m p a r a l l e l to the surface - in several two-component systems. A survey of some 22 metal pairs at room temperature showed that only four - Cu-Te, Ag-Te, Cu-Se and Ag-Se - gave suitable d i f f u s i o n zones. Even i n these systems only d i f f u s i o n in Se and Te could be studied. It had o r i g i n a l l y been hoped to study d i f -fusion along thin films produced from the bulk. However, i t proved impracticable to produce such films in Se and Te, the only metals in which l a t e r a l d i f f u s i o n could be seen. This portion of the work was therefore abandoned. The e f f e c t of varying the thicknesses of both components on the d i f f u s i o n rate constant was examined. Also the temperature dependence of the rate constant in each system was determined. In addition a detailed study of the d i f f u s i o n front and the nature of i t s movement as well as the microstructure and composition of the d i f f u s i o n zone was carried out using transmission electron microscopy. 5 1.3 Diffusion Theory 1»3.1 Atomic Models f o r Diffusion Aa Lattice Diffusion Some proposed mechanisms for l a t t i c e d i f f u s i o n are i l l u s t r a t e d i n Figure 1.1, A b r i e f description of each model i s given belows (1) Interchange mechanism; It i s now generally agreed that direct interchange of atoms does not occur in view of the large l a t t i c e d istortions involved. (2) I n t e r s t i t i a l mechanism: " I n t e r s t i t i a l d i f -fusion can take place when the two atom sizes are markedly d i f f e r e n t . For example, in. i o n i c compounds, where there i s often a great size difference between anion and cation, d i f f u s i o n i s usually due to the smaller cation. (3) Vacancy mechanism: Diffusion i s usually considered to take place by a vacancy mechanism. If an atom i s missing i n the l a t t i c e , atomic motion w i l l result i f any of the adjacent atoms jump into the vacant s i t e , interchanging positions with the vacancy. The vacancy w i l l thereby advance one atomic distance and enable other atoms to move i n the next jump, B. The Kirkendall E f f e c t Point defects such as i n t e r s t i t i a l s and vacancies permit net tr a n s l a t i o n a l motion of atoms r e l a t i v e to a fixed l a t t i c e under the driving force of a o o o o o o o o o o o # > o o o o o °o0o0^o0o0o°c|%0  0o0o0o0o0o0o0J°£0  0o0o0o0oGo0o0o°o0 a) Interchange p a i r and ri n g of four o o o o o o o o o O O O O O O O O °o0o0o°o0 °o0o°o0  Oo0o0o0o0o*o0o°o0 0o0o0o0o0o0o°o0o0 b) Vacancy O O O O O O O O O o o o o o o o o ° o ° o ° o ° o 0 o 0 o ° o 0 o ° Oo056o0o0o0o2o0o0 0o0o0o0o0o°oVo0 c) I n t e r s t i t i a l Figure I d Models for Diffusion 7 chemical or thermal gradient, In other words, r e l a t i v e to the c r y s t a l l a t t i c e , the atomic species in a binary a l l o y diffuse at unequal rates, This phenomenon i s 17 18 c a l l e d the Kirkendall e f f e c t * and i s evidenced by a macroscopic s h i f t i n the center of gravity of an i n i t i a l concentration gradient with respect to inert markers fixed i n the l a t t i c e . The Kirkendall s h i f t s observed i n some oxide layers and i n t e r m e t a l l i c compounds can be very large. In these cases only one species diffuses and the s h i f t can therefore be nearly the f u l l width of the d i f f u s i o n zone. The Kirkendall experiment demonstrates that a net flow of atoms can take place during d i f f u s i o n . It has often been observed that voids, or pores, form in that region of the d i f f u s i o n zone from which there i s a flow of mass. This i s c a l l e d Kirkendall porosity - i t s o r i g i n being a vacancy flux which moves in a direction opposite to the net mass flow during d i f f u s i o n , C, Short C i r c u i t Diffusion The d i f f u s i o n rate of atoms along grain boundaries, surfaces, and dislocations i s considerably greater than the rate of bulk d i f f u s i o n . Figure 1,2 shows the apparent s e l f - d i f f u s i o n c o e f f i c i e n t s i n s i l v e r as determined by a radioactive s i l v e r t r acer experiment f o r s i n g l e - c r y s t a l 19 and p o l y c r y s t a l samples , It can be seen that the same value of the d i f f u s i o n c o e f f i c i e n t i s obtained for both types of samples at high temperature. Below 700°C, how-8 ever, the d i f f u s i o n c o e f f i c i e n t values obtained using a pol y c r y s t a l l i e consistently above the values obtained with a single c r y s t a l . This graph i l l u s t r a t e s that the activ a t i o n energy for grain boundary d i f f u s i o n i s about 60% of the value for bulk d i f f u s i o n and also that grain boundary d i f f u s i o n becomes increasingly important at low temperatures. The apparent l a t t i c e d i f f u s i o n c o e f f i c i e n t can also be affected by dislocations e s p e c i a l l y i f t h e i r density i s high. The e f f e c t of dislocations on d i f f u -s i v i t y also becomes more important at lower temperatures. o o b0 O H -8 -10 -12 -14 1 900 1 1 1 800 700 600 i i i 500 450 400 Temperature(°C) - _ 5 26,400 =(2,3x10 °)exp(- n m ) RT D =0,895 exp( Li i . i ^45950^ X8T N1 i 1,00 1,20 1000 _ i 1,40 I, 50 Figure 1 , 2 S e l f - d i f f u s i o n i n Single-Crystal and 20 P o l y c r y s t a l l i n e S i l v e r , (After Turnbull ) Many workers report that the d i f f u s i o n c o e f f i c i e n t along a surface i s greater than both the grain boundary and l a t t i c e d i f f u s i o n c o e f f i c i e n t s . The driv i n g force for 9 s u r f a c e d i f f u s i o n may be s u r f a c e t e n s i o n or s u r f a c e f r e e energy. Two of the main methods f o r determining the s u r f a c e d i f f u s i o n c o e f f i c i e n t are s u r f a c e s c r a t c h smoothing 21 and g r a i n boundary gr o o v i n g „ Surface contamination can l e a d to tremendous s c a t t e r i n the r e s u l t s o b t a i n e d . For example, a comparison o f the a c t i v a t i o n e n e r g i e s f o r s u r f a c e , g r a i n boundary and l a t t i c e d i f f u s i o n f o r s e l f 22 d i f f u s i o n o f Ag i s given i n the t a b l e below : Me chanism E(kcal/mole) Surface Grain boundary Volume 10,3 26,4 4 5 , 9 In c o n t r a s t to these r e s u l t s the g r a i n boundary 2 3 24 g r o o v i n g a n a l y s i s o f Mullin's * f o r D s on copper gi v e s an a c t i v a t i o n energy o f 4 9 kcal/mole which i s n e a r l y the same as the a c t i v a t i o n energy f o r bulk s e l f d i f f u s i o n (46,8 k c a l / m o l e ) . T h i s h i g h value found by surface smoothing i s not too s u r p r i s i n g s i n c e a copper atom moving on the s u r f a c e i s w e l l on i t s way to being an evaporated atom. Thus the a c t i v a t i o n energy f o r i t s motion i s r e -l a t e d more c l o s e l y to the heat o f v a p o r i z a t i o n (80 kcal/mole f o r Cu) than to the bulk a c t i v a t i o n energy. I t would appear, however, t h a t more work on very c l e a n s u r f a c e s must be done to remove some o f the i n c o n s i s t e n c i e s from s u r f a c e d i f f u s i o n r e s u l t s . 10 D, Diffusion i n Intermetallic Compounds Intermetallic compounds which are present i n most binary systems often have only small deviations from stoichiometry associated with them. Such deviations are usually due to a defect structure i n which some of the atoms of one species are missing from t h e i r normal l a t t i c e positions. For example, Zr02 can exist from i t s s t o i c h i o -metric composition to ZrO2_ o00l° This i s probably a Schottky defect structure with oxygen vacancies. Another example of a defect i n t e r m e t a l l i c compound i s Cu^^gSe which i s a copper deficient form of C^Se. As might be expected, d i f f u s i o n tin such compounds i s often greatly dependent on the exact deviation from stoichiometry since t h i s determines the vacancy and i n t e r s t i t i a l concentrations. The "open" structures which occur i n defect i n t e r m e t a l l i c compounds can r e s u l t i n very high atomic m o b i l i t i e s . It i s known, for example, that Ag ions i n the high temperature modification of Ag 2S (a-Ag2S) possess extremely high 9 m o b i l i t i e s , The reason for this i s that the cations do not occupy fixed l a t t i c e positions in t h i s structure and can migrate from s i t e to s i t e just l i k e in a l i q u i d . 1,3,2 Mathematics of Diffusion Fick's f i r s t and second laws of d i f f u s i o n i n one-dimensional form are s J =«D — (1,1) 11 and ^ = L. ( D l £ ) 3t 3x 3x (1.2) Equation (1.2) becomes as , D 3t 3£c 3x2 i f D i s not a function of concentration. A. Single-phase Diffusion-Consider a semi-infinite d i f f u s i o n couple i n a single-phase binary system (Figure 1.3). If the trans-formation X - x//t~ i s applied to Fick's second law (equation 1.2) then the following equation r e s u l t s : X dc _ _d 2 dt " dX dc dX (1.3) This has eliminated x and t as independent variables. Hence one concentration p r o f i l e i s applicable at a l l times in a semi-infinite couple. That i s , the p r o f i l e can be Cone, X Figure 1.3 Concentration P r o f i l e s with Increasing Time i n a Single-phase Binary System. given as C = C(X) instead of a whole series of p r o f i l e s with C = C(x,t), The equation for t h i s single p r o f i l e can be found by integrating equation 1 03 twice. If D i s taken to be constant then a p a r t i c u l a r solution to t h i s equation for a semi-infinite d i f f u s i o n couple i s : C-C r — = l / 2 [ l - e r f X/2/D] (1.4) fX/2/D 2 where e r f X/2/TJ = — B. Multi-Phase Diffusion 2 e~ n dn J o Consider now a d i f f u s i o n couple composed of two pure metals A and B with no s o l i d s o l u b i l i t y in the parent phases but having an intermediate compound y with a region of s o l u b i l i t y from C-j_ to C2 at T 0 After time t a homo-geneous region of y phase extends from x-j_ to x 2. In the y-phase the composition p r o f i l e w i l l be a portion of an error function of the form C = A - B erf X/2/LT (1,5) That i s , the p r o f i l e can be drawn in X-space (Figure 1,4) and so the growth of the y-phase w i l l be parabolic. The constants A and B in equation (1,5) may be determined by the boundary conditions at X = a-j_ and X = a 2 ; namely, C = C-^  at X = a-L and C = C2 at X = a 2. 13 Figure 1,4 Diffusion Couple in an Intermediate Phase System with no Terminal Solid Solubility, 14 The r e s u l t i n g concentration p r o f i l e i s : C = CL+ ( C g " ^ ) erf erf X / 2 / J T e r f ^ / 2 / i T - e r f a 2 / 2 / F (1.6) C = c 2 + ( C j - ^ ) e r f - a 2 / 2 ^ 5 ~ - e r f X/2/5" erf a 1 / 2 / f T - e r f a9/2/D~ (1.7) To obtain expressions f o r and mass balance conditions across the interface can be applied and equations (1.6) and (1.7) used to derive the f i n a l r e s ult. Simplified Method, for. Finding and If the composition range of the intermediate phase i s assumed to be small ( 5% or l e s s ) , the concentra-tion gradient i n the phase may be taken to be l i n e a r to a f i r s t approximation. Figure 1.5 shows the re s u l t i n g p r o f i l e i n X-space, C„ Cone, X = CL. X = 0 X X= ou Figure 1.5 Concentration P r o f i l e of an Intermediate Phase System in X-Space, 15 From t h i s figure i t can be seen that dc C 2 " C l — = - — (lo 8) dX a - a 2 The interface mass balance condition at i s that the flux across the boundary i n a time dt causes the phase boundary to move a distance d5 i n the dir e c t i o n of the net mass flow. Thus, at the interface, the condition becomes: - D j — dt = ( C . . - C )dS (1.9) Setting £ = a/t and X = x//t leads to - D — = (c - C ) — ( l o l O ) dX 1 o 2 Substituting (1,8) into (1,10) gives (Co-Cx) a , ( a . - o J = 2 D — - — — (1.11) 1 1 2 «o.-c0> S i m i l a r l y the mass balance condition at the a 2 interface gives: ( C - C ) a„(a -a ) = -2D — - — i - (1.12) ( c 3 - c 2 ) Using equations (1,11) and (1,12) i t can be found that Thus may be set equal to the d i f f u s i o n c o e f f i c i e n t times some constant y» say, which depends only on con-centration. This may be written as a x 2 = Dy s K (1.14) where K i s henceforth referred to as the d i f f u s i o n rate 7 9 i constant , Since = x-^  / t , we can write that x 1 = /K^t. Equation 1,13 shows that x-^  i s proportional to both /D and /C2-C^, If C^-C-^ tends to zero - that i s , the stoichiometry range of the i n t e r m e t a l l i c compound tends to zero - then x^ w i l l become very small, A large value of x^ under these 'circumstances would imply an exceptional-l y large value for D, A s i m i l a r expression to 1,13 may be derived for a 2 giving X 2 = /K^t, E f f e c t of Temperature The d i f f u s i o n c o e f f i c i e n t , D, changes with temperature according to the Arrhenius-type equation D = D exp (-E-./RT) (1.15) o 1 In most systems having an intermediate phase the composi-tion l i m i t s change l i t t l e with temperature. Thus in equation (1,13) the difference (C 2~C^) i s not expected to vary s i g n i f i c a n t l y with temperature and so the temperature dependence of and c*2 w i l l be due to the variation of the d i f f u s i o n c o e f f i c i e n t . Even i f there i s a change in composition range with temperature, a straight l i n e 17 Arrhenius plot for a-^  arid would s t i l l be expected since 2 7 (C^C-^) should t h e o r e t i c a l l y vary with temperature accord-ing to an exponential law; namely, (C 2-C 1 ) • ;= y 3 exp (-E2/RT) (1.16 ) Substituting i n thi s equation using equation (1.13) gives: K " = (D6A)exp(-E 2/RT) (1.17) with A.• = ,• ( c 3 - c 2 ) ; ^ G 0 : ) X C 3 - G 2 + C 1-C 0) The terms (C 3-C 2)» ^ ci~ C 0^» a n d ^ C 3 " C 2 + C i " C o ^ i n t h i s ex-pression w i l l change by neg l i g i b l e amounts compared to ((-:2~C-|_) o Thus i t can be seen that K = K exp(-E/RT) (1.18) 1 o where E = E + E„. 1 2 In systems having more than one intermediate phase, the motion of the indi v i d u a l phases i s s t i l l para-b o l i c . Diffusion i n such a system w i l l be q u a l i t a t i v e l y similar to the special, case discussed above. A solution to the n-component d i f f u s i o n couple i s complex but has 2 8 2 9 been derived by Buckle and Kidson 18 1»4 The Structure of Evaporated Thin Films 2 1,4,1 Thin Film Nucleation The i n i t i a l stage of growth of most deposited films consists of the formation of three-dimensional nuclei. 30 The theoretical treatment is concerned with the nucleation of a thin film condensed from the vapour phase on a sub-strate held at a temperature lower than that of the eva-porating source. After impingement on the substrate the vapour atoms can either adsorb and stick permanently to the substrate, they can adsorb and re-evaporate in a fini t e time, or they can immediately rebound off the sub-strate. The f i r s t two cases are by far the most common. An atom adsorbed on a substrate can migrate over the surface giving rise to collisions with other atoms, and aggregates of adsorbed atoms can now exist. Aggregates should be more stable toward re-evaporation than single adsorbed atoms, since they are bound to each other by the condensation energy. While the aggregates are very small however, their surface-to-volume ratio is very high and the resulting high total surface energy causes them to have a higher vapour pressure than the bulk material and thus to dissociate again. Consequent-ly there i s a size at which the s t a b i l i t y of the aggre-gate is a minimum. Adding another atom to an aggregate of c r i t i c a l size makes i t more stable. This may occur by direct impingement and incorporation of atoms from the 19 gas phase, or by c o l l i s i o n with adsorbed atoms d i f f u s i n g over the substrate surface. The c r i t i c a l radius r* of a stable aggregate i s calculated by considering the t o t a l free energy of the aggregate as a function of size. This free energy involves the free energy of condensation, the surface energies of both aggregate and substrate, and the i n t e r f a c i a l energy between the aggregate and substrate. It i s possible to f i n d both the c r i t i c a l mean l i n e a r dimension of the aggre-gate and the c r i t i c a l free energy of formation (AF*) of the stable aggregate. Figure 1,6 shows the dependence of the free energy of an aggregate on i t s s i z e . The r e l a t i v e magnitudes of r* and i\F* determine the basic structure of the thin f i l m deposit. Films having a nucleation b a r r i e r , that i s , a large r* and a high free energy of formation w i l l be coarse-grained having an i s l a n d structure up to r e l a t i v e l y high average f i l m thicknesses. In the low nucleation barrier regime the f i l m i s generally much finer-grained since a dense population of small islands grow together at an early stage i n the deposition process and become continuous at low average f i l m thicknesses. The tendency to form an i s l a n d structure i s greater i n a low boiling-point material due to the weak bounding between atoms and hence the high volume free energy of condensation. Elements such as Cd, Zn, Se, Te, and Sb w i l l therefore remain as i s l a n d structures up to large f i l m thicknesses size Figure 1,6 The Free energy of Formation of an Aggregate of Film Material as a Function of Size, The aggregate has minimum s t a b i l i t y at the c r i t i c a l radius r A„ while Au and Ag, for example, w i l l tend to form continuous films. Other factors promoting the formation of island structures include: (1) a high substrate temperature, (2) a low deposition rate, (3) weak binding forces between f i l m and substrate, (4) a high surface energy of the f i l m material, and (5) a low surface energy of the substrate. These factors, although mentioned only b r i e f l y , have a very profound influence on the sub-structure of a thin ,.,4,5,31 fxlm ' ' , 5 32 1,4,2 The Growth-of- Thin Films ' The c h a r a c t e r i s t i c stages i n the growth of a thin f i l m are: (1) the formation of a surface d i s t r i -bution of small three-dimensional n u c l e i , (2) the growth in size of these nuclei without any increase i n t h e i r numbers, (3) further increases i n size of the nuclei or islands accompanied by a gradual but considerable de-crease i n t h e i r numbers, (4) the formation of a connected network of deposit usually rapidly developing into a channelled structure, (5) a continuous deposit f i l m free of holes (see Fig, 1,7), This sequence of growth events i s generally the same for both e p i t a x i a l films deposited on s i n g l e - c r y s t a l substrates and p o i y e r y s t a l l i n e films evaporated onto amorphous substrates. The average f i l m thickness of the films at each growth stage are usually d i f f e r e n t , however. One of the most s t r i k i n g phenomena which occur during the growth of a f i l m i s the l i q u i d - l i k e 22 Figure 1,7 Growth of an Ag Film ( a f t e r Sennett and Scott 1") 23 coalescence of randomly oriented nuclei and islands which takes place as the n u c l e i or islands touch one another. i Figure 1,8 Manner of Coalescence of Two Small Rounded Nuclei. (Pasfhley32) The e f f e c t i s i l l u s t r a t e d i n Figure 1,8 for the case of n u c l e i which have round p r o f i l e s . When the islands are small (say less than 200 % across) the complete coalescence appears to take place instantaneously and the compound is l a n d has a greater thickness than the two i n i t i a l islands. The composite islan d has a single orientation that may d i f f e r from the orientations of the parent islands. The mechanism of coalescence i s completely ana-logous to that of s i n t e r i n g and i s explained i n terms of the surface mobility of deposit atoms over the deposit (rather than the substrate) with the dr i v i n g force for the transfer of material between islands being the surface energy. As the coverage of the substrate becomes high, the islands have increasing d i f f i c u l t y i n assuming t h e i r favoured crystallographic shapes, and an open network structure i s eventually formed. F i n a l l y the elongated channels i n the network become f i l l e d i n and a continuous f i l m i s formed. The three predominant deposition parameters are chamber pressure, deposition rate and substrate tempera-ture. While most of the investigations of the e f f e c t of these variables on a deposit have been done for s i n g l e -32 34 c r y s t a l films ' , there i s some evidence available for 5 32 p o l y c r y s t a l l i n e films as well ' , The chamber pressure determines the quantity of residual gases present during evaporation. Adsorbed impurity gas atoms on the substrate can decrease surface m o b i l i t i e s and result in small grain sizes. The deposit f i l m may be porous and highly d i s -ordered i f gas atoms are trapped by the deposit or impure i f any residual gases with a high chemical a f f i n i t y for the f i l m are present. With increasing substrate tempera-ture the size of the c r y s t a l l i t e s (islands) increases due to a higher surface mobility of the deposit atoms and the grain size of the deposit becomes larger. For a given substrate temperature the grain size of a p o l y c r y s t a l l i n e f i l m i s usually f i n e r and less agglomerated the higher the rate of deposition. This i s because highly mobile surface atoms at high deposition rates become buried in random sit e s by successively a r r i v i n g atoms before finding 25 appropriate l a t t i c e s i t e s . 1.4.3 The Properties of Thin Films A, L a t t i c e Defects The main classes of l a t t i c e defects may be l i s t e d as follows: (1) d i s l o c a t i o n l i n e s , (2) stacking f a u l t s , (3) microtwins, (4) aggregation of point defects, (e.g. d i s l o c a t i o n loops and stacking-fault tetrahedra). At the stages before a continuous hole-free f i l m i s formed, there are few d i s l o c a t i o n s , and the i n i t i a l nuclei 5 32 are completely free of dislocations ' „ The way i n which the d i s l o c a t i o n density increases during growth of the f i l m i s shown i n Figure 1,9, Appreciable numbers of dislocations appear only when the network stage of growth i s reached,, Five proposed mechanisms for the i n t r o -o o H X >> +J •H CQ c CD TD 0 •rl •P O o rH • r l Q 100 -80 60 40 20 0 1 -1 1 Coalescence j Network j Channel 1 I Continu-1 1 1 Stage , Stage | and Hole | Stage ous Film 1 b0, 4->' CO 1 1 | l_ 1 | / 1 i X 1 1 1 -coalescence 1 | / 1 1 / 1 / 1 / 1 Pre-- — i — — • — i i .j 0 100 200 300 400 Approx. Gold Thickness (&) 500 Figure 1.9 The Density of Dislocations (per unit area of substrate) in a Gold Deposit o 26 duction of growth imperfections are: (1) The extension of imperfections already ex-i s t i n g at the substrate surface, (2) The formation of imperfections to accommo-date any orientation differences between j o i n i n g nuclei, (3) The formation of imperfections to accommo-date displacement m i s f i t s between j o i n i n g n u c l e i , (4) The formation of point defects and t h e i r aggregation to form d i s l o c a t i o n loops and other imper-fect ions, (5) P l a s t i c deformation of the f i l m at various stages of growth, B, Stresses i n Thin Films Vacuum deposited films can be in a state of high mechanical stress. The magnitude of the stress can be very high and i n some instances exceeds the normal bulk y i e l d 7 stress of the material , The o r i g i n of t h i s stress i s not c l e a r l y understood. There are two components of the stress, the f i r s t due to any temperature differences between substrate and deposit during deposition (thermal stress) and the second any additional stress due to structure ( i n t r i n s i c s t r e s s ) . I n t r i n s i c stress can be generated by enclosed gas atoms or impurities, by freez-ing-in of l a t t i c e defects during condensation, or by surface e f f e c t s due to the small thicknesses involved (for example, surface tension). Also, oxides or other c h e m i c a l l y bound s u r f a c e l a y e r s can c o n t r i b u t e t o the s t r e s s i n a manner s i m i l a r t o the i n t e r f a c e between sub-31,35 s t r a t e and f i l m , S t r e s s r e s u l t i n g from l a t t i c e d i s o r d e r s w h i c h a c c o u n t s f o r most o f t h e i n t r i n s i c s t r e s s on a f i l m can be r e l i e v e d by a n n e a l i n g o r by the c h o i c e o f a h i g h e r d e p o s i t i o n t e m p e r a t u r e . CHAPTER 2 EXPERIMENTAL PROCEDURE 2 o1 Vacuum Equipment Thin f i l m depositions were carried out in a CVC-14 vacuum unit capable of an ultimate pressure of -8 . . . 5x10 Torr i n the working chamber, Modifications were made to the basic system so that four evaporation sources were available,, An aluminum masking plate was i n s t a l l e d at a distance of 25 cm. above the base-plate giving an e f f e c t i v e source-to-specimen spacing of 22 on. A rotation seal was machined so as to impart both a l i f t i n g and rotation motion to a l l specimen holders. This enabled specimens to be set i n place on a mask d i r e c t l y above any one of four sources during a single pump-down, A 1/8" diameter Al wire was i n s t a l l e d i n the b e l l j a r at a distance of 1 1/2" from the specimen plane to provide glow-discharge cleaning during the roughing part of the pump-down cycle. This wire was inserted into one of the main base-plate plugs. P r i o r to evacuation of the vacuum chamber, an 85 mm. glass cylinder was placed around each evaporation source so as to prevent contamination of other sources and samples. Slides were attached to the specimen holder with scotch tape. Glass cover s l i d e s ,0 015" thick were used f o r masking. A mask could be i n any desired shape depending on the experiment. Figure 2,1 shows the de t a i l s of the vacuum equipment, 2.2 Film Deposition 2,2,1 Sample Preparation Specimens were prepared on glass microscope s l i d e s . Each s l i d e was rinsed with a detergent solution, polished with lens ti s s u e , and subjected to 'the breath test 5' 5 before being inserted into the vacuum chamber. To 3 6 complete the cleaning process the sl i d e was exposed to a glow discharge inside the vacuum system for 10 minutes during the f i r s t part of the pumping cycle. The evapora-—6 tions were ca r r i e d out i n a vacuum of 2x10 Torr using resistance heated ,010" molybdenum boats, The substrates, mounted 2 2 cm, above the evaporation sources, could be rotated so as to l i e d i r e c t l y above each source in turn, 30 • It was calculated that at this source to specimen d i s -tance the var i a t i o n i n thickness across the slid e would be less than 2%, In k i n e t i c studies two d i f f u s i o n couples were evaporated onto a single microscope sli d e using suitable * Breath t e s t : Slide i s clean to within one or two mono-layers of contamination when a breath mark on i t d i s -appears rapidly, LEGEND A e v a p o r a t i o n s o u r c e s e l e c t o r s w i t c h B m a s k i n g p l a t e C s p e c i m e n h o l d e r D r o t a t i o n c o n t r o l E #4 e v a p o r a t i o n s o u r c e F Mo b o a t G #3 e v a p o r a t i o n s o u r c e H #2 e v a p o r a t i o n s o u r c e I m a i n b a s e p l a t e J b r a s s b a s e - p l a t e K #1 e v a p o r a t i o n s o u r c e L g l o w d i s c h a r g e r i n g F i g u r e 2,1 Vacuum E q u i p m e n t Ag or Cu Se or Te Figure 2,2 Main Evaporation Configuration 31 masks above each source. Figure 2,2 (a) shows the main experimental configuration used to observe l a t e r a l d i f -fusion and Figure 2.2 (b) shows the layout of samples on the microscope s l i d e substrate. A f i l m of Ag or Cu was f i r s t deposited over part of the sli d e and allowed to cool for a minimum of 15 minutes i n order to ensure that the sub-strate would be at room temperature for successive eva-porations. The s l i d e was then rotated into place over two Te or two Se sources i n succession and evaporation across the e x i s t i n g Ag or Cu step was carried out. A time of 3 minutes was allowed between the two evaporations, 2,2,2 Film Thicknesses For purposes of measurement of f i l m thicknesses an opaque s t r i p of Al was evaporated across the f i l m steps at the c l e a r edge of the s l i d e (Figure 2,2 (b))„ The method of Fizeau fringes of constant thickness as describ-37 • ed by Tolansky was used to determine the f i l m thickness. In this technique a p a r t i a l l y s i l v e r e d (4-6% transmission) o p t i c a l f l a t i s brought close to the Al over-layered step. If the r e l a t i v e positions of s l i d e and f l a t are adjusted so as to form a wedge shaped a i r gap, and the i n t e r f e r o -meter i s illuminated by a beam of p a r a l l e l monochromatic l i g h t , a series of dark fringes can be made to run i n straight l i n e s perpendicular to the steps on the opaque f i l m . These fringes trace out the points of equal a i r gap thickness and t h e i r separation corresponds to an i n -crease in gap thickness of X/2 where X i s the wavelength of the l i g h t . The fringes show a displacement as they pass over the step edge and measuring t h i s as a fr a c t i o n of the fringe spacing gives the f i l m thickness in units of X/2. Figure 2,3 shows the interferometry arrangement and some t y p i c a l fringe systems observed. 2.2.3 Temperature Tests Temperature tests i n the range 3 0-100°C were car r i e d out i n a water bath controlled to +_ 1.5°C by ins e r t i o n of the sample s l i d e into a 1" diameter t e s t -tube immersed i n the water. The test-tube was sealed with a rubber stopper to reduce convection heat losses. Tests at 0°C were carried out in an ice-water mixture. Thermometer readings were made on the bath every hour during a run as a check on the temperature c o n t r o l l e r . 2.2.4 Measurement of Diffusion Rate Constants The d i f f u s i o n rate constant was determined by measuring the width (x) of the l a t e r a l d i f f u s i o n zone as a function of time. Measurements were made using a cali b r a t e d t r a v e l l i n g eyepiece on a metallurgical micro-scope , 33 Eyepiece and ocular lens for viewing fringe system Hg source Wratten #72 f i l t e r (1% yellow transmission) P a r t i a l l y s i l v e r e d o p t i c a l f l a t Step of f i l m to be measured glass opaque r e f l e c t i n g coating of Ag or Al Observed Fringe Patterns Ag step of 1990 % Ag step of 260 A Figure 2,3 Measurement of Film Thicknesses 34 2.2.5 Electron Microscopy A thin evaporated carbon f i l m floated onto a 150 mesh specimen g r i d i n d i s t i l l e d water provided a sub-strate f o r an evaporated d i f f u s i o n couple that could be studied by transmission electron microscopy. The specimen gri d with i t s attached carbon support f i l m was taped by one edge to a microscope sli d e and a di f f u s i o n couple was deposited on i t i n the configuration shown i n Figure 2,4. The s l i d e was masked so as to f a c i l i t a t e f i l m thickness measurements. A cooling time of at least 15 minutes was allowed between the two required evapora-tions. Figure 2.4 Evaporation Configuration for Electron Microscopy Specimens, 35 2,3 Different Evaporation Configurations Three other evaporation configurations in Cu-Te were investigated to see i f any l a t e r a l d i f f u s i o n occurred. The geometries involved are shown in Figure 2,5, The occurrence of l a t e r a l d i f f u s i o n i n 2,5 (a) or (b) - that i s , the advance of a d i f f u s i o n zone into the pure Cu f i l m - would be due to the d i f f u s i o n of the Te into Cu, In samples prepared i n these two configurations no l a t e r a l d i f f u s i o n was ever observed e i t h e r by o p t i c a l or electron microscopy even after annealing at 50°C for 2-3 hours. The reason that d i f f u s i o n i n this d i r e c t i o n i s not observ-ed i s probably due to the development of Kirkendall porosity (see page 7, Introduction) on the Cu/Cu-Te interface causing i t s rupture. The geometry of 2,5 (c) should be exactly equivalent to that described i n Section 2.1. Diffusion of Cu into the pure Te f i l m should res u l t i n the formation and growth of a l a t e r a l d i f f u s i o n zone. While there was some indicati o n that l a t e r a l d i f f u s i o n was proceeding immediately a f t e r the d i f f u s i o n couple formation, the inevitable result of forming a sample in t h i s way was that the entire Cu side became detached from the glass substrate and l i f t e d away from the surface. With the fi-re s u i t ing discontinuity between Cu-rich side and Te, d i f -fusion could not proceed. The immediate and rapid loss of adhesion was probably due to both the poor adhesion Cu Te Cu Glass (a) Te Cu Glass (b) Cu l e _ Glass (c) gure 2,5 Alternative Evaporation Geometries 37 of the i n t e r m e t a l l i c compound produced by downward di f f u s i o n on the Cu side (which extends right to the glass surface) and the aggregation of the Te substrate f i l m during the deposition of Cu. The evaporation of Cu requires a high power input to the source for s u f f i c i e n t lengths of time to produce 40-50°C temperature increases at the substrate. It was observed that the application of a thin Cr substrate to the glass before evaporating Te and Cu seemed to s t a b i l i z e the Cu side for about 15 minutes during which time a thin l a t e r a l zone de-v e l o p e d . At longer periods, however, the Cu side peeled o f f and d i f f u s i o n ceased. Because of this adhesion problem -common to a l l four systems - a study of d i f f u s i o n i n this configuration was extremely d i f f i c u l t and further work was not attempted, 2,4 Other Systems Table 2,1 l i s t s 18 systems i n which room tempera-ture l a t e r a l d i f f u s i o n was looked for without success. For a system X-Y, the evaporation configuration was as shown i n the table and was generally arranged so that the f a s t e r d i f f u s i n g atom would be i n a position X, This was to avoid the development of porosity at the boundary of the d i f f u s i o n zone. In a l l the additional systems investigated i t was concluded that no l a t e r a l d i f f u s i o n took place because the expected d i f f u s i o n c o e f f i c i e n t s at room temperature were too small. Table 2,2 l i s t s the expected d i f f u s i o n c o e f f i c i e n t s 9 as found i n t h i n films ( a f t e r Brown where available) i n Table 2.1 Other Systems i n which the P o s s i b i l i t y of Lateral Diffusion Was Investigated y Y Glass Pb-Te Pb-Se Ag-Cd Ag-Sb Cu-Sn Al-Te Al-Se Cu-Cd Cu-Sb Au-Pb Fe-Te Bi-Se Cu-Ge* Bi-Te Cu-Al Cd-Te Ag-Al** Au-Te i Annealed at 200°C f o r 4 hours ** Observed at 600°C i n electron microscope hot-stage „ TABLE 2.2 Expected Diffusion Coefficients i n some Possible Thin Film Diffusion Systems System Faster. Diffusing Atom*' T(°C) 2 D (cm /sec) Ag-Al Ag 21 -22 3x10 Cu-Al Cu . ' 21 -29 8.4x10 . Ag-Cd Ag 21 1.5xl0~ 1 6 Au-Pb Au 21 2.17xl0" 1 5 Cu-Sn Cu 21 1.13xl0" 3 6 Cu-Cd Cu 21 -16^ 5x10 t Au-Te Au 90 2x10-" Cu-Ge Cu 700 3 x l 0 _ 5 ^ i Bulk d i f f u s i o n data some of these systems. At higher temperatures movement of the phase boundary interface would be expected but t h i s was never observed even i n the electron microscope hot stage due to interface rupture, diffuse interfaces, aggreg t i o n , oxidation, etc. 41 CHAPTER 3 LATERAL DIFFUSION IN Ag-Se 3«,1 Introduction Figure 3=1 shows the equilibrium phase diagram for 40 Ag-Se , At low temperatures only the phase Ag 2Se i s thermally stable and i t i s expected that d i f f u s i o n i n the Ag-Se system w i l l result i n i t s formation, Ag 2Se undergoes an a l l o t r o p i c transformation at about 130°C„ The low tempera-ture 3 modification has been described as having either an orthorhombic or monoclinic structure while the a modifica-41 t i o n , stable above 130°C, has a CaF 2 structure , 42 4 3 Pure bulk Se has several a l l o t r o p i c forms * The two most important modifications are the hexagonal, the most common form stable below the melting point, and the amorphous form which i s induced by supercooling l i q u i d Sec A l l of the evaporated thin films of Se observed i n th i s work were amorphous i n nature. The colour of the Se de-posits varied from l i g h t orange for the very thin films (< 100&) to deep red for the very thick films (> 4000 X ) . The experimental configuration of a l l Ag-Se thin f i l m d i f f u s i o n couples investigated i s shown.in Figure 3,2, 42 1000 10 I 15 i 20 _ l WEIGHT PER CENT SELENIUM 25 30 40 50 60 ' ' L _1_ 70 _L_ 60 i 90 960.5° 900 l I I / TWO MELTS / -690" l 897s 800 12 (9) 840° 700 600 500 £ 4 0 0 300 200 100-sr. -44.5-(37) TWO MELTS 616° 217° 128*5° 0 10 20 30 40 50 60 70 80 90 100 Aq ATOMIC PER CENT SELENIUM S« Figure 3.1 Equilibrium Phase Diagram f o r Ag-Se (Hansen 4 0), Figure 3 „ 2 Ag-Se Diffusion Couple Evaporation of the Se across the Ag step resulted i n the immediate formation of the i n t e r m e t a l l i c compound Ag 2Se on the Ag side of the couple. During deposition t h i s was evidenced by an immediate colour change ranging from blue-purple f o r very thin Se films to l i g h t grey fo r thick Se films, A white d i f f u s i o n zone was observed at the i n t e r -face A (figure 3.2) immediately a f t e r the sample was re-'s moved from the vacuum chamber. The growth of the d i f f u s i o n zone proceeded rapidly at room temperature (21 +_ 3°C) with a planar phase boundary interface advancing into the pure Se, The interface was seen to remain planar even afte r a long ageing time (750 hours), 3.2 Diffusion Kinetics 3.2,1 Growth Rate A t y p i c a l plot of the d i f f u s i o n zone width x as of a function^time i s shown in Figure 3,3, In Figure 3.4, x i s plotted against /F and the l i n e a r dependence i l l u s t r a t e s • • 9 that the phase boundary motion obeys the parabolic law x =Kt where K i s the d i f f u s i o n rate, constant. V i r t u a l l y a l l of the d i f f u s i o n zones measured i n the Ag-Se system exhibited this parabolic behaviour. As discussed in the "Introduction" parabolic growth i s c h a r a c t e r i s t i c of d i f f u s i o n control. The series of photographs i n Figure 3.5, made on an o p t i c a l microscope, shows the growth of the Ag 2Se phase fromtr= 0 to t = 4 hours. The white- band appearing between the d i f f u s i o n zone and the Ag-Se region of the d i f f u s i o n Figure 3 . 5 Growth of a D i f f u s i o n Zone i n Ag-Se (x!88) 4 8 couple has been c a l l e d a "white Zone"„ T h i s r e g i o n w i l l be d i s c u s s e d i n the Appendix where i t i s shown t h a t the "white zone" i s o f no s i g n i f i c a n c e i n the l a t e r a l d i f f u s i o n process, 3,2,2 E f f e c t o f Se Thickness on the Rate Constant F i g u r e 3,6 shows a s e r i e s o f x versus / t " p l o t s f o r Ag-Se d i f f u s i o n couples i n which the Se t h i c k n e s s ranged o from 0 to 1300 A, In every case p a r a b o l x c growth was ob-served i n d i c a t i n g d i f f u s i o n c o n t r o l . In Figure 3,7 the r a t e c o n s t a n t , K, determined from the growth k i n e t i c s o f samples i n which t g e was v a r i e d from 0 to 2 2 60 X i s p l o t t e d as a f u n c t i o n o f Se t h i c k n e s s . The r a t i o o f Ag to Se t h i c k n e s s ( t ^ g / t ^ ) w a s S r e a ' t e r than 1,1 i n a l l these samples. The reason f o r e x c l u d i n g samples i n which ^ A g ^ s e < w - ^ 1 1 be d i s c u s s e d i n the next s e c t i o n . These r e s u l t s show t h a t i n the Se t h i c k n e s s regime 20 0 to 2260 ft, the r a t e constant has a constant value o f 1,1x10 ^ cm 2/sec. Between 0 and 20 0 A*, the rate constant r i s e s s h a r p l y to reach a maximum at about 15 0 A then drops o to the constant value above 2 00 A, I t appears, t h e r e f o r e , t h a t the d i f f u s i o n r a t e i s enchanced i n the t h i c k n e s s regime 90 to 170 A*, T h i s maximum i n the curve a t t a i n s a value o n l y 3,5 times g r e a t e r than the constant r a t e constant value and appears to be a genuine e f f e c t s i n c e s i m i l a r peaks were a l s o found i n the o t h e r three systems i n v e s t i g a t e d , and i n the Te systems a much l a r g e r d i f f e r e n c e between peak and constant r a t e values was observed. 0,0 1,0 2.0 .3.0 4.0 / t - (/hrs) Figure 3.6 Effect of Se Thickness on Growth Rate o o o o ° O o Q f e ° o o o o oo o _u X I X X x 0 100 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 o t (A) Figure 3/7 Rate Constant a§ a Function of Se Thickness 3,2.3 The Structure of Se Films A suggested explanation of the fas t e r d i f f u s i o n rate at low Se thickness i s that a disproportionate number of high d i f f u s i v i t y paths are present i n these films. An electron microscopy study of very t h i n Se films was carried out to see i f , i n fa c t , h i g h - d i f f u s i v i t y channels did exist i n the amorphous Se films. Although the general growth stages of a thi n f i l m have been well documented for such metals as Au and Ag (see Introduction, page 21) , no s p e c i f i c reference to Se could be found i n the l i t e r a t u r e . I n i t i a l l y , thin Se films o between 50 and 300 A were examxned by transmission electron microscopy both at room temperature and l i q u i d nitrogen temperature using the microscope cold stage. In the thicknes o range 50 to 90 A the Se films appeared to consist of massive, disconnected islands with some tendency to be coalesced at o higher thicknesses (~ 100 A), There appeared to be no material present between the islands, however. Cr-shadowed carbon re p l i c a s were then made of the same Se films observed by transmission electron microscopy. Electron micrographs o showed that at t Q = 5 0 A, the Se f i l m consisted of large islands 2000 to 5000 % i n diameter with a fine i n t e r - i s l a n d substructure i n evidence. At 90 A" coalescence of the large Se islands had begun and the substructure between the islands was well defined, This inter-network layer was calculated o to be about 30 A thick. Figure 3,8 shows both the trans-mission and r e p l i c a electron microscopy results for very 52 o (5) 300 A Se f i l m (transmission) (6) Cr-shadowed glass surface (replica) Figure 3,8 Structure of Se Films thin Se films. In both cases the size of the Se aggregates i s equivalent i n d i c a t i n g that the i s o l a t e d islands i n the transmission micrographs are not the result of melting by the electron beam and that the microstructure of the Se films i s not influenced by the substrate (glass versus carbon). Also shown i n Figure 3,8 i s an electron micro-graph of a Cr-shadowed r e p l i c a of a glass surface. The absence of any fine structure indicates that the substructure seen i n the Se re p l i c a s i s due s t r i c t l y to the structure of the Se f i l m and not to i r r e g u l a r i t i e s on the glass sub-o . strate. The micrograph of a 300 A Se f i l m characterizes continuous Se f i l m s ; the large islands present during the early growth stages are f a i n t l y v i s i b l e within the amo rpho us mate r i a l , The e f f e c t of a very thin Se f i l m possessing a structure l i k e that shown i n Figure 3,8(4) on the d i f f u s i o n zone interface i s shown i n the series of o p t i c a l micrographs o in Figure 3,9, Up to 150 A the phase boundary interface consists of many minute projections suggesting the tendency for d i f f u s i o n to proceed s l i g h t l y faster i n the i n t e r -i s l a n d channels, A c a l c u l a t i o n of the wavelength of the interface fluctuations made from Figures 3,9 (1), (2), (3) o shows that i t i s approximately 3000 to 5000 A which i s approximately the same as the p a r t i c l e size indicated i n the electron micrographs. By contrast the interface i n Figure o 3,9 (4) where t = 900 A i s very planar. The Se f i l m at th i s thickness i s continuous having the microstructure Ag 2Se — » 54 > Se Ag 0Se J > Se Figure 3„9 Appearance of Phase Boundary at Varying Se Thickness 55 shown i n Figure 3.8 (5). The electron microscope results on very thin Se films lead to the suggested growth sequence shown i n Figure 3.10. Enfchanced short c i r c u i t d i f f u s i o n occurs mainly i n the network stage of growth when the i n t e r - i s l a n d sub-structure i s very th i n but s t i l l continuous. The substructure part of the f i l m i s l i k e l y a region of high disorder contain-ing a large number of grain boundary-like regions. Diffusion i n the substructure i s probably analogous to 18 grain boundary d i f f u s i o n . In terms of Fischer's model (Figure 3,11) the i n t e r i s l a n d f i l m would correspond to a grain boundary although, of course, i t i s very much wider. The large islands would be equivalent to bulk material. Even though grain boundary d i f f u s i o n i n bulk metals i s about 10 times greater than i n the l a t t i c e the e f f e c t i s f a i r l y small because l a t e r a l d i f f u s i o n from the grain boundary into the l a t t i c e e s s e n t i a l l y "damps" the fas t e r d i f f u s i o n process taking place i n the boundary, 3,2,4 Effe c t of Thickness Ratio on the Rate Constant Figures 3,12 and 3.13 show the e f f e c t of the r a t i o of Ag to Se on the r a t i o constant for Se films greater than o 200 A thick. It can be seen that below a r a t i o of 1,1, the di f f u s i o n rate constant i s zero while at values of ^Ag^Se greater than 1.1, the rate constant tends to a constant — 8 2 value of 1,1x10 cm /sec. The value of t^g/tgg above which d i f f u s i o n occurs and below which d i f f u s i o n does not occur 56 < o g o r Pre-coalescence stage ( \(\r\f \r\r\l i 0 i s o l a t e d islands of amorphous material o < 50 A Coalescence stage: 2. some islands begin to j o i n 0 50-90 A Network stage: large coalesced 3. islands and i n t e r -island substructure 90-150 A Channel and hole stage: i n t e r - i s l a n d 4 , sub-structure i n -creases in thickness , 150-180 A Continuous amorphous film. o > 180 A Figure 3.10 Stages i n the Formation of a Continuous Amorphous Se Film. 57 Grain Boundary Figure 3.11 Fischer's Model for Grain Boundary Diffusion, 250 200 150 100 50 0 — • — o o tAg / tSe W^e = 1.1 = 9.7 1 ^- • W^e V'se = 2.4 <_ 1.1 0,0 1.0 2.0 3.0 / t ~ (/hours) Figure 3.12 E f f e c t of Thickness Ratio on Growth Rate 2o 00 o cu cn S o lo 50 o l o 0 0 y; Oo 50 1 • m ® fl i i 1 i i m i < • V c r i t i c a l r a t i o = 1„ i i i Ool 0„ 5 lo 0 2o0 3.0 4 . 0 5.0 10o 0 Figure 3 0 13 Growth Rate as a Function of Thickness Ratio 60 has been ca l l e d the c r i t i c a l r a t i o (R c)° An investigation of the c r i t i c a l r a t i o value over a range of Se thicknesses showed that It was independent of the absolute Se thickness. The result of this study i s shown i n Table 3,1, TABLE 3,1 C r i t i c a l Ratio Dependence on the Absolute Se Thickness R c t S e (A) ,95-1,15 125 l . l + o l M B 390 1.0 3+.1 740 l . l l + . l 15 70 The o r i g i n of a c r i t i c a l r a t i o of Ag to Se which must be exceeded i n order for d i f f u s i o n to proceed i s due primarily to the stoichiometry i n the Ag-Se overlap region of the d i f f u s i o n couple, 3,2,5 Theoretical Determination of the C r i t i c a l Ratio Consider the thin f i l m d i f f u s i o n couple M-Y shown i n Figure 3,14 where M i s the fa s t e r d i f f u s i n g species. In rapidly d i f f u s i n g systems such as Ag-Se a d i f f u s i o n reaction occurs very quickly i n the region where Y overlaps M to form 61 Figure 3„14 Theoretical Diffusion Couple M-Y 62 a compound M^Y, say. Knowing the exact composition of t h i s d i f f u s i o n compound i t i s possible to calculate on the basis of stoichiometry the r a t i o of thickness of M to Y at which the entire volume of M w i l l be used up i n forming MxY, When thi s occurs there i s no excess M available to diffuse 2 l a t e r a l l y . Consider, now, a unit area (1 cm ); the c r i t i c a l r a t i o i s the r a t i o of t., (M thickness) to t v M Y (Y thickness) at which the entire volume of M in t h i s unit area combines with a s u f f i c i e n t amount of Y to form M Y, x The molar volume (a) i s given by P a = - (3 ,1 ) A where p = density and A = atomic weight i n grams/mole. In dealing with t h i n films i t i s assumed, therefore, that the bulk and thin f i l m densities are equivalent. In unit area 3 3 there w i l l be t cm of M and t„ cm of Y, Neglecting any M Y o -/ volume change i n Y as M diffuses into i t , the c r i t i c a l thickness r a t i o Rc = ( t ^ / t Y ) c r i t which must be exceeded for any excess M to be l e f t for l a t e r a l d i f f u s i o n i s given by: Moles/cc of M x ( t M ) ^ Moles of M reacting to give M^Y Moles/cc of Y x ( t v ) • +. * c r i t Moles of Y reacting to give MxY (3.2) 63 I f a M and ay are the molar volumes of M and Y respectively and B^, $y a r e the number of moles of M and Y required to form MY, then we may write that 3 M a y (3.3) To correct for any volume expansion or contraction of Y as M diffuses i n to form MY, i t i s necessary to multiply the value of Rc obtained from equation (3,3) by the r a t i o aMxY H H (3.4) ajvj ay where x i s the stoichiometric r a t i o between M and Y i n the compound M Y, Notice that the units of 1/ot are cm /mole x and that ct y i s the'. actual molar volume of the compound MXY as defined i n equation (3,1). For Ag2Se, the only i n t e r m e t a l l i c compound i n the Ag-Se system, a t h e o r e t i c a l value for Rc of 1 ,0 5 i s obtained using equations (3,3) and (3,4), This i s i n good agreement with the observed experi-mental value of 1,1 +_ d a The close agreement between the o r e t i c a l and experimental values of Rc found i n Ag-Se appeared to j u s t i f y the application of the theory to pre-d i c t i n g the intermediate compound formed i n the other three systems i n which more than one i n t e r m e t a l l i c phase i s stable at room temperature. 64 3,2 o 6 Temperature Dependence of the Rate Constant The temperature dependence of the rate constant for samples having t<,^  > 180 A* and t^g^Se > l o 1 ^ n t n e temperature range 0-55°C was determined. Figures 3.15 and 3.16 show the results of the study. The upper l i m i t of the temperature range was kept below 60°C since Se films heated above th i s temperature became aggregated*. The Arrhenius-type expression obtained for the rate constant K from Figure 3,15 was K = 67 exp[- ] F RT To see i f the di f f u s i o n process i n thin films was comparable to that which occurs i n bulk couples, the d i f -fusion rate constant was measured at 50, 100, and 130°C in bulk d i f f u s i o n couples of Ag and c r y s t a l l i n e Se, Since d i f f u s i o n rates i n t h i s system are controlled by the d i f -fusion of s i l v e r through the c r y s t a l l i n e kg^Se d i f f u s i o n zone, the use of c r y s t a l l i n e Se rather than the amorphous material should not have affected the re s u l t s . Some couples were made using amorphous Se, but even at temperatures as low as 50°C, the Se became p l a s t i c and flowed a f t e r short *N0TE: The fals e o r i g i n i n the 3°C tes t was due to the inclusi o n of the white zone width in the d i f f u s i o n zone width. This was necessary because the exact start of the d i f f u s i o n zone was not well defined i n t h i s specimen, 67 annealing times (2-4 hours). The results of the bulk temperature study are plotted i n Figure 3.17 along with the thin f i l m data. From t h i s graph the temperature de-pendence of the rate constant for bulk couples i s found to be K = 24 expC-iZl0-0-] RT The large difference i n growth rates between bulk and thin f i l m couples (about 3 orders of magnitude) and the difference in a c t i v a t i o n energies implies that the d i f f u s i o n mechanism i s not the same. It would seem l i k e l y that some form of short-c i r c u i t d i f f u s i o n process i s operative i n thin films which results i n a lower a c t i v a t i o n energy, 3,3 Electron Microscopy The advance of the Ag^Se phase boundary was ob-served d i r e c t l y i n the electron microscope. The interface appeared to be quite planar even at high magnification and i t s motion was rapid. Although the Se f i l m i n front of the d i f f u s i o n zone was amorphous in nature, the d i f f u s i o n zone i t s e l f was c r y s t a l l i n e with elongated or columnar grains aligned p a r a l l e l to the interface growth di r e c t i o n . Figure 3.18 shows a series of electron micrographs made of the moving phase boundary as i t swept across the f i e l d of view, The elapsed time between micrographs 1 and 3 in this figure was about 4 minutes. This figure i l l u s t r a t e s 68 one of the major d i f f i c u l t i e s encountered i n the electron microscopy of Se f i l m s ; namely, that the heating of the f i l m by the electron beam i s s u f f i c i e n t to produce aggre-gation of the Se, In photographing the moving interface i t was impossible to prevent aggregation even when very low illumination l e v e l s were used. Aggregation of the Se accounts for the minute black specks seen i n the micrograph of Figure 3,18, The white areas i n 3,18 (2), (3) appear a f t e r the electron beam induces a l o c a l i z e d temperature i n -crease and are probably depleted regions produced by Se aggregation or re-evaporation. This explanation i s sub-stantiated by the coincidence of the white areas in Figure 3.18 (2) and 3,18 ( 3 ) . The general appearance of the d i f f u s i o n zone and phase boundary interface at high magnification i s shown i n Figure 3,19, The major contributing factor to the contrast between the dark d i f f u s i o n zone and the l i g h t Se i s the d i f ference i n thickness r e s u l t i n g from volumetric expansion.of the Se when Ag diffuses i n to form Ag^Se, The volume change brought about in t h i s case i s about 5 7%. It should also be pointed out that t h i s volumetric expansion causes the d i f f u s i o n zone to become quite rumpled and distorted and to become p a r t i a l l y detached from i t s underlying sub-strate. Evidence of t h i s d i s t o r t i o n i s provided by the large number of bend and thickness contours seen in Figure 3.19 (a), A further contribution to contrast between the 71 (b) Phase Boundary interface showing elongated grains in the diffusion zone Figure 3.19 Diffusion Zone in Ag-Se 72 d i f f u s i o n zone and pure Se may be the large difference in 44 atomic scattering factors of Ag and Se. Selected area d i f f r a c t i o n patterns were made of the d i f f u s i o n zone. Subsequent analyses showed that the d-spacings calculated from the pattern rings were in good agreement with the known d-spacings of B-Ag2Se, the low temperature modification. Figure 3.20 shows a t y p i c a l set of d i f f r a c t i o n r e s u l t s . While the electron microscopy results enabled the composition of the d i f f u s i o n zone to be determined and while the direct observation of the moving phase boundary was i n i t s e l f i n t e r e s t i n g , p a r t i c u l a r l y since r e l a t i v e l y l i t t l e i s known about the actual motion of phase boundaries, the results provided l i t t l e information concerning the mechanism for d i f f u s i o n i n Ag-Se, 73 (a) S,A.D, of d i f f u s i o n zone (b) Au Standard i n an Ag-Se thin f i l m couple o o Calculated d-spacings (A) d-spacings for 3-Ag2Se (A) 7,25 _ _ 4, 32 4.15 3.76 3. 77 3. 42 3. 30 2 . 84 2.89 2, 76 2. 72 2.66 2,67 2.57 2.20 2.23 2.10 2.11 2.04 2.07 2,00 1. 84 1, 87 1, 77 1, 82 Figure 3,20 Selected Area D i f f r a c t i o n Pattern of Diffusion Zone 74 CHAPTER 4 LATERAL DIFFUSION IN Cu-Te 4„1 Introduction The equilibrium phase diagram for Cu-Te i s shown i n Figure 4.1. Unlike Ag-Se, i n which only one i n t e r m e t a l l i c phase i s thermally stable at room temperature, Cu-Te has at least 3 possible stable phases at room temperature. The main i n t e r m e t a l l i c compounds are Cu2Te, Cu 2 xTe with x~0.6 (Cu^'Te^), and CuTe, In addition Hansen 4 0 has pointed out the possible existence of a phase (X) whose composition l i e s at about 36-3 7. at. % Te. It i s shown in section 4.3 that the d i f f u s i o n of copper along a Te f i l m results i n the formation of only one phase, Cu 0 vTe. This phase z —x has a defect structure of the Cu 2Sb type (tetragonal) and undergoes a polymorphic transformation at about 367°C. The phase diagram indicates that Cu 2_ xTe ranges i n compo-s i t i o n from C.u^  3 5 T e to Cu-^  ^ T e so that 0.59 < x > 0.65. At temperatures below the melting point Te has a 42 4 3 stable hexagonal form ' , The structure i s highly an-i s o t r o p i c due to different bonding perpendicular and p a r a l l e l to the c-axis. This anisotropy i s r e f l e c t e d i n 7 5 10 20 30 J I 40 WEIGHT PER CENT TELLURIUM 50 60 70 60 J _ l , I . L 90 L 0 Cu 10 20 30 40 50 60 70 ATOMIC PEA CENT TELLURIUM 80 90 100 T« Figure 4.1 Equilibrium Phase Diagram of Cu-Te (af t e r Hansen 4 0) 76 both the l i n e a r expansion c o e f f i c i e n t , which is negative p a r a l l e l to the c-axis, and p o s i t i v e perpendicular to i t , and the e l e c t r i c a l r e s i s t i v i t y which attains a value twice a as great i n the p a r a l l e l direction as i n the perpendicular. Figure 4.2 i s a selected area d i f f r a c t i o n pattern made on a pure evaporated Te thin f i l m . The d-spacings calculated from this pattern are i n good agreement with the known d-spacings for hexagonal Te. Because of the c r y s t a l l i n e nature of a l l Te films encountered i n t h i s work, the re-sults obtained i n Cu-Te, although completely analogous to those f o r Ag-Se, w i l l be discussed i n some d e t a i l . 4.2 Kinetics 4,2.1 Growth Rate Figure 4.3 i s a t y p i c a l plot of the d i f f u s i o n zone width as a function of / t obtained for the d i f f u s i o n of Cu into Te. The l i n e a r dependence shows a parabolic growth law which implies that growth i s d i f f u s i o n controlled. 4.2,2. Effe c t of Te Thickness on the Kinetics Figures 4,4 and 4,5 i l l u s t r a t e the e f f e c t of Te thickness on the growth rate for samples having t^/t-p e>R c, Beyond Te thicknesses of about 200 X, the d i f f u s i o n rate -9 2 constant has a constant value of 2.1x10 cm /sec. In thinner films, however, the growth rate i s much fas t e r and -9 2 Q approaches a value of 9x10 cm /sec at a thickness of 110 A. Figure 4.2 Selected Area D i f f r a c t i o n Patte of Pure Te 79 0 1.0 2,0 3.0 4.0 5.0 6.0 7.0 / t ~(/hr) Figure 4,4 E f f e c t of Te Thickness on Kinetics 10.0 o 7> o 6> ° o o ° o ± [For t C u / t * 0.693, Room Temperature] o o o _L _L 100 200 400 600 800 1000 1200 1400 t T e (A) 1600 O TT 1800 2000 3200 3400 Figure 4 . 5 Rate Constant as a Function o f Te Thickness 81 4.2,3 The Structure of a Te Film The early growth stages of a Te f i l m before i t becomes continuous account for the apparent peak i n the rate constant versus Te thickness graph. The steps i n the formation of the Te f i l m closely p a r a l l e l those of a Se f i l m as discussed i n section 3,2,3, but a major difference i s that the islands of Te observed i n the pre-coalescence stage (see page 25 of Introduction) are randomly oriented o c r y s t a l l i t e s about 200 A i n diameter rather than the large o (2000 - 5000 A diameter) amorphous islands observed in Se films, A transmission electron microscopy investigation of the microstructure of Te films 50 - 1200 X thick was carried out. The re s u l t s of t h i s study, shown i n Figure 4,6, suggest that enhanced d i f f u s i o n occurs when the Te f i l m i s in the network and channel stages of growth. In t h i s thickness o regime, between 90 and 130 A, the Te f i l m consists of coalesced islands with a highly disordered i n t e r — i s l a n d net-work, probably analogous to grain boundaries, where d i f f u s i o n can occur more rapidly. The exact mechanism i s probably s i m i l a r to that which occurs i n Ag-Se as discussed i n section 3,2,3. Film continuity and the onset of a d e f i n i t e o grain structure i s seen at about 200 A and p e r s i s t s up to o the thickest f i l m studied - 1200 A, The microstructure of o Te films greater than 400 A thick closely resembles that of o bulk material except that films between 400 and 900 A are characterized by numerous thickness contours. 82 Figure 4,6 The Growth of a Te Thin Film 83 4,2.4 C r i t i c a l Ratio Figure 4.7 shows a plot of the room temperature d i f -fusion rate constant as a function of the r a t i o of Cu to Te o thickness (t ( - . u / t n [ - e ) f o r couples i n which t ^ > 180 A. This figure indicates that the c r i t i c a l r a t i o (R c) i s 0.63; that i s , when ^ c u^Te > u , ,63 d i f f u s i o n proceeds at a constant rate -9 2 of about 2.1x10 cm /sec while f o r t ^ / t ^ , < 0.63, d i f f u s i o n does not occur. The th e o r e t i c a l values of RQ for each of the three i n t e r m e t a l l i c phases i n Cu-Te were calculated using the methods outlined i n section 3.2.5, Table 4.1 l i s t s the t h e o r e t i c a l values for each phase. From this i t would appear that the growing phase should have the composition C^Te. As w i l l be discussed in section 4.3, the phase forming i n the d i f f u s i o n zone was p o s i t i v e l y i d e n t i f i e d by electron d i f -f r a c t i o n analysis as Cu2_ xTe. The reason why the c r i t i c a l thickness r a t i o i s in error in t h i s system i s uncertain, since the technique yielded excellent results i n the other systems investigated. The value f o r the c r i t i c a l r a t i o i s not dependent on the absolute thickness of the Te f i l m (see Table 4.2) and so i s independent of the f i l m structure. The actual percentage error i s f a i r l y small (~ 30%) and i t i s perhaps unfortunate i n t h i s system that the three i n t e r -m e t a l l i c compounds occur at f a i r l y equivalent compositions. o ( t T e 180>A, Room Temperature) 4. 00 <o 3,00 W ^ e Figure 4,7 Rate Constant as a Function of Thickness Ratio 0 0 85 TABLE 4,1 R for Intermetallic Phases i n Cu-Te c Phase Cu-Te 0, 35 Cu 2_ xTe 0,47 Cu 2Te 0,63 86 TABLE 4.2 C r i t i c a l Ratio as a Function of Absolute Te Thickness t T e (X) 0.58-0.70 270 0.66+0.1 800 0.6 2 + 0.1 3350 0.63+0.1 5000 4,2.5 Temperature Dependence of the Rate Constant The temperature dependence of the rate constant f o r f i l m couples h a v i n g t T e > 180 A* and t £ U / t T e > R c was de-termined over the range 0-100°C. Since Te tends to be f a r less aggregated on a glass substrate than does Se , i t was possible to extend the temperature range of investigation i n both Cu-Te and Ag-Te up to 10 0°C without encountering aggregation problems. Figure 4,8 shows the Arrhenius plot obtained. From this graph the dependence of the d i f f u s i o n rate constant on temperature was found to be K = .0017 exp[-I£H] RT Also shown i n Figure 4,9 i s the Arrhenius plot obtained by .250 ,270 ,290 .310 .330 .350 100 7T (0 K-1) Figure 4,8 Arrhenius Plot f o r Cu-Te F i g u r e 4 „ 9 Comparison o f B u l k to T h i n F i l m T e m p e r a t u r e Dependence 89 "I C Parkinson f o r Cu-Te thin films« His results gave K = .0755 e x p [ - 1 0 0 0 0 3 RT i n the temperature range 0-105°C. The agreement between the two sets of re s u l t s i s somewhat disappointing since b a s i c a l l y the same technique was used i n both instances. It i s f e l t that the r e s u l t s obtained i n the present investigation are probably more r e l i a b l e since a more complete range of temperatures has been used and the effects of thickness r a t i o and Te f i l m thickness have been properly understood. Figure 4,9 shows an Arrhenius plot of the rate constant for growth of Cu2_xTe i n bulk Cu-Te couples as found 45 46 by Wayman and Bennett , Sanderson, St. John, and Brown This system i s one i n which d i f f u s i o n i s sensitive to any compressive stress applied to the d i f f u s i o n zone. The work of Sanderson et a l has shown that during d i f f u s i o n a t h i r d phase, C^Te, appears i n the d i f f u s i o n zone i n addition to Cu2_xTe and Cu-Te, i f the magnitude of the applied stress i s great enough. At zero . applied stress C^Te i s not de-tected. In the thin f i l m couples studied, only the phase ^ u 2 - x T e w a s e v e r present. The absence of any Cu 2Te i n d i -cates that the thin f i l m couples were comparable to bulk couples at "zero pressure". Therefore, a v a l i d comparison between the temperature dependence of the growth rates of Cu 0 Te i n bulk and thin films can be made. If the Arrhenius plot for bulk specimens in Figure 90 4.9 i s compared to the thin f i l m curve, i t can be seen that although the activation energies are quite d i f f e r e n t , the d i f f u s i o n rate constants i n bulk and thin f i l m couples are quite comparable i n the 300-4 50°C temperature range. The convergence of the two curves at these temperatures suggests that some short c i r c u i t d i f f u s i o n mechanism such as grain boundary d i f f u s i o n i s operative at lower temperatures (see Figure 1.2). The activation.energy predicted by the bulk graph i s 150 00 cal/mole, nearly twice as great as the thin f i l m a c t i v a t i o n energy of 7800 cal/mole. This i s again i n d i c a t i v e of a short c i r c u i t mechanism in the thin films. 4.3 Electron Microscopy The advance of a phase boundary along a Te f i l m suggests a somewhat di f f e r e n t picture from that presented by the Ag-Se system due to the c r y s t a l l i n e structure of the Te, As viewed by transmission microscopy, the phase bound-ary motion i s s t i l l quite rapid but the phase interface in general i s seen to be more i r r e g u l a r at high magnification. This i s i l l u s t r a t e d i n Figures 4,10 and 4.11 which show respectively the interface motion along a Te f i l m 4 90 % o thick and one of only 200 A thickness. An in t e r e s t i n g feature of the l a t t e r series of micrographs i s that the Te f i l m i s s t i l l so thin that a well-defined grain structure i s not present. The t o t a l elapsed time between pictures #1 and #4 i n both series i s about 6 minutes. A l l of the micro-91 (3) ( 4 ) Figure 4,10 Motion of the Cu 2 ^Te Phase Boundary ( x 2 2 , 0 0 0 ) 92 o Figure 4.11 Diffusion into a 200 A Te Film 93 graphs indicate that the grains i n the d i f f u s i o n zone are equiaxed rather than columnar as i n Ag-Se. The micro-graphs of Figure 4,12 are enlargements of the phase boundary interfaces of the previous two figures. Figure 4.12 (b) , i n p a r t i c u l a r , suggests that there i s some tendency f o r the advancing phase boundary to surround some of the Te grains. This phenomenon i s more c l e a r l y demonstrated i n Figure 4.13 and i t s accompanying schematic sketch (Figure 4.14) which depicts the surrounding of a Te grain by the advancing phase boundary. These observations suggest that there i s a tendency for grain boundary d i f f u s i o n to occur i n Cu-Te. The results of an electron d i f f r a c t i o n study of the d i f f u s i o n zone i n Cu-Te showed that only the phase Cu2_xTe was formed during d i f f u s i o n . A t y p i c a l selected area d i f f r a c t i o n pattern and the calculated d-spacings obtained from i t are shown i n Figure 4.15. Electron microscopy results on the motion of the Cu 9 Te phase boundary suggest that grain boundary d i f f u s i o n i s important i n the room temperature dif f u s i o n process which occurs i n Cu-Te. Grain boundary d i f f u s i o n would account for the i r r e g u l a r nature of the phase boundary interface. The equiaxed grain structure of the d i f f u s i o n zone suggests that i t s formation may be due to l a t e r a l d i f f u s i o n from the grain boundaries into the pure Te grains. Also the peak i n the o growth rate at a Te thickness of about 110 A i s i n agreement Figure 4,12 Phase Boundary Interfaces at High Magnification Figure 4.13 The Surrounding of a Grain of Te by the Diffusion Zone Interface 9 6 Bend or thickness contour Figure U014 Schematic Sketch of the Surrounding of a Te Grain by the Phase Boundary Interface (a) S o A o D 0 of d i f f u s i o n zone of Cu-Te thin f i l m couple Calculated d-spacings d-spacings (A*) for Cu„ Te (h 2-X 8 0 29 7, 82 6 0 08 6,05 3,70 3,1+2 3, 35 2, 88 2. 81 2 ,62 2o 54 2,48 2,42 2 d l 2o 07 1„ 85 I, 82 I, 76 I, 70 Figure 4,15 Selected Area D i f f r a c t i o n Pattern of the Diffusion Zone of a Cu-Te Thin Film Couple 98 with a grain boundary mechanism. No quantitative estimate of the r e l a t i v e rates of grain boundary to volume d i f f u s i o n could be made on the basis of the electron micrographs. Nevertheless, the microscopy results provide strong evidence to support the idea that grain boundary d i f f u s i o n i s an important mechanism i n thin f i l m Cu-Te couples. 99 CHAPTER 5 LATERAL DIFFUSION IN Ag-Te 5o1 Introduction The o v e r a l l r e s u l t s found in the Ag-Te system close-l y p a r a l l e l e d those of Cu-Te and for this reason they w i l l be reviewed only b r i e f l y . The equilibrium phase diagram, 40 seen i n Figure 5,1 , shows that two in t e r m e t a l l i c phases, Ag Te and Ag Te^Cx ~ 0,2 ), may be thermally stable at Z b —X ^ room temperature. The phase Ag 2Te undergoes a polymorphic t r a n s i t i o n between 135 and 149°C„ The low temperature 4 7 modification, S-Ag^Te , with which we are concerned here, 40 i s reported by Hansen to possess an orthorhombic structure, Ag Telx - 0,2 ) , the other stable phase i n this,system, has a hexagonal structure, 5,2 Kinetics In a l l d i f f u s i o n zones studied in Ag-Te the phase boundary motion was found to be parabolic. The rate of ad-vance of the interface was quite rapid - nearly an order of magnitude greater than i n Cu-Te - and the interface i t s e l f was observed to remain very planar even when the d i f f u s i o n 100 WEIGHT PER CENT TELLURIUM 10 20 30 40 50 60 70 80 SO I l ' l l i . L—. 1—| . L-Figure 5„1 Equilibrium Phase Diagram of Ag-Te (after HanserT U) 101 zone width was 700-800 u, o For Te thicknesses between 50 and 180 A (with t. / t > R ) the d i f f u s i o n rate constant attained sub-Ag Te c s t a n t i a l l y higher values than at greater thicknesses, o Between 2 00 and 1750 A the rate constant tended to a -8 2 constant value of about 1,9x10 cm /sec. Figure 5,2 i l l u s t r a t e s the experimental dependence of the rate constant on the Te thickness. The peak value observed l i e s at about o 80 A and i s over twenty times the constant value found at o thicknesses of 20 0 A and greater. This i s a much larger e f f e c t than that seen i n any of the other three systems i n -vestigated. It i s probably due to the network structure of very thin Te films which gives high d i f f u s i o n rates between islands as discussed i n section 4,2,3, Figure 5,3 shows the dependence of the rate constant on the Ag to Te thick-o ness r a t i o (t^g/trpg) f ° r couples in which t ^ > 180 A, The c r i t i c a l r a t i o was found to be 1,0 +_ 0,1, This agrees closely with the t h e o r e t i c a l value of 1.00 which would be given by the phase Ag 2Te, I f Ag^^Te^x -.0,2 ) were the i n t e r m e t a l l i c phase formed during d i f f u s i o n , the calcu-lated c r i t i c a l r a t i o would be 0,715, i n poor agreement with the experimental value. The results indicated, therefore, that the composition of the d i f f u s i o n zone was Ag^Te. A determination of the c r i t i c a l r a t i o at tellurium thicknesses o of 105 and 2 730 A gave the same value of 1,0 +_ 0.1, The c r i t i c a l r a t i o was thus taken to be independent of the Te f i l m thickness over the thickness range under investigation. [ t A g / t T e > l , 0 , Room Temperature] 0 100 200 400 600 800 1000 1200 1400 1600 1800 2000 Figure. 502 Rate Constant as a Function of Te Thickness [ t r r . e > 2 5 0 A*, Room Temperature] i : c r i t i c a l r a t i o = 1 . 0 0 *4 1 . 0 2 3 4 5 1 0 . 0 t A / t Ag Te Figure 5 . 3 Growth Rate as a Function of Thickness Ratio 104 The temperature dependence of the rate constant was determined i n the range 0-100°C. From the Arrhenius plot shown i n Figure 5,4 the d i f f u s i o n rate constant was found to be 10000., K = 0.6 3 exp [- 3 RT 1 3 Also plotted i n this figure i s Mohr's data which gives X = 5 79 exp [-13820] RT Although s i m i l a r techniques were used i n the two i n v e s t i -gations, the agreement between the two sets of results i s disappointing, e s p e c i a l l y at high temperatures where there i s almost a one order of magnitude difference in the two measured rates, Mohr applied a correction to his growth rates to correct for volume expansion of the Te as Ag d i f -fused i n . No d e t a i l s of t h i s correction are given i n Mohr's paper but i t would not be expected to a l t e r the activation energy s i g n i f i c a n t l y . It should be mentioned that in the two systems in which comparison was possible with the results of other workers, agreement at high temperatures was not good with the present work giving much slower rates than the other i n -vestigations. It i s f e l t that there can be no experimental error i n the present investigation which could explain anything l i k e the observed differences in the growth rates. If there i s a genuine difference i n growth rates between 105 77515 T77Q 2791) 3,10 3, 30 3,50 3,7 0 1000/T (0 K-1) Figure 5,4 Arrhenius Plot f o r Ag-Te 106 between the two cases, t h i s must presumably be due to some difference i n structures which gives d i f f e r e n t contributions to grain boundary and volume d i f f u s i o n . This might be due to d i f f e r e n t residual gas pressures, evaporation rates, or one of the many other variables which can affect f i l m structure (see Introduction, section 1,4), 38 Behera has shown that a study of d i f f u s i o n i n bulk Ag-Te couples i s impossible because a proper d i f f u s i o n zone i s not formed. The bulk d i f f u s i o n rate plotted i n Figure 5,4 at 13 0°C i s a very approximate value obtained from his work, A complete temperature study in bulk Ag-Te was not undertaken due to the i r r e g u l a r nature of the d i f -fusion zones involved. However, the low value of activation energy obtained for the thi n f i l m couples does seem to i n d i -cate that some short c i r c u i t mechanism i s important i n the di f f u s i o n process, 5,3 Electron Microscopy Transmission electron micrographs made of the Ag^Te phase boundary showed that grain boundary d i f f u s i o n plays a role i n the d i f f u s i o n process. The micrograph of the boundary interface i n Figure 5.5 (a) shows many colonies of Ag^Te l y i n g ahead of the main d i f f u s i o n zone but connected to i t by "st r i n g e r s " of Ag 2Te centered predominantly at the Te grain boundaries. Figure 5,5 (b) i s the same interface a f t e r two hours showing e s s e n t i a l l y the same general features. The remaining two micrographs i n Figure 5.5, made 107 (c) Cd) o Figure 5,5 Phase Boundary Interface i n a 210 A Te Film 108 at 1 minute i n t e r v a l s a f t e r 5.5 (b), show how the ef f e c t of l o c a l i z e d heating by the electron beam tends to obscure the grain boundary d i f f u s i o n and makes the phase boundary interface very planar. The Te thickness i n t h i s series of o pictures i s about 20 0 A. Figure 5.6 shows the phase boundary interface i n a sample having a Te thickness of o about 10 0 0 A, Once again, hg^Ze has formed in Te grains ahead of the main body of the d i f f u s i o n zone with stringers extending along the Te grain boundaries. In this micro-graph i t appears that some Ag^Te colonies have begun t h e i r development at the grain boundary corners. This obvious tendency for grain boundary d i f f u s i o n to occur i s i n f u l l agreement with the large e f f e c t observed i n 80-100 %. films i n t h i s system. It i s probably due to a very large grain boundary d i f f u s i o n c o e f f i c i e n t i n this system. The grain boundary effects i n Ag-Te are much more pronounced than those i n Cu-Te, which probably accounts for the higher growth rates observed i n Ag-Te. Selected area d i f f r a c t i o n patterns were made of the d i f f u s i o n zone of Ag-Te couples. The d-spacings c a l -culated were i n good agreement with the known d-spacings for g-Ag^Te, the low temperature form of Ag2Te. This substantiates the k i n e t i c evidence i n section 5.2 for growth of Ag^Te rather than Ag^^Te^ on the basis of agree-ment between experimental and theore t i c a l values of the c r i t i c a l r a t i o . A t y p i c a l set of d i f f r a c t i o n results i s 109 110 shown i n Figure 5.7. Figure 5.8 (a) shows the res u l t of an experiment i n which high illumination levels were used i n the electron microscope and the beam was focused on the Ag 2Te interface for a r e l a t i v e l y long time; a thin band of the Te-rich phase Ag,. Te (x - 0,2) appeared at the edge of the normal d i f f u s i o n zone and began to grow into the Te at a rapid rate due to heating by.the electron beam. This i n t e r -m e t a l l i c phase was p o s i t i v e l y i d e n t i f i e d by a selected area d i f f r a c t i o n pattern. The microstructure of the Ag 2Te phase in the main body of the d i f f u s i o n zone i s i l l u s t r a t e d i n Figure 5,8 (b), The Te thickness i n t h i s sample i s about o 200 A, The exact temperature increase induced by the electron beam spot i n such a small l o c a l i z e d area i s impossible to measure. It i s to be expected, however, that i f the appearance of this second phase during d i f f u s i o n were due to thermal effects alone, a second phase would be observed i n thin f i l m couples annealed at high temperatures. Since t h i s second phase was not present i n the d i f f u s i o n zones of samples heated up to 100°C, i t i s concluded that eit h e r the e f f e c t i v e temperature r i s e produced by beam heating was greater than 100°C, or the growth of the phase was not e n t i r e l y due to thermal e f f e c t s . The electron microscopy results suggest that grain boundary d i f f u s i o n i s an important factor i n room temperature d i f f u s i o n i n Ag-Te, As the electron beam brings about a I l l (a) S.A.D. of dif f u s i o n (b) Au Standard zone i n Ag-Te Calculated d-spacings (A*) d-for spacings e-Ag2Te (A) 7 0 1 4 7 d 4 6 0 8 5 4 o 6 0 4 , 5 3 3 . 7 1 3 . 7 4 3 o 4 0 3 . 1 9 3 d 9 3 o 0 1 3 . 0 1 2 . 88 2 . 8 7 2 o 7 3 2 . 8 0 2 . 6 9 2 , 4 5 2 . 4 5 Figure 5 . 7 Selected Area D i f f r a c t i o n Pattern of the Diffusion Zone i n Ag-Te (a) Ag (x ~ 0.2) induced by electron beam heating (b) Appearance of Ag Te phase i n thi s sample Figure 5,8 Electron Beam Heat-Induced Second Phase i n Ag-Te 113 l o c a l i z e d temperature increase at the phase boundary i n t e r -face the grain boundary d i f f u s i o n i s obscured by rapid ad-vance of an interface that has become increasingly planar as the temperature rose. This implies that grain boundary di f f u s i o n i s not important at higher temperatures. Since the presence of a second phase was not detected during normal d i f f u s i o n experiments at 100°C, i t i s conceivable that the electron beam heating produced by high illumination levels results i n a temperature r i s e of greater than 100°C. 114 CHAPTER 6 LATERAL DIFFUSION IN Cu-Se 6,1 Introduction A complete equilibrium phase diagram i s not yet available for Cu-Se, The three intermediate phases that can be i n thermal equilibrium at room temperature are 40 Cu 2_ xSe (0.0 < x < 0,2), Cu 3Se ?, and CuSe . Cu 2_ xSe i s a copper d e f i c i e n t form of the stoichiometric i n t e r m e t a l l i c compound Cu2Se (33,3 at % Se), The high temperature polymorph of this phase has an anti-isomorphous CaF 2 structure i n which Se atoms replace Ca atoms. As the deviation from stoichiometry i n Cu 2Se increases, the transformation temperature decreases, so that the cubic structure becomes stable at room temperature. At the stoichiometric compo-s i t i o n , however, the transformation temperature i s around 10 0°C, Below t h i s temperature, a number of metastable tetragonal or B.C.C, structures are encountered depending on 40 ,48,49 the heating and cooling history , The t r u l y stable low temperature structure i s not known, CUgSe2 has a tetragonal structure. There i s a strong p o s s i b i l i t y that t h i s phase i s a grossly defective Cu u Se compound 115 only approximating Cu.gSe2 i n composition. CuSe has a hexa-gonal structure, 6.2 Kinetics 6.2,1 Growth Rate The graph of d i f f u s i o n zone width (x) as a function of /t for about 85% of a l l d i f f u s i o n couples studied was of the form of curve I i n Figure 6.1, Most of the remaining 15% exhibited the behaviour of curve II in t h i s figure with only a small f r a c t i o n being s t r i c t l y parabolic i n nature (curve I I I ) , The e s s e n t i a l features of curves I and II are i l l u s t r a t e d i n Figure 6,2. The dependence of x on /T i n each "stage" of both curves was l i n e a r suggesting that growth was d i f f u s i o n controlled. The basic difference between curves I and II i s that stage 2 i n the l a t t e r i s much shorter, degenerating into stage 3, a region of more rapid growth. It should be emphasized that the physical implication of growth curves l i k e I and II i s that a very wide d i f f u s i o n zone - 500 to 6 00 u i n some cases - develops in about one hour, A period of slower parabolic growth then follows. This may p e r s i s t over a long time as curve I suggests or may be followed by a period of rapid growth (curve I I ) , Such behaviour may, at f i r s t glance, appear to be due to the formation of a second phase during d i f -fusion. However, no evidence of more than one phase was ever seen by o p t i c a l microscopy. Therefore t h i s explana-x(u) /t~~(/hr) Figure 6,1 Typical Room Temperature Kinetics Plots H H CD 117 (a) Curve I (b) Curve II Figure 6 02 General Form of Majority of Growth Plotso 118 tio n does not account f o r the observed behaviour, A d i f f u s i o n rate constant was calculated from each of the l i n e a r regions of both types of curves I and II. I t was found that i n stage 1, the rate constants were widely variable bearing no apparent relationship to Se thickness or thickness r a t i o . S i m i l a r l y , the rate constants determined i n stage 3 showed a large degree of scatter, although the magnitudes of the slopes were of course much smaller than those i n stage 1, Using the rate constants of stage 2, however, a set of results f o r the dependence of rate constant on Se thickness and on the ra t i o of Cu to Se thickness (t /tg g) was obtained that was completely analogous to the other three systems. For t h i s reason the rate constants calculated from stage 2 were taken as being representative of the l a t e r a l d i f f u s i o n process in Cu-Se, although i t may well be that the d i f f u s i o n controlled region i s i n fact stage 1 with stage 2 being a region showing certain i n h i b i t i o n s to d i f f u s i o n , 6,2,2 Dependence of Rate Constant on Se Thickness Figure 6,3 shows the d i f f u s i o n rate constant plotted as a function of Se thickness. At thicknesses greater than o 180 A the rate constant tends to a constant value of _8 2 uohi'e, 3t /oiuer thicknttois it nses io a _ 8 2 0,80x10 cm /sec^peak value of approximately 3.3x10 cm / sec at about 100 ft. This possible tendency for higher d i f -fusion rates to occur i n thi n Se films appears to be con-sis t e n t with the eff e c t observed i n Ag-Se where the maximum 3,00 h -CO 2,00 1,00 0 100 200 400 600 800 1000 1200 1400 1600 1800 Figure 6,3 Rate Constant as a Function of Se Thickness 120 d i f f u s i o n rate i s also about four times the constant value obtained at Se thicknesses exceeding 180 A*, This i s not unexpected since the structure of the Se films i s the same in both cases. Therefore the same mechanism proposed for enhanced d i f f u s i o n i n Ag-Se (section 3,2.3) should be a p p l i -cable to Cu-Se as well. The o p t i c a l micrograph in Figure 6.4 i l l u s t r a t e s the i r r e g u l a r nature of the phase boundary interface i n a sample having a Se thickness of 125 A*. The wavelength of the minute projections on the interface i s about 1 u which i s consistent with the i n t e r - i s l a n d spacing i n the Se at t h i s stage of growth. 6 , 2 1 , 3 C r i t i c a l Ratio The c r i t i c a l r a t i o i n Cu-Se was found to be between 0,63 and 0.71, Below this range d i f f u s i o n did not occur while above i t , d i f f u s i o n proceeded at a constant value of — 8 2 0.80x10 cm /sec for couples i n which the Se thickness was greater than 180 A*, The results of the thickness r a t i o (t_ / t 0 ) study are shown i n Figure 6.5, The t h e o r e t i c a l Cu Se J ° values of R were calculated f o r each of the phases Cu 0 vSe, c z. —x Cu Se , and CuSe and are l i s t e d i n Table 6,1, Comparing 3 2 these values with the experimental value f o r Rc, i t was seen that the composition o f the d i f f u s i o n zone should be Cu2_xSe. A determination o f the c r i t i c a l r a t i o at Se thicknesses of 350 and 2380 % gave values o f 0.71 and 0,63 respectively. Thus the c r i t i c a l r a t i o was taken t o be independent of the absolute Se thickness. 121 Figure 6o4 Phase Boundary Interface i n a 125 A Se Film (x71) Figure 6,5 Rate Constant as a Function of Thickness Ratio 123 TABLE 6.1 Theoretical C r i t i c a l Ratios i n Cu-Se Phase Theoretical R c Cu„ Se, x=0,0 .720 2-x * Cu„ Se, x=0,2 .645 2-x ' Cu 3Se 2 ,513 CuSe , 375 6,2,4 Temperature Dependence The temperature dependence of the rate constant was determined over the range 0-50°C. Higher temperatures were not used i n order to avoid any aggregation of Se on the glass substrates. The shapes of the x versus /t~ curves were not observed to change with temperature, most showing the two stages of parabolic growth discussed i n section 6.2.1. Although growth rates i n this system at room temperature are comparable with rates i n other systems, the increase i n growth rate with increasing temperature i s much greater than that found i n any other system. Taking the growth rate characterized by the second stage of the x versus /E~ curves the temperature dependence of the rate constant determined from the Arrhenius plot i n Figure 6.6 i s given by 125 K = 3,9 x 10 e x p [ — — ] RT The very large activation energy r e f l e c t s the large increase in growth rate with temperature i n t h i s system. The pre-exponential term i s also extremely large and t h i s i s con-sistent with the fast growth rate observed at low temperatures r e l a t i v e to the high activation energy. It i s indeed d i f f i c u l t to give any convincing ex-planation f o r the very high activation energy and pre-exponential term i n t h i s system since the other Se-base system, Ag-Se, gave much more reasonable values. It seems possible that the large increase i n growth rate with tempera-ture i s due not only to an increase i n the d i f f u s i o n co-e f f i c i e n t D, but to some other e f f e c t which may be, for example, a progressive change i n c r y s t a l structure of the in t e r m e t a l l i c compound, with temperature^ or c r y s t a l l i z a t i o n of the amorphous Se f i l m immediately ahead of the phase boundary. A combination of two such thermally activated processes would give a very high apparent activation energy for the system 2^ , 2^, In any case i t would appear that the d i f f u s i o n mechanism i n Cu-Se i s very complicated and bears l i t t l e resemblance to the mechanism for d i f f u s i o n in the other three systems. 126 6 ,3 Electron Microscopy 6,3.1 Normal Growth The dominant feature of the electron microscopy results i n Cu-Se was the high s e n s i t i v i t y of the d i f f u s i o n zone to heating by the electron beam. This was also observed to some extent i n Ag-Te, i n which, as discussed i n Chapter 5, a second i n t e r m e t a l l i c phase formed at the d i f f u s i o n zone front. In Cu-Se, however, the e f f e c t was much more pro-nounced. I f extremely low illumination levels were used, the phase boundary motion appeared as shown i n Figure 6,7, The interface appeared to be quite i r r e g u l a r and moved rapidly. The d i f f u s i o n zone behind i t consisted of columnar grains which increased i n size the longer the beam was focused on the interface. The r e s u l t i n g difference i n grain s i z e i s i l l u s t r a t e d by micrographs 6,7 (1) and 6,7 (4), The elapsed time between these photographs was about two minutes. Figure 6,8 shows the d i r e c t i o n a l nature of the elongated grains i n the d i f f u s i o n zone at higher magnification. The large arrow on t h i s micrograph indicates the direction of the phase boundary advance, A selected area d i f f r a c t i o n pattern made from the d i f f u s i o n zone showed that i t s composi-tion was Cu„ Se, This was i n agreement with the composition 2-x c predicted by the c r i t i c a l r a t i o study i n Section 6.2.3. A selected area d i f f r a c t i o n pattern and the d-spacing calculated from i t are shown i n Figure 6,9, Figure 6„7 Motion of the Phase Boundary Interface i n Cu-Se 128 Figure 6.8 Columnar Grains in Diffusion Zone (a) S.A.D. of Diffusion Zone (b) Au Standard Calculated d- spacings d-spacings (A) for Cu ?_ xSe (A) 3. 34 3.33 2, 88 2, 88 2.24 2.03 2. 02 1,73 1, 73 1, 65 1,65 1,42 1,43 1. 31 1, 32 1.28 1,17 1,17 1.11 1,105 1.02 1, 01 0, 972 , 969 Figure 6,9 Selected Area D i f f r a c t i o n Pattern of the Diffusion Zone 130 At high magnification the phase boundary interface appeared to consist of a series of p a r a l l e l growth tips of varying size l i k e that shown i n Figure 6.10. The d i f f u s i o n couple was cooled to -150°C i n the microscope cold stage in order to prevent the interface from advancing. Selected area d i f f r a c t i o n patterns were made on several of these t i p s . The patterns were s i n g l e - c r y s t a l l i n e i n nature and exhibited 50 pronounced streaking of the spots . Two such d i f f r a c t i o n patterns and t h e i r associated growth t i p s are shown i n Figure 6.11, An in t e r e s t i n g feature of these t i p s was that i n each of them a series of fine s t r i a t i o n s running nearly p a r a l l e l to the growth di r e c t i o n could be seen. These are c l e a r l y shown i n Figures 6,10 and 6,11. In order to e s t a b l i s h a growth d i r e c t i o n on the d i f f r a c t i o n patterns, a rotation c a l i b r a t i o n of the intermediate lens of the micro-scope was ca r r i e d out with the same accelerating voltage and projector lens polepiece as was used to make the actual . 45,50 micrograph of the growth t i p s . Analysis of the d i f -f r a c t i o n patterns of Figure 6,11 i l l u s t r a t e d that the growth dir e c t i o n of the ti p s lay within 9° of the <111> direction and that the steaking d i r e c t i o n of the spots was almost exactly perpendicular to t h i s . Further analysis of other tip s confirmed those relationships; i n every case the growth d i r e c t i o n of the t i p s was close to <111> and the st r i a t i o n s were associated with {110} planes. These s t r i a t i o n s were the apparent cause of the streaking of the pattern spots. 131 Figure 6 010 Growth Tip at High Magnification P a r a l l e l fringes i n th i s micrograph are believed to be due to astigmatism i n the objective lens of the microscope. 132 133 Figure 6,12 shows schematically the indexing of the single-c r y s t a l d i f f r a c t i o n patterns of Figure 6,11, In summary i t was found that the grains of Cu 0 Se possessed a preferred growth di r e c t i o n , growing in a <111> d i r e c t i o n . The fine s t r i a t i o n s appearing i n the growth ti p s were related to {110} planes and were responsible for streaking of the d i f f r a c t i o n patterns. The two main sources of streaking of d i f f r a c t i o n spots are stacking 51 fa u l t s and twins , It i s unlikely that the s t r i a t i o n s observed here are stacking f a u l t s . On the other hand {110} planes are not twinning planes in an anti-isomorphous CaF 2 structure l i k e Cu 2 x S e 4 1 , Therefore these s t r i a t i o n s must be due to some other source. The growth dir e c t i o n i s also d i f f i c u l t ' to account for by crystallographic considerations since the <111> direction i s not a close-packed direction i n the Cu 2_ xSe l a t t i c e , It should be noted, however, that the growth direction during formation of columnar crystals from the l i q u i d (e,g, i n steels) i s not a close-packed direction. Apparently t h i s i s related to the a b i l i t y of l i q u i d atoms to " s t i c k " more e a s i l y to planes other than the close-packed ones, 6,3,2 Dendritic Growth When high illumination l e v e l s were used to observe the phase boundary interface i n Cu-Se, a second phase appear-ed at the interface which grew rapidly i n a dendritic manner. Once nucleated, t h i s phase continued to grow even when i l l u -131 022 113 134 111 113 ^ 022 ft 131 [211] Zone (a) Indexing of 6 „ 11 (1) Growth direction 13.1 ^ 022 113 111 111 ± i 113 022 131 (b) Indexing of 6,11 (2) Growth direction Figure 6,12 Schematic Indexing of D i f f r a c t i o n Patterns 135 mination was greatly reduced. The structure was t r u l y d e n d r i t i c , e x h i b i t i n g primary arms and numerous side-branches. Figure 6.13 shows the advance of the dendritic phase into the pure Se. The electron micrographs of Figure 6,14 c l e a r l y i l l u s t r a t e the appearance of a single primary dencrite at the phase boundary interface and the dendritic structure within the body of the phase. The boundary between the normal non-dendritic Cu2_xSe and the dendritic phase induced by electron beam heating i s shown i n Figure 6.15. This effect was found to be completely reproducible. A selected area d i f f r a c t i o n pattern made from the dendritic phase showed that i t was the tetragonal i n t e r m e t a l l i c com-pound Cu,jSe2. A t y p i c a l d i f f r a c t i o n pattern and i t s associ-ated d-spacings are given i n Figure 6.16, These "d" values are in good agreement with the known d-spacings for Cu3Se2 l i s t e d in the same figure. To determine the dendritic growth direction selected area d i f f r a c t i o n patterns were made i n the primary arms at -110°C using the cold stage. It was found that cooling of the sample to t h i s temperature resulted in the dendritic structure being transformed into one consisting of only p a r a l l e l primary arms with no side branches, s i m i l a r i n appearance to non-dendritic Cu 0 Se. The composition and C. " 1% c r y s t a l structure was s t i l l that of Cu 3Se2» however. Because the primary arms were quite narrow i t was nearly impossible to obtain a pure s i n g l e - c r y s t a l d i f f r a c t i o n pattern. There-(1) 137 (2) I n t e r i o r Microstructure of the Dendritic Phase Figure 6,14 Nature of the Dendritic Phase 138 Figure 6„15 Boundary Between Dendritic and Non-dendritic Phase 139 (a) S.A.D. of Diffusion (b) Au Standard Zone Calculated d-spacings (A) d-spacings for CugSe2 4.28 4.28 3.56 3.56 3.20 3.11 2.97 2. 97 2. 86 2. 86 2.62 2.56 2,56 2.49 2,49 2.38 2. 38 2.26 2.26 2.14 2.14 2.10 2, 08 2. 02 2.00 2, 00 1.93 1,93 1.91 1.83 1. 83 Figure 6,16 S.A.D. Pattern of the Dendritic Phase i n Cu-Se 14 0 fore, the d i f f r a c t i o n patterns were invariably a super-position of at least two s i n g l e - c r y s t a l patterns and t h e i r indexing was d i f f i c u l t . Pronounced streaking was i n evidence on a l l the patterns. Figures 6.17 and 6,18 i l l u s t r a t e t y p i c a l d i f f r a c t i o n patterns obtained, t h e i r corresponding . . . 52 microstructures, and the schematic indexing of each Analyses of the d i f f r a c t i o n patterns give the growth d i r e c t i o n as being <101> and indicate that the streaks arise from fine s t r i a t i o n s (see Figure 6,18) associated with {111} planes. An investigation of possible twinning planes i n the s p e c i f i c tetragonal structure of Cu^Se^ was not carried out. Therefore i t i s not possible to say whether the s t r i a -tions present i n the micrographs are due to twins. It i s unl i k e l y , however, that they are stacking f a u l t s , since {111} i s not a close-packed plane in t h i s structure. 19,5 3 The occurrence of dendritic growth in a s o l i d state d i f f u s i o n reaction i s a very rare phenomenon, Malcolm 54 and Purdy observed the dendritic growth of y brass from supersaturated 3-brass in the s o l i d state. In t h e i r work, however, a very favourable morphology existed between"pre-c i p i t a t e and parent grain. In the present investigation the observed growth of a dendritic phase appears to be due to thermal rather than crystallographic e f f e c t s . Focusing of an intense beam of electrons on the normal d i f f u s i o n zone interface results i n rapid dendritic growth. Once the beam is removed from the interface, growth of the dendritic phase proceeds slowly ( i f at a l l ) . 141 Figure 6,17 Dendrite Analysis Figure 6,18 Dendrite Analysis 143 A p o s s i b l e e x p l a n a t i o n f o r the observed behaviour i s t h a t the l o c a l i z e d h e a t i n g produced by the beam at the i n t e r f a c e e x c i t e s Se atoms i n the immediate v i c i n i t y making them q u i t e mobile. The poor thermal conduction p r o p e r t i e s o f Se prevents the beam heat from b e i n g conducted away r e a d i l y from t h i s r e g i o n . Se i s observed t o aggregate at o n l y 60°C s u g g e s t i n g that Se atoms are capable o f s u r f a c e m i g r a t i o n even at t h i s low temperature. T h i s p i c t u r e o f h i g h m o b i l i t y i s a l s o c o n s i s t e n t with the d e s c r i p t i o n o f the amorphous . 55 s t a t e as b e i n g a h i g h l y v i s c o u s l i q u i d , The observed t e n -dency o f bulk amorphous Se to become p l a s t i c and flow at temperatures below 100°C (see page 30, Chapter 3) f i t s t h i s d e s c r i p t i o n w e l l . The net r e s u l t o f poor thermal con-d u c t i v i t y i n the Se and r e l a t i v e l y good conduction i n the i n t e r m e t a l l i c compound i s t h a t a l a y e r o f very mobile atoms i s c r e a t e d ahead o f the i n t e r f a c e . The system then wants to tr a n s f o r m as q u i c k l y as p o s s i b l e to form Cu2Se2» P l a t e -shaped o r p o i n t e d p r e c i p i t a t e s can t r a n s f o r m a g r e a t e r volume per second than p l a n a r boundaries. Therefore a d e n d r i t i c i n t e r f a c e develops, p r o v i d e d the decrease i n volume f r e e energy more than counterbalances.the i n c r e a s e i n s u r f a c e energy and the m o b i l i t y o f the d i f f u s i n g s p e c i e s i s s u f f i c i e n t l y h i g h . Another c o n c e i v a b l e e x p l a n a t i o n o f the r e s u l t s i s 4 0 4 8 that Cu^Se^ i s a h i g h temperature d e r i v a t i v e o f Cu2_ xSe ' I f t h i s were so, the r a p i d l a t e r a l d i f f u s i o n produced by 144 5 6 beam heating could be due to a polymorphic transformation At the present time, however, there i s i n s u f f i c i e n t i n f o r -mation available to say whether Cu,jSe2 could be a high temperature form of Cu 2 xSe r e s u l t i n g from an increased homogeneity range, In summary i t has been found that Cu-Se i s a much more complicated system than the other three investigated. The growth k i n e t i c s are not s t r i c t l y parabolic and the ac t i v a t i o n energy appears to be abnormally high for a system i n which d i f f u s i o n proceeds so rapidly. In addition the electron microscopy results indicate that the phase bound-ary interface i s very sensitive to high illumination l e v e l s ; i f these become large enough, a second phase i s i n i t i a t e d at the interface which moves very rapidly and grows dendri-t i c a l l y . These results suggest that the actual d i f f u s i o n mechanism i n Cu-Se i s quite complex. 145 CHAPTER 7 SUMMARY AND CONCLUSIONS 7,1 Discussion and Summary 7,1,1 Growth Kinetics In each of the three systems Ag-Se, Cu-Te, and Ag-Te the graphs of dif f u s i o n zone width (x) as a function of /t were l i n e a r implying that the growth of the dif f u s i o n zones was d i f f u s i o n controlled. As discussed i n section 5,2,1, most of the growth rate plots i n Cu-Se were not s t r i c t l y parabolic but instead appeared to consist of two or three stages of parabolic growth. The exact reason for this behaviour remains obscure, but i t would seem that the dif f u s i o n zone growth i n each stage i s d i f f u s i o n controlled. Lateral d i f f u s i o n at room temperature was very rapid i n a l l four systems investigated, The r e s u l t i n g d i f f u s i o n zones tended to be very wrinkled or folded i n nature and became p a r t i a l l y detached from t h e i r underlying substrates. This e f f e c t was no doubt due to the volume expansion of the Se or 4 6 Te l a t t i c e as Ag or Cu diffused i n , since very large i n -creases i n a unit volume of Se and Te resu l t when an i n t e r -metallic compound with Ag or Cu i s formed. In Cu-Te, for 14 6 example, the volume expansion of the Te i s about 40%, 2 7.1.2 Rate Constant Dependence on Film Thickness The o r i g i n a l purpose of investigating the ef f e c t of Se and Te f i l m thickness on the rate constant for couples in which the thickness r a t i o was greater than R c was to see i f the l a t e r a l d i f f u s i o n process involved any surface d i f -fusion along the Se or Te. It would be expected that the occurrence of surface d i f f u s i o n should be re f l e c t e d i n a general decrease of the rate constant with increasing Se or Te thickness since the surface to volume ra t i o of a f i l m i s reduced as the thickness becomes greater. In each of the systems studied, however, i t was found that beyond a certain Se or Te thickness, the rate constant was e s s e n t i a l l y independent of the thickness while below the thickness the rate constant tended to a peak value. This phenomenon was attributed to the structure of the thin films. An electron microscopy investigation of very thin Se and Te films showed that they consisted of coalesced islands with an i n t e r -i s l a n d network that undoubtedly contained many structural imperfections. This would be conducive to a short c i r c u i t d i f f u s i o n process between the islands, The eff e c t of low Se and Te thicknesses on the rate constant was seen to be much greater i n the Te systems than i n the Se ones. This was consistent with the def i n i t e evidence of grain boundary d i f -fusion at a l l Te thicknesses observed i n both Ag-Te and Cu-Te 147 using transmission electron microscopy, 7.1.3 C r i t i c a l Ratio The existence of a c r i t i c a l thickness r a t i o for the d i f f u s i o n couple components was v e r i f i e d in a l l four systems. Above th i s thickness r a t i o d i f f u s i o n proceeded at a rate independent of the Se or Te thickness, and below i t , no d i f -fusion took place. It was found that the experimentally ob-served c r i t i c a l r a t i o was independent of the absolute Se or Te thickness over the range of thickness i n which growth rates were measured. Theoretical determinations of the c r i t i c a l ratios from stoichiometric considerations were i n excellent agreement with the experimental values obtained except i n the case of Cu-Te where a 30% difference was found. In Ag-Se, Cu-Se, and Ag-Te the compositions of the d i f f u s i o n zones predicted by the k i n e t i c s were confirmed by electron d i f f r a c t i o n studies. 7.1.4 Temperature Dependence Table 7,1 summarizes the results obtained i n each system f o r the temperature dependence of the rate constant. The three systems Ag-Se, Cu-Te, and Ag-Te a l l have r e l a t i v e l y low activation energies. In Ag-Se and Cu-Te, comparison with activation energies for bulk d i f f u s i o n couples was possible. The thin f i l m activation energies were lower than the bulk activation energies. Thus the activation energies i n the thin f i l m results not only constitute very low values i n them-14 8 TABLE 7,1 Activation Energies for Thin Film Couples System Temperature Range Investigated ( ° C ) Thin Film Activation Energy ' (Kcal/mole) Bulk Act ivation Energy (Kcal/mole! Ag-Se 0-50 12 ,200 17,600 Cu-Te 0-100 7, 800 15 ,000 Ag-Te 0-100 10,000 * Cu-Se 0-5 0 23,000 * Not available 14 9 selves, but also tend to be much below the observed bulk activation energies. This suggests that a short c i r c u i t mechanism i s responsible for d i f f u s i o n . Examination of the phase boundary interfaces i n Cu-Te and Ag-Te by electron microscopy provided d e f i n i t e evidence of grain boundary d i f f u s i o n , The high ac t i v a t i o n energy f o r d i f f u s i o n i n Cu-Se i s not consistent with the other r e s u l t s . The most probable explanation for t h i s i s that the d i f f u s i o n i n t h i s system involves more than one process so that i t i s improper to 2 8 2 9 ascribe an a c t i v a t i o n energy to i t ' , 7,1,5 Electron Microscopy The direct observation of the moving phase boundary interfaces i n the electron microscope was i n i t s e l f i n t e r e s t -ing since very l i t t l e work of t h i s type has been done before. In Cu-Te and Ag-Te there were definite indications that grain boundary d i f f u s i o n was taking place. This was consistent with the low ac t i v a t i o n energy values obtained for d i f f u s i o n in these systems. In the Se systems the microscopy results did not provide any d e f i n i t e information as to the nature of the d i f f u s i o n mechanism. I t was observed, however, that l o c a l i z e d heating by the electron beam at the phase boundary interface resulted i n some aggregation of the Se i n the case of Ag-Se, and i n Cu-Se to the nucleation of a second phase which grew d e n d r i t i c a l l y , The formation of a second phase by beam heating was also seen to a less marked degree i n Ag-Te, Such phenomena may suggest that the l e v e l of l o c a l -150 ized heating produced i n the electron beam i s much greater than previously thought. Temperature increases of 10 0°C could well be involved. Despite the evidence for grain boundary d i f f u s i o n obtained i n the Te systems, i t was disappointing that a quantitative estimate of the r e l a t i v e rate of grain boundary to l a t e r a l d i f f u s i o n could not be made. In Cu-Te, the grain boundary effect was not pronounced enough to assess the d i f -fusion rate, while i n Ag-Te, beam heating tended to obscure the grain boundary d i f f u s i o n before any useful measurements could be made. General Summary The important features of the l a t e r a l d i f f u s i o n process i n each of Ag-Se, Cu-Te, Ag-Te and Cu-Se as outlined in the preceeding discussion are summarized in Table 7,2, 7 • 2. Estimation of Diffusion Coefficients / In the "Introduction" (page 15) i t was shown that the rate constant found by measuring the width of the d i f -fusion zone was related to the di f f u s i o n c o e f f i c i e n t by the formula 2(0,-0, ) (Co-C 9) K = D 6 (7.1) (C -C )(C«-C 0+0_C_) 1 o d ^ 1 o i f the composition range of the intermediate phase involved i s small. This i s a v a l i d approximation i n the case of each TABLE 7.2 Summary of Lateral Diffusion i n the Four Systems Investigated System Diffusion Zone Composition Room Temperature Growth Rate (cm^/sec) Kinetics C r i t i c a l Ratio for Diffusion Proposed Diffusion Mechanism Special Characteristics Ag-Se Ag 2Se -8 • 1,1x10 parabolic l . l + . l Short c i r c u i t (e.g, grain boundary) Se i s amorphous Growth rate higher in thin Se films. Cu-Te C u 2 - x T e (x~Q,6) 2 , l x l 0 - 9 parabolic 0,6 3^.1 Grain boundary Growth rate higher in thin Te fil m s ; e f f e c t i s much more pronounced than i n Se systems. Ag-Te Ag 2Te -8 1.9x10 parabolic 1,0+.1 Grain boundary Effect of very th i n Te films on growth i s extremely marked. Cu-Se Cu 2_ xSe (0<x<0. 2 ) -8 0,80x10 separate stages of parabolic growth 0.63-0,71 --Very large d i f f u s i o n zone widths-observed. Electron beam heating induces second phase at phase boundary interface which grows d e n d r i t i c a l l y . of the systems studied so that i t i s possible to use equation 7,1 to estimate the d i f f u s i o n c o e f f i c i e n t s in each system. This has been done using the room temperature value of the rate constant; that i s , the value obtained for couples in which the thickness r a t i o i s greater than the c r i t i c a l r a t i o and the Se or Te thickness i s beyond the region where the structure of the f i l m r e s u l t s in higher growth rates. The calculated values of D are given i n Table 7.3, From t h i s i t can be seen that the d i f f u s i o n c o e f f i c i e n t s are about two orders of magnitude greater than the rate constants except f o r the system Ag-Se i n which the difference involves a factor of 500 due to the very small composition range of Ag 2Se, It i s obvious, therefore, that the d i f f u s i o n c o e f f i c i e n t s i n a l l these systems are very large indeed. Although very l i t t l e i s known about the variation with temperature of the composition ranges of the i n t e r m e t a l l i c compounds formed during d i f f u s i o n in each of the four 4 0 4 8 systems, present evidence ' suggests that the phase boundary compositions do not change s i g n i f i c a n t l y up to temperatures of 500-600°C. Therefore the activation energies observed represent those of the d i f f u s i o n process alone. 153 TABLE 7 o 3 Calculation of Diffusion Coefficients System Steady State Rate Constant K (cm /sec) Inter-metallic Phase Present Composition Range of Phase (C 9-C, ) (at %) 1 1 Calculated Diffusion Coefficient D ( cm2/sec) Ag-Se -8 l o 1 x 1 0 Ag 2Se 0„2 -6 5 o 5x10 Cu-Te -9 2 o l x l 0 Cu 2_ xTe (x~0, 6) 0.9 -7 1.6x10 Ag-Te -8 lo 9x10 Ag 2Te 0o 9 -6 2,1x10 Cu-Se -8 Oo 80x10 Cu„ Se 2 - x (0<x<0 o 2) 2,4 -7 2.9x10 154 7 0 ^  The Mechanism of Rapid Diffusion Rapid d i f f u s i o n at room temperature i s a rarely-occurring phenomenon. In the present work i t was observed in only four systems out of the 22 investigated. Therefore i t i s natural to raise the question as to why very rapid d i f -fusion i s observed i n these systems and not i n others. Present results i n thin f i l m d i f f u s i o n couples suggest that grain boundary d i f f u s i o n and possibly "pipe" d i f f u s i o n are the predominant mechanisms in Ag-Se, Cu-Te, and Ag-Te, The bulk data available i n these systems, how-ever, shows that high growth rates are also encountered at r e l a t i v e l y low temperatures (100-200°C) i n bulk d i f f u s i o n couples. In Cu-Se the d i f f u s i o n mechanism does not appear to be consistent with that of the other three systems and i t s exact nature remains obscure. Nevertheless, very large growth rates are observed i n t h i s system as well. A l l of the i n t e r m e t a l l i c phases formed during d i f -fusion have several i n t e r e s t i n g features i n common. They are known to be small band gap semiconducting compounds i n 4 2 4 8 5 7 which cation vacancies act as acceptors ' ' , Each of the compounds exists i n at least two stable polymorphs in 2 6 diffe r e n t temperature ranges , In every case both the high temperature and low temperature modifications are regarded as being defect i n t e r m e t a l l i c compounds with cation vacancies constituting the main inperfection. F i n a l l y , the bonding in a l l four compounds i s e s s e n t i a l l y covalent rather 155 than m e t a l l i c . This i s not surprising, however, i n compounds involving Se and Te which have been referred to by various authors as "metalloids" or semiconductors. The high temperature modifications of Ag2Se, Ag 2Te, Cu„ Se, and Cu, QS are s i m i l a r to a-Ag s (see Introduction, 2-x. 1. o °2 page 10) i n that they are substances i n which only the anions occupy a regular l a t t i c e while the cations are p r a c t i c a l l y "molten" and are not bound to d e f i n i t e l a t t i c e 2 B positions , Measurements of e l e c t r i c a l conductivities and transference numbers i n a-Ag 2S, for example, have shown that the cations possess abnormally high mobility equal to that of ions i n aqueous solution while the anions are e s s e n t i a l l y immobile. This behaviour i s probably due to: (1) The large size difference between cation and anion which enables the smaller cation to readily occupy an i n t e r s t i t i a l l a t t i c e s i t e , (2) The inherent defect structure of these com-pounds which tend to be deficient i n the cation species. This creates extra s i t e s to which cations in the l a t t i c e can migrate, (3) The nature of the covalent bonding i s such as to f a c i l i t a t e the breaking of cation ranion bonds. In this regard i t should be pointed out that' the order of increasing m e t a l l i c character (decreasing e l e c t r o n e g a t i v i t y ^ ' ^ ) of the anions i s S, Se, Te, and a l l . o f these are much less e l e c t r o -negative than any of the halides. The room temperature 156 structures of these compounds have not been studied as extensively as the high temperature modifications , but i t would be expected that there i s a strong p o s s i b i l i t y that the cation p a r t i a l l a t t i c e s contain a large number of l a t t i c e defects. In these low temperature modifications, however, the cations are now r e s t r i c t e d to definite l a t t i c e s i t e s . Nevertheless, the cation mobility, although much less than i n the high temperature structure, w i l l s t i l l be comparatively high. The present work indicates that d i f f u s i o n i n Ag-Se, Cu-Se, and Cu-Te i s controlled by the migration of Ag or Cu through the d i f f u s i o n zone which i n each case involves an i n t e r m e t a l l i c compound analogous i n composition and structure to Ag^S, I t i s doubtful that the rapid growth rates encountered are related to the free energy of formation 60 of the various i n t e r m e t a l l i c phases , Sulphide formation studies i n Cu and Ag alleys involving various impurity C -I CO additions ' have shown that the rate of sulphide attack i s comparable i n both cases despite the large difference in the standard free energy of formation of AgjS and Cu2S (-17,8 kcal/mole versus -=28,2 kcal/mole). From this i t i s concluded that only the d i f f u s i v i t y of Ag and Cu in the sulphide layers i s s i g n i f i c a n t i n the sulphidation process. By analogy with this i t i s expected that the r a t e - c o n t r o l l i n g process i n the systems Ag-Se, Cu-Te, Ag-Te, and possibly Cu-Se i s the d i f f u s i v i t y of Cu and Ag in the d i f f u s i o n zone compound, Scaling experiments in the Ag-S system ' have revealed that the sulphide phase forms as a result of d i f -fusion of Ag ions through the Ag 2S layer. This i s accompan-ied by a motion of electrons i n the same direction as the ion flux. The electrons move rapidly i n large numbers, causing an additional e l e c t r i c a l potential gradient i n ad-d i t i o n to the chemical potential gradients due to the Ag ions which are already present; t h i s i n turn causes an increase i n the transport rate of the s i l v e r ions through the tarnishing layer. Similar experiments on Ag and Cu with Se and T e ^ ' ^ have not led to any consistent data on the d i f f u s i o n process. The p o s s i b i l i t y that the d i f f u s i o n of Ag and Cu i n the Se and Te systems i s increased by the existence of an additional e l e c t r i c a l potential cannot be ruled out. However the e f f e c t of t h i s potential i s merely 6 3 to double or t r i p l e the d i f f u s i o n rate It i s proposed, therefore, that the mechanism for rapid d i f f u s i o n i n the four systems investigated i n this work i s a combination of high Ag and Cu d i f f u s i v i t y in the i n t e r m e t a l l i c compounds that are formed during d i f f u s i o n and the short c i r c u i t d i f f u s i o n processes which occur rea d i l y at low temperatures in t h i n films. The high atomic d i f f u s i v i t i e s i n each of the i n t e r m e t a l l i c compounds are the r e s u l t of the unique chemical properties of the compounds and s p e c i f i c a l l y , t h e i r defect structures, i n which cations tend to be abnormally mobile. 158 7 o4 Conclusions The observations and interpretations of l a t e r a l d i f f u s i o n i n the four systems Ag-Se, Cu-Te, Ag-Te, and Cu-Se lead to the following conclusions: (1) The growth rate i n Ag-Se, Cu-Te, and Ag-Te i s d i f -fusion controlled. In Cu-Se two or three stages of dif f u s i o n controlled growth occur with the i n i t i a l growth rate being much faster than succeeding ones, (2) In a l l four systems the di f f u s i o n rates of Cu and Ag are much greater than those of Se and Te, This would lead to the development of extensive Kirkendall porosity on the Se or Te side of a di f f u s i o n couple • and would impede the d i f f u s i o n of these atoms across the i n t e r f a c e . For t h i s reason, a study of the l a t e r a l d i f f u s i o n of Se or Te along Cu or Ag was not possible, (3) The l a t e r a l d i f f u s i o n process i n each system i s con-t r o l l e d by the motion of Cu or Ag ions through the di f f u s i o n zone which i s c r y s t a l l i n e i n nature. Thus, i n the Se systems, d i f f u s i o n i s not affected by the amorphous microstructure of the Se, (4) The d i f f u s i o n rate constant i s independent of the Se or Te f i l m thicknesses for any thickness at which the f i l m i s continuous. This implies that surface di f f u s i o n i s not involved in the l a t e r a l d i f f u s i o n along the Se or Te since the surface to volume 159 ra t i o decreases as the f i l m thickness increases, (5) Se and Te films become continuous at about 180 to o 200 A. Below this thickness the structure of the films i s such that the d i f f u s i o n rate constant tends to a peak value due to s h o r t - c i r c u i t d i f f u s i o n in the i n t e r -i s l a n d channels. The eff e c t of structure i s much more pronounced i n Cu-Te and Ag-Te due to the fact that grain boundary d i f f u s i o n takes place quite readily in these systems, (6) In order for l a t e r a l d i f f u s i o n to occur, a d e f i n i t e r a t i o of Cu or Ag thickness to that of Se or Te must be exceeded. This c r i t i c a l thickness r a t i o i s de-termined only by the stoichiometry of the i n t e r m e t a l l i c phase formed during d i f f u s i o n and i s independent of the structure of the Se or Te f i l m . (7) A grain boundary d i f f u s i o n mechanism accounts for the rapid room temperature growth rates in Cu-Te and Ag-Te, Short c i r c u i t d i f f u s i o n such as grain boundary or "pipe" d i f f u s i o n i s also responsible for rapid growth i n Ag-Se, Therefore, i n these systems, the growth rates observed i n the thin f i l m couples are considerably greater than those observed i n bulk couples at room temperature, (8) The occurrence of rapid room temperature d i f f u s i o n along a f i l m i s r e s t r i c t e d to the four Se and Te systems investigated. There are no obvious extensions 160 of the present work on l a t e r a l d i f f u s i o n to other systems, (9) The rapid d i f f u s i o n processes taking place i n Ag, Cu-Se and Ag, Cu-Te are due to t h e i r unique chemical properties and to the defect structures of the com-pounds formed during d i f f u s i o n . In thin f i l m d i f -fusion couples involving these systems short c i r c u i t d i f f u s i o n processes res u l t i n an acceleration of normal growth rates and enable d i f f u s i o n to proceed rapidly at room temperature. 161 APPENDIX WHITE ZONE The "white zone" described in section 3,2.1 was observed i n a l l of the systems studied and i t s width was observed to decrease as the r e l a t i v e thicknesses of the d i f f u s i o n couple components (e.g. Ag and Se) became compar-able. In any given sample the white zone width remained constant at a l l times and was not included i n the d i f f u s i o n zone width i n the kinetics graphs. Figure A . l , a growth plot i n Ag-Te, shows the true d i f f u s i o n zone width and the t o t a l d i f f u s i o n zone plus white zone width plotted against /t". It can be seen that the d i f f u s i o n zone graph i s parabolic passing through t=0 while the t o t a l width plot, although s t i l l parabolic, i s displaced from the other curve by about 18 u and does not pass through the o r i g i n . It was thus concluded that the white zone was associated with the downward d i f f u s i o n process rather than with l a t e r a l d i f f u s i o n . The o r i g i n of the white zone i s probably due to the masking of the substrate i n order to produce a Ag step. Consider Figure A,2 which represents the Ag vapour incident on the mask and substrate configuration (A,2(a)), and the 162 Figure A„2 Eff e c t of Non-Ideal Masking on Resulting Film Step 164 r e s u l t i n g Ag step produced (A„2(b)), In practice i t i s not possible to achieve perfect contact between mask and sub-strate so that there i s always a narrow gap between them. This permits a small f r a c t i o n of Ag atoms to occupy s i t e s in region B of the substrate. This may occur when atoms such as X and Y in A.2(a) st r i k e the substrate at a high angle of incidence due to rebounding of the chimney walls or c o l l i s i o n with other atoms in the beam. Some Ag atoms (e,g, Z in A,2(a)) may migrate from region A to region B by surface d i f f u s i o n especially i f t h e i r k i n e t i c energy on c o l l i s i o n with the substrate i s s u f f i c i e n t l y high to enable them to move out of bound surface s i t e s , but insuf-f i c i e n t to cause them to re-evaporate. The result of these two processes i s a f i l m structure which becomes increasingly aggregated and porous towards the edge of the Ag ' Figure A,3 i l l u s t r a t e s what happens when Se i s evaporated over such a step to produce a di f f u s i o n couple. The Se in the aggregated portion of the step e s s e n t i a l l y " f i l l s i n " the pores i n the Ag r e s u l t i n g in an e f f e c t i v e reduction of the Se thickness in thi s region. Diffusion s t i l l takes place between the Ag and Se to form Ag 2Se but because the o net Se thickness i s less i n t h i s region the o p t i c a l contrast i s d i f f e r e n t and t h i s area i s observed as the white zone. Evaporation of thicker and thicker Se films reduces the white zone by building up a thick layer of Se at either end of the step d i s t r i b u t i o n and so decreasing the area of ef f e c t i v e Se thickness reduction. This argument was con-165 Se Ag Mask edge White zone < > Lateral d i f f u s i o n ^ ( a ) " ^ g No white zone Se Glass substrate (b) t a t. Se Ag Figure A.3 Evaporation of Se across an Actual Ag Step 166 firmed by evaporating a Ag-Te couple with the mask raised 2 mm above the substrate at one end and in contact with the substrate at the opposite end. The width of the white zone at the "poor mask" end was about 150 u while at the "good" end i t was 18 p, The d i f f u s i o n zone at the "poor mask" end appeared very porous or diffuse i n the early stages of growth making the exact position of x = 0 very d i f f i c u l t to est a b l i s h . The beginning of the l a t e r a l d i f f u s i o n zone, however, appeared to coincide with the very edge of the i l l - d e f i n e d Ag step on the glass immediately adjacent to the Se fi l m . No difference i n the di f f u s i o n rate was de-tected at the "good" and "poor" mask ends, confirming that the white zone i s of no significance i n the l a t e r a l d i f -fusion process,, 167 BIBLIOGRAPHY 1, "Physics of Thin Films", Vol, 2, Ed, by G, Hass and R.E. 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C h r i s t i a n , "The Theory of Transformations i n Metals and A l l o y s " , Permagon Press, p, 5 94 (1965), 57, S.G, E l l i s , J, Appl, Phys,, 3j3_, No, 7, p. 2906 (1967), 58, C, K i t t e l i , "Introduction to S o l i d State Physics", John Wiley and Sons, New York, p, 63 (1962), 59, E,S, Gould, "Inorganic Reactions and Structure", Henry Holt and Company, New'York, p, 134 (1958). 60, 0, Kubaschewski, E,H, Evans and C B , Al cock, "Metallurgical Thermochemistry", Pergamon Press, p, 304 (1967), ( 61, R,T, Foley, M,J, Bolton, and W, M o r i l l , J, Electrochem, S o c , 100, p, 538 (1953), 62, B,D, Lichter and C, Wagner, J, Electrochem, S o c , 10 7, p, 168 (1960), 63, K, Hauffe, "Oxidation of Metals", Plenum Press, New York, p. 365 f f (1965), Bibliography (Cont'd) Reinhold and H. Seidel, Z, Physik. Che., B (38), p. 245 (1937). I, Arkharov and S. Mardeshev, Dokl. Akad. Nauk. SSSR, SS, 517 (1954). M, Niewenhuizen and H,B._Haanstra, P h i l i p s Research Laboratories S c i e n t i f i c and Anal y t i c a l Equipment B u l l e t i n , 79.177/EM9, (1967). 

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