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UBC Theses and Dissertations

Diffusion in thin films Johnson, Dale Bernard 1968

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DIFFUSION IN THIN FILMS  by  DALE BERNARD JOHNSON B„Se,(Hons), The U n i v e r s i t y o f 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 i n the Department of METALLURGY  We accept t h i s t h e s i s as conforming to the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA March, 196 8  In p r e s e n t i n g  this  advanced degree at  Library  shall  agree that  thesis  the  in p a r t i a l  University  make i t f r e e l y  permission  be  granted  by  tatives.  It  is understood  financial  gain  not  the  be  for  requirements f o r  copying or  I agree that  r e f e r e n c e and  copying of  Head o f my  that  the  B r i t i s h Columbia,  available  for extensive  p u r p o s e s may  shall  of  f u l f i l m e n t of  this  thesis  Department o r  publication  a l l o w e d w i t h o u t my  study.  written  by  of  I  the  further  for  scholarly  his  represen-  this  thesis  permission.  Dale Bernard Johnson  Department of  Metallurgy  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  Date  A p r i l 10,  Columbia  I968  an  for  1  ABSTRACT  The nature o f d i f f u s i o n a l o n g t h i n evaporated f i l m s has been s t u d i e d by o p t i c a l and t r a n s m i s s i o n e l e c t r o n microscopy,,  The t h i c k n e s s e s o f the f i l m s were measured by m u l t i p l e -  beam i n t e r f e r o m e t r y o A p r e l i m i n a r y survey o f some 2 2 binary metal systems  showed t h a t o n l y f o u r - Ag-Se, Cu-Se, Cu-Te, and  Ag-Te - d i f f u s e d measurably  at room temperature,  -In these  four systems i t was found p o s s i b l e t o study o n l y the d i f f u s i o n o f Cu o r Ag i n t o Se and Te; experiments f a i l e d , presumably  the r e v e r s e d i f f u s i o n  because o f e x t e n s i v e  K i r k e n d a l l p o r o s i t y which developed on the Se o r Te side of  the d i f f u s i o n c o u p l e s , impeding the motion of these  atoms c The room temperature  growth r a t e s i n each  system  were observed to be h i g h e r when the s t r u c t u r e of the Se o r Te c o n s i s t e d o f i s o l a t e d i s l a n d s w i t h a h i g h l y i n t e r - i s l a n d network. short c i r c u i t ary  disordered  T h i s e f f e c t was a t t r i b u t e d to a  d i f f u s i o n process analogous to g r a i n bound-  d i f f u s i o n which took p l a c e 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 e l e c t r o n microscopy o b s e r v a t i o n s of the phase boundary  i n t e r f a c e s showed a marked tendency f o r g r a i n  ii boundary d i f f u s i o n t o o c c u r at a l l Se and Te t h i c k n e s s e s . For continuous  f i l m s o f Se and Te, the growth r a t e s were  found to be independent  o f the absolute t h i c k n e s s .  Because o f the e v a p o r a t i o n geometry used i n dep o s i t i n g the couples, there was a c r i t i c a l t h i c k n e s s r a t i o of for  Ag or Cu t o Se o r Te that had to be exceeded i n o r d e r d i f f u s i o n to proceed.  T h e o r e t i c a l treatment  o f the  problem, based on the s t o i c h i o m e t r y o f the phases formed d u r i n g d i f f u s i o n , gave p r e d i c t i o n s o f the c r i t i c a l  ratio  that were g e n e r a l l y i n good agreement w i t h the e x p e r i mental values obtainedo  In each system the c r i t i c a l  was found to be independent thickness. ion  ratio  o f the a b s o l u t e Se o r Te  I t was a l s o p o s s i b l e to p r e d i c t the composit-  o f the phase formed d u r i n g d i f f u s i o n u s i n g the c r i t i c a l  ratio.  In every  system but Cu-Te, the composition de-  termined i n t h i s way was i n agreement w i t h that given by e l e c t r o n d i f f r a c t i o n a n a l y s i s o f the d i f f u s i o n The  a c t i v a t i o n e n e r g i e s f o r d i f f u s i o n i n Ag-Se,  Cu-Te, and Ag-Te were f a i r l y circuit  zone.  low s u g g e s t i n g t h a t short  d i f f u s i o n was the predominant mechanism i n these  systems.  The a c t i v a t i o n energy  (2 3 k c a l / m o l e ) , and i t appears  i n Cu-Se was q u i t e l a r g e that the d i f f u s i o n mechanism  i n t h i s case i s not c o n s i s t e n t with that i n the o t h e r systems. microscopy  An i n t e r e s t i n g o b s e r v a t i o n made during e l e c t r o n s t u d i e s i n Cu-Se was the formation o f a second  phase when h i g h e l e c t r o n beam i n t e n s i t i e s were used. phase (CUgSe2), not observed  This  i n normal d i f f u s i o n e x p e r i -  ments up to 5 0°C, grew d e n d r i t i c a l l y i n the presence o f the e l e c t r o n beam.  iv  TABLE OF CONTENTS Page CHAPTER 1  INTRODUCTION . . . . . . . . , . . . . .  1  1.1  Previous Work, » . . » » - . . . . . . .  1  1.2  Object o f the Present  4  1, 3  D i f f u s i o n Theory . . . . . . . . . . . .  5  1.3.1  Atomic Models for. D i f f u s i o n  5  1.3.2  Mathematics o f D i f f u s i o n .  1,4  The S t r u c t u r e o f Evaporated 1.4.1 1.4.2 1.4.3  CHAPTER 2  Investigation. . ,  , . .  . . . .  Thin Films  10 .  18  Thin F i l m N u c l e a t i o n , . . . . . . The Growth o f Thin Films. . . . . The P r o p e r t i e s o f Thin Films. , .  18 21 25  EXPERIMENTAL PROCEDURE . . . . . . . . .  28  2.1  Vacuum Equipment  . . . . . . . . . . . .  28  2.2  Film Deposition,  , , , , . . . . . . .  2.2.1 2.2.2 2.2.3 2.2.4 2.2.5  Sample P r e p a r a t i o n . . . . F i l m Thicknesses. . . . . Temperature T e s t s . . . . Measurement o f D i f f u s i o n Rate Constant . . . . . E l e c t r o n Microscopy . . .  .  29  . . . . . . . . . . . .  29 31 32  . . . . . . . .  32 34  2.3  D i f f e r e n t Evaporation  2.4  Other Systems, . . . . . . . . . . . . .  37  LATERAL DIFFUSION IN Ag-Se . . . . . . .  41  3.1  Introduction , „ . . , . . , , . . . . »  41  3.2  Diffusion  CHAPTER 3  Configurations . »  35  V  Table o f Contents (Cont'd) Page 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3,3 CHAPTER 4  Growth Rate, , . . . . . . . . . E f f e c t o f Se Thickness on Rate Constant. . . . . . . . . The S t r u c t u r e o f Se F i l m s . . . . E f f e c t o f Thickness Ratio 6n the Rate Constant . . . . . T h e o r e t i c a l Determination o f the C r i t i c a l Ratio. . , , . Temperature Dependence of the Rate Constant . . . . .  55 60 64 67  LATERAL DIFFUSION IN Cu-Te,  . . . . . .  74  . . . . . . . . . . . . .  74  Introduction  4.2  Diffusion Kinetics,  CHAPTER 5  48 51  E l e c t r o n Microscopy . . . . . . . . . .  4.1  4.3  4 1 4  .  ,  0  ,  0  0  .  ,  .  76  .  4.2.1 4.2.2  Growth R a t e . . . . . . . . . . . E f f e c t o f Te Thickness on  76  4.2.3 4.2.4 4.2.5  The S t r u c t u r e o f Te F i l m s . . . . C r i t i c a l Ratio . , , . , . . „ . Temperature Dependence o f the Rate Constant . . . . .  8 1 83  E l e c t r o n Microscopy  . . . . . . . .  0  LATERAL DIFFUSION IN Ag-Te.  .  86 90  . . . . . .  99  . . . . . . . . . . . . .  99  5,1  Introduction,  5o2  Kinetics.  5,3  E l e c t r o n Microscopy , , . „ . . 0 . . .  1 0 6  LATERAL DIFFUSION IN Cu-Se, . . . . . .  1 1 4  6.1  Introduction,  . . . . . 0 . . . . . . .  1 1 4  G &2  r\iriG"tlCSo  0  CHAPTER 6  602.1 6.2.2  0  0  ,  o  0  ,  0  0  0  o  0  0  0  0  0  o  0  0  0  o  .  o  ,  o  0  0  o  99  ,  o  Growth Rate. . . . . . . . . . . Dependence o f the Rate Constant on Se Thickness . . .  115  1 1 5 1 1 8  vi Table o f Contents (Cont'd) Page 6.2.3 6.2.4 6,3  C r i t i c a l Ratio, , . . Temperature Dependence 0  E l e c t r o n Microscopy 0 6.3.1 6.3.2  0  0  Normal Growth . 0 D e n d r i t i c Growth 0  SUMMARY AND CONCLUSIONS 0  CHAPTER 7 7,1  Discussion 7.1.1 7.1.2  0  0  0  0  0  0  0  0  0  0  and Summary  0  9  0  0  0  0  0  0  0  0  0  0  120 123  0  126  0  0  0  0  0  0  126 133  0  0  0  0  145  0  145  0  Growth K i n e t i c s . . . . Rate Constant Dependence on F i l m Thickness . . 0 C r i t i c a l Ratio, . . . . 0 Temperature Dependence. 0 E l e c t r o n Microscopy . . 0  7.1.3 7.1.4 7.1.5  0  0  14 5 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  146 147 147 14 9  lik  Estimation  of Diffusion Coefficients . .  150  7,D  The Mechanism o f Rapid D i f f u s i o n . . . .  154  7,4  Conclusions,  158  APPENDIX , 0 0 0 0 . 0 BIBLIOGRAPHY  0  0  0 " '0  , . . , . , . . . » . » . .  0 0 0 0 0 0 0 0 0 0 0  0  0  0 0  0 0  o  0  oo  0  0  0  0  0  0  0  161  0  167  vii  LIST OF FIGURES Page 1.1  Models f o r D i f f u s i o n ,  1.2  S e l f - d i f f u s i o n i n S i n g l e C r y s t a l and Poly c r y s t a l l i n e S i l v e r , . . „ » . , . . . . . .  8  C o n c e n t r a t i o n P r o f i l e s with I n c r e a s i n g Time i n a Single-Phase Binary System . . . . . .  11  D i f f u s i o n Couple i n an Intermediate Phase System w i t h No Terminal S o l i d S o l u b i l i t y  . . . .  13  C o n c e n t r a t i o n P r o f i l e o f an Intermediate Phase System i n X-Space. . . . . . . . . . . . .  14  1.3 1.4 1.5 1.6  .  . » . » . . o . . . . . .  0  The Free Energy o f Formation o f an Aggregate o f F i l m M a t e r i a l as a Function o f Size  1.7  Growth o f an Ag F i l m ,  1.8  Manner o f Coalescence o f Two N l i C X S l  1.9  6  o  o  o  o  o  o  . . . . .  20 22  o  o  o  o  Small Rounded o  o  o  o  o  o  o  o  o  o  23  o  The Density o f D i s l o c a t i o n s i n a Gold D6 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. ,  2.2  Main E v a p o r a t i o n C o n f i g u r a t i o n . . . . . . . . . . .  30  2.3  Measurement  33  2.4  Evaporation Configuration f o r Electron  0  , . . , , , »  . . . . . . .  .  o f F i l m Thicknesses  Microscopy  Specimen, . . . . . . . . . . . . . .  -JD  34  2.5  A l t e r n a t i v e E v a p o r a t i o n Geometries,  . . . . . . . .  36  3.1  E q u i l i b r i u m Phase Diagram f o r Ag-Se . . . . . . . .  42  3.2  Ag-Se D i f f u s i o n Couple,  3.3  T y p i c a l P l o t o f x versus t at Room Tsinpsx^s'tviiir's o o o a o o o o o o o P l o t o f x versus -ft  3.4  ,  0  . . . . . . . . . . .  o  o  o  o  o  o  o  .  o  43 45 46  viii L i s t o f F i g u r e s (Cont'd) Page 3.5  Growth o f a D i f f u s i o n Zone i n Ag-Se.  3.6  E f f e c t o f Se Thickness on Growth Rate,  49  3.7  Rate Constant as a F u n c t i o n o f Se Thickness. . . .  50  3.8  S t r u c t u r e o f Se F i l m s . . . . . . . . . . . . . . .  52  3.9  Appearance o f Phase Boundary at Varying S 6  3.10  Tin x c Jen 6  S  S  0  0  0  0  0  0  0  0  0  0  . . . . . . .  0  0  0  0  0  0  0  47  0  54  Amorphous Se F i l m . . . . . . . . . . . . . . .  56  Stages i n the Formation o f a Continuous  3.11  F i s c h e r ' s Model f o r Grain Boundary D i f f u s i o n  . . .  57  3.12  E f f e c t o f Thickness Ratio on Growth Rate . . . . .  58  3.13  Growth Rate as a Function o f Thickness Rcl"tlO  o  o  o  o  o  o  o  o  o  o  o  o  o  o  3.14  T h e o r e t i c a l D i f f u s i o n Couple M-Y  3.15  Temperature Dependence o f the Rate C O I'l S "t c l X l "t  3.16 3.17  X Tl  "  S  S  o  o  o  o  o  o  o  o  o  o  o  o  59  61  o  o  o  o  o  o  o  o  o  o  65  A r r h e n i u s P l o t f o r Ag-Se . . . o o . . . . . . . . Comparison o f Thin F i l m to Bulk Temperature JOS p  6J"1  dS IlCS  O  O  O  O  O  O  O  O  O  O  O  O  O  O  O  66  O  O  O  Q  3.18  Advance o f the Phase Boundary i n Ag-Se . . . . . .  69  3.19  D i f f u s i o n Zone i n Ag-Se,  . . . . . . . . . . . . .  71  3.20 4.1  S e l e c t e d Area D i f f r a c t i o n P a t t e r n o f D i f f u s i o n Zons o o o o o o o o o o o o o o o o o E q u i l i b r i u m Phase Diagram o f Cu-Te . . . . . . . .  "73 75  4.2  S e l e c t e d Area D i f f r a c t i o n  77  4.3  T y p i c a l P l o t o f x versus -ft i n Cu-Te . . . . . . .  78  4.4  E f f e c t o f Te Thickness on K i n e t i c s  79  4.5  Rate Constant as a Function o f Te 'Pi*lXClCri6 S S  o  o  o  o  o  o  P a t t e r n of Pure Te „ . .  o  o  o  o  o  . . . . . . . . o  o  o  o  o  o  o  o  80  68  ix L i s t o f Figures  (Cont'd) Page  4.6  The Growth o f a Te Thin F i l m ,  . . . . . . . . . . ,  4.7  Growth Rate as a Function o f 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  4.8  Arrhenius Plot  f o r Cu-Te, . . . . . . . . . . . . . .  4.9  Comparison o f Bulk t o Thin  4.10  Temperature Dependence . . . . . . . . . . . . . Motion o f the Cu„ Te Phase Boun d c L r y o o o o o o o o  82  84  87  Film 88 31  O  4.11  D i f f u s i o n Into a 200 A Te F i l m ,  . . . . . . . . . .  4.12  Phase Boundary I n t e r f a c e s at High M a g n i f i C3. "tXOn o o o o o o o o o o Q o o o o o o o  4.13 4.14  4.15  92 34  The Surrounding o f a Grain o f Te by the D i f f u s i o n Zone I n t e r f a c e . . . . . . . . . . . .  95  Schematic Sketch o f the Surrounding o f a Te G r a i n by the Phase Boundary I n t e r f a c e Shown i n Figure 4„13 . . . . . . . , .  96  S e l e c t e d Area D i f f r a c t i o n P a t t e r n o f the D i f f u s i o n Zone o f a Cu-Te Thin F i l m Couple . . .  97  5.1  E q u i l i b r i u m Phase Diagram o f Ag-Te. . . . . . . . .  100  5.2  Growth Rate as a F u n c t i o n o f Te T h i c k n e s s . , . „ „  102  5.3  Growth Rate as a Function o f T h i c k n e s s R a t i o ,  , . .  103  5.4  Arrhenius Plot  f o r Ag-Te, . . . . . . . . . . . . . o Phase Boundary I n t e r f a c e i n a 210 A Te F i l m . . . . Evidence o f Grain Boundary D i f f u s i o n i n a 1000 ft Te F i l m . „ » . . . . . . . . . . . . .  105  5.5 5.6 5.7 5.8  S e l e c t e d Area D i f f r a c t i o n P a t t e r n o f the D i f f u s i o n Zone i n Ag-Te, . . . . . . . . . . . . E l e c t r o n Beam Heat-Induced Second 11*1  ^§ T S  o  0  0  O  0  107 109 I l l  Phase  o o o o O O 0 0 O 0 O O O 0 o  112  6.1  T y p i c a l K i n e t i c s P l o t s i n Cu-Se . . . . . . . . . .  116  6.2  General Form o f the M a j o r i t y o f Growth P l o t s .  117  . . .  X  L i s t o f F i g u r e s (Cont'd) Page 6.3  Rate Constant as a Function o f 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  9  O  6.4  o Phase Boundary I n t e r f a c e i n a 125 A Se F i l m . . . .  6.5  Rate Constant as a F u n c t i o n o f 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  A r r h e n i u s P l o t f o r Cu-Se, . . . . . . . . . . . . .  6.7  Motion o f the Phase Boundary I n t e r f a c e XXI  C\i*"" SS  O  O  O  O  O  O  O  Q  0  0  0  0  9  0  Q  O  O  O  O  121  o  6.6  6.9  S e l e c t e d - A r e a D i f f r a c t i o n P a t t e r n o f the  128  D x f f vis xon Zon6 o o o o o o o o o o o o o o <> <> o  6.11  S e l e c t e d Area D i f f r a c t i o n P a t t e r n s o f S i n g l e Growth  2  127  Columnar Grains i n D i f f u s i o n Zone . . . . . . . . .  Growth T i p a t High M a g n i f i c a t i o n ,  12  124  O  6.8  6.10  119  . . . . . . . . .  12 9 131  Tips  132  6.12  Schematic Indexing o f D i f f r a c t i o n P a t t e r n s .  6.13  Motion o f D e n d r i t i c Phase I n t e r f a c e  . . . . . . . .  136  6.14  Nature o f the D e n d r i t i c Phase . . . . . . . . . . .  137  6.15  Boundary Between D e n d r i t i c and NonDGndi^xizic Phciss o o o o o o o o o o S e l e c t e d Area D i f f r a c t i o n P a t t e r n o f  138  6.16  ©  o  o  . „ . ,  o  o  o  ©  the D e n d r i t i c Phase i n Cu-Se . . . . . . . . . . Dendrite A n a l y s i s  6.18  Dendrite A n a l y s i s  A.l  Plot o f x against  A,2  E f f e c t o f Non-Ideal Masking on R e s u l t i n g  A.3  E v a p o r a t i o n o f Se Across an A c t u a l 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  S "tS p 0  O  0  . . . . . . . . . .  139  6.17  F XllTl  . . . . .  0  .  . . . . . . . .  .  >[t i n Ag-Te . . . . . . . . . . .  0  0  O  O  O  O  0  0  O  Q  0  O  O  0  o  o  134  141 142 162  o  163  165  xi  LIST OF TABLES Page 2ol  Other Systems i n which the P o s s i b i l i t y . .  of L a t e r a l D i f f u s i o n was I n v e s t i g a t e d , 2„2 3.1  Expected D i f f u s i o n C o e f f i c i e n t s i n Some P o s s i b l e Thin F i l m D i f f u s i o n Systems , , Critical S 6  4.1 4.2  Ratio Dependence  ThlClCTlG S  S  o  o  o  o  . .  .  ,  .  38  . .  39  on the Absolute o  o  o  o  o  o  o  o  o  o  o  o  o  o  R f o r I n t e r m e t a l l i c Phases i n Cu-Te. . . . . . . . c C r i t i c a l Ratio as a Function o f 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  SO  85  85  6,1  Theoretical  7.1  A c t i v a t i o n E n e r g i e s f o r Thin F i l m Couples . . . . .  148  7.2  Summary o f L a t e r a l D i f f u s i o n i n the Four Systems I n v e s t i g a t e d , . . . . . . . . . . . Calculation of Diffusion Coefficients . . . . . . .  151 153  7.3  Critical  Ratios i n Cu-Se,  123  ACKNOWLEDGEMENT  The his research  author would l i k e  d i r e c t o r , Dr,  L,.C,  to express h i s g r a t i t u d e to Brown, f o r h i s advice  and  couragement d u r i n g the course o f t h i s r e s e a r c h p r o j e c t . a l s o wishes to thank other students  f a c u l t y members and  f o r many u s e f u l and  enHe  f e l l o w graduate  stimulating discussions.  The  a s s i s t a n c e o f the t e c h n i c a l s t a f f i s g r a t e f u l l y acknowledged. T h i s r e s e a r c h was  f i n a n c e d i n part by a N a t i o n a l  C o u n c i l Studentship,  a Cominco F e l l o w s h i p , and  Research Board Research A s s i s t a n t s h i p .  Research  a Defense  1  CHAPTER 1  INTRODUCTION  In r e c e n t years t h i n f i l m s have a c q u i r e d a wide range of a p p l i c a t i o n s electronics  »,  film electronics  The  i n the  f i e l d s of o p t i c s  development o f the  and  technology of t h i n  d e v i c e s , i n p a r t i c u l a r , has  l e d to a q  great deal o f i n t e r e s t i n t h e i r s t r u c t u r e  and  properties  c  [I  '  9  T h e r e f o r e , many i n v e s t i g a t i o n s have been centered around t h e i r fundamental p r o p e r t i e s  and  how  they compare with  7  those of bulk material.„ been c a r r i e d out, studies  Comparatively l i t t l e work  however, on  thin film diffusion.  are o f c o n s i d e r a b l e p o t e n t i a l i n t e r e s t  evaporated t h i n f i l m s are of h i g h p u r i t y , can both s i n g l e - c r y s t a l and  because any quantity  generally  inapplicable  method of s e c t i o n i n g  of material  be grown i n can  be  microscopy,  methods used to i n v e s t i g a t e  bulk couples are  Such  since  p o i y e r y s t a l l i n e form, and  observed by t r a n s m i s s i o n e l e c t r o n 1,1 Previous Work The  has  diffusion in  to evaporated  i s impossible and  films  the  a v a i l a b l e i s inadequate f o r chemical  »  2  analysis. since  R a d i o a c t i v e t r a c e r techniques cannot be used  the a b s o r p t i o n o f the f i l m s i s n e g l i g i b l e even f o r  low energy B-rays.  Consequently no changes i n emission  can be d e t e c t e d as r a d i o a c t i v e the  p a r t i c l e s d i f f u s e through  films. In the p a s t , most measurements o f d i f f u s i o n i n q  t h i n f i l m s have i n v o l v e d technique employed  the use o f o p t i c a l methods ,  t o study d i f f u s i o n i n two  t h i n f i l m s uses v a r i a t i o n s fusion  surface, .  .  have i n v e s t i g a t e d  i n superimposed Au-Al f i l m s by t h i s method. that  superimposed  i n r e f l e c t i v i t y as the d i f -  zone reaches the metal 9 Weaver and Brown  diffusion They found  changes i n r e f l e c t i v i t y at the metal surface were  due to a s h a r p l y d e f i n e d phase boundary and that  the  compound formed during d i f f u s i o n was A ^ A l .  The  growth  o f the d i f f u s i o n l a y e r obeyed the p a r a b o l i c  law x  where k i s the d i f f u s i o n r a t e rate  One  constant.  The  = kt  diffusion  constant and a c t i v a t i o n energy f o r d i f f u s i o n o f A l  i n t o a Au f i l m were independent o f the Au f i l m t h i c k n e s s i n the range 70 ft. to 3000 8 i n d i c a t i n g that mechanism f o r the very t h i n f i l m s was thicker  Schopper  the d i f f u s i o n  the same as f o r  ones. 10  R e f l e c t i v i t y measurements were a l s o used by 9 and Weaver and Brown to i n v e s t i g a t e t h i n 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 o f a d i f f u s e phase boundary.  The growth r a t e , however, was  still  3  p a r a b o l i c 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 o f AuPb2 d u r i n g diffusion, The p o s s i b i l i t y o f i n v e s t i g a t i n g 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 s u r f a c e was by Monch"^,, to produce  first  demonstrated  The work apparently s t a r t e d with radiation detectors,  attempts  A f i l m o f Te was  ed so as to form a b r i d g e between two  evaporat-  t h i c k Ag e l e c t r o d e s  which had themselves been evaporated onto a c o l l o d i o n film.  On ageing, the Ag d i f f u s e d i n t o the Te, forming a  yellowish-brown band of Ag2Te spreading outwards from the 12 sxlver.  Mohr  13 •  measured the c o e f f x c i e n t o f dxffusxon  of the Ag by determining the widths o f the d i f f u s i o n zone as a f u n c t i o n o f time, Te was  A v a r i a t i o n with the t h i c k n e s s of  a t t r i b u t e d to a f o l d i n g o r c r i n k l i n g o f the t h i c k e r  f i l m s which became detached strates. D = D  Q  from t h e i r u n d e r l y i n g sub-  Measurements o v e r a range of temperature  expC-B/T) where D  Q  = 5xl0  S i m i l a r experiments i n s t e a d o f Te by K i e n e l ' ^  7  gave  cm /day and B = 6010  deg"" .  2  1  were c a r r i e d out u s i n g Se  and Zorll"'"^ but the f i l m s were  d e p o s i t e d on s u b s t r a t e s at l i q u i d n i t r o g e n temperatures because  o f the r e l a t i v e v o l a t i l i t y o f the Se.  Measure-  ments o f d i f f u s i o n r a t e were again made by determining the width o f the d i f f u s i o n  zone as a f u n c t i o n of time  the r e s u l t s , although approximate,  and  were i n g e n e r a l agree-  ment with the e a r l i e r r e s u l t s 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 e l e c t r o n microscopy.  Observations  were made on the moving d i f f u s i o n zone i n t e r f a c e and no evidence o f g r a i n boundary f u s i o n was  seen.  Volume d i f -  the proposed mechanism f o r d i f f u s i o n i n the  f i l m couples with K = K cm /sec and E = 10.0 1.2  d i f f u s i o n was  expC-E/RT] where K  Q  Q  =  7,55xl0~  2  kcal/mole.  Object o f the Present I n v e s t i g a t i o n The main purpose o f t h i s study was  a thorough i n v e s t i g a t i o n o f l a t e r a l  to c a r r y out  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 t o the surface - i n s e v e r a l two-component systems. p a i r s at room temperature  A survey of some 22 metal  showed that o n l y f o u r - Cu-Te,  Ag-Te, Cu-Se and Ag-Se - gave s u i t a b l e d i f f u s i o n  zones.  Even i n these systems o n l y d i f f u s i o n i n Se and Te could be s t u d i e d .  I t had o r i g i n a l l y been hoped to study d i f -  f u s i o n along t h i n f i l m s produced  from the bulk.  i t proved i m p r a c t i c a b l e to produce  However,  such f i l m s i n Se and  Te, the o n l y metals i n which l a t e r a l d i f f u s i o n could be seen.  T h i s p o r t i o n o f the work was  t h e r e f o r e abandoned.  The e f f e c t of v a r y i n g the t h i c k n e s s e s o f both components on the d i f f u s i o n r a t e constant was temperature system was  examined.  A l s o the  dependence o f the r a t e constant i n each determined.  In a d d i t i o n a d e t a i l e d study o f  the d i f f u s i o n f r o n t and the nature o f i t s movement as w e l l as the m i c r o s t r u c t u r e and composition o f the d i f f u s i o n zone was  carried  out u s i n g t r a n s m i s s i o n e l e c t r o n microscopy.  5  1.3  D i f f u s i o n Theory 1»3.1  A  a  Atomic Models f o r D i f f u s i o n  Lattice Diffusion Some proposed mechanisms f o r 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 brief description of  each model i s given belows (1)  Interchange mechanism;  I t i s now  generally  agreed that d i r e c t interchange o f atoms does not o c c u r i n view o f the l a r g e l a t t i c e (2)  distortions  I n t e r s t i t i a l mechanism:  involved.  "Interstitial  dif-  f u s i o n can take place when the two atom s i z e s a r e markedly different.  For example, in. i o n i c compounds, where there  i s o f t e n a great  s i z e d i f f e r e n c e between anion and c a t i o n ,  d i f f u s i o n i s u s u a l l y due to the s m a l l e r (3)  Vacancy mechanism:  considered to take place  cation.  Diffusion i s usually  by a vacancy mechanism.  I f an  atom i s m i s s i n g i n the l a t t i c e , atomic motion w i l l r e s u l t i f any o f the adjacent atoms jump i n t o the vacant interchanging  p o s i t i o n s with the vacancy.  w i l l thereby advance one atomic d i s t a n c e  site,  The vacancy and enable o t h e r  atoms t o move i n the next jump, B.  The K i r k e n d a l l 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 t r a n s l a t i o n a l motion o f atoms r e l a t i v e to a f i x e d l a t t i c e under the d r i v i n g f o r c e o f a  o  o  o  o  o  o o #>o  o o  0  0  o o  o o  o o  °o o ^o o o°c|% o o o o o o J°£ o o o o o o o°o 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  G  0  0  0  a)  o  O  Interchange p a i r and r i n g o f  o  O  o  O  o  O  o  O  o  O  o  O  o  O  four  o  °o o o°o °o o°o o o o o o*o o°o o o o o o o°o o 0  0  0  0  O  0  0  0  0  0  0  0  0  0  b)  Vacancy  O  O  O  O  O  o  o  o  0  0  0  0  0  O O O O o o o o o  ° o ° o ° o ° o O  0  0  0  o  0  o ° o  0  o °  o 5 o o o o2o o o o o o o°oVo 0  0  6  0  0  0  0  c)  Figure I d  0  0  0  Interstitial  Models f o r D i f f u s i o n  0  0  7  chemical to  or thermal g r a d i e n t ,  In o t h e r words, r e l a t i v e  the c r y s t a l l a t t i c e , the atomic s p e c i e s i n a binary  a l l o y d i f f u s e at unequal r a t e s , 17 c a l l e d the K i r k e n d a l l e f f e c t  T h i s phenomenon i s 18  *  and  i s evidenced  macroscopic s h i f t i n the c e n t e r o f g r a v i t y o f an  by a initial  c o n c e n t r a t i o n gradient with r e s p e c t to i n e r t markers f i x e d i n the l a t t i c e . some oxide  The  K i r k e n d a l l s h i f t s observed i n  l a y e r s and i n t e r m e t a l l i c compounds can  very l a r g e .  In these  cases o n l y one  the s h i f t can t h e r e f o r e be n e a r l y the d i f f u s i o n zone.  The  be  species d i f f u s e s and f u l l width o f the  K i r k e n d a l l experiment demonstrates  that a net flow o f atoms can take place d u r i n g  diffusion.  I t has o f t e n been observed that v o i d s , or pores,  form i n  that r e g i o n o f the d i f f u s i o n zone from which there i s a flow o f mass.  This i s c a l l e d K i r k e n d a l l p o r o s i t y - i t s  o r i g i n b e i n g a vacancy f l u x which moves i n a d i r e c t i o n opposite C,  Short  to the net mass flow d u r i n g  diffusion,  Circuit Diffusion The  d i f f u s i o n r a t e o f atoms along g r a i n  boundaries,  s u r f a c e s , and d i s l o c a t i o n s i s c o n s i d e r a b l y g r e a t e r than the r a t e of bulk d i f f u s i o n .  F i g u r e 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 r a d i o a c t i v e s i l v e r t r a c e r 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 value  ,  I t can be seen that the same  o f the d i f f u s i o n c o e f f i c i e n t i s o b t a i n e d  types o f samples at h i g h temperature.  f o r both  Below 700°C,  how-  8  ever, the d i f f u s i o n polycrystal  l i e consistently  with a s i n g l e activation 60%  c o e f f i c i e n t values o b t a i n e d u s i n g a  crystal.  above the values o b t a i n e d  T h i s graph i l l u s t r a t e s that the  energy f o r gra i n  boundary d i f f u s i o n  o f the value f o r bulk d i f f u s i o n  and a l s o  boundary d i f f u s i o n becomes i n c r e a s i n g l y temperatures. can  also  be a f f e c t e d  also 1  o  o  by d i s l o c a t i o n s  grain  important at low coefficient  especially  The e f f e c t o f d i s l o c a t i o n s  i f their  on d i f f u -  becomes more important at lower temperatures. 1 700  1  900  -8  that  The apparent l a t t i c e d i f f u s i o n  density i s high. sivity  i s about  800  1  i 500  600  -10 -  i  i  450 400 Temperature(°C)  _ 26,400 =(2,3x10 °)exp() RT 5  b0  n  O H  -12  m  D =0,895 exp( ^45950^ 8T Li X  i  -14  .  1,00  i 1,20  1000 Figure 1 , 2  N1 1,40  i  I, 50  _ i  S e l f - d i f f u s i o n i n S i n g l e - C r y s t a l and 20 Polycrystalline Silver, (After Turnbull )  Many workers r e p o r t that the d i f f u s i o n along a s u r f a c e i s g r e a t e r than both the g r a i n lattice diffusion  coefficients.  The d r i v i n g  coefficient  boundary and  force f o r  9  surface  d i f f u s i o n may  energy.  Two  surface  of the  diffusion  be  surface  tension  or  surface  main methods f o r d e t e r m i n i n g  coefficient  are  surface  free  the  scratch  smoothing  21 and  g r a i n boundary g r o o v i n g  lead  „  Surface  t o t r e m e n d o u s s c a t t e r i n the  example, a comparison o f t h e surface,  g r a i n b o u n d a r y and  d i f f u s i o n o f Ag  i s given  r e s u l t s obtained.  a c t i v a t i o n energies  i n the  diffusion for 22 t a b l e below :  Surface  10,3  Grain  26,4  boundary  to t h e s e  r e s u l t s the  23 a n a l y s i s o f Mullin's  grain  boundary  24 *  for D  s  on  copper  gives  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  same as (46,8  the  a c t i v a t i o n energy f o r bulk  kcal/mole).  smoothing i s not the  surface  atom. lated for  self  45,9  In c o n t r a s t  on  For  E(kcal/mole)  Volume  an  Thus t h e  This high too  value  i s w e l l on  i t s way  a c t i v a t i o n energy  than t o the  bulk  self  f o u n d by  s u r p r i s i n g since  more c l o s e l y t o t h e  Cu)  can  for  lattice  Me c h a n i s m  grooving  contamination  the  diffusion surface  a c o p p e r atom m o v i n g  to being  an  evaporated  f o r i t s motion i s r e -  heat o f v a p o r i z a t i o n a c t i v a t i o n energy.  kcal/mole  I t would  a p p e a r , h o w e v e r , t h a t more work on  very  must be  done t o  i n c o n s i s t e n c i e s from  surface  diffusion  remove some o f t h e results.  clean  (80  surfaces  10  D,  D i f f u s i o n i n I n t e r m e t a l l i c Compounds I n t e r m e t a l l i c compounds which are present  binary  systems o f t e n have only  stoichiometry u s u a l l y due  a s s o c i a t e d with them.  metric  from  Such d e v i a t i o n s  to a defect s t r u c t u r e i n which some of  atoms o f one positions.  small d e v i a t i o n s  s p e c i e s are m i s s i n g  i n most  are  the  from t h e i r normal  lattice  For example, Zr02 can e x i s t from i t s s t o i c h i o -  composition to ZrO2_ 00l°  This i s probably a  o  Schottky defect  s t r u c t u r e with oxygen v a c a n c i e s .  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 d e f i c i e n t form o f C ^ S e .  As might  expected, d i f f u s i o n tin such compounds i s o f t e n dependent on the exact t h i s determines the The  greatly  d e v i a t i o n from s t o i c h i o m e t r y  vacancy and  interstitial  be  since  concentrations.  "open" s t r u c t u r e s which o c c u r 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 . i s known, f o r example, that Ag modification  ions i n the h i g h  o f Ag S (a-Ag2S) possess extremely 2  It  temperature high  9 mobilities  ,  The  reason f o r t h i s i s that the c a t i o n s  not occupy f i x e d l a t t i c e p o s i t i o n s i n t h i s s t r u c t u r e  do  and  can migrate from s i t e to s i t e j u s t l i k e i n a l i q u i d . 1,3,2 Mathematics o f D i f f u s i o n F i c k ' s f i r s t and  second laws o f d i f f u s i o n i n  one-  dimensional form are s J =«D  —  (1,1)  11  = L.  ^  and  3t Equation  l£)  (1.2)  3x  (1.2) becomes  as, 3t if A.  ( D  3x  D  3£c 3x  2  D i s not a f u n c t i o n o f c o n c e n t r a t i o n .  Single-phase  Diffusion-  Consider a s e m i - i n f i n i t e d i f f u s i o n couple s i n g l e - p h a s e b i n a r y system ( F i g u r e 1.3).  in a  I f the t r a n s -  formation X - x//t~ i s a p p l i e d t o F i c k ' s second law (equation 1.2) then the f o l l o w i n g equation  X dc _ _d 2 dt " dX  results:  dc dX  (1.3)  T h i s has e l i m i n a t e d x and t as independent v a r i a b l e s . Hence one c o n c e n t r a t i o n p r o f i l e i s a p p l i c a b l e at a l l times i n a s e m i - i n f i n i t e couple.  That i s , the p r o f i l e can be  Cone,  X  F i g u r e 1.3  Concentration P r o f i l e s with I n c r e a s i n g Time i n a Single-phase Binary System.  given as C = C(X)  i n s t e a d of a whole s e r i e s o f p r o f i l e s  with C = C ( x , t ) ,  The  equation f o r t h i s s i n g l e  can be found by i n t e g r a t i n g equation 1 3 0  profile  twice.  If D i s  taken to be constant then a p a r t i c u l a r s o l u t i o n to t h i s equation f o r a s e m i - i n f i n i t e 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  2 where  e r f X/2/TJ =  e~  — J  B.  Multi-Phase  n  dn  o  Diffusion  Consider now  a d i f f u s i o n couple composed o f  two  pure metals A and B with no s o l i d s o l u b i l i t y i n the parent phases but having an intermediate compound y with a r e g i o n of s o l u b i l i t y  from C-j_ to C2 at T  geneous r e g i o n o f y phase extends  0  A f t e r time t a homofrom x-j_ to x . 2  In the  y-phase the composition p r o f i l e w i l l be a p o r t i o n o f an e r r o r f u n c t i o n o f the  form  C = A - B e r f X/2/LT That i s , the p r o f i l e  (1,5)  can be drawn i n X-space (Figure  and so the growth o f the y-phase w i l l be p a r a b o l i c . constants A and B i n equation  (1,5) may  the boundary c o n d i t i o n s at X = a-j_ and  be determined  X = a  C = C-^ at X = a-L and C = C2 at X = a . 2  2  ;  namely,  1,4) The by  13  Figure 1,4  Diffusion Couple in an Intermediate Phase System with no Terminal Solid S o l u b i l i t y ,  14 The r e s u l t i n g  C = C+ L  concentration p r o f i l e i s :  (Cg"^)  erf  2  (Cj-^)  X/2/JT  (1.6) erf  C = c +  erf  ^ / 2 / i T -  erf a / 2 / F 2  erf-a /2^5~-  e r f X/2/5"  2  erf  a /2/fT-  e r f a /2/D~  1  To o b t a i n e x p r e s s i o n s f o r  (1.7)  9  and  mass balance c o n d i t i o n s  a c r o s s the i n t e r f a c e can be a p p l i e d and equations and  (1.7) used to d e r i v e the f i n a l  S i m p l i f i e d Method, f o r . F i n d i n g  I f the composition  (1.6)  result.  and  range o f the i n t e r m e d i a t e  phase i s assumed t o be small ( 5%  o r l e s s ) , the concentra-  t i o n g r a d i e n t i n the phase may be taken to be l i n e a r to a first  approximation.  profile  Figure 1.5 shows the r e s u l t i n g  i n X-space, C„  Cone,  X = CL. F i g u r e 1.5  X=0  X= ou  X C o n c e n t r a t i o n P r o f i l e o f an Phase System i n X-Space,  Intermediate  15  From t h i s f i g u r e i t can be seen that  dc  —  dX  The  C  = -  2 "  a  l —  C  - a  (lo 8) 2  i n t e r f a c e mass balance c o n d i t i o n at  across  t h e boundary i n a time dt causes the phase boundary  to move a d i s t a n c e flow.  i s t h a t the f l u x  d5 i n the d i r e c t i o n o f the net mass  Thus, at the  -  i n t e r f a c e , the c o n d i t i o n becomes:  D j —  dt  =  (C..-C  )dS  (1.9)  S e t t i n g £ = a / t and X = x / / t leads to -  D—  dX  = (c  1  -C )— o 2  (lolO)  S u b s t i t u t i n g (1,8) i n t o (1,10) gives (Co-Cx)  a,(a.-oJ 1  1  2  = 2D—-——  (1.11)  «o.-c > 0  S i m i l a r l y the mass balance c o n d i t i o n at the a  2  interface  gives: (C  - C  )  a„(a -a ) = -2D — - — i -  (c -c ) 3  (1.12)  2  Using equations (1,11) and (1,12) i t can be found t h a t  Thus  may be s e t equal t o the d i f f u s i o n  coefficient  times some constant y» say, which depends o n l y on concentration.  T h i s may be w r i t t e n as a  where K  = Dy  2 x  s  K  (1.14)  i s h e n c e f o r t h r e f e r r e d to as the d i f f u s i o n 7  constant ,  9  Since  rate i  = x-^ / t , we can w r i t e t h a t x = /K^t. 1  Equation 1,13 shows t h a t x-^ i s p r o p o r t i o n a l t o both and  /C -C^,  I f C^-C-^ tends t o zero - t h a t i s , the  2  s t o i c h i o m e t r y range o f the i n t e r m e t a l l i c to  /D  compound  zero - then x^ w i l l become very s m a l l ,  tends  A l a r g e value  of x^ under these 'circumstances would imply an e x c e p t i o n a l l y l a r g e value f o r D,  A s i m i l a r e x p r e s s i o n to 1,13  may be d e r i v e d f o r a  g i v i n g X 2 = /K^t,  2  E f f e c t o f Temperature The temperature  d i f f u s i o n c o e f f i c i e n t , D, changes with  a c c o r d i n g t o the Arrhenius-type  equation  D = D exp (-E-./RT) o 1  (1.15)  In most systems having an i n t e r m e d i a t e phase the composit i o n l i m i t s change l i t t l e w i t h temperature. equation  (1,13) the d i f f e r e n c e  vary s i g n i f i c a n t l y with dependence o f the d i f f u s i o n  Thus i n  (C ~C^) i s not expected to 2  temperature  and so the  temperature  and c* w i l l be due to the v a r i a t i o n o f 2  coefficient.  Even i f there i s a change i n  composition range w i t h temperature,  a straight  line  17  Arrhenius p l o t  f o r a-^ arid  would s t i l l  be expected  since  27  (C^C-^) should t h e o r e t i c a l l y i n g to an e x p o n e n t i a l law;  vary with temperature namely,  ( C - C ) • ;= y 3 exp (-E /RT) 2  1  (1.16 )  2  S u b s t i t u t i n g i n t h i s equation u s i n g equation  (1.13) g i v e s :  K " = (D6A)exp(-E /RT)  (1.17)  2  with  A.• = ;  The terms ( C - C ) » 3  pression w i l l (-2~C-|_) o (  ^G  ,•  (c -c )  0 :  )XC -G  ^ i~ ^» c  2  C  0  accord-  3  2  3  a  n  d  2+  C -C )  ^ 3" 2 C  change by n e g l i g i b l e  C  1  + C  0  i" o^ C  i  n  t  h  i s ex-  amounts compared t o  Thus i t can be seen t h a t  :  K  where E = E  1  = K exp(-E/RT) o  (1.18)  + E„. 1  2  In systems having more than one i n t e r m e d i a t e phase, the motion o f t h e i n d i v i d u a l phases i s s t i l l bolic.  Diffusion  i n such a system w i l l be q u a l i t a t i v e l y  s i m i l a r to t h e special, case d i s c u s s e d above. to the n-component  para-  A  solution  d i f f u s i o n couple i s complex but has 28 29 been d e r i v e d 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 t h e o r e t i c a l treatment  i s concerned with the nucleation  of a thin f i l m condensed from the vapour phase on a substrate held at a temperature lower than that of the evaporating source.  After impingement on the substrate the  vapour atoms can either adsorb and s t i c k permanently to the substrate, they can adsorb and re-evaporate i n a f i n i t e time, or they can immediately rebound o f f the substrate.  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 r i s e to c o l l i s i o n s 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, t h e i r surface-to-volume r a t i o i s very high and the r e s u l t i n g high t o t a l surface energy causes them to have a higher vapour pressure than the bulk material and thus to dissociate again.  Consequent-  l y there i s a size at which the s t a b i l i t y of the aggregate i s 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 s u b s t r a t e The  surface.  critical  r a d i u s r * o f a s t a b l e aggregate i s  c a l c u l a t e d by c o n s i d e r i n g the t o t a l f r e e energy o f  the  aggregate as a f u n c t i o n of s i z e .  involves  the  This  f r e e energy  f r e e energy of condensation, the surface energies  both aggregate and  s u b s t r a t e , and  between the aggregate and f i n d both the c r i t i c a l gate and  the c r i t i c a l  the s t a b l e aggregate.  the i n t e r f a c i a l energy  substrate.  I t i s p o s s i b l e to  mean l i n e a r dimension o f the f r e e energy of formation Figure  of  1,6  aggre-  (AF*)  of  shows the dependence o f  the f r e e energy o f an aggregate on i t s s i z e . The  r e l a t i v e magnitudes o f r * and i\F*  the b a s i c s t r u c t u r e of the t h i n f i l m d e p o s i t .  f r e e energy of formation  having an i s l a n d s t r u c t u r e up f i l m thicknesses. the  In the  w i l l be  and  coarse-grained  to r e l a t i v e l y high  average  low n u c l e a t i o n b a r r i e r regime  f i l m i s g e n e r a l l y much f i n e r - g r a i n e d since a dense  population  o f small i s l a n d s grow t o g e t h e r  stage i n the low  Films  b a r r i e r , that i s , a l a r g e r*  having a n u c l e a t i o n a high  determine  d e p o s i t i o n process and  average f i l m t h i c k n e s s e s .  The  become continuous at tendency to form an  i s l a n d s t r u c t u r e i s g r e a t e r i n a low m a t e r i a l due  at an e a r l y  boiling-point  to the weak bounding between atoms  and  hence the h i g h volume f r e e energy o f condensation. Elements such as Cd,  Zn,  Se, Te,  and  Sb w i l l  remain as i s l a n d s t r u c t u r e s up to l a r g e f i l m  therefore thicknesses  size  Figure  1,6  The Free energy o f Formation o f an Aggregate o f F i l m M a t e r i a l as a Function o f S i z e , 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, films.  f o r example, w i l l tend to form  Other f a c t o r s promoting the formation  structures include: (2) a low f i l m and  (1)  a high s u b s t r a t e  continuous  of  island  temperature,  d e p o s i t i o n r a t e , (3) weak b i n d i n g f o r c e s between s u b s t r a t e , (4) a h i g h s u r f a c e energy of the  m a t e r i a l , and  (5) a low  s u r f a c e energy o f the  film  substrate.  These f a c t o r s , although mentioned o n l y b r i e f l y , have a very profound i n f l u e n c e on the s u b - s t r u c t u r e o f a t h i n ,.,4,5,31 fxlm ' ' ,  1,4,2  The  5 32 Growth-of- Thin Films ' The  thin f i l m are:  c h a r a c t e r i s t i c stages i n the growth o f a (1) the formation  b u t i o n o f small three-dimensional i n s i z e o f these n u c l e i without  of a surface nuclei,  any  distri-  (2) the growth  increase i n t h e i r  numbers, (3) f u r t h e r i n c r e a s e s i n s i z e o f the n u c l e i o r i s l a n d s accompanied by a gradual but crease  considerable  i n t h e i r numbers, (4) the formation  o f a connected  network o f d e p o s i t u s u a l l y r a p i d l y developing channelled o f holes  s t r u c t u r e , (5) a continuous  (see F i g , 1,7),  de-  into a  deposit f i l m free  This sequence o f growth events  i s g e n e r a l l y the same f o r both e p i t a x i a l f i l m s deposited on s i n g l e - c r y s t a l s u b s t r a t e s and p o i y e r y s t a l l i n e f i l m s evaporated onto amorphous s u b s t r a t e s .  The  average  film  t h i c k n e s s o f the f i l m s at each growth stage are u s u a l l y d i f f e r e n t , however.  One  o f the most s t r i k i n g phenomena  which occur during the growth o f a f i l m i s the  liquid-like  22  Figure 1,7  Growth o f an Ag F i l m ( a f t e r Sennett and S c o t t " ) 1  23 coalescence o f randomly o r i e n t e d n u c l e i and i s l a n d s which takes p l a c e as the n u c l e i or i s l a n d s touch one  another.  i  F i g u r e 1,8  Manner o f Coalescence o f Two Small Rounded N u c l e i . (Pasfhley32)  The e f f e c t i s i l l u s t r a t e d i n F i g u r e 1,8 n u c l e i which have round p r o f i l e s .  f o r the case o f  When the i s l a n d s are  small (say l e s s than 200 % across) the complete appears  coalescence  to take p l a c e i n s t a n t a n e o u s l y and the compound  i s l a n d has a g r e a t e r t h i c k n e s s than the two  initial  islands.  orientation  that may islands.  The  composite  i s l a n d has  a single  d i f f e r from the o r i e n t a t i o n s of the parent The mechanism o f coalescence i s completely  ana-  logous to t h a t o f s i n t e r i n g and i s e x p l a i n e d i n terms of the s u r f a c e m o b i l i t y o f d e p o s i t atoms over the d e p o s i t ( r a t h e r than the s u b s t r a t e ) w i t h the d r i v i n g f o r c e f o r the t r a n s f e r o f m a t e r i a l between i s l a n d s b e i n g the s u r f a c e  energy.  As the coverage o f the s u b s t r a t e becomes high,  the i s l a n d s have i n c r e a s i n g d i f f i c u l t y favoured  i n assuming t h e i r  c r y s t a l l o g r a p h i c shapes, and an open network  s t r u c t u r e i s e v e n t u a l l y formed.  F i n a l l y the  channels i n the network become f i l l e d i n and  elongated a continuous  f i l m i s formed. The  three predominant d e p o s i t i o n parameters are  chamber p r e s s u r e , ture.  d e p o s i t i o n r a t e and  substrate  tempera-  While most of the i n v e s t i g a t i o n s o f the e f f e c t  of  these v a r i a b l e s on a deposit have been done f o r s i n g l e 32 crystal films  34 '  , there i s some evidence a v a i l a b l e f o r 5 32  p o l y c r y s t a l l i n e f i l m s as w e l l  '  ,  The  chamber  determines the q u a n t i t y o f r e s i d u a l gases present evaporation. can  Adsorbed i m p u r i t y  gas  decrease s u r f a c e m o b i l i t i e s and  sizes.  The  ordered  i f gas  i f any  deposit  f i l m may  the f i l m are present.  substrate  r e s u l t i n small g r a i n  by the deposit o r impure  a h i g h chemical  affinity  With i n c r e a s i n g s u b s t r a t e  t u r e the s i z e o f the c r y s t a l l i t e s to a h i g h e r  during  be porous and h i g h l y d i s -  atoms are trapped  r e s i d u a l gases with  atoms on the  pressure  for  tempera-  (islands) increases  due  s u r f a c e m o b i l i t y o f the d e p o s i t atoms and  the  g r a i n s i z e of the deposit becomes l a r g e r .  For a  given  s u b s t r a t e temperature the g r a i n s i z e o f a p o l y c r y s t a l l i n e f i l m i s u s u a l l y f i n e r and the r a t e o f d e p o s i t i o n .  l e s s agglomerated the  higher  T h i s i s because h i g h l y mobile  s u r f a c e atoms at h i g h d e p o s i t i o n r a t e s become b u r i e d i n random s i t e s by s u c c e s s i v e l y a r r i v i n g atoms before f i n d i n g  25 appropriate l a t t i c e 1.4.3 A,  The  sites.  P r o p e r t i e s o f Thin Films  Lattice  Defects  The main c l a s s e s o f l a t t i c e d e f e c t s may l i s t e d as f o l l o w s : faults,  (1) d i s l o c a t i o n l i n e s ,  (3) microtwins,  be  (2) s t a c k i n g  (4) aggregation o f p o i n t d e f e c t s ,  (e.g. d i s l o c a t i o n loops and s t a c k i n g - f a u l t t e t r a h e d r a ) . 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 5 32 are completely  free of dislocations  '  „  The way  nuclei  in  which the d i s l o c a t i o n d e n s i t y i n c r e a s e s d u r i n g growth o f the f i l m i s shown i n Figure 1,9,  A p p r e c i a b l e numbers o f  d i s l o c a t i o n s appear o n l y when the network stage o f growth i s reached,,  F i v e proposed mechanisms f o r the  1  o  1  100 -  1  o  c  80 60  CD TD 0  40  •rl •P  O  o rH •rl Q  4->' CO  20  01-  0  1  j Channel I Continu| and Hole o u s F i l m | Stage 1  Network Stage  1  |  1  1  i  1  1/  |  1 1 -  —  i  100  Figure 1.9  —  —  •  —  i  l_  |  1  1  1 1 1 Pre--coalescence  >> +J  •H CQ  1  b0,  1  H X  j ,  Coalescence Stage  1  intro-  / X  /  /  / i  200 300 400 Approx. Gold Thickness (&) The Density o f D i s l o c a t i o n s (per u n i t area o f s u b s t r a t e ) i n a Gold Deposit o  .j  500  26 duction o f growth i m p e r f e c t i o n s a r e : (1)  The e x t e n s i o n o f i m p e r f e c t i o n s a l r e a d y ex-  i s t i n g at the s u b s t r a t e s u r f a c e , (2) date  The formation o f i m p e r f e c t i o n s t o accommo-  any o r i e n t a t i o n d i f f e r e n c e s between j o i n i n g n u c l e i , (3)  The formation o f i m p e r f e c t i o n s t o accommo-  date displacement (4) aggregation  m i s f i t s between j o i n i n g n u c l e i ,  The formation o f p o i n t d e f e c t s and t h e i r  to form d i s l o c a t i o n loops and o t h e r  imper-  fect ions, (5)  P l a s t i c deformation  o f the f i l m at v a r i o u s  stages o f growth, B,  S t r e s s e s i n Thin  Films  Vacuum d e p o s i t e d f i l m s can be i n a s t a t e o f h i g h mechanical s t r e s s .  The magnitude o f the s t r e s s can be very  high and i n some i n s t a n c e s exceeds the normal bulk  yield  7  s t r e s s o f the m a t e r i a l , not c l e a r l y understood. s t r e s s , the f i r s t  The o r i g i n o f t h i s s t r e s s i s There are two components o f the  due to any temperature d i f f e r e n c e s  between s u b s t r a t e and d e p o s i t d u r i n g d e p o s i t i o n  (thermal  s t r e s s ) and the second any a d d i t i o n a l s t r e s s due t o structure  (intrinsic stress).  I n t r i n s i c s t r e s s can be  generated  by e n c l o s e d gas atoms o r i m p u r i t i e s , by f r e e z -  i n g - i n o f l a t t i c e d e f e c t s d u r i n g condensation,  o r by  surface e f f e c t s due t o the small t h i c k n e s s e s i n v o l v e d ( f o r example, s u r f a c e t e n s i o n ) .  A l s o , oxides o r o t h e r  chemically  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 t h e  s t r e s s i n a manner s i m i l a r t o t h e i n t e r f a c e b e t w e e n s u b 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  lattice  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 on a f i l m  c a n be r e l i e v e d by a n n e a l i n g  of a higher  deposition  temperature.  o r by t h e  stress choice  CHAPTER 2  EXPERIMENTAL PROCEDURE  2 o1  Vacuum Equipment Thin f i l m d e p o s i t i o n s were c a r r i e d out  CVC-14 vacuum u n i t capable  o f an ultimate pressure  -8 5x10  in a of  . . . T o r r i n the working chamber,  M o d i f i c a t i o n s were  made to the b a s i c system so t h a t f o u r evaporation were available,,  An aluminum masking p l a t e was  at a d i s t a n c e of 25 cm.  above the b a s e - p l a t e  installed  g i v i n g an  e f f e c t i v e source-to-specimen s p a c i n g o f 22 on. s e a l was  machined so as to impart  A rotation  both a l i f t i n g  r o t a t i o n motion to a l l specimen h o l d e r s .  sources  This  and enabled  specimens to be set i n p l a c e on a mask d i r e c t l y above one o f four sources  d u r i n g a s i n g l e pump-down,  diameter A l wire was d i s t a n c e o f 1 1/2"  main base-plate  1/8"  i n s t a l l e d i n the b e l l j a r at a  from the specimen plane  glow-discharge c l e a n i n g d u r i n g the roughing pump-down c y c l e .  A  any  T h i s wire was plugs.  to  provide  p a r t of  i n s e r t e d i n t o one  P r i o r to evacuation  chamber, an  85 mm.  g l a s s c y l i n d e r was  evaporation  source  so as to prevent  the  o f the  o f the vacuum  placed around each  contamination  of  o t h e r sources and samples.  S l i d e s were attached to the  specimen h o l d e r with s c o t c h tape. t h i c k were used f o r masking.  Glass cover s l i d e s  ,0 015"  A mask could be i n any d e s i r e d  shape depending on the experiment.  Figure 2,1 shows the  d e t a i l s o f the vacuum equipment, 2.2  Film Deposition 2,2,1  Sample P r e p a r a t i o n Specimens were prepared on g l a s s  slides.  microscope  Each s l i d e was r i n s e d with a detergent  solution,  p o l i s h e d w i t h l e n s t i s s u e , and subjected t o 'the breath test ' 5  5  before being i n s e r t e d i n t o the vacuum chamber. 36  complete the c l e a n i n g process  To  the s l i d e was exposed t o  a glow discharge i n s i d e the vacuum system f o r 10 minutes d u r i n g the f i r s t  p a r t o f the pumping c y c l e .  The  evapora-  —6  t i o n s were c a r r i e d out i n a vacuum o f 2x10 r e s i s t a n c e heated  ,010" molybdenum boats,  Torr using The s u b s t r a t e s ,  mounted 2 2 cm, above the e v a p o r a t i o n sources, c o u l d be r o t a t e d so as t o l i e d i r e c t l y above each source i n t u r n , 30 I t was c a l c u l a t e d  • t h a t at t h i s source to specimen d i s -  tance the v a r i a t i o n i n t h i c k n e s s a c r o s s the s l i d e would be l e s s than 2%, In k i n e t i c s t u d i e s two d i f f u s i o n couples were evaporated *  onto a s i n g l e microscope  slide using suitable  Breath t e s t : S l i d e i s c l e a n to w i t h i n one o r two monol a y e r s o f contamination when a breath mark on i t d i s appears r a p i d l y ,  LEGEND  Figure  2,1  Vacuum  A  evaporation source selector switch  B  masking  C  specimen  holder  D  rotation  control  E  #4  evaporation  F  Mo  boat  G  #3  evaporation  source  H  #2  evaporation  source  I  main base  J  brass  K  #1  L  glow d i s c h a r g e  Equipment  plate  source  plate  base-plate  evaporation  source ring  Ag o r  Cu  Se o r Te  F i g u r e 2,2  Main Evaporation  Configuration  31 masks above each source. experimental  F i g u r e 2,2  (a) shows the main  c o n f i g u r a t i o n used to observe l a t e r a l  f u s i o n and F i g u r e 2.2  dif-  (b) shows the l a y o u t o f samples on  microscope s l i d e s u b s t r a t e .  A f i l m o f Ag o r Cu was  the  first  d e p o s i t e d over p a r t o f the s l i d e and allowed to c o o l f o r a minimum o f 15 minutes i n o r d e r to ensure that the subs t r a t e would be at room temperature f o r s u c c e s s i v e evaporations. Te o r two  The  s l i d e was  Se sources  then r o t a t e d i n t o p l a c e over  i n s u c c e s s i o n and evaporation  the e x i s t i n g Ag o r Cu step was minutes was 2,2,2  Film  c a r r i e d out.  allowed between the two  evaporations,  Thicknesses  an opaque s t r i p o f A l was  evaporated  the c l e a r edge o f the s l i d e  (b))„  In t h i s technique flat  steps  The  t h i c k n e s s as d e s c r i b -  37 ed by Tolansky  thicknesses  across the f i l m  (Figure 2,2  method o f F i z e a u f r i n g e s o f constant  optical  across  A time of 3  For purposes o f measurement o f f i l m  at  two  • was  used to determine the f i l m t h i c k n e s s .  a partially silvered  (4-6%  transmission)  i s brought c l o s e to the A l o v e r - l a y e r e d  I f the r e l a t i v e p o s i t i o n s o f s l i d e and so as to form a wedge shaped a i r gap,  flat  are  and the  step.  adjusted  interfero-  meter i s i l l u m i n a t e d by a beam o f p a r a l l e l monochromatic l i g h t , a s e r i e s o f dark f r i n g e s can be made to run i n straight film.  l i n e s p e r p e n d i c u l a r to the steps on the opaque  These f r i n g e s t r a c e out the p o i n t s o f equal a i r  gap t h i c k n e s s and t h e i r s e p a r a t i o n corresponds t o an i n crease i n gap t h i c k n e s s o f X/2 where X i s the wavelength of the l i g h t .  The f r i n g e s show a displacement as they  pass over the step edge and measuring  t h i s as a f r a c t i o n  o f the f r i n g e spacing g i v e s the f i l m t h i c k n e s s i n u n i t s of  X/2.  F i g u r e 2,3 shows the i n t e r f e r o m e t r y arrangement  and some t y p i c a l f r i n g e systems observed. 2.2.3  Temperature T e s t s Temperature t e s t s i n the range  3 0-100°C were  c a r r i e d out i n a water bath c o n t r o l l e d t o +_ 1.5°C by i n s e r t i o n o f the sample s l i d e i n t o a 1" diameter tube immersed i n the water. a rubber stopper  test-  The t e s t - t u b e was s e a l e d with  to reduce convection heat  losses.  Tests at 0°C were c a r r i e d o u t i n an ice-water mixture. Thermometer readings were made on the bath every during a run as a check on the temperature 2.2.4  Measurement o f D i f f u s i o n Rate  hour  controller.  Constants  The d i f f u s i o n rate constant was determined by measuring  the width  a f u n c t i o n o f time.  (x) o f the l a t e r a l d i f f u s i o n zone as Measurements were made u s i n g a  c a l i b r a t e d t r a v e l l i n g eyepiece on a m e t a l l u r g i c a l microscope ,  33 Eyepiece and ocular lens f o r viewing f r i n g e system  Hg  source  Wratten #72 f i l t e r (1% y e l l o w t r a n s m i s s i o n ) Partially silvered optical flat  Step o f f i l m to be measured glass  opaque r e f l e c t i n g c o a t i n g o f Ag o r A l  Observed Fringe P a t t e r n s  Ag step o f 1990 % Ag step o f 260 A  Figure 2,3  Measurement o f F i l m Thicknesses  34  2.2.5  Electron  Microscopy  A t h i n evaporated carbon  film floated  onto a  150 mesh specimen g r i d i n d i s t i l l e d water p r o v i d e d a substrate  f o r an evaporated  diffusion  couple that c o u l d be  s t u d i e d by t r a n s m i s s i o n e l e c t r o n microscopy.  The  specimen g r i d with i t s a t t a c h e d carbon support f i l m taped by one edge to a microscope couple was Figure 2,4.  diffusion  d e p o s i t e d on i t i n the c o n f i g u r a t i o n shown i n The  s l i d e was  t h i c k n e s s measurements. minutes was  s l i d e and a  was  masked so as to f a c i l i t a t e  A c o o l i n g time o f at l e a s t  allowed between the two  15  r e q u i r e d evapora-  tions.  Figure 2.4  Evaporation Configuration f o r E l e c t r o n Microscopy Specimens,  film  35 2,3  D i f f e r e n t Evaporation Configurations Three o t h e r e v a p o r a t i o n c o n f i g u r a t i o n s i n Cu-Te  were i n v e s t i g a t e d to see i f any l a t e r a l d i f f u s i o n  occurred.  The geometries  The  i n v o l v e d are shown i n Figure 2,5,  occurrence o f l a t e r a l d i f f u s i o n i n 2,5  (a) o r (b) - t h a t  i s , the advance o f a d i f f u s i o n zone i n t o the pure Cu f i l m - would be due to the d i f f u s i o n o f the Te i n t o In samples prepared i n these two d i f f u s i o n was microscopy  ever observed  c o n f i g u r a t i o n s no  lateral  e i t h e r by o p t i c a l or e l e c t r o n  even a f t e r a n n e a l i n g at 50°C f o r 2-3  hours.  The reason t h a t d i f f u s i o n i n t h i s d i r e c t i o n i s not ed i s probably porosity  Cu,  observ-  due to the development o f K i r k e n d a l l  (see page  7, I n t r o d u c t i o n ) on the Cu/Cu-Te  i n t e r f a c e causing i t s rupture. The geometry o f 2,5  (c) should be e x a c t l y  e q u i v a l e n t to t h a t d e s c r i b e d i n S e c t i o n 2.1.  Diffusion  o f Cu i n t o the pure Te f i l m should r e s u l t i n the and growth o f a l a t e r a l d i f f u s i o n zone.  While there  some i n d i c a t i o n t h a t l a t e r a l d i f f u s i o n was immediately  formation was  proceeding  a f t e r the d i f f u s i o n couple f o r m a t i o n , the  i n e v i t a b l e r e s u l t o f forming a sample i n t h i s way that the e n t i r e Cu s i d e became detached  was  from the g l a s s  s u b s t r a t e and l i f t e d away from the s u r f a c e .  With the  re s u i t i n g d i s c o n t i n u i t y between C u - r i c h s i d e and Te, f u s i o n could not proceed. of adhesion was  The  immediate and r a p i d  probably due to both the poor  fidif-  loss  adhesion  Cu Te Cu Glass  (a)  Te Cu  Glass  (b)  Cu  le_ Glass  (c)  gure 2,5  A l t e r n a t i v e Evaporation  Geometries  37  of the  i n t e r m e t a l l i c compound produced by  on  Cu  the  the  (which extends r i g h t to the  a g g r e g a t i o n of the  of Cu. the  side  The  Te  glass surface)  s u b s t r a t e f i l m during the  deposition to  source f o r s u f f i c i e n t lengths of time to produce 40-50°C  application  e v a p o r a t i n g Te  substrate.  I t was  of a t h i n Cr s u b s t r a t e to the and  Cu  observed  v e l o p e d . At  seemed to s t a b i l i z e the  l o n g e r p e r i o d s , however, the  d i f f u s i o n ceased.  that  g l a s s before Cu  side  for  about 15 minutes during which time a t h i n l a t e r a l zone  and  and  e v a p o r a t i o n of Cu r e q u i r e s a h i g h power input  temperature i n c r e a s e s at the the  downward d i f f u s i o n  de-  Cu side peeled o f f  Because of t h i s adhesion problem -  common to a l l f o u r systems - a study of d i f f u s i o n i n t h i s configuration not  was  extremely d i f f i c u l t  and  f u r t h e r work  attempted,  2,4  Other Systems Table 2,1  l i s t s 18  ture l a t e r a l d i f f u s i o n was  systems i n which room temperalooked f o r without success.  a system X-Y,  the  evaporation configuration  the  was  g e n e r a l l y arranged so that  table  and  d i f f u s i n g atom would be the  was  in a position  development of p o r o s i t y  zone.  In a l l the  concluded that  no  additional  at the  X,  was  For  as shown i n  the  faster  T h i s was  boundary of the  systems i n v e s t i g a t e d  to  avoid  diffusion it  was  l a t e r a l d i f f u s i o n took p l a c e 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 small. as  Table 2,2  l i s t s the  found i n t h i n f i l m s  expected d i f f u s i o n  ( a f t e r Brown  9  too  coefficients  where a v a i l a b l e )  in  Table 2.1  Other Systems i n which the P o s s i b i l i t y of Lateral Was  Diffusion  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 e l e c t r o n hot-stage „  microscope  TABLE 2.2  Expected D i f f u s i o n C o e f f i c i e n t s i n some  Possible  Thin F i l m D i f f u s i o n Systems  System  Faster. D i f f u s i n g Atom*'  T(°C)  2 D (cm /sec) -22 3x10 -29 8.4x10  Ag-Al  Ag  21  Cu-Al  Cu  . ' 21  . Ag-Cd  Ag  21  1.5xl0~  Au-Pb  Au  21  2.17xl0"  Cu-Sn  Cu  21  Cu-Cd  Cu  21  1.13xl0" -16^ 5x10 t  Au-Te  Au  90  2x10-"  Cu-Ge  Cu  700  3xl0 ^  i  Bulk d i f f u s i o n data  1 6  15  36  _ 5  some o f these systems. of the phase boundary  At h i g h e r temperatures movement i n t e r f a c e would be expected but t h i s  was never observed even i n the e l e c t r o n  microscope hot  stage due t o i n t e r f a c e r u p t u r e , d i f f u s e i n t e r f a c e s , aggreg tion, oxidation, e t c .  41  CHAPTER 3  LATERAL DIFFUSION IN Ag-Se  3«,1  Introduction Figure  3=1 shows the e q u i l i b r i u m phase diagram f o r  40 Ag-Se  ,  thermally  At low temperatures only the phase Ag Se i s 2  s t a b l e 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 r e s u l t i n i t s formation, an a l l o t r o p i c t r a n s f o r m a t i o n ture  2  at about 130°C„  3 m o d i f i c a t i o n has been d e s c r i b e d  orthorhombic o r m o n o c l i n i c  Ag Se undergoes  structure  t i o n , s t a b l e above 130°C, has a CaF  2  The low tempera-  as having e i t h e r an  while the a m o d i f i c a 41 structure , 42 4 3  Pure bulk Se has s e v e r a l a l l o t r o p i c forms The  two most important m o d i f i c a t i o n s  *  are the hexagonal, the  most common form s t a b l e below the m e l t i n g  p o i n t , and the  amorphous form which i s induced by s u p e r c o o l i n g  l i q u i d Se  c  A l l o f the evaporated t h i n f i l m s o f Se observed i n t h i s work were amorphous i n nature.  The c o l o u r o f the Se de-  p o s i t s v a r i e d from l i g h t orange f o r the very t h i n f i l m s (< 100&) to deep r e d f o r the very t h i c k f i l m s The  (> 4000 X ) .  experimental c o n f i g u r a t i o n o f a l l Ag-Se t h i n  f i l m d i f f u s i o n couples i n v e s t i g a t e d i s shown.in Figure  3,2,  42  10 I  1000  l  I  960.5°  / /  900  15  20  i  _l  WEIGHT 25 30 _1_  PER CENT SELENIUM 40 50 60  '  '  L  70 _L_  60  90  i  I TWO  MELTS  -690"  l  897  s  12 (9) 840° 800  TWO MELTS 700  sr.  600  616°  -44.5(37)  500  £400  300 217° 200 128*5°  100-  0 Aq  10  20  Figure 3.1  30  40 50 60 70 ATOMIC PER CENT SELENIUM  80  90  100 S«  E q u i l i b r i u m Phase Diagram f o r Ag-Se (Hansen ), 40  Figure 3 „ 2  Ag-Se D i f f u s i o n  Couple  E v a p o r a t i o n o f the  Se across the  immediate formation o f the the Ag  s i d e o f the  evidenced by  an  in  the  compound Ag Se  on  2  During d e p o s i t i o n t h i s  was  immediate c o l o u r change ranging from b l u e f i l m s to l i g h t  A white d i f f u s i o n zone was  face A ( f i g u r e  step r e s u l t e d  intermetallic  couple.  purple f o r very t h i n Se films,  Ag  3.2)  grey f o r t h i c k  observed at the  immediately a f t e r the  Se  inter-  sample was  re-  's  moved from the  vacuum chamber.  zone proceeded r a p i d l y  The  at room temperature (21  a p l a n a r phase boundary i n t e r f a c e Se,  The  interface  was  l o n g ageing time (750 3.2 3.2,1  Diffusion  growth o f the  +_ 3°C)  advancing i n t o the  pure a  hours),  Kinetics  Growth Rate diffusion  of a f u n c t i o n ^ t i m e i s shown i n Figure 3,3, is plotted  against  /F and  the  zone width x  as  In Figure 3.4,  x  l i n e a r dependence i l l u s t r a t e s  •  the  •  phase boundary motion obeys the  where K i s the the  with  seen to remain p l a n a r even a f t e r  A t y p i c a l p l o t o f the  that  diffusion  d i f f u s i o n rate, constant.  d i f f u s i o n zones measured i n the  this parabolic parabolic  behaviour.  As  parabolic  law  d i s c u s s e d i n the  fromtr= 0 to t = 4 hours. the d i f f u s i o n zone and  The  =Kt  diffusion  exhibited  "Introduction" control.  s e r i e s o f photographs i n Figure 3.5,  an o p t i c a l microscope, shows the  x  V i r t u a l l y a l l of  Ag-Se system  growth i s c h a r a c t e r i s t i c o f The  9  made on  growth of the Ag Se phase 2  white- band appearing between  the Ag-Se r e g i o n of the  diffusion  Figure 3 . 5  Growth o f a D i f f u s i o n Zone  i n Ag-Se  (x!88)  48  couple  has  discussed  been c a l l e d  a "white  Zone"„  This region w i l l  i n t h e A p p e n d i x where i t i s shown t h a t the  zone"  i s o f no  3,2,2  Effect  significance  i n the l a t e r a l  o f Se T h i c k n e s s  Figure  3,6  on t h e  shows a s e r i e s  f o r Ag-Se d i f f u s i o n  couples  Rate  "white  diffusion  process,  Constant  o f x versus  i n which the  be  /t" p l o t s  Se t h i c k n e s s  ranged  o from  0 t o 1300  A,  In every  served i n d i c a t i n g  diffusion  rate  determined  c o n s t a n t , K,  samples  i n which t g  was  e  case  control. from  varied  The be  (t^g/t^)  reason  w  a  S  s  r e a  '  The than  t e r  f o r e x c l u d i n g samples  d i s c u s s e d i n the next These r e s u l t s  rises  ^ cm /sec. 2  to the that 90  the  times  appears also  value  diffusion  t o 170  3,5  Te  constant  A*,  found  rate  above 2 00  the  1,1  o f Ag  to  Se  i n a l l these  Se  i n the o t h e r t h r e e  observed.  samples.  <  w  -^  1 1  t h i c k n e s s regime  a constant  20 0 A*, t h e  A,  value  rate  I t appears,  curve  constant  a genuine e f f e c t  v a l u e s was  ratio  of  constant  a maximum a t a b o u t 15 0 A then o  s y s t e m s a much l a r g e r  of  0 t o 2 2 60 X i s p l o t t e d  show t h a t i n t h e  T h i s maximum i n t h e  t o be  the  growth k i n e t i c s  r a t e i s enchanced i n the  g r e a t e r than  ob-  section.  Between 0 and  s h a r p l y to reach  3,7  i n which ^ A g ^ s e  20 0 t o 2260 ft, t h e r a t e c o n s t a n t has 1,1x10  g r o w t h was  In F i g u r e  the  from  as a f u n c t i o n o f Se t h i c k n e s s . thickness  parabolxc  drops  therefore,  t h i c k n e s s regime  attains  a value  rate constant  value  only and  s i n c e s i m i l a r p e a k s were systems i n v e s t i g a t e d ,  difference  between peak and  and  in  the  constant  0,0  1,0  2.0  .3.0 / t (/hrs) -  F i g u r e 3.6  E f f e c t o f Se Thickness on Growth Rate  4.0  o o OoQfe°o  o o ° I  X  _u  0 100 200  400  600  F i g u r e 3/7  o  oo  o 800  1000  X  1200 t  o (A)  o  1400  X  1600  x  1800  2000  Rate Constant a§ a F u n c t i o n o f Se Thickness  o  2200  2400  3,2.3  The S t r u c t u r e o f Se Films A suggested e x p l a n a t i o n o f the f a s t e r d i f f u s i o n r a t e  at low Se t h i c k n e s s i s t h a t a d i s p r o p o r t i o n a t e number o f h i g h d i f f u s i v i t y paths are present  i n these  films.  An e l e c t r o n  microscopy study o f very t h i n Se f i l m s was c a r r i e d out to see i f , i n f a c t , h i g h - d i f f u s i v i t y amorphous  channels d i d e x i s t i n the  Se f i l m s . Although the general  growth stages o f a t h i n  film  have been w e l l documented f o r such metals as Au and Ag (see I n t r o d u c t i o n , page 21) , no s p e c i f i c reference to Se c o u l d be found i n the l i t e r a t u r e . I n i t i a l l y , t h i n Se f i l m s o between 50 and 300 A were examxned by t r a n s m i s s i o n e l e c t r o n microscopy both a t room temperature and l i q u i d n i t r o g e n temperature u s i n g the microscope c o l d stage. In the t h i c k n e s o range 50 t o 90 A the Se f i l m s appeared t o c o n s i s t o f massive, disconnected  i s l a n d s with some tendency t o be c o a l e s c e d at o  higher thicknesses  (~ 100 A ) ,  There appeared to be no  m a t e r i a l present between the i s l a n d s , however.  Cr-shadowed  carbon r e p l i c a s were then made o f the same Se f i l m s observed by t r a n s m i s s i o n e l e c t r o n microscopy. o showed that at t  Q  E l e c t r o n micrographs  = 5 0 A, the Se f i l m c o n s i s t e d o f l a r g e  i s l a n d s 2000 to 5000 % i n diameter with a f i n e  inter-island  s u b s t r u c t u r e i n evidence.  o f the l a r g e  At 90 A" coalescence  Se i s l a n d s had begun and the s u b s t r u c t u r e between the i s l a n d s was w e l l d e f i n e d , o  T h i s inter-network  to be about 30 A t h i c k . mission  l a y e r was c a l c u l a t e d  F i g u r e 3,8 shows both the t r a n s -  and r e p l i c a e l e c t r o n microscopy r e s u l t s  f o r very  52  o  (5) 300 A Se f i l m ( t r a n s m i s s i o n ) Figure  3,8  (6) Cr-shadowed glass surface ( r e p l i c a )  S t r u c t u r e o f Se Films  t h i n Se f i l m s .  In both cases  the s i z e o f the Se aggregates  i s e q u i v a l e n t i n d i c a t i n g that the i s o l a t e d i s l a n d s i n the t r a n s m i s s i o n micrographs are not the r e s u l t o f m e l t i n g by the e l e c t r o n beam and t h a t the m i c r o s t r u c t u r e f i l m s i s not i n f l u e n c e d by the s u b s t r a t e carbon).  Also shown i n Figure  (glass  o f the Se versus  3,8 i s an e l e c t r o n micro-  graph o f a Cr-shadowed r e p l i c a o f a g l a s s s u r f a c e .  The  absence o f any f i n e s t r u c t u r e i n d i c a t e s t h a t the substructure seen i n the Se r e p l i c a s i s due s t r i c t l y to the s t r u c t u r e o f the Se f i l m and not t o i r r e g u l a r i t i e s on the glass subo . strate.  The micrograph o f a 300 A Se f i l m c h a r a c t e r i z e s  continuous  Se f i l m s ;  the l a r g e i s l a n d s present  the e a r l y growth stages  during  are f a i n t l y v i s i b l e w i t h i n the  amo rpho us mate r i a l , The  e f f e c t o f a very t h i n Se f i l m p o s s e s s i n g a  s t r u c t u r e l i k e that shown i n Figure  3,8(4) on the d i f f u s i o n  zone i n t e r f a c e i s shown i n the s e r i e s o f o p t i c a l micrographs o i n Figure  3,9,  Up to 150 A the phase boundary i n t e r f a c e  c o n s i s t s o f many minute p r o j e c t i o n s suggesting f o r d i f f u s i o n to proceed s l i g h t l y i s l a n d channels,  f a s t e r i n the i n t e r -  A c a l c u l a t i o n o f the wavelength o f the  i n t e r f a c e f l u c t u a t i o n s made from F i g u r e s shows t h a t i t i s approximately approximately  the tendency  3,9 ( 1 ) , ( 2 ) , o  (3)  3000 to 5000 A which i s  the same as the p a r t i c l e s i z e i n d i c a t e d i n the  e l e c t r o n micrographs. 3,9 (4) where t  By c o n t r a s t the i n t e r f a c e i n Figure o  = 900 A i s very p l a n a r .  t h i s t h i c k n e s s i s continuous  having  The Se f i l m at  the m i c r o s t r u c t u r e  54  Ag Se — » > Se 2  F i g u r e 3„9  Ag Se 0  Appearance o f Phase Boundary a t V a r y i n g Se T h i c k n e s s  J  > Se  55 shown i n Figure 3.8 ( 5 ) . The e l e c t r o n microscope f i l m s l e a d t o the suggested 3.10.  Enfchanced  r e s u l t s on very t h i n Se  growth sequence shown i n Figure  short c i r c u i t  d i f f u s i o n occurs mainly i n  the network stage o f growth when the i n t e r - i s l a n d subs t r u c t u r e i s very t h i n but s t i l l  continuous.  The s u b s t r u c t u r e  p a r t o f the f i l m i s l i k e l y a r e g i o n o f h i g h d i s o r d e r c o n t a i n i n g a l a r g e number o f g r a i n boundary-like r e g i o n s . D i f f u s i o n i n the s u b s t r u c t u r e i s probably analogous to 18 g r a i n boundary d i f f u s i o n .  In terms o f F i s c h e r ' s model  (Figure 3,11) the i n t e r i s l a n d f i l m would correspond t o a g r a i n boundary although, o f course, i t i s very much wider. The l a r g e i s l a n d s would be e q u i v a l e n t to bulk m a t e r i a l .  Even  though g r a i n boundary d i f f u s i o n i n bulk metals i s about 10 times g r e a t e r 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 g r a i n boundary i n t o  the l a t t i c e e s s e n t i a l l y "damps" the f a s t e r d i f f u s i o n  process  t a k i n g p l a c e i n the boundary, 3,2,4  E f f e c t o f Thickness Ratio on the Rate  Constant  F i g u r e s 3,12 and 3.13 show the e f f e c t o f the r a t i o of Ag t o Se on the r a t i o constant f o r Se f i l m s g r e a t e r than o 200 A t h i c k . I t can be seen t h a t below a r a t i o o f 1,1, the d i f f u s i o n r a t e constant i s zero while at values o f ^ A g ^ S e g r e a t e r than 1.1, the r a t e constant tends t o a constant —8 value o f 1,1x10  2 cm /sec.  The value o f 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  <ogo  (  \(\r\f  r  \r\r\l  i  0  Pre-coalescence stage i s o l a t e d i s l a n d s of amorphous m a t e r i a l  Coalescence stage: 2. some i s l a n d s begin to j o i n  o < 50 A  50-90 A  0  Network stage: l a r g e coalesced 3. i s l a n d s and i n t e r i s l a n d substructure  4,  Channel and hole stage: i n t e r - i s l a n d sub-structure i n 150-180 A creases i n t h i c k n e s s ,  Continuous amorphous film.  Figure  3.10  90-150 A  Stages i n the Formation o f a Continuous Amorphous Se Film.  o > 180 A  57  Grain  Figure  3.11  F i s c h e r ' s Model f o r Grain Boundary D i f f u s i o n ,  Boundary  250 — •  200  150  —  100  o  50  0  ^-  1 0,0  2.0  1.0 /t~ F i g u r e 3.12  t  A g S e = 1.1 / t  o  W^e  = 9.7  •  W^e  = 2.4  V'se  <_ 1.1 3.0  (/hours)  E f f e c t o f Thickness  Ratio on Growth Rate  2o  00  1 o  lo  •  50  cu cn  ®  m  fl  S o o  i i  l 00 o  •  1 i  y;  i i i  Oo 50  m <  V  c r i t i c a l r a t i o = 1„  i i Ool  0„ 5  Figure 3 13 0  lo 0  2o0  3.0  4.0  5.0  10o  Growth Rate as a Function o f Thickness Ratio  0  60  has been c a l l e d the c r i t i c a l of the c r i t i c a l  ratio  (R )° c  An  investigation  r a t i o value over a range o f Se t h i c k n e s s e s  showed t h a t I t was independent o f the absolute Se t h i c k n e s s . The  r e s u l t o f t h i s study i s shown i n Table  3,1,  TABLE 3,1  Critical  Ratio Dependence  on the Absolute  R  Se Thickness  t  c  S e  (A)  ,95-1,15  125  l . l + o l  390  MB  740  1.0 3+.1  15 70  l . l l + . l  The o r i g i n o f a c r i t i c a l  r a t i o o f Ag to Se which must be  exceeded i n o r d e r f o r d i f f u s i o n t o proceed  i s due  p r i m a r i l y to the s t o i c h i o m e t r y i n the Ag-Se o v e r l a p r e g i o n o f the d i f f u s i o n 3,2,5  couple,  T h e o r e t i c a l Determination  o f the C r i t i c a l  Consider the t h i n f i l m d i f f u s i o n in  Ratio  couple M-Y  shown  Figure 3,14 where M i s the f a s t e r d i f f u s i n g s p e c i e s .  rapidly  In  d i f f u s i n g systems such as Ag-Se a d i f f u s i o n r e a c t i o n  occurs very q u i c k l y i n the r e g i o n where Y o v e r l a p s M t o form  61  Figure 3„14  T h e o r e t i c a l D i f f u s i o n Couple  M-Y  62  a compound M^Y,  say.  Knowing the exact composition  of this  d i f f u s i o n compound i t i s p o s s i b l e to c a l c u l a t e on the of  basis  s t o i c h i o m e t r y the r a t i o o f t h i c k n e s s o f M to Y at which  the e n t i r e volume o f M w i l l be used up i n forming M Y,  When  x  t h i s occurs there i s no excess laterally.  M a v a i l a b l e to d i f f u s e 2  a u n i t area (1  Consider, now,  cm  );  critical  the  r a t i o i s the r a t i o o f t., (M t h i c k n e s s ) to t M Y (Y t h i c k n e s s ) at which the e n t i r e volume o f M i n t h i s u n i t v  area combines with a s u f f i c i e n t The molar volume (a) i s given  amount o f Y to form M Y, x  by  P a = A  (3,1)  where p = d e n s i t y and A = atomic weight i n grams/mole. In d e a l i n g with t h i n f i l m s i t i s assumed, t h e r e f o r e , that the bulk and t h i n f i l m d e n s i t i e s are e q u i v a l e n t . there w i l l be t  M  cm  3  o f M and t„ cm Y  3  o f Y,  In u n i t Neglecting  any  o  -/  volume change i n Y as M d i f f u s e s i n t o i t , the thickness r a t i o R for  any excess  c  = (t^/t )  M to be l e f t  Y  c r  area  critical  i t which must be exceeded  f o r 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 o f M r e a c t i n g to give  M^Y  Moles/cc of Y x ( t ) • +. * crit Moles o f Y r e a c t i n g to give M Y v  x  (3.2)  63 If a  M  and  and  B^,  ay are the molar volumes o f M and Y r e s p e c t i v e l y  $y  a  form MY,  r  the number o f moles o f M and Y r e q u i r e d to  e  then we may  write that 3  M  a  y  (3.3)  To  c o r r e c t f o r any volume expansion  M d i f f u s e s i n to form MY, value o f R  obtained  c  i t i s necessary  from equation  a  o r c o n t r a c t i o n o f Y as  (3,3)  to m u l t i p l y the  by the  ratio  M Y x  H  H  ajvj  ay  (3.4)  where x i s the s t o i c h i o m e t r i c r a t i o between M and Y i n the compound M Y, x and that ct MY X  y  N o t i c e t h a t the u n i t s o f 1/ot are cm /mole i s the'. a c t u a l molar volume of the compound  as d e f i n e d 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 f o r R (3,4),  c  o f 1,0 5 i s o b t a i n e d u s i n g equations  (3,3)  and  This i s i n good agreement w i t h the observed e x p e r i -  mental value o f 1,1  +_ d a  The  t h e o r e t i c a l and experimental  c l o s e agreement between  values o f R  c  found  i n Ag-Se  appeared to j u s t i f y the a p p l i c a t i o n o f the theory to pred i c t i n g the i n t e r m e d i a t e compound formed i n the o t h e r three systems i n which more than one s t a b l e at room  temperature.  i n t e r m e t a l l i c phase i s  64  3,2 o 6  Temperature  Dependence o f the Rate Constant  The temperature dependence o f the r a t e constant f o r samples h a v i n g t<,^ > 180 A* and t ^ g ^ S e range 0-55°C was determined. r e s u l t s o f the study.  >  l  o  1  ^  n t  n  e  temperature  F i g u r e s 3.15 and 3.16 show the  The upper l i m i t o f the temperature  range was kept below 60°C s i n c e Se f i l m s heated above t h i s temperature became aggregated*.  The A r r h e n i u s - t y p e e x p r e s s i o n  o b t a i n e d f o r the r a t e constant K from Figure 3,15 was  K = 67 exp[F  ] RT  To see i f the d i f f u s i o n process i n t h i n comparable  f i l m s was  to t h a t which occurs i n bulk couples, the d i f -  f u s i o n r a t e constant was measured a t 50, 100, and 130°C in  bulk d i f f u s i o n couples o f Ag and c r y s t a l l i n e Se,  diffusion  r a t e s i n t h i s system are c o n t r o l l e d  f u s i o n o f s i l v e r through the c r y s t a l l i n e kg^Se  Since  by the d i f diffusion  zone, the use o f c r y s t a l l i n e Se r a t h e r than the amorphous m a t e r i a l should not have a f f e c t e d the r e s u l t s .  Some  couples were made u s i n g 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  *N0TE:  short  The f a l s e o r i g i n i n the 3°C t e s t was due t o the i n c l u s i o n o f the white zone width i n the d i f f u s i o n zone width. T h i s was necessary because t h e exact s t a r t o f the d i f f u s i o n zone was not w e l l d e f i n e d i n t h i s specimen,  67 a n n e a l i n g times temperature  (2-4 h o u r s ) .  The r e s u l t s o f the bulk  study are p l o t t e d i n F i g u r e 3.17  the t h i n f i l m data.  along with  From t h i s graph the temperature  de-  pendence o f the r a t e constant f o r bulk couples i s found to be  K = 24 expC-iZl - -] 0 0  RT  The l a r g e d i f f e r e n c e i n growth r a t e s between bulk and f i l m couples  (about 3 orders o f magnitude) and the  thin  difference  i n a c t i v a t i o n e n e r g i e s i m p l i e s that the d i f f u s i o n mechanism i s not the same. I t would seem l i k e l y t h a t some form o f s h o r t circuit  d i f f u s i o n process i s o p e r a t i v e i n t h i n f i l m s which  r e s u l t s i n a lower a c t i v a t i o n 3,3  Electron  energy,  Microscopy  The advance o f the Ag^Se phase boundary was served d i r e c t l y i n the e l e c t r o n microscope. appeared  The  ob-  interface  to be q u i t e p l a n a r even at h i g h m a g n i f i c a t i o n and  i t s motion was diffusion  rapid.  zone was  i t s e l f was  Although the Se f i l m i n f r o n t o f the  amorphous i n n a t u r e , the d i f f u s i o n  zone  c r y s t a l l i n e with elongated or columnar g r a i n s  a l i g n e d p a r a l l e l to the i n t e r f a c e growth d i r e c t i o n . Figure 3.18  shows a s e r i e s o f e l e c t r o n micrographs  made of  the moving phase boundary as i t swept across the f i e l d o f view,  The elapsed time between micrographs  t h i s f i g u r e was  about 4 minutes.  1 and  This f i g u r e  3 in  illustrates  68  one o f the major d i f f i c u l t i e s encountered i n the e l e c t r o n microscopy o f Se f i l m s ;  namely, that the h e a t i n g o f the  f i l m by the e l e c t r o n beam i s s u f f i c i e n t to produce g a t i o n o f the Se, was  aggre-  In photographing the moving i n t e r f a c e i t  i m p o s s i b l e to prevent a g g r e g a t i o n even when very low  i l l u m i n a t i o n l e v e l s were used.  Aggregation o f the Se  accounts f o r the minute b l a c k specks seen i n the micrograph o f Figure 3,18,  The white areas i n 3,18  ( 2 ) , (3) appear  a f t e r the e l e c t r o n beam induces a l o c a l i z e d temperature i n crease and are probably d e p l e t e d r e g i o n s produced by Se aggregation or r e - e v a p o r a t i o n . T h i s e x p l a n a t i o n i s subs t a n t i a t e d by the c o i n c i d e n c e o f the white areas i n Figure 3.18  (2) and 3,18  (3).  The g e n e r a l appearance o f the d i f f u s i o n zone phase boundary F i g u r e 3,19,  and  i n t e r f a c e at h i g h m a g n i f i c a t i o n i s shown i n The major c o n t r i b u t i n g f a c t o r to the c o n t r a s t  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 t h i c k n e s s r e s u l t i n g from v o l u m e t r i c expansion.of the Se when Ag d i f f u s e s i n to form Ag^Se,  The volume  change brought about i n t h i s case i s about 5 7%.  I t should  a l s o be p o i n t e d out that t h i s v o l u m e t r i c expansion causes the d i f f u s i o n zone to become q u i t e rumpled and and to become p a r t i a l l y strate.  distorted  detached from i t s u n d e r l y i n g sub-  Evidence o f t h i s d i s t o r t i o n i s p r o v i d e d by the  l a r g e number o f bend and t h i c k n e s s contours seen i n Figure 3.19  (a),  A f u r t h e r c o n t r i b u t i o n to c o n t r a s t between the  71  (b)  Phase Boundary interface showing elongated grains i n the diffusion zone  Figure 3.19  Diffusion Zone i n Ag-Se  72 diffusion  zone and  pure Se may  be  the  o f Ag  and  large difference  in  44  atomic s c a t t e r i n g  factors  Se.  S e l e c t e d area d i f f r a c t i o n p a t t e r n s were made o f the  diffusion  zone.  spacings c a l c u l a t e d agreement w i t h the  Subsequent analyses showed t h a t the from the  known d-spacings o f  temperature m o d i f i c a t i o n . of d i f f r a c t i o n  composition o f the  was  electron  B-Ag2Se, the  low  shows a t y p i c a l  microscopy r e s u l t s  diffusion  zone to be  d i r e c t o b s e r v a t i o n of the  in i t s e l f interesting,  little the  Figure 3.20  were i n good  set  results.  While the  while the  pattern rings  d-  i s known about the  enabled  determined  the  and  moving phase boundary  p a r t i c u l a r l y since r e l a t i v e l y actual  results provided l i t t l e  motion of phase boundaries,  i n f o r m a t i o n concerning  mechanism f o r d i f f u s i o n i n Ag-Se,  the  73  (a)  S,A.D, o f d i f f u s i o n zone i n an Ag-Se t h i n f i l m couple  Calculated  o d-spacings (A) 7,25 4, 32 3.76 3. 42 2 . 84 2, 76 2.66 2.20 2.10 2.04 1. 84 1, 77  Figure  3,20  (b)  Au Standard  o d-spacings f o r 3-Ag Se (A) 2  _ _  4.15 3. 77 3. 30 2.89 2. 72 2,67 2.57 2.23 2.11 2.07 2,00 1, 87 1, 82  S e l e c t e d Area D i f f r a c t i o n o f D i f f u s i o n Zone  Pattern  74  CHAPTER 4  LATERAL DIFFUSION IN Cu-Te  4„1  Introduction The e q u i l i b r i u m phase diagram f o r Cu-Te i s shown  i n F i g u r e 4.1.  U n l i k e Ag-Se, i n which o n l y one  intermetallic  phase i s t h e r m a l l y s t a b l e at room temperature, Cu-Te has at least  3 p o s s i b l e s t a b l e phases at room temperature.  main i n t e r m e t a l l i c compounds are Cu2Te, Cu x~0.6 out  (Cu^'Te^), and CuTe,  2  x  Te  In a d d i t i o n H a n s e n  the p o s s i b l e e x i s t e n c e o f a phase  l i e s at about 36-3 7. a t . % Te.  The  with  40  (X) whose  has p o i n t e d composition  I t i s shown i n s e c t i o n 4.3  that the d i f f u s i o n o f copper along a Te f i l m  results  i n the formation  T h i s phase  o f o n l y one phase, Cu  Te. z —x  0  v  has a defect s t r u c t u r e o f the Cu Sb type ( t e t r a g o n a l ) and 2  undergoes  a polymorphic t r a n s f o r m a t i o n  at about  367°C.  The phase diagram i n d i c a t e s t h a t C u _ T e ranges i n compo2  s i t i o n from C.u^ 3 5  T e  to Cu-^ ^ T e  x  so t h a t 0.59  < x >  0.65.  At temperatures below the m e l t i n g p o i n t Te has a 42 4 3 s t a b l e hexagonal form  '  ,  The s t r u c t u r e i s h i g h l y an-  i s o t r o p i c due to d i f f e r e n t bonding p e r p e n d i c u l a r p a r a l l e l to the c - a x i s .  and  This a n i s o t r o p y i s r e f l e c t e d i n  75  10  0  Cu  20  30  J  I  10  F i g u r e 4.1  WEIGHT PER CENT TELLURIUM 50 60 70 60  40  20  J  30  _l  ,  I  .  L  40 50 60 70 ATOMIC PEA CENT TELLURIUM  90 L  80  90  E q u i l i b r i u m Phase Diagram o f Cu-Te (after Hansen ) 40  100 T«  76  both the l i n e a r expansion c o e f f i c i e n t , which i s negative p a r a l l e l t o the  c - a x i s , and p o s i t i v e p e r p e n d i c u l a r 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 a t t a i n s a value twice as great i n the p a r a l l e l d i r e c t i o n as i n the Figure 4.2  a  perpendicular.  i s a s e l e c t e d area d i f f r a c t i o n p a t t e r n made on  a pure evaporated Te t h i n f i l m .  The  d-spacings c a l c u l a t e d  from t h i s p a t t e r n are i n good agreement with the known dspacings nature  f o r hexagonal Te.  crystalline  o f a l l Te f i l m s encountered i n t h i s work, the r e -  s u l t s obtained to those 4.2  Because o f the  i n Cu-Te, although  f o r Ag-Se, w i l l be  completely  analogous  d i s c u s s e d i n some d e t a i l .  Kinetics  4,2.1  Growth Rate F i g u r e 4.3  i s a t y p i c a l p l o t o f the  zone width as a f u n c t i o n o f o f Cu i n t o Te.  The  / t  obtained  diffusion  f o r the  diffusion  l i n e a r dependence shows a p a r a b o l i c  growth law which i m p l i e s t h a t growth i s d i f f u s i o n c o n t r o l l e d . 4.2,2.  E f f e c t o f Te Thickness F i g u r e s 4,4  and 4,5  on the K i n e t i c s  i l l u s t r a t e the e f f e c t o f Te  t h i c k n e s s on the growth r a t e f o r samples having Beyond Te t h i c k n e s s e s o f about 200  X,  has  a constant  e  value o f 2.1x10  2 cm /sec.  In  t h i n n e r f i l m s , however, the growth r a t e i s much f a s t e r -9 approaches a value o f 9x10  c  the d i f f u s i o n r a t e -9  constant  t^/t-p >R ,  and  2 cm /sec at a t h i c k n e s s of 110  Q  A.  Figure 4.2  S e l e c t e d Area D i f f r a c t i o n o f Pure Te  Patte  79  0  1.0  2,0  3.0  4.0  5.0  6.0  /t~(/hr) Figure 4,4  E f f e c t o f Te Thickness on  Kinetics  7.0  [For t  C u  /t  * 0.693, Room Temperature]  10.0  o 6> 100  200  400  600  o  7>  ° o o °  800  ±  1000  1200 t  Figure  4.5  o  o  T e  o  o  _L  _L  1400  1600  TT  O 1800  (A)  Rate C o n s t a n t as a F u n c t i o n o f Te T h i c k n e s s  2000  3200  3400  81  4.2,3  The  S t r u c t u r e o f a Te  Film  The e a r l y growth stages o f a Te f i l m before i t becomes continuous  account  f o r the apparent  peak i n the  r a t e constant versus Te t h i c k n e s s graph.  The  formation o f the Te f i l m c l o s e l y p a r a l l e l  those o f a Se  f i l m as d i s c u s s e d i n s e c t i o n  steps i n the  3,2,3, but a major d i f f e r e n c e  i s that the i s l a n d s o f Te observed i n the  pre-coalescence  stage (see page 25 o f I n t r o d u c t i o n ) are randomly o r i e n t e d o c r y s t a l l i t e s about 200 A i n diameter r a t h e r than the l a r g e o (2000 - 5000 A diameter) films,  amorphous i s l a n d s observed  A t r a n s m i s s i o n e l e c t r o n microscopy  the m i c r o s t r u c t u r e o f Te f i l m s 50 - 1200 out.  i n Se  i n v e s t i g a t i o n of  X t h i c k was  The r e s u l t s o f t h i s study, shown i n Figure 4,6,  carried suggest  t h a t enhanced d i f f u s i o n occurs when the Te f i l m i s i n the network and channel stages o f growth. o regime, between 90 and 130  In t h i s t h i c k n e s s  A, the Te f i l m c o n s i s t s o f  c o a l e s c e d i s l a n d s with a h i g h l y d i s o r d e r e d i n t e r — i s l a n d  net-  work, probably analogous  to g r a i n boundaries, where d i f f u s i o n  can o c c u r more r a p i d l y .  The exact mechanism i s probably  s i m i l a r to t h a t which occurs i n Ag-Se as d i s c u s s e d i n section  3,2,3.  F i l m c o n t i n u i t y and the onset o f a d e f i n i t e o g r a i n s t r u c t u r e i s seen at about 200 A and p e r s i s t s up to o the t h i c k e s t f i l m s t u d i e d - 1200 A, The m i c r o s t r u c t u r e o f o Te f i l m s g r e a t e r than 400 A t h i c k c l o s e l y resembles that o f o bulk m a t e r i a l except t h a t f i l m s between 400  and  c h a r a c t e r i z e d by numerous t h i c k n e s s contours.  900 A are  82  Figure 4,6  The Growth of a Te Thin Film  83 4,2.4  Critical  Ratio  F i g u r e 4.7  shows a p l o t o f the room temperature  dif-  f u s i o n r a t e constant as a f u n c t i o n o f the r a t i o o f Cu to Te o thickness  f o r couples i n which t ^  (t(-. /tn[- ) u  e  f i g u r e i n d i c a t e s t h a t the c r i t i c a l r a t i o is, of  when ^ c u ^ T e -9  >  u,,  about 2.1x10  does not occur.  63 2  (R )  d i f f u s i o n proceeds  c  theoretical  A.  This  i s 0.63;  that  at a constant  cm /sec while f o r t ^ / t ^ , The  > 180  < 0.63,  values o f R  Q  rate  diffusion  f o r each o f the  three i n t e r m e t a l l i c phases i n Cu-Te were c a l c u l a t e d u s i n g the methods o u t l i n e d i n s e c t i o n  3.2.5,  Table 4.1  t h e o r e t i c a l values f o r each phase.  l i s t s the  From t h i s i t would appear  t h a t the growing phase should have the composition w i l l be d i s c u s s e d i n s e c t i o n 4.3, diffusion  zone was  positively  f r a c t i o n a n a l y s i s as Cu2_ Te. x  C^Te.  As  the phase forming i n the  i d e n t i f i e d by e l e c t r o n The  thickness r a t i o i s i n e r r o r i n t h i s  reason why system  dif-  the c r i t i c a l  i s uncertain,  s i n c e the technique y i e l d e d e x c e l l e n t r e s u l t s i n the o t h e r systems i n v e s t i g a t e d .  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 a b s o l u t e t h i c k n e s s o f the Te f i l m Table 4.2)  and so i s independent  a c t u a l percentage  (see  o f the f i l m s t r u c t u r e .  e r r o r i s f a i r l y small (~  perhaps unfortunate i n t h i s system  30%) and  t h a t the three  The  i t is  inter-  m e t a l l i c compounds occur at f a i r l y e q u i v a l e n t compositions.  (t  T e  o 180>A, Room Temperature)  4. 00  <o 3,00  W^e Figure 4,7  Rate Constant as a Function o f Thickness  Ratio  00  85  TABLE 4,1  R  c  f o r Intermetallic  Phases i n Cu-Te  Phase Cu-Te  0, 35  Cu _ Te  0,47  Cu Te  0,63  2  2  x  86  TABLE 4.2  Critical  Ratio as a Function  o f Absolute  Te Thickness  t (X) T e  4,2.5  0.58-0.70  270  0.66+0.1  800  0.6 2 + 0.1  3350  0.63+0.1  5000  Temperature Dependence o f the Rate The  temperature dependence o f the r a t e constant f o r  f i l m couples h a v i n g t termined  Constant  T e  > 180 A* and t £ / t U  over the range 0-100°C.  l e s s aggregated  T e  > R  c  was de-  Since Te tends t o be f a r  on a g l a s s s u b s t r a t e than does Se  , i t was  p o s s i b l e t o extend the temperature range o f i n v e s t i g a t i o n i n both Cu-Te and Ag-Te up to 10 0°C without aggregation problems. obtained.  encountering  Figure 4,8 shows the Arrhenius  plot  From t h i s graph the dependence o f the d i f f u s i o n  r a t e constant on temperature was found t o be K = .0017 e x p [ - I £ H ] RT A l s o shown i n Figure 4,9 i s the Arrhenius p l o t o b t a i n e d by  .250  ,270  ,290 100 7T  Figure  4,8  Arrhenius  .310  (0 -1) K  Plot  f o r Cu-Te  .330  .350  Figure  4„ 9  C o m p a r i s o n o f B u l k to T h i n T e m p e r a t u r e Dependence  Film  89 "I  Parkinson  C  f o r Cu-Te t h i n films«  His r e s u l t s gave  K = .0755 e x p [ RT  1 0 0 0 0  i n the temperature two  range 0-105°C.  The  3  agreement between the  s e t s o f r e s u l t s i s somewhat d i s a p p o i n t i n g s i n c e b a s i c a l l y  the same technique was  used i n both i n s t a n c e s .  It i s f e l t  that the r e s u l t s o b t a i n e d i n the present i n v e s t i g a t i o n probably more r e l i a b l e temperatures  are  s i n c e a more complete range o f  has been used and the e f f e c t s o f t h i c k n e s s  r a t i o and Te f i l m t h i c k n e s s have been p r o p e r l y F i g u r e 4,9  understood.  shows an Arrhenius p l o t o f the r a t e  constant f o r growth o f Cu2_ Te i n bulk Cu-Te couples as found 45 46 by Wayman and Bennett , Sanderson, St. John, and Brown x  T h i s system i s one compressive  i n which d i f f u s i o n i s s e n s i t i v e to any  s t r e s s a p p l i e d to the d i f f u s i o n zone.  The work  o f 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 ^ T e ,  appears  i n the d i f f u s i o n zone i n a d d i t i o n to  Cu2_ Te and Cu-Te, i f the magnitude o f the a p p l i e d s t r e s s x  i s great enough. tected. ^ 2-x u  T e  At zero . a p p l i e d s t r e s s C ^ T e  i s not  de-  In the t h i n f i l m couples s t u d i e d , o n l y the phase w  a  s  e  v  e  r  present.  The  absence o f any  Cu Te 2  indi-  cates t h a t the t h i n f i l m couples were comparable to bulk couples at "zero p r e s s u r e " . between the temperature Cu  0  Therefore, a v a l i d  comparison  dependence o f the growth r a t e s o f  Te i n bulk and t h i n f i l m s can be made. I f the Arrhenius p l o t f o r bulk specimens i n Figure  90 4.9  i s compared t o the t h i n f i l m curve, i t can be seen that  although the a c t i v a t i o n e n e r g i e s are q u i t e d i f f e r e n t , the d i f f u s i o n r a t e constants i n bulk and t h i n f i l m couples are q u i t e comparable  i n the 300-4 50°C temperature range.  convergence o f the two  The  curves at these temperatures suggests  t h a t some short c i r c u i t d i f f u s i o n mechanism such as g r a i n boundary  d i f f u s i o n i s o p e r a t i v e at lower temperatures (see  F i g u r e 1.2).  The a c t i v a t i o n . e n e r g y p r e d i c t e d by the bulk  graph i s 150 00 cal/mole, n e a r l y twice as great as the t h i n f i l m a c t i v a t i o n energy o f 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 i n the t h i n 4.3  films.  E l e c t r o n Microscopy The advance o f a phase  boundary  along a Te  film  suggests a somewhat d i f f e r e n t p i c t u r e from that presented by the Ag-Se system due to the c r y s t a l l i n e s t r u c t u r e o f the Te, ary  As viewed by t r a n s m i s s i o n microscopy, the phase motion i s s t i l l  q u i t e r a p i d but the phase  bound-  interface in  general i s seen to be more i r r e g u l a r at h i g h m a g n i f i c a t i o n . T h i s i s i l l u s t r a t e d i n F i g u r e s 4,10  and 4.11  which show  r e s p e c t i v e l y the i n t e r f a c e motion along a Te f i l m 4 90 % o t h i c k and one o f o n l y 200 A t h i c k n e s s .  An  interesting  f e a t u r e o f the l a t t e r s e r i e s o f micrographs i s t h a t the Te film i s s t i l l  so t h i n t h a t a w e l l - d e f i n e d g r a i n s t r u c t u r e i s  not  The t o t a l e l a p s e d time between p i c t u r e s  present.  and #4 i n both s e r i e s i s about 6 minutes.  #1  A l l o f the micro-  91  (3)  F i g u r e 4,10  (4)  M o t i o n o f the C u Boundary  2  ^Te Phase  (x22,000)  92  o  Figure 4.11  Diffusion  i n t o a 200  A Te  Film  93 graphs i n d i c a t e t h a t the g r a i n s i n the d i f f u s i o n equiaxed r a t h e r than columnar as i n Ag-Se. graphs o f Figure 4,12  zone are  The micro-  are enlargements o f the phase boundary  i n t e r f a c e s o f the previous two f i g u r e s .  Figure 4.12  (b) , i n  p a r t i c u l a r , suggests that t h e r e i s some tendency f o r the advancing phase boundary to surround some o f the Te g r a i n s . T h i s 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 d e p i c t s the surrounding o f a Te g r a i n by the advancing phase boundary.  These o b s e r v a t i o n s suggest t h a t there i s a  tendency f o r g r a i n boundary d i f f u s i o n to o c c u r i n Cu-Te. The r e s u l t s o f an e l e c t r o n d i f f r a c t i o n study o f the d i f f u s i o n zone i n Cu-Te showed that only the phase Cu2_ Te was x  formed during d i f f u s i o n .  A typical  selected  area d i f f r a c t i o n p a t t e r n and the c a l c u l a t e d d-spacings o b t a i n e d from i t are shown i n Figure  4.15.  E l e c t r o n microscopy r e s u l t s on the motion o f the Cu  9  Te phase boundary suggest t h a t g r a i n boundary d i f f u s i o n  i s important i n the room temperature d i f 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 f o r  the i r r e g u l a r nature o f the phase boundary i n t e r f a c e .  The  equiaxed g r a i n s t r u c t u r e o f the d i f f u s i o n zone suggests that i t s formation may  be due t o l a t e r a l  boundaries i n t o the pure Te g r a i n s .  diffusion  from the g r a i n  Also the peak i n the o growth r a t e at a Te t h i c k n e s s o f about 110 A i s i n agreement  Figure 4,12  Phase Boundary I n t e r f a c e s at High M a g n i f i c a t i o n  Figure 4.13  The Surrounding o f a Grain o f Te by the D i f f u s i o n Zone I n t e r f a c e  96  Bend o r thickness contour  Figure  U 14 0  Schematic Sketch o f the Surrounding o f a Te Grain by the Phase Boundary I n t e r f a c e  (a)  SoAoD of diffusion t h i n f i l m couple  zone o f Cu-Te  Calculated  d-spacings  0  d-spacings (A*) 8 29 7, 82 6 0 08 3,70  f o r Cu„  2-X  Te  (h  0  3,1+2  2, 88 2,62 2,48 2d l 1„ 85 I, 76  Figure 4,15  6,05 3, 35 2. 81 2o 54 2,42 2o 07 I, 82 I, 70  S e l e c t e d Area D i f f r a c t i o n P a t t e r n o f the D i f f u s i o n Zone o f a Cu-Te Thin Film Couple  98  w i t h a g r a i n boundary mechanism.  No  quantitative  estimate  o f the r e l a t i v e r a t e s o f g r a i n boundary to volume d i f f u s i o n could be made on  the b a s i s o f the e l e c t r o n micrographs.  N e v e r t h e l e s s , the microscopy r e s u l t s provide strong to support the  evidence  i d e a that g r a i n boundary d i f f u s i o n i s an  important mechanism i n t h i n 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 i n the Ag-Te system  close-  l y p a r a l l e l e d those o f Cu-Te and f o r t h i s reason they w i l l be reviewed only b r i e f l y .  The e q u i l i b r i u m phase  diagram,  40 seen i n F i g u r e 5,1 Ag Te and Ag  phases,  Te^Cx ~ 0,2 ), may be t h e r m a l l y s t a b l e at b —X  Z  , shows that two i n t e r m e t a l l i c  ^  room temperature. The phase Ag Te undergoes a polymorphic t r a n s i t i o n between 135 and 149°C„ The low temperature 47 m o d i f i c a t i o n , S-Ag^Te , with which we are concerned h e r e , 40 2  i s r e p o r t e d by Hansen Ag  Telx -  structure,  0,2 ) , the o t h e r s t a b l e phase i n t h i s , s y s t e m ,  has a hexagonal 5,2  to possess an orthorhombic  structure,  Kinetics In a l l d i f f u s i o n zones s t u d i e d i n Ag-Te the phase  boundary  motion was found to be p a r a b o l i c .  The r a t e o f ad-  vance o f t h e i n t e r f a c e was q u i t e r a p i d - n e a r l y an o r d e r o f magnitude g r e a t e r than i n Cu-Te - and t h e i n t e r f a c e  itself  was observed t o remain very p l a n a r even when the d i f f u s i o n  100  10 I  20 l  F i g u r e 5„1  30 '  WEIGHT PER CENT TELLURIUM 40 50 60 70 l l i . L—.  80 1—|  E q u i l i b r i u m Phase Diagram o f Ag-Te ( a f t e r HanserT ) U  .  SO L-  101 zone width was  700-800 u, o A (with  For Te t h i c k n e s s e s between 50 and 180  t. / t > R ) the d i f f u s i o n r a t e constant a t t a i n e d subAg Te c s t a n t i a l l y h i g h e r values than at g r e a t e r t h i c k n e s s e s , o Between 2 00 and 1750 A the r a t e constant tended to a -8 constant value o f about 1,9x10 cm /sec. Figure 5,2 2  i l l u s t r a t e s the experimental  dependence o f the rate constant  on the Te t h i c k n e s s . 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 t h i c k n e s s e s o f 20 0 A and g r e a t e r .  This i s a much l a r g e r  e f f e c t than t h a t seen i n any o f the o t h e r three systems i n vestigated.  It  i s probably due to the network s t r u c t u r e o f  very t h i n Te f i l m s which g i v e s h i g h d i f f u s i o n r a t e s between i s l a n d s as d i s c u s s e d i n s e c t i o n 4,2,3,  Figure 5,3  shows  the dependence o f the r a t e constant on the Ag to Te  thicko  ness r a t i o  A,  critical  (t^g/trpg) f °  r a t i o was  r  found  couples  i n which t ^  to be 1,0  +_ 0,1,  c l o s e l y with the t h e o r e t i c a l value o f 1.00 given by the phase Ag Te, 2  > 180  This  The  agrees  which would be  I f A g ^ ^ T e ^ 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 c a l c u lated c r i t i c a l  r a t i o would be 0,715, i n poor agreement w i t h  the experimental  value.  that the composition  The  of the d i f f u s i o n zone was  determination o f the c r i t i c a l o of  105  results indicated, therefore,  r a t i o was  A  r a t i o at t e l l u r i u m t h i c k n e s s e s  and 2 730 A gave the same value o f 1,0  critical  Ag^Te.  +_ 0.1,  The  thus taken to be independent o f the Te  f i l m t h i c k n e s s over the t h i c k n e s s range under i n v e s t i g a t i o n .  [t  0 100 200  400  600  Figure. 5 2 0  800  1000  1200  1400  A g  /t  T e  > l , 0 , Room Temperature]  1600  1800  Rate Constant as a Function o f Te Thickness  2000  [trr. >25 0 e  i  A*, Room Temperature]  :  c r i t i c a l ratio = 1.0 0  *4  1.0  2  t  Figure 5 . 3  3  4  5  /t Ag Te A  Growth Rate as a Function o f Thickness Ratio  10.0  104  The was  temperature dependence o f the  determined i n the  p l o t shown i n Figure found to  range 0-100°C. 5,4  the  rate  From the  constant Arrhenius  d i f f u s i o n rate constant  was  be K = 0.6 3 exp  [-  10000., 3 RT 13  Also p l o t t e d i n t h i s f i g u r e i s Mohr's X = 5 79 exp  data which  [-13820] RT  Although s i m i l a r techniques were used i n the gations,  the  agreement between the two  disappointing,  gives  two  investi-  sets o f r e s u l t s i s  e s p e c i a l l y at h i g h temperatures where there  i s almost a one  order o f magnitude d i f f e r e n c e  i n the  two  measured r a t e s ,  Mohr a p p l i e d a c o r r e c t i o n to h i s growth  r a t e s to c o r r e c t  f o r volume expansion o f the Te as Ag  fused  in.  paper but  No  dif-  d e t a i l s o f t h i s c o r r e c t i o n are given i n Mohr's  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 . I t should be mentioned that which comparison was  i n the  p o s s i b l e w i t h the  two  systems i n  r e s u l t s of other  workers, agreement at high temperatures was  not  good with  the present work g i v i n g much slower r a t e s than the o t h e r i n vestigations.  It i s felt  that t h e r e can  be no  e r r o r i n the p r e s e n t i n v e s t i g a t i o n which could anything l i k e the observed d i f f e r e n c e s  i n the  experimental explain growth r a t e s .  I f there i s a genuine d i f f e r e n c e i n growth r a t e s between  105  77515  T77Q  2791)  3,10  3, 30  1000/T ( 0 - 1 ) K  Figure 5,4  Arrhenius P l o t f o r Ag-Te  3,50  3,7 0  106  between the two cases, t h i s must presumably be due t o some d i f f e r e n c e i n s t r u c t u r e s which g i v e s d i f f e r e n t c o n t r i b u t i o n s to g r a i n 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 r e s i d u a l gas p r e s s u r e s , e v a p o r a t i o n r a t e s , o r one o f the many o t h e r v a r i a b l e s which can a f f e c t structure  film  (see I n t r o d u c t i o n , s e c t i o n 1,4), 38 Behera  has shown t h a t a study o f d i f f u s i o n i n  bulk Ag-Te couples i s i m p o s s i b l e because a proper zone i s not formed.  diffusion  The bulk d i f f u s i o n r a t e p l o t t e d i n  Figure 5,4 at 13 0°C i s a very approximate value o b t a i n e d from h i s work,  A complete temperature  was not undertaken  due t o the i r r e g u l a r nature o f t h e d i f -  f u s i o n zones i n v o l v e d . energy  study i n bulk Ag-Te  However, the low value o f a c t i v a t i o n  o b t a i n e d f o r the t h i n f i l m couples does seem to i n d i -  cate t h a t some short c i r c u i t mechanism i s important i n the diffusion 5,3  process,  Electron  Microscopy  Transmission e l e c t r o n micrographs  made o f the  Ag^Te phase boundary showed t h a t g r a i n boundary d i f f u s i o n p l a y s a r o l e i n the d i f f u s i o n p r o c e s s . the boundary i n t e r f a c e i n F i g u r e 5.5  The micrograph o f  (a) shows many c o l o n i e s  o f Ag^Te l y i n g ahead o f the main d i f f u s i o n zone but connected to i t by " s t r i n g e r s " o f Ag Te centered predominantly 2  Te g r a i n boundaries.  F i g u r e 5,5  at the  (b) i s t h e same i n t e r f a c e  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)  Figure 5,5  Cd)  o Phase Boundary I n t e r f a c e i n a 210 A Te F i l m  108  at 1 minute i n t e r v a l s a f t e r 5.5  ( b ) , show how  the e f f e c t  l o c a l i z e d h e a t i n g by the e l e c t r o n beam tends t o  of  obscure  the g r a i n boundary d i f f u s i o n and makes the phase boundary i n t e r f a c e very p l a n a r .  The Te t h i c k n e s s i n t h i s s e r i e s o f  o p i c t u r e s i s about 20 0 A.  Figure 5.6  shows the phase  boundary i n t e r f a c e i n a sample having a Te t h i c k n e s s o f o about 10 0 0 A,  Once a g a i n , hg^Ze has formed i n Te g r a i n s  ahead o f the main body o f the d i f f u s i o n zone with  stringers  extending along the Te g r a i n boundaries.  micro-  graph i t appears  In t h i s  t h a t some Ag^Te c o l o n i e s have begun t h e i r  development at the g r a i n boundary c o r n e r s . tendency  This obvious  f o r g r a i n boundary d i f f u s i o n t o o c c u r i s i n f u l l  agreement with the l a r g e e f f e c t observed i n 80-100 %. f i l m s i n t h i s system.  I t i s probably due to a very l a r g e g r a i n  boundary d i f f u s i o n c o e f f i c i e n t i n t h i s system.  The  grain  boundary e f f e c t s i n Ag-Te are much more pronounced than those i n Cu-Te, which probably accounts growth r a t e s observed  f o r the h i g h e r  i n Ag-Te.  S e l e c t e d area d i f f r a c t i o n p a t t e r n s were made o f the d i f f u s i o n zone o f Ag-Te couples.  The  d-spacings  c u l a t e d were i n good agreement with the known for  g-Ag^Te,  the low temperature  cal-  d-spacings  form o f Ag2Te.  s u b s t a n t i a t e s the k i n e t i c evidence i n s e c t i o n 5.2  This for  growth o f Ag^Te r a t h e r than A g ^ ^ T e ^ on the b a s i s o f  agree-  ment between experimental and t h e o r e t i c a l values o f the critical ratio.  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 r e s u l t o f an experiment i n  which h i g h i l l u m i n a t i o n l e v e l s were used i n the e l e c t r o n microscope and the beam was f o r a r e l a t i v e l y l o n g time; phase Ag,.  Te  diffusion  (x - 0,2)  focused on the Ag Te i n t e r f a c e 2  a t h i n band o f the T e - r i c h  appeared at the edge o f the normal  zone and began to grow i n t o the Te at a r a p i d  r a t e due to h e a t i n g by.the e l e c t r o n beam.  This  inter-  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 s e l e c t e d area d i f f r a c t i o n pattern.  The m i c r o s t r u c t u r e o f the Ag Te phase 2  i n the main body o f 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 F i g u r e 5,8 o 200 A,  (b),  The Te t h i c k n e s s i n t h i s sample i s about  The exact temperature i n c r e a s e induced by the  e l e c t r o n beam spot i n such a small l o c a l i z e d area i s i m p o s s i b l e to measure.  I t i s t o be expected, however,  t h a t i f the appearance o f t h i s second phase  during d i f f u s i o n  were due t o thermal e f f e c t s a l o n e , a second phase would  be  observed i n t h i n f i l m couples annealed at h i g h temperatures. Since t h i s second phase was not p r e s e n t i n the d i f f u s i o n zones o f samples heated up t o 100°C, i t i s concluded t h a t e i t h e r the e f f e c t i v e temperature r i s e produced by beam h e a t i n g was was  g r e a t e r than 100°C, o r the growth o f the phase  not e n t i r e l y due t o thermal e f f e c t s . The e l e c t r o n microscopy r e s u l t s suggest that  boundary  grain  d i f f u s i o n i s an important f a c t o r i n room temperature  d i f f u s i o n i n Ag-Te,  As the e l e c t r o n beam b r i n g s about a  Ill  (a) S.A.D. o f d i f f u s i o n zone i n Ag-Te  Calculated d-spacings (A*) 7  0  1 4  60  85  4o  60  3.  71  (b) Au Standard  d- spacings for  e-Ag Te (A) 2  7 d 4  4 , 5 3 3.  74  3 o 4 0 3 . 1 9 3 o 0 1 2 .  88  2 o 7 3  3 d 9 3.  01  2 .  87  2 .  80  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 D i f f u s i o n Zone i n Ag-Te  (a)  Ag beam  (b)  Figure  (x ~ 0 . 2 )  induced by e l e c t r o n  heating  Appearance o f Ag Te phase i n t h i s  5,8  sample  E l e c t r o n Beam Heat-Induced Second Phase i n Ag-Te  113  localized  temperature i n c r e a s e at the phase boundary  face the g r a i n boundary  inter-  d i f f u s i o n i s obscured by r a p i d ad-  vance o f an i n t e r f a c e that has become i n c r e a s i n g l y p l a n a r as the temperature rose.  This implies that grain  d i f f u s i o n i s not important a t h i g h e r temperatures.  boundary Since  the presence o f a second phase was not detected d u r i n g normal d i f f u s i o n experiments at 100°C, i t i s conceivable t h a t the e l e c t r o n beam h e a t i n g produced by h i g h i l l u m i n a t i o n l e v e l s r e s u l t s i n a temperature r i s e o f g r e a t e r than 100°C.  114  CHAPTER 6  LATERAL DIFFUSION IN Cu-Se  6,1  Introduction A complete e q u i l i b r i u m phase  a v a i l a b l e f o r Cu-Se,  The three  diagram i s not y e t  intermediate  phases  that  can be i n thermal e q u i l i b r i u m at room temperature are 40 Cu _ Se 2  x  (0.0 < x < 0,2), C u S e , and CuSe 3  .  ?  copper d e f i c i e n t form o f the s t o i c h i o m e t r i c compound Cu Se (33,3 at % Se), 2  polymorph  The high  Cu _ Se i s a 2  x  intermetallic  temperature  o f t h i s phase has an anti-isomorphous CaF  i n which Se atoms r e p l a c e stoichiometry  Ca atoms.  i n Cu Se i n c r e a s e s , 2  structure  2  As the d e v i a t i o n  the  from  transformation  temperature decreases, so t h a t the c u b i c s t r u c t u r e  becomes  s t a b l e at room temperature.  compo-  At the s t o i c h i o m e t r i c  s i t i o n , however, the t r a n s f o r m a t i o n 10 0°C,  temperature i s around  Below t h i s temperature, a number o f metastable  t e t r a g o n a l o r B.C.C, s t r u c t u r e s the h e a t i n g  are encountered depending on 40 ,48,49  and c o o l i n g h i s t o r y  ,  low temperature s t r u c t u r e i s not known, has a t e t r a g o n a l  structure.  The t r u l y CUgSe  There i s a strong  that t h i s phase i s a g r o s s l y d e f e c t i v e C u  u  Se  stable  2  possibility compound  115  o n l y approximating Cu.gSe2 i n composition.  CuSe has a hexa-  gonal s t r u c t u r e , 6.2  Kinetics  6.2,1  Growth Rate The  graph o f d i f f u s i o n zone width  o f /t f o r about  (x) as a f u n c t i o n  85% o f a l l d i f f u s i o n couples s t u d i e d was  the form o f curve I i n Figure 6.1,  of  Most o f the remaining  15% e x h i b i t e d the behaviour o f curve I I i n t h i s  figure  with o n l y a small f r a c t i o n b e i n g s t r i c t l y p a r a b o l i c i n nature (curve I I I ) , The e s s e n t i a l f e a t u r e s o f curves I and I I are i l l u s t r a t e d i n F i g u r e 6,2.  The  /T i n each "stage" o f both curves was that growth was  diffusion controlled.  dependence o f x on l i n e a r suggesting The b a s i c  difference  between curves I and I I i s t h a t stage 2 i n the l a t t e r i s much s h o r t e r , degenerating i n t o stage 3, a r e g i o n o f more r a p i d growth.  I t should be emphasized  t h a t the p h y s i c a l  i m p l i c a t i o n o f 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 i n about one hour, then f o l l o w s .  T h i s may  suggests or may (curve I I ) ,  A p e r i o d o f slower p a r a b o l i c growth p e r s i s t over a long time as curve I  be f o l l o w e d by a p e r i o d o f r a p i d growth  Such behaviour may,  at f i r s t  glance, appear  to be due t o the formation o f a second phase d u r i n g d i f fusion.  However, no evidence o f more than one phase  ever seen by o p t i c a l microscopy.  was  Therefore t h i s explana-  x(u)  /t~~(/hr) F i g u r e 6,1  T y p i c a l Room Temperature K i n e t i c s  Plots H H  CD  117  (a)  Curve I  Figure 6 2 0  (b)  Curve I I  General Form o f M a j o r i t y o f Growth Plotso  118 tion  does not account  f o r the observed  behaviour,  A d i f f u s i o n r a t e constant was c a l c u l a t e d  from  each o f the l i n e a r r e g i o n s o f both types o f curves I and II.  I t was found t h a t i n stage 1, the r a t e constants were  widely v a r i a b l e b e a r i n g no apparent thickness or thickness r a t i o . determined  r e l a t i o n s h i p t o Se  S i m i l a r l y , the r a t e constants  i n stage 3 showed a l a r g e degree o f s c a t t e r ,  although the magnitudes o f the slopes were o f course much s m a l l e r than those i n stage 1,  Using the r a t e constants o f  stage 2, however, a s e t o f r e s u l t s f o r the dependence o f r a t e constant on Se t h i c k n e s s and on the r a t i o o f Cu t o Se t h i c k n e s s ( t analogous  / t g ) was o b t a i n e d t h a t was g  to the o t h e r t h r e e systems.  r a t e constants c a l c u l a t e d  completely  For t h i s reason the  from stage 2 were taken as being  r e p r e s e n t a t i v e o f t h e l a t e r a l d i f f u s i o n process i n Cu-Se, although i t may w e l l be t h a t the d i f f u s i o n r e g i o n i s i n f a c t stage  1 with stage  2  controlled  being a r e g i o n 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 o f Rate Constant on Se Thickness F i g u r e 6,3 shows t h e d i f f u s i o n r a t e constant 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 . At t h i c k n e s s e s g r e a t e r than o 180 A the r a t e constant tends to a constant value o f _8 2 uohi'e, 3t /oiuer thicknttois it n s e s i o a _ 0,80x10 cm /sec^peak value o f approximately 3.3x10 cm / 8  sec at about 100 ft. T h i s p o s s i b l e tendency  f o r higher d i f -  f u s i o n r a t e s t o o c c u r i n t h i n Se f i l m s appears s i s t e n t with the e f f e c t observed  2  to be con-  i n Ag-Se where the maximum  3,00 h  CO  -  2,00  1,00  0  100  200  400  Figure 6,3  600  800  Rate Constant  1000  1200  1400  as a Function o f Se Thickness  1600  1800  120 d i f f u s i o n r a t e i s a l s o about f o u r times the constant value o b t a i n e d at Se t h i c k n e s s e s exceeding unexpected  180  A*,  T h i s i s not  s i n c e the s t r u c t u r e o f the Se f i l m s i s the same  i n both cases.  Therefore the same mechanism proposed  for  enhanced d i f f u s i o n i n Ag-Se ( s e c t i o n 3,2.3) should be cable to Cu-Se as w e l l . 6.4  The o p t i c a l micrograph  appli-  i n Figure  i l l u s t r a t e s the i r r e g u l a r nature o f the phase boundary  i n t e r f a c e i n a sample having a Se t h i c k n e s s o f 125  A*.  The  wavelength o f the minute p r o j e c t i o n s on the i n t e r f a c e i s about 1 u which i s c o n s i s t e n t with the i n t e r - i s l a n d  spacing  i n the Se at t h i s stage o f growth. Critical  6 , 2 1 , 3  The 0,63  critical  and 0.71,  —8  r a t i o i n Cu-Se was  found to be between  Below t h i s range d i f f u s i o n d i d not occur  while above i t , 0.80x10  Ratio  d i f f u s i o n proceeded  at a constant value o f  2 cm /sec f o r couples i n which the Se t h i c k n e s s  g r e a t e r than 180 A*,  The  r e s u l t s o f the t h i c k n e s s r a t i o  ( t _ / t ) study are shown i n F i g u r e 6.5, Cu Se ° 0  values o f R  J  c  was  The  theoretical  were c a l c u l a t e d f o r each o f the phases Cu  Cu Se , and CuSe and are l i s t e d i n Table 6,1, 3 2 these values with the experimental  Se,  z. —x  0  v  Comparing  value f o r R , c  i t was  that the composition o f the d i f f u s i o n zone should be  seen  Cu2_ Se. x  A determination o f the c r i t i c a l r a t i o at Se t h i c k n e s s e s o f 350  and 2380 % gave values o f 0.71  Thus the c r i t i c a l r a t i o was absolute Se t h i c k n e s s .  and  0,63  respectively.  taken t o be independent  o f the  121  Figure 6o4  Phase Boundary I n t e r f a c e i n a 125 A Se F i l m ( x 7 1 )  Figure 6,5  Rate Constant as a Function of Thickness  Ratio  123  TABLE 6.1  Theoretical C r i t i c a l  Phase  Ratios i n Cu-Se  Theoretical R c  Cu„ Se, x=0,0 2-x * Cu„ Se, x=0,2 2-x ' Cu Se  .645  CuSe  , 375  3  6,2,4  .720  ,513  2  Temperature Dependence The temperature  determined  dependence o f the r a t e constant was  over the range 0-50°C.  Higher temperatures  were  not used i n o r d e r t o a v o i d any aggregation o f Se on the glass substrates. observed  The shapes o f the x versus /t~ curves were not  to change with temperature,  most showing the two  stages o f p a r a b o l i c growth d i s c u s s e d i n s e c t i o n 6.2.1. Although  growth r a t e s i n t h i s system at room temperature are  comparable with r a t e s i n o t h e r systems, the i n c r e a s e i n growth r a t e with i n c r e a s i n g temperature that found i n any o t h e r system.  i s much g r e a t e r than  Taking the growth r a t e  c h a r a c t e r i z e d by the second stage o f the x versus /E~ curves the temperature  dependence o f the r a t e constant  determined  from t h e Arrhenius p l o t i n Figure 6.6 i s given by  125  K = 3,9 x 10  exp[——  ] RT  The very l a r g e a c t i v a t i o n energy r e f l e c t s the l a r g e i n growth r a t e with temperature i n t h i s system.  increase  The pre-  e x p o n e n t i a l term i s a l s o extremely l a r g e and t h i s i s cons i s t e n t w i t h the f a s t  growth r a t e observed at low temperatures  r e l a t i v e to the h i g h a c t i v a t i o n energy. I t i s indeed d i f f i c u l t  to give any c o n v i n c i n g ex-  p l a n a t i o n f o r the very h i g h a c t i v a t i o n energy and p r e e x p o n e n t i a l term i n t h i s system s i n c e the o t h e r Se-base system, Ag-Se, gave much more reasonable values.  I t seems  p o s s i b l e t h a t the l a r g e i n c r e a s e i n growth r a t e with temperature i s due not o n l y t o an i n c r e a s e i n the d i f f u s i o n e f f i c i e n t D, but to some o t h e r e f f e c t which may example,  co-  be, f o r  a p r o g r e s s i v e change i n c r y s t a l s t r u c t u r e o f the  intermetallic  compound, w i t h t e m p e r a t u r e ^ o r 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 o f the phase boundary.  A combination of two such t h e r m a l l y  activated  processes would give a very h i g h apparent a c t i v a t i o n energy f o r the s y s t e m ^ ^ , 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 little  resemblance to the mechanism f o r d i f f u s i o n  o t h e r three  systems.  i n the  126  6 ,3  E l e c t r o n Microscopy  6,3.1  Normal  Growth  The dominant f e a t u r e o f the e l e c t r o n microscopy r e s u l t s i n Cu-Se was the h i g h s e n s i t i v i t y o f the d i f f u s i o n zone to h e a t i n g by the e l e c t r o n beam.  This was a l s o observed  to some extent i n Ag-Te, i n which, as d i s c u s s e d 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. nounced.  In Cu-Se, however, the e f f e c t was much more proI f extremely low i l l u m i n a t i o n l e v e l s were used,  the phase boundary motion appeared as shown i n Figure  6,7,  The i n t e r f a c e appeared to be q u i t e 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 c o n s i s t e d o f columnar  g r a i n s which i n c r e a s e d i n s i z e the l o n g e r the beam was focused on the i n t e r f a c e .  The r e s u l t i n g d i f f e r e n c e i n g r a i n  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 o f the  e l o n g a t e d grains i n the d i f f u s i o n zone at h i g h e r m a g n i f i c a t i o n . The l a r g e arrow on t h i s micrograph i n d i c a t e s the d i r e c t i o n o f the phase boundary advance,  A s e l e c t e d area  diffraction  p a t t e r n made from the d i f f u s i o n zone showed that i t s composit i o n was  Cu„  Se,  T h i s was i n agreement with the composition  2-x p r e d i c t e d by the c r i t i c a l  c  r a t i o study i n S e c t i o n 6.2.3.  s e l e c t e d area d i f f r a c t i o n p a t t e r n and the d-spacing from i t are shown i n Figure  6,9,  A  calculated  Figure 6 „ 7  Motion o f the Phase Boundary I n t e r f a c e i n Cu-Se  128  Figure 6.8  Columnar Grains i n D i f f u s i o n  Zone  (b) Au Standard  (a) S.A.D. o f D i f f u s i o n Zone  Calculated d-spacings (A) 3. 34 2, 88 2.24 2.03 1,73 1, 65 1,42 1. 31 1.28 1,17 1.11 1.02 0, 972  Figure 6,9  d- spacings f o r Cu _ Se (A) ?  x  3.33 2, 88 2. 02 1, 73 1,65 1,43 1, 32 1,17 1,105 1, 01 , 969  S e l e c t e d Area D i f f r a c t i o n o f the D i f f u s i o n Zone  Pattern  130  At h i g h m a g n i f i c a t i o n t h e phase boundary i n t e r f a c e appeared t o c o n s i s t o f a s e r i e s o f p a r a l l e l  growth t i p s o f  v a r y i n g s i z e l i k e t h a t shown i n F i g u r e 6.10.  The d i f f u s i o n  couple was c o o l e d t o -150°C i n the microscope c o l d stage i n o r d e r to prevent  the i n t e r f a c e from advancing.  Selected  area d i f f r a c t i o n p a t t e r n s were made on s e v e r a l o f these The  p a t t e r n s were s i n g l e - c r y s t a l l i n e i n nature  tips.  and e x h i b i t e d  50 pronounced s t r e a k i n g o f the spots  .  Two such  diffraction  p a t t e r n s and t h e i r a s s o c i a t e d growth t i p s are shown i n F i g u r e 6.11,  An i n t e r e s t i n g f e a t u r e o f these t i p s was  that i n each o f them a s e r i e s o f f i n e s t r i a t i o n s  running  n e a r l y p a r a l l e l t o the growth d i r e c t i o n c o u l d be seen. These are c l e a r l y shown i n F i g u r e s 6,10 and 6,11.  In o r d e r  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 r o t a t i o n c a l i b r a t i o n o f t h e intermediate  l e n s o f t h e micro-  scope was c a r r i e d out with the same a c c e l e r a t i n g voltage and p r o j e c t o r l e n s p o l e p i e c e as was used t o make the a c t u a l . 45,50 micrograph o f the growth t i p s .  Analysis  o f the d i f -  f r a c t i o n p a t t e r n s o f Figure 6,11 i l l u s t r a t e d that the growth d i r e c t i o n o f the t i p s l a y w i t h i n 9° o f the <111> d i r e c t i o n and that the s t e a k i n g d i r e c t i o n o f the spots was almost exactly perpendicular to t h i s . t i p s confirmed  those  Further analysis o f other  relationships;  i n every  case the  growth d i r e c t i o n o f the t i p s was c l o s e t o <111> and the s t r i a t i o n s were a s s o c i a t e d with  {110} planes.  These s t r i a t i o n s  were the apparent cause o f the s t r e a k i n g o f t h e p a t t e r n  spots.  131  Figure 6 10 0  Growth T i p at High  Magnification  P a r a l l e l f r i n g e s i n t h i s micrograph are b e l i e v e d to be due to astigmatism i n the o b j e c t i v e l e n s of the microscope.  132  133 Figure 6,12  shows s c h e m a t i c a l l y the i n d e x i n g o f the  c r y s t a l d i f f r a c t i o n p a t t e r n s of F i g u r e In summary i t was possessed  single-  6,11,  found t h a t the g r a i n s o f Cu  a p r e f e r r e d growth d i r e c t i o n , growing i n a  direction.  The  Se  0  <111>  f i n e s t r i a t i o n s appearing i n the growth  t i p s were r e l a t e d to {110}  planes and were r e s p o n s i b l e f o r  s t r e a k i n g of the d i f f r a c t i o n p a t t e r n s .  The two  main  sources o f s t r e a k i n g o f d i f f r a c t i o n spots are s t a c k i n g 51 f a u l t s and twins  ,  I t i s u n l i k e l y t h a t the  observed here are s t a c k i n g f a u l t s .  striations  On the o t h e r hand  planes are not twinning planes i n an anti-isomorphous s t r u c t u r e l i k e Cu  2  x  Se  4 1  ,  s i n c e the <111> x  The  growth d i r e c t i o n i s a l s o  f o r by c r y s t a l l o g r a p h i c c o n s i d e r a t i o n s  I t should be noted, however, that the  growth d i r e c t i o n d u r i n g formation o f columnar c r y s t a l s the l i q u i d  2  d i r e c t i o n i s not a close-packed d i r e c t i o n i n  the C u _ S e l a t t i c e , 2  CaF  Therefore these s t r i a t i o n s must  be due to some o t h e r source. d i f f i c u l t ' to account  {110}  (e,g, i n s t e e l s ) i s not a close-packed  from  direction.  Apparently t h i s i s r e l a t e d to the a b i l i t y o f l i q u i d atoms to " s t i c k " more e a s i l y to planes o t h e r than the  close-  packed ones, 6,3,2  D e n d r i t i c Growth When h i g h i l l u m i n a t i o n l e v e l s were used to  observe  the phase boundary i n t e r f a c e i n Cu-Se, a second phase appeared at the i n t e r f a c e which grew r a p i d l y i n a d e n d r i t i c manner. Once n u c l e a t e d , t h i s phase continued t o grow even when i l l u -  134 131 022 113  111  Growth d i r e c t i o n 113  ^ 022  ft  131 [211] (a)  Zone  Indexing o f 6 „ 11 (1)  13.1  ^ 022 113  111  Growth 111  ± 113  (b)  Figure 6,12  i 022  131  Indexing o f 6,11 (2)  Schematic Patterns  Indexing o f D i f f r a c t i o n  direction  135 mination  was g r e a t l y reduced.  The s t r u c t u r e was  truly  d e n d r i t i c , e x h i b i t i n g primary arms and numerous s i d e branches.  Figure 6.13 shows the advance o f the d e n d r i t i c  phase i n t o the pure Se.  The e l e c t r o n micrographs o f Figure  6,14 c l e a r l y i l l u s t r a t e the appearance o f a s i n g l e primary d e n c r i t e at the phase boundary i n t e r f a c e and the d e n d r i t i c s t r u c t u r e w i t h i n the body o f the phase.  The boundary  between the normal n o n - d e n d r i t i c Cu2_ Se and the d e n d r i t i c x  phase induced 6.15.  by e l e c t r o n beam h e a t i n g i s shown i n F i g u r e  T h i s e f f e c t was found to be completely  reproducible.  A s e l e c t e d area d i f f r a c t i o n p a t t e r n made from the d e n d r i t i c phase showed t h a t i t was the t e t r a g o n a l i n t e r m e t a l l i c compound Cu,jSe2.  A t y p i c a l d i f f r a c t i o n p a t t e r n and i t s a s s o c i -  ated d-spacings are given i n Figure 6.16,  These "d" values  are i n good agreement with the known d-spacings f o r Cu Se2 3  l i s t e d i n the same f i g u r e . To determine the d e n d r i t i c growth d i r e c t i o n s e l e c t e d area d i f f r a c t i o n p a t t e r n s were made i n the primary arms at -110°C u s i n g the c o l d stage.  I t was found t h a t c o o l i n g o f  the sample to t h i s temperature r e s u l t e d i n the d e n d r i t i c s t r u c t u r e b e i n g transformed  i n t o one c o n s i s t i n g o f o n l y  p a r a l l e l primary arms with no s i d e branches, s i m i l a r i n appearance to n o n - d e n d r i t i c C u  0  C.  c r y s t a l s t r u c t u r e was s t i l l  Se.  The composition  and  " 1%  t h a t o f Cu Se2» however. 3  the primary arms were q u i t e narrow i t was n e a r l y  Because  impossible  to o b t a i n 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 p a t t e r n .  There-  (1)  137  (2)  I n t e r i o r M i c r o s t r u c t u r e o f the D e n d r i t i c Phase  Figure 6,14  Nature o f the D e n d r i t i c Phase  138  Figure 6„15  Boundary Between D e n d r i t i c and N o n - d e n d r i t i c Phase  139  (a)  S.A.D. o f D i f f u s i o n Zone  (b) Au Standard  Calculated  d-spacings  d-spacings (A)  f o r CugSe2  4.28 3.56 3.20  4.28 3.56  2.97 2. 86 2.56 2.49 2.38 2.26 2.14  2.00 1.93 1.91 1.83  Figure 6,16  3.11 2. 97 2. 86 2.62 2,56 2,49 2. 38 2.26 2.14 2.10 2, 08 2. 02 2, 00 1,93 1. 83  S.A.D. P a t t e r n o f the D e n d r i t i c Phase i n Cu-Se  14 0  f o r e , the d i f f r a c t i o n p a t t e r n s were i n v a r i a b l y a superp o s i t i o n o f at l e a s t two  s i n g l e - c r y s t a l p a t t e r n s and  i n d e x i n g was  Pronounced s t r e a k i n g was  difficult.  on a l l the p a t t e r n s . typical  F i g u r e s 6.17  and 6,18  m i c r o s t r u c t u r e s , and the schematic  .  i n evidence  illustrate  d i f f r a c t i o n patterns obtained, t h e i r .  their  corresponding  .  52  i n d e x i n g o f each  Analyses o f the d i f f r a c t i o n p a t t e r n s give the growth d i r e c t i o n as b e i n g <101> from f i n e s t r i a t i o n s planes.  and i n d i c a t e that the s t r e a k s a r i s e  (see F i g u r e 6,18)  a s s o c i a t e d with  An i n v e s t i g a t i o n o f p o s s i b l e twinning planes i n  the s p e c i f i c t e t r a g o n a l s t r u c t u r e o f Cu^Se^ was out.  {111}  not  carried  T h e r e f o r e i t i s not p o s s i b l e to say whether the  t i o n s p r e s e n t i n the micrographs  are due  to twins.  stria-  It i s  u n l i k e l y , however, t h a t they are s t a c k i n g f a u l t s , s i n c e {111}  i s not a close-packed plane i n t h i s  structure. 19,5 3 The occurrence o f d e n d r i t i c growth in a solid  s t a t e d i f f u s i o n r e a c t i o n i s a very r a r e phenomenon,  Malcolm  54 and Purdy  observed  supersaturated  the d e n d r i t i c growth o f y brass  3-brass  i n the s o l i d s t a t e .  from  In t h e i r work,  however, a very f a v o u r a b l e morphology e x i s t e d between"prec i p i t a t e and parent  grain.  In the present i n v e s t i g a t i o n  observed growth o f a d e n d r i t i c phase appears thermal r a t h e r than c r y s t a l l o g r a p h i c e f f e c t s .  to be due to Focusing o f  an i n t e n s e beam o f e l e c t r o n s on the normal d i f f u s i o n i n t e r f a c e r e s u l t s i n r a p i d d e n d r i t i c growth.  the  zone  Once the beam  i s removed from the i n t e r f a c e , growth of the d e n d r i t i c phase proceeds  slowly ( i f at  all).  141  Figure  6,17  Dendrite A n a l y s i s  Figure  6,18  Dendrite  Analysis  143  A possible is  that  e x p l a n a t i o n f o r the observed  the l o c a l i z e d h e a t i n g produced  interface  excites  Se  them q u i t e m o b i l e .  region.  suggesting that even at t h i s is  also  Se  vicinity  making  poor thermal conduction p r o p e r t i e s  Se p r e v e n t s t h e beam h e a t from t h i s  by t h e beam a t the  atoms i n t h e i m m e d i a t e The  behaviour  from b e i n g conducted  i s observed t o aggregate  away  of  readily  a t o n l y 60°C  Se atoms a r e c a p a b l e o f s u r f a c e m i g r a t i o n  low  temperature.  consistent  with the  This picture  description  of high  o f the  mobility  amorphous  . 55 state  as b e i n g a h i g h l y  viscous l i q u i d  ,  The  dency o f b u l k amorphous Se t o become p l a s t i c temperatures this  description well.  ductivity  i n t h e Se  intermetallic is  below 1 0 0 ° C ( s e e page  created  transform shaped  as q u i c k l y  as p o s s i b l e  f r e e energy  is  sufficiently Another  fits con-  good c o n d u c t i o n i n the  The  system  atoms  t h e n wants t o Plate-  transform a greater Therefore a  develops, p r o v i d e d the decrease i n more t h a n  and  counterbalances.the increase  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  high. 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  Cu^Se^ i s a h i g h t e m p e r a t u r e  this  3)  o f poor thermal  than p l a n a r b o u n d a r i e s .  interface  s u r f a c e energy  Chapter  to f o r m Cu2Se2»  can  ten-  and f l o w a t  a l a y e r o f very mobile  ahead o f t h e i n t e r f a c e .  in  If  and r e l a t i v e l y  or pointed precipitates  dendritic  that  net r e s u l t  compound i s t h a t  volume p e r s e c o n d  volume  The  30,  observed  were s o , t h e r a p i d  lateral  derivative diffusion  results i s 40 48  o f Cu2_ Se x  produced  by  '  144  56  beam At  h e a t i n g c o u l d be due to a polymorphic t r a n s f o r m a t i o n  the p r e s e n t time, however, there i s i n s u f f i c i e n t  infor-  mation a v a i l a b l e to say whether Cu,jSe2 could be a high temperature  form o f C u  homogeneity  range,  In  2  x  Se  r e s u l t i n g from an i n c r e a s e d  summary i t has been found t h a t Cu-Se i s a much  more complicated system than the o t h e r t h r e e i n v e s t i g a t e d . The growth k i n e t i c s are not s t r i c t l y p a r a b o l i c and the a c t i v a t i o n energy appears to be abnormally h i g h f o r a system i n which d i f f u s i o n proceeds so r a p i d l y .  In a d d i t i o n the  e l e c t r o n microscopy r e s u l t s i n d i c a t e t h a t the phase boundary  i n t e r f a c e i s very s e n s i t i v e to h i g h i l l u m i n a t i o n l e v e l s ;  i f these become l a r g e enough, a second phase i s i n i t i a t e d at  the i n t e r f a c e which moves very r a p i d l y and grows d e n d r i -  tically.  These r e s u l t s suggest t h a t the a c t u a l  mechanism i n Cu-Se i s q u i t e complex.  diffusion  145  CHAPTER 7  SUMMARY AND CONCLUSIONS  7,1 7,1,1  Discussion  and Summary  Growth K i n e t i c s In each o f the three  systems Ag-Se, Cu-Te, and  Ag-Te the graphs o f d i f f u s i o n zone width (x) as a f u n c t i o n of / t were l i n e a r i m p l y i n g  that the growth o f the d i f f u s i o n  zones was d i f f u s i o n c o n t r o l l e d .  As d i s c u s s e d  i n section  5,2,1, most o f the growth rate p l o t s i n Cu-Se were not s t r i c t l y p a r a b o l i c but i n s t e a d appeared to c o n s i s t o f two or three  stages o f p a r a b o l i c growth.  The exact reason f o r  t h i s behaviour remains obscure, but i t would seem that the d i f f u s i o n zone growth i n each stage i s d i f f u s i o n c o n t r o l l e d . L a t e r a l d i f f u s i o n at room temperature was very r a p i d i n a l l f o u r systems i n v e s t i g a t e d ,  The r e s u l t i n g d i f f u s i o n zones  tended to be very w r i n k l e d  o r f o l d e d i n nature and became  p a r t i a l l y detached from t h e i r u n d e r l y i n g  substrates.  This  e f f e c t was no doubt due t o the volume expansion o f t h e Se o r 46 Te l a t t i c e as Ag o r Cu  d i f f u s e d i n , s i n c e very l a r g e i n -  creases i n a u n i t volume o f Se and Te r e s u l t when an i n t e r m e t a l l i c compound with Ag o r Cu i s formed.  In Cu-Te, f o r  14 6  example, the volume expansion o f the Te i s about 40%,  7.1.2  Rate Constant Dependence The  2  on F i l m  Thickness  o r i g i n a l purpose o f i n v e s t i g a t i n g the e f f e c t o f  Se and Te f i l m t h i c k n e s s on the r a t e constant  f o r couples  i n which the t h i c k n e s s r a t i o was g r e a t e r than R if  the l a t e r a l  d i f f u s i o n process  f u s i o n along the Se o r Te. occurrence  c  was to see  i n v o l v e d any s u r f a c e  dif-  I t would be expected t h a t the  o f s u r f a c e d i f f u s i o n should be r e f l e c t e d i n a  general decrease o f the r a t e constant with i n c r e a s i n g Se o r Te t h i c k n e s s s i n c e the s u r f a c e to volume r a t i o o f a f i l m i s reduced as the t h i c k n e s s becomes g r e a t e r .  In each o f the  systems s t u d i e d , however, i t was found that beyond a c e r t a i n Se o r Te t h i c k n e s s , the r a t e constant was e s s e n t i a l l y independent o f t h e t h i c k n e s s while below the t h i c k n e s s the r a t e constant  tended t o a peak value.  This phenomenon was  a t t r i b u t e d to the s t r u c t u r e o f the t h i n f i l m s .  An e l e c t r o n  microscopy i n v e s t i g a t i o n o f very t h i n Se and Te f i l m s showed that they  c o n s i s t e d o f c o a l e s c e d i s l a n d s with an i n t e r -  i s l a n d network t h a t undoubtedly contained many s t r u c t u r a l imperfections.  T h i s would be conducive t o a short  d i f f u s i o n process  between the i s l a n d s ,  circuit  The e f f e c t o f low Se  and Te t h i c k n e s s e s on the r a t e constant was seen to be much g r e a t e r i n the Te systems than i n the Se ones. c o n s i s t e n t with the d e f i n i t e evidence  This was  o f g r a i n boundary  dif-  f u s i o n at a l l Te t h i c k n e s s e s observed i n both Ag-Te and Cu-Te  147  using t r a n s m i s s i o n e l e c t r o n 7.1.3  Critical The  microscopy,  Ratio  existence of a c r i t i c a l thickness r a t i o  d i f f u s i o n couple components was  v e r i f i e d i n a l l f o u r systems.  Above t h i s t h i c k n e s s r a t i o d i f f u s i o n proceeded independent  f o r the  at a r a t e  o f the Se o r Te t h i c k n e s s , and below i t , no  f u s i o n took p l a c e . served c r i t i c a l  I t was  r a t i o was  dif-  found t h a t the e x p e r i m e n t a l l y obindependent  o f the absolute Se o r  Te t h i c k n e s s over the range o f t h i c k n e s s i n which growth r a t e s were measured. critical  ratios  T h e o r e t i c a l determinations o f the  from s t o i c h i o m e t r i c c o n s i d e r a t i o n s were i n  e x c e l l e n t agreement with the experimental except i n the case o f Cu-Te where a 30% found.  values o b t a i n e d  difference  In Ag-Se, Cu-Se, and Ag-Te the compositions  was o f the  d i f f u s i o n zones p r e d i c t e d 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 r e s u l t s o b t a i n e d i n each  system f o r the temperature The  dependence o f the r a t e constant.  three systems Ag-Se, Cu-Te, and Ag-Te a l l have  low a c t i v a t i o n e n e r g i e s .  In Ag-Se and Cu-Te, comparison with  a c t i v a t i o n e n e r g i e s f o r bulk d i f f u s i o n couples was The  thin  relatively  possible.  f i l m a c t i v a t i o n e n e r g i e s were lower than the bulk  a c t i v a t i o n energies.  Thus the a c t i v a t i o n e n e r g i e s i n the  t h i n f i l m r e s u l t s not o n l y c o n s t i t u t e very low values i n them-  14 8  TABLE 7,1  A c t i v a t i o n E n e r g i e s f o r Thin F i l m Couples  System  Temperature Range I n v e s t i g a t e d (°C)  Thin F i l m A c t i v a t i o n Energy ' (Kcal/mole)  Bulk Act i v a t i o n Energy (Kcal/mole!  12 ,200  17,600  0-100  7, 800  15 ,000  Ag-Te  0-100  10,000  Cu-Se  0-5 0  23,000  Ag-Se  0-50  Cu-Te  *  Not a v a i l a b l e  *  14 9  s e l v e s , but a l s o tend to be much below the observed a c t i v a t i o n energies.  bulk  T h i s suggests t h a t a short c i r c u i t  mechanism i s r e s p o n s i b l e f o r d i f f u s i o n .  Examination  o f the  phase boundary i n t e r f a c e s i n Cu-Te and Ag-Te by e l e c t r o n microscopy  p r o v i d e d d e f i n i t e evidence o f g r a i n boundary  diffusion,  The h i g h a c 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 c o n s i s t e n t with the o t h e r r e s u l t s .  The most probable  e x p l a n a t i o n f o r t h i s i s t h a t the d i f f u s i o n i n t h i s system i n v o l v e s more than one process so t h a t i t i s improper 28 29 a s c r i b e an a c t i v a t i o n energy to i t ' , 7,1,5  Electron The  to  Microscopy  d i r e c t o b s e r v a t i o n o f the moving phase boundary  i n t e r f a c e s i n the e l e c t r o n microscope  was  in itself  interest-  i n g s i n c e very l i t t l e work o f t h i s type has been done before. In Cu-Te and Ag-Te there were d e f i n i t e i n d i c a t i o n s t h a t g r a i n boundary d i f f u s i o n was  taking place.  with the low a c t i v a t i o n energy i n these systems.  T h i s was c o n s i s t e n t  values o b t a i n e d f o r d i f f u s i o n  In the Se systems the microscopy  results  d i d not provide any d e f i n i t e i n f o r m a t i o n as to the nature o f the d i f f u s i o n mechanism.  I t was  observed, however, t h a t  l o c a l i z e d h e a t i n g by the e l e c t r o n beam at the phase boundary i n t e r f a c e r e s u l t e d i n some aggregation o f the Se i n the  case  o f Ag-Se, and i n Cu-Se to the n u c l e a t i o n o f a second phase which grew d e n d r i t i c a l l y , by beam h e a t i n g was Ag-Te,  The  formation o f a second  phase  a l s o seen to a l e s s marked degree i n  Such phenomena may  suggest  that the l e v e l o f l o c a l -  150  i z e d h e a t i n g produced i n the e l e c t r o n beam i s much g r e a t e r than p r e v i o u s l y thought.  Temperature i n c r e a s e s o f  10 0°C  could w e l l be i n v o l v e d . Despite obtained  the evidence f o r g r a i n boundary  diffusion  i n the Te systems, i t was d i s a p p o i n t i n g t h a t a  q u a n t i t a t i v e estimate o f the r e l a t i v e rate o f g r a i n boundary to l a t e r a l d i f f u s i o n c o u l d not be made.  In Cu-Te, the g r a i n  boundary e f f e c t was not pronounced enough t o assess f u s i o n r a t e , while  i n Ag-Te, beam h e a t i n g  the g r a i n boundary d i f f u s i o n before  the d i f -  tended to obscure  any u s e f u l measurements  could be made. General Summary The  important f e a t u r e s o f t h e l a t e r a l  diffusion  process i n each o f Ag-Se, Cu-Te, Ag-Te and Cu-Se as o u t l i n e d i n the p r e c e e d i n g d i s c u s s i o n are summarized i n Table 7,2, 7 • 2. E s t i m a t i o n  of Diffusion Coefficients /  In the " I n t r o d u c t i o n " the  r a t e constant  (page 15) i t was shown that  found by measuring the width o f the d i f -  f u s i o n zone was r e l a t e d to the d i f f u s i o n  c o e f f i c i e n t by the  formula 2(0,-0, ) ( C o - C ) 9  K = D  6  (C -C ) ( C « - C + 0 _ C _ ) 1 o d ^ 1 o  (7.1)  0  if  the composition range o f the intermediate  is  small.  phase i n v o l v e d  T h i s i s a v a l i d approximation i n the case o f each  TABLE  Summary o f L a t e r a l D i f f u s i o n  System  Ag-Se  Cu-Te  Ag-Te  Diffusion Zone Composition  Ag Se 2  2-x (x~Q,6)  C u  T e  Ag Te 2  1,1x10  2,lxl0  - 9  -8 1.9x10  -8 Cu-Se  Cu _ Se 2  x  (0<x<0. 2 )  i n the Four Systems  Room Temperature Growth Rate (cm^/sec) Kinetics  -8 •  0,80x10  7.2  parabolic  parabolic  parabolic  Critical Ratio f o r Diffusion  Investigated  Proposed Diffusion Mechanism  Special  Characteristics  Se i s amorphous Growth r a t e h i g h e r i n t h i n Se f i l m s .  l.l+.l  Short c i r c u i t (e.g, g r a i n boundary)  0,6 3^.1  Growth r a t e higher i n t h i n Te f i l m s ; e f f e c t i s much more pronounced Grain boundary than i n Se systems.  1,0+.1  E f f e c t o f very t h i n Te f i l m s on growth i s Grain boundary extremely marked.  separate stages o f parabolic growth 0.63-0,71  --  Very l a r g e d i f f u s i o n zone widths-observed. E l e c t r o n beam heating induces second phase at phase boundary i n t e r f a c e which grows dendritically.  o f the systems s t u d i e d so t h a t i t i s p o s s i b l e to use 7,1  to estimate the d i f f u s i o n  coefficients  i n each system.  This has been done u s i n g the room temperature rate constant;  equation  value o f the  that i s , the value o b t a i n e d f o r couples i n  which the t h i c k n e s s r a t i o i s g r e a t e r than the c r i t i c a l  ratio  and the Se o r Te t h i c k n e s s i s beyond the r e g i o n where the s t r u c t u r e o f the f i l m r e s u l t s  i n h i g h e r growth r a t e s .  c a l c u l a t e d values o f D are given i n Table 7.3, can be seen t h a t the d i f f u s i o n  coefficients  The  From t h i s i t  are about  o r d e r s o f magnitude g r e a t e r than the r a t e constants  two  except  f o r the system Ag-Se i n which the d i f f e r e n c e i n v o l v e s a f a c t o r o f 500 Ag Se, 2  I t i s obvious, t h e r e f o r e , t h a t the  coefficients Although  due to the very small composition  diffusion  i n a l l these systems are very l a r g e indeed.  very l i t t l e  temperature  range o f  i s known about the v a r i a t i o n  of the composition  ranges o f the  compounds formed during d i f f u s i o n  with  intermetallic  i n each o f the f o u r  40 48 systems, present evidence boundary compositions temperatures observed  '  suggests that the phase  do not change s i g n i f i c a n t l y up to  o f 500-600°C.  Therefore the a c t i v a t i o n  represent those o f the d i f f u s i o n process  energies  alone.  153  TABLE 7 o 3  System  Calculation  of Diffusion  Steady State Rate Constant K (cm /sec)  Intermetallic Phase Present  Ag-Se  lo1x10  Cu-Te  2olxl0  -8  Composition Range o f Phase (C -C, ) (at %) 9  1  1  Calculated Diffusion Coefficient D  (cm2/sec)  Ag Se  0„2  -6 5 o 5x10  Cu _ Te  0.9  1.6x10  0o 9  2,1x10  2,4  2.9x10  2  -9  Coefficients  2  x  -7  ( x ~ 0 , 6) -8  Ag-Te  l o 9x10  Cu-Se  Oo 8 0 x 1 0  Ag Te 2  -8  Cu„  2-x  Se  (0<x<0 o 2 )  -6  -7  154 70  ^  The Mechanism o f Rapid  Diffusion  Rapid d i f f u s i o n at room temperature o c c u r r i n g phenomenon.  i s a rarely-  In the present work i t was observed  i n o n l y f o u r systems out o f the 22 i n v e s t i g a t e d . it  Therefore  i s n a t u r a l to r a i s e the q u e s t i o n as t o why very r a p i d  f u s i o n i s observed  dif-  i n these systems and not i n o t h e r s .  Present r e s u l t s i n t h i n f i l m d i f f u s i o n  couples  suggest t h a t g r a i n boundary d i f f u s i o n and p o s s i b l y "pipe" d i f f u s i o n are the predominant mechanisms i n Ag-Se, Cu-Te, and Ag-Te,  The bulk data a v a i l a b l e i n these systems, how-  ever, shows t h a t h i g h growth r a t e s are also encountered at r e l a t i v e l y low temperatures couples.  (100-200°C) i n bulk  diffusion  In Cu-Se the d i f f u s i o n mechanism does not appear  to be c o n s i s t e n t w i t h that o f the o t h e r three systems and i t s exact nature remains obscure. growth r a t e s are observed  N e v e r t h e l e s s , very l a r g e  i n t h i s system as w e l l .  A l l o f the i n t e r m e t a l l i c phases formed d u r i n g d i f f u s i o n have s e v e r a l i n t e r e s t i n g f e a t u r e s i n common. are known to be s m a l l band gap semiconducting  They  compounds i n  42 48 5 7 which c a t i o n vacancies a c t as acceptors ' ' ,  Each o f  the compounds e x i s t s i n at l e a s t two s t a b l e polymorphs i n 26 d i f f e r e n t temperature temperature  ranges  and low temperature  ,  In every case both the high m o d i f i c a t i o n s are regarded  as being d e f e c t i n t e r m e t a l l i c compounds with vacancies c o n s t i t u t i n g the main i n p e r f e c t i o n . bonding  cation F i n a l l y , the  i n a l l f o u r compounds i s e s s e n t i a l l y c o v a l e n t r a t h e r  155  than m e t a l l i c .  This i s not  s u r p r i s i n g , however, i n compounds  i n v o l v i n g Se and Te which have been r e f e r r e d to by authors  various  as " m e t a l l o i d s " o r semiconductors. The h i g h temperature m o d i f i c a t i o n s o f Ag2Se, Ag Te, 2  Cu„ Se, and 2-x.  Cu, S 1. o  are s i m i l a r to a-Ag  Q  s (see °2  Introduction,  page 10) i n that they are substances i n which o n l y anions occupy a r e g u l a r l a t t i c e while practically  the  the c a t i o n s are  "molten" and are not bound to d e f i n i t e  lattice  2B positions  ,  Measurements o f e l e c t r i c a l  c o n d u c t i v i t i e s and  t r a n s f e r e n c e numbers i n a-Ag S, f o r example, have shown that 2  the c a t i o n s possess abnormally high m o b i l i t y equal to t h a t o f ions i n aqueous s o l u t i o n while immobile.  the anions  T h i s behaviour i s probably (1)  The  (2)  pounds which tend  to: and  the s m a l l e r c a t i o n to r e a d i l y occupy an  lattice The  essentially  l a r g e s i z e d i f f e r e n c e between c a t i o n  anion which enables interstitial  due  are  site,  inherent d e f e c t s t r u c t u r e o f these comto be d e f i c i e n t i n the c a t i o n s p e c i e s .  T h i s c r e a t e s e x t r a s i t e s to which c a t i o n s i n the l a t t i c e  can  migrate, (3)  The  nature  o f the covalent bonding i s such as  to f a c i l i t a t e the breaking o f c a t i o n a n i o n r  bonds.  In t h i s  r e g a r d i t should be p o i n t e d out that' the o r d e r o f i n c r e a s i n g m e t a l l i c character anions  (decreasing e l e c t r o n e g a t i v i t y ^ ' ^ ) o f the  i s S, Se, Te, and a l l . o f these are much l e s s  negative  than any o f the h a l i d e s .  The  electro-  room temperature  156  s t r u c t u r e s o f these compounds have not  been s t u d i e d  as  e x t e n s i v e l y as the h i g h temperature m o d i f i c a t i o n s , but i t would be expected t h a t there  i s a strong p o s s i b i l i t y  the c a t i o n p a r t i a l l a t t i c e s contain l a t t i c e defects.  In these low  however, the c a t i o n s are now sites.  Nevertheless,  a l a r g e number o f  temperature  modifications,  r e s t r i c t e d to d e f i n i t e l a t t i c e  the c a t i o n m o b i l i t y , although much  l e s s than i n the high temperature s t r u c t u r e , w i l l comparatively The Cu-Se, and  still  be  high. present  work i n d i c a t e s that d i f f u s i o n i n Ag-Se,  Cu-Te i s c o n t r o l l e d by the m i g r a t i o n  through the  that  o f Ag o r  d i f f u s i o n zone which i n each case i n v o l v e s  i n t e r m e t a l l i c compound analogous i n composition s t r u c t u r e to Ag^S,  Cu  an  and  I t i s d o u b t f u l t h a t the r a p i d growth  r a t e s encountered are r e l a t e d to the f r e e energy o f  formation  60  of the v a r i o u s  i n t e r m e t a l l i c phases  ,  Sulphide  s t u d i e s i n Cu and Ag a l l e y s i n v o l v i n g various C  impurity  CO  -I  additions  formation  '  have shown that the r a t e of sulphide  attack  i s comparable i n both cases d e s p i t e the l a r g e d i f f e r e n c e i n the standard  f r e e energy o f formation  o f AgjS and  Cu S (-17,8 2  kcal/mole versus -=28,2 kcal/mole).  From t h i s i t i s concluded  that o n l y the d i f f u s i v i t y o f Ag and  Cu i n the  sulphide  l a y e r s i s s i g n i f i c a n t i n the s u l p h i d a t i o n process.  By  analogy with t h i s 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 Cu-Se i s the d i f f u s i v i t y o f Cu and compound,  possibly  Ag i n the d i f f u s i o n zone  S c a l i n g experiments i n the Ag-S  system  '  have  r e v e a l e d t h a t the s u l p h i d e phase forms as a r e s u l t o f f u s i o n of Ag ions through the Ag S l a y e r .  dif-  T h i s i s accompan-  2  i e d by a motion of e l e c t r o n s i n the same d i r e c t i o n as ion flux. causing  The  the  e l e c t r o n s move r a p i d l y i n l a r g e numbers,  an a d d i t i o n a l e l e c t r i c a l p o t e n t i a l gradient i n ad-  d i t i o n to the chemical  p o t e n t i a l g r a d i e n t s due  ions which are already present;  to the  Ag  t h i s i n turn causes an  i n c r e a s e i n the t r a n s p o r t r a t e o f the s i l v e r ions through the t a r n i s h i n g l a y e r . Se and T e ^ ' ^  have not  d i f f u s i o n process. Ag and  S i m i l a r experiments on Ag and  The  Cu i n the Se and  existence  l e d to any  Cu  c o n s i s t e n t data on  the  p o s s i b i l i t y that the d i f f u s i o n Te systems i s i n c r e a s e d by  with  of  the  of an a d d i t i o n a l e l e c t r i c a l p o t e n t i a l cannot be  r u l e d out.  However the e f f e c t o f t h i s p o t e n t i a l i s merely 6 3  to double o r t r i p l e  the d i f f u s i o n  rate  It i s proposed, t h e r e f o r e , t h a t the mechanism f o r r a p i d d i f f u s i o n i n the f o u r systems i n v e s t i g a t e d i n t h i s work i s a combination o f h i g h Ag and  Cu d i f f u s i v i t y i n the  i n t e r m e t a l l i c compounds that are formed during and  the short c i r c u i t  r e a d i l y at low  d i f f u s i o n processes  which  temperatures i n t h i n f i l m s .  The  diffusion occur high  atomic d i f f u s i v i t i e s i n each o f 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 compounds and  p r o p e r t i e s o f the  s p e c i f i c a l l y , t h e i r defect structures, i n  which c a t i o n s tend  to be abnormally mobile.  158  7 o4  Conclusions The o b s e r v a t i o n s and i n t e r p r e t a t i o n s o f l a t e r a l  d i f f u s i o n i n the f o u r systems Ag-Se, Cu-Te, Ag-Te, and Cu-Se l e a d to the f o l l o w i n g c o n c l u s i o n s : (1)  The growth r a t e i n Ag-Se, Cu-Te, and Ag-Te i s d i f fusion controlled.  In Cu-Se two o r three stages o f  d i f f u s i o n c o n t r o l l e d growth occur with the i n i t i a l growth r a t e being much f a s t e r than succeeding ones, (2)  In a l l f o u r systems the d i f f u s i o n r a t e s o f Cu and Ag are much g r e a t e r than those o f Se and Te,  T h i s would  l e a d to the development o f e x t e n s i v e K i r k e n d a l l p o r o s i t y on the Se o r Te side o f a d i f f u s i o n couple • and would impede the d i f f u s i o n o f these atoms across the i n t e r f a c e .  For t h i s reason, a study o f the  l a t e r a l d i f f u s i o n o f Se o r Te along Cu o r 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 cont r o l l e d by the motion o f Cu o r Ag ions through the d i 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 a f f e c t e d by the amorphous m i c r o s t r u c t u r e o f the Se, (4)  The d i f f u s i o n r a t e constant i s independent o f the Se o r Te f i l m t h i c k n e s s e s f o r any t h i c k n e s s at which the f i l m i s continuous.  This implies that surface  d i f f u s i o n i s not i n v o l v e d i n the l a t e r a l along the Se o r Te  diffusion  s i n c e the surface to volume  159 r a t i o decreases as the f i l m t h i c k n e s s (5)  increases,  Se and Te f i l m s become continuous at about 180 to o 200 A.  Below t h i s t h i c k n e s s the s t r u c t u r e o f the f i l m s  i s such that the d i f f u s i o n r a t e constant tends t o a peak value due to s h o r t - c i r c u i t i s l a n d channels.  diffusion  i n the i n t e r -  The e f f e c t o f s t r u c t u r e i s much more  pronounced i n Cu-Te and Ag-Te due t o the f a c t grain  that  boundary d i f f u s i o n takes p l a c e q u i t e r e a d i l y i n  these systems, (6)  In o r d e r f o r l a t e r a l d i f f u s i o n t o o c c u r , a d e f i n i t e r a t i o o f Cu o r Ag t h i c k n e s s t o t h a t o f Se o r Te must be exceeded.  T h i s c r i t i c a l t h i c k n e s s r a t i o i s de-  termined only by the s t o i c h i o m e t r y o f the i n t e r m e t a l l i c phase formed d u r i n g d i f f u s i o n and i s independent o f the s t r u c t u r e o f the Se o r Te f i l m . (7)  A grain the  rapid  Ag-Te, or  boundary d i f f u s i o n mechanism accounts f o r room temperature growth r a t e s i n Cu-Te and  Short c i r c u i t  diffusion  "pipe" d i f f u s i o n i s also  growth i n Ag-Se,  such as g r a i n  boundary  responsible f o r rapid  T h e r e f o r e , i n these systems, the  growth r a t e s observed i n the t h i n  f i l m couples are  c o n s i d e r a b l y g r e a t e r than those observed i n bulk couples at room temperature, (8)  The occurrence o f r a p i d  room temperature  diffusion  along a f i l m i s r e s t r i c t e d to the f o u r Se and Te systems i n v e s t i g a t e d .  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 o t h e r systems, (9)  The r a p i d d i f f u s i o n processes t a k i n g place i n Ag, Cu-Se and Ag, Cu-Te are due t o t h e i r unique  chemical  p r o p e r t i e s and to the d e f e c t s t r u c t u r e s o f the compounds formed during d i f f u s i o n .  In t h i n f i l m  dif-  f u s i o n couples i n v o l v i n g these systems s h o r t c i r c u i t d i f f u s i o n processes r e s u l t i n an a c c e l e r a t i o n of normal growth r a t e s and enable rapidly  at room  temperature.  diffusion  to proceed  161  APPENDIX  WHITE ZONE  The "white zone" d e s c r i b e d i n s e c t i o n 3,2.1 observed i n a l l o f the systems  s t u d i e d and i t s width  was was  observed to decrease as the r e l a t i v e t h i c k n e s s e s o f the diffusion able.  couple components (e.g. Ag and Se) became compar-  In any given sample the white zone width  constant at a l l times and was zone width i n the k i n e t i c s  remained  not i n c l u d e d i n the  graphs.  diffusion  F i g u r e A . l , a growth  p l o t i n Ag-Te, shows the t r u e d i f f u s i o n zone width and the  total diffusion  a g a i n s t /t".  zone p l u s white zone width p l o t t e d  I t can be seen that the d i f f u s i o n  zone graph  i s p a r a b o l i c p a s s i n g through t=0 while the t o t a l width p l o t , although s t i l l  p a r a b o l i c , i s d i s p l a c e d from the o t h e r  curve by about 18 u and does not pass through the o r i g i n . I t was  thus concluded that the white zone was  associated  with the downward d i f f u s i o n process r a t h e r than with lateral  diffusion. The o r i g i n o f the white zone i s probably due to  the  masking o f the s u b s t r a t e i n o r d e r to produce  a Ag step.  Consider Figure A,2 which r e p r e s e n t s the Ag vapour on the mask and s u b s t r a t e c o n f i g u r a t i o n  incident  ( A , 2 ( a ) ) , and the  162  F i g u r e A„2  E f f e c t o f Non-Ideal Masking on R e s u l t i n g F i l m Step  164  r e s u l t i n g Ag step produced (A„2(b)), p o s s i b l e to achieve  In p r a c t i c e i t i s not  p e r f e c t c o n t a c t between mask and sub-  s t r a t e so t h a t there i s always a narrow gap between them. T h i s permits in  a small f r a c t i o n o f Ag atoms t o occupy  r e g i o n B o f the s u b s t r a t e .  sites  T h i s may occur when atoms  such as X and Y i n A.2(a) s t r i k e the s u b s t r a t e at a high angle o f i n c i d e n c e due t o rebounding o f the chimney w a l l s or c o l l i s i o n with o t h e r atoms i n the beam.  Some Ag atoms  (e,g, Z i n A,2(a)) may migrate from region A t o r e g i o n B by s u r f a c e d i f f u s i o n e s p e c i a l l y 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 s u b s t r a t e i s s u f f i c i e n t l y high t o enable them to move out o f bound s u r f a c e s i t e s , but i n s u f f i c i e n t t o cause them to re-evaporate. two  processes  The r e s u l t o f these  i s a f i l m s t r u c t u r e which becomes i n c r e a s i n g l y  aggregated and porous towards the edge o f the Ag ' F i g u r e A,3 i l l u s t r a t e s what happens when Se i s evaporated over such a step t o produce a d i f f u s i o n couple. in  The Se  the aggregated p o r t i o n o f the step e s s e n t i a l l y  "fills in"  the pores i n the Ag r e s u l t i n g i n an e f f e c t i v e r e d u c t i o n o f the Se t h i c k n e s s i n t h i s r e g i o n .  Diffusion s t i l l  takes  place between the Ag and Se t o form Ag Se but because the 2  o  net Se t h i c k n e s s i s l e s s i n t h i s region the o p t i c a l is  contrast  d i f f e r e n t and t h i s area i s observed as the white zone.  Evaporation  o f t h i c k e r and t h i c k e r Se f i l m s reduces the  white zone by b u i l d i n g up a t h i c k l a y e r o f Se at e i t h e r end  o f the step d i s t r i b u t i o n and so decreasing  e f f e c t i v e Se t h i c k n e s s r e d u c t i o n .  the area o f  T h i s argument was con-  165  Mask edge  <  White zone  "  ( a )  >  Lateral ^  diffusion  ^g  No white zone  Se  Ag  Se  Glass s u b s t r a t e  (b)  t  a t. Se  Figure A.3  Ag  E v a p o r a t i o n o f Se across an A c t u a l Ag Step  166  firmed by e v a p o r a t i n g a Ag-Te couple with the mask r a i s e d 2 mm above the s u b s t r a t e at one end and i n contact with the s u b s t r a t e at the o p p o s i t e end.  The width o f the white  zone  at the "poor mask" end was about 150 u while a t the "good" end i t was 18 p, appeared  The d i f f u s i o n zone at the "poor mask" end  very porous o r d i f f u s e i n the e a r l y stages o f  growth making the exact p o s i t i o n o f x = 0 very d i f f i c u l t t o establish.  The beginning o f the l a t e r a l  however, appeared  diffusion  to c o i n c i d e with the very edge o f the  i l l - d e f i n e d Ag step on the g l a s s immediately the Se f i l m .  zone,  adjacent to  No d i f f e r e n c e i n the d i f f u s i o n r a t e was de-  t e c t e d at the "good" and "poor" mask ends, c o n f i r m i n g that 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  f u s i o n process,,  dif-  167  BIBLIOGRAPHY  1, "Physics o f T h i n F i l m s " , V o l , 2, Ed, by G, Hass and R.E. Thun, Academic Press, New York S London (1964), 2,  J,C, Anderson, "The Use o f Thin Films i n P h y s i c a l I n v e s t i g a t i o n s " , Academic P r e s s , New York S London (1966),  3,  R.W,  4,  R.E, Thun, "Physics o f Thin F i l m s " , V o l , 1, Ed. by G, Hass, Academic P r e s s , New York S London, p. 187 (1963),  5,  "Thin F i l m s " , A,S.M, Seminar, Ed, by H. W i l s d o r f (1963).  6,  0,S, Heavens, " O p t i c a l P r o p e r t i e s o f Thin S o l i d Butterworths P u b l i c a t i o n s , London, (1955).  7,  " S t r u c t u r e and P r o p e r t i e s o f Thin F i l m s " , Ed, by C,A. Neugebauer, J,B, Newkirk, D,A, Vermilyea, Wil&y and Sons, New York, (1959),  8,  C, Weaver and R, M, H i l l ,  Hoffman, "Physics o f Thin F i l m s " , V o l , 3, Ed. by G, Hass and R, E, Thun, Academic P r e s s , New York S London, p, 211 (1966),  p, 9,  Phil,  Mag,  Films",  Supplement, _8, No,  32,  375 (1959),  C, Weaver and L,C„ Brown, P h i l ,  Mag., _8, p, 1379 (1963),  10,  H, Schopper, Z, Physik, 14 3, p, 93 (1955),  11,  G,C,  12,  T. Mohr, Wiss, Z,. Martin-Luther  Monch, I b i d , , 14_, p, 363 (1954),  Wittenberg,  Univ,, H a l l e -  2_, p, 601 (1952),  13,  T, Mohr, I b i d , , 14, p. 377 (1954),  14,  G, K i e n e l , Ann, Phys,, Lpz, , 6_, p. 1 (1955),  15,  V, Z o r l l , I b i d , , 16, p, 7 (1955),  168 Bibliography  (Cont'd)  16,  D.T, Parkinson, U n i v e r s i t y o f S t r a t h c l y d e , unpublished work (1963),  17,  A.D, L e C l a i r e , "Progress i n Metal P h y s i c s " , V o l . 4, Ed. by B, Chalmers, Pergamon P r e s s , London (19 53).  18,  P.G, Shewmon, " D i f f u s i o n i n S o l i d s " , McGraw-Hill, p. 116 (1963),  19,  R,E, R e e d - H i l l , " P h y s i c a l M e t a l l u r g y P r i n c i p l e s " , Van Nostrand Company, New J e r s e y , p. 378 (1964),  20,  D, T u r n b u l l , "Atom Movements", A,S,M,, C l e v e l a n d , p. 129 (1951),  21,  N,A, G j o s t e i n , "Metal S u r f a c e s " , A.S,M, Seminar, Ed. by W,D, Robertson and N,A, G j o s t e i n , p, 114 (1962).  22,  R,A„ Nickerson and E,R, Parker, Trans, A.S.M., 42, p,  376 (1950).  23,  W,W.  M u l l i n s , J , Appl. P h y s i c s , 2j8, p, 333 (195 7).  24, 25,  J , Choi and P. Shewmon, Trans, AIME, 224, p, 5 89 (1962). D, Lazarus, " E n e r g e t i c s i n M e t a l l u r g i c a l Phenomena", V o l , 1, Ed, by W,M, M u e l l e r , Gordon and Breach, p. 1 (1965),  26,  W, J o s t , " D i f f u s i o n i n S o l i d s , L i q u i d s , Gases", Academic Press, New York, p, 87 (1952),  27,  A.H. C o t t r e l l , " T h e o r e t i c a l S t r u c t u r a l M e t a l l u r g y " , Edward A r n o l d P u b l i s h e r s , London, p, 154 (1954),  28,  H, Buckle, Colloquium on S o l i d State D i f f u s i o n : Saclay, France, North H o l l a n d Publ, Co., Amsterdam, p, 170 (1958) .  29,  G.V. Kidson, J , Nuc, Mat,, 3_, No. 1, p. 21 (1960).  30,  J,P, H i r t h and G.U, Pound, "Condensation Pergamon P r e s s , New York, (196 3),  31,  L, H o l l a n d , "Vacuum D e p o s i t i o n o f Thin F i l m s " , Chapman and H a l l L t d , , London (195 8),  32,  D.W,  and E v a p o r a t i o n " ,  Pasfchley, Advances i n Phys,, 14, p. 330 (1965).  169 Bibliography  (Cont'd)  33<>  R.S, Sennett and G.D. S c o t t , J . Opt. Soc. Amer,, 40, p, 203 (1950),  34,  L.E, Mure and M.C. Inman, P h i l , Mag,, 13_, p„ 135 (1966,  35,  J.S, H a l l i d a y , T.B, Rymer, and K.H.R, Wright, Proc. Royal S o c , A 224, p. 548 (1954),  36,  R.B, B e l s e r , J , Appl, Phys,,  37,  S, Tolansky, "Multiple-Beam I n t e r f e r o m e t r y " , Clarendon P r e s s , Oxoford, p. 147 (1948). S.K. Behera, P r i v a t e Communication,  3 8,  31, p. 562 (1960).  39,  S.D, G e r t s r i k e n , I, Ya, Dekhtyar, " S o l i d State D i f f u s i o n i n Metals and A l l o y s " , U n i t e d S t a t e s Atomic Energy Commission,translation o f a p u b l i c a t i o n o f t h e State P u b l i s h i n g House f o r P h y s i c a l - M a t h e m a t i c a l L i t e r a t u r e , Moscow, p. 478 (1960),  40,  M, Hansen, C o n s t i t u t i o n o f Binary A l l o y s , New York (1958),  41,  C,S, B a r r e t t , " S t r u c t u r e o f M e t a l s " , McGraw-Hill, New York, p. 230 (1952).  42,  N.B, Hannay, "Semiconductors", New York, (1960),  43,  C A , Hampel, "Rare Metals Handbook", Reinhold P u b l i s h i n g Corp,, pp, 447 and 519 (1961),  44,  G, Thomas, "Transmission E l e c t r o n Microscopy o f Metals", John Wiley and Sons, New York (19 62),  45,  M, Wayman and R, Bennett, U n i v e r s i t y o f B r i t i s h unpublished work (1964),  46,  L.C. Brown, C.S. Sanderson, and C. S t . John, Trans. AIME, 226, p, 1539 (1966),  47,  R, Dalven, J , Appl, Phys,,  48,  R.P, E l l i o t , " C o n s t i t u t i o n o f Binary A l l o y s , Supplement", McGraw-Hill, p, 3 84 (19 65).  McGraw-Hill,  Reinhold P u b l i s h i n g Co.,  37_, N  o  ° » P° 6  2 2  Columbia,  7 1 (1966 ), First  170 Bibliography  (Cont'd)  4 9,  W.B,  50,  R.W.  51,  P,B, H i r s c h , A, Howie, R,B, N i c h o l s e n , P,W, Paschley, N,J, Whelan, " E l e c t r o n Microscopy o f Thin C r y s t a l s " , Butterworths, London, pp, 133 f f and 320 f f (1965).  52,  A, T a y l o r , "x-Ray Metallography", John Wiley and Sons, New York (1964),  53,  R,W,  54,  J.A, Malcolm and G,R, p, 1391 (1967),  55,  L,H, Van V l a c k , "Elements o f M a t e r i a l s Science", AddisonWesley P u b l i s h i n g Co,, Reading, Massachusetts, p, 67 (1960),  56,  J.W.  of  Pearson, "Handbook o f L a t t i c e Spacings and S t r u c t u r e s M e t a l s " , 2., Pergamon P r e s s , p, 885 (196 7),  H i l l , " R e a c t i v i t y o f S o l i d s " , Ed, by J.H. De Boer, Proceedings o f the 4th I n t e r n a t i o n a l Symposium on the R e a c t i v i t y o f S o l i d s , E l s e v i e r Pubo Co., New York, p. 294 (1961),  Cahn, " P h y s i c a l M e t a l l u r g y " , North-Holland P u b l i s h i n g Co,, Amsterdam (1965), Purdy, Trans, AIME, 239, No,  9,  C h r i s t i a n , "The Theory o f Transformations i n Metals and A l l o y s " , Permagon P r e s s , p, 5 94  57,  S.G,  58,  C, K i t t e l i , " I n t r o d u c t i o n to S o l i d State P h y s i c s " , John Wiley and Sons, New York, p, 63 (1962), E,S, Gould, " I n o r g a n i c Reactions and S t r u c t u r e " , Henry H o l t and Company, New'York, p, 134 (1958).  59, 60,  Ellis,  J , Appl, Phys,,  3j3_, No,  (1965),  7, p. 2906 (1967),  0, Kubaschewski, E,H, Evans and C B , A l cock, " M e t a l l u r g i c a l Thermochemistry", Pergamon P r e s s , p, 304 (1967), (  61,  R,T, F o l e y , M,J, B o l t o n , and W, S o c , 100, p, 538 (1953),  M o r i l l , J , Electrochem,  62,  B,D, L i c h t e r and C, Wagner, J , Electrochem, S o c , p, 168 (1960),  63,  K, Hauffe, " O x i d a t i o n o f Metals", Plenum P r e s s , New p. 365 f f (1965),  10 7, York,  Bibliography  (Cont'd)  Reinhold and H. S e i d e l , 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 L a b o r a t o r i e s S c i e n t i f i c and A n a l y t i c a l Equipment B u l l e t i n , 79.177/EM9, (1967).  

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