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Mechanisms of voltage controlled reactive sputtering and physical properties of reactively sputtered… Affinito, John David 1984

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MECHANISMS OF VOLTAGE CONTROLLED REACTIVE SPUTTERING AND PHYSICAL PROPERTIES OF REACTIVELY SPUTTERED CERMET FILMS By JOHN DAVID AFFINITO B . S c , Lawrence I n s t i t u t e of Techology, 1975 B.Sc. , Lawrence I n s t i t u t e of T e c h o l o g y , 1975 M . S c , Wayne S t a t e U n i v e r s i t y , 1978  THIS THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of P h y s i c s We accept t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d  THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1984 © John D a v i d A f f i n i t o ,  1984  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e for reference  and  study.  I  further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be  department o r by h i s o r her  granted by  the head o f  representatives.  my  It i s  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be  allowed w i t h o u t my  permission.  Department of The U n i v e r s i t y o f B r i t i s h 1956 Main Mall Vancouver, Canada V6T 1Y3  Columbia  written  ABSTRACT  T h i s t h e s i s d e a l s w i t h the mechanisms i n v o l v e d i n r e a c t i v e l y s p u t t e r i n g a m e t a l t a r g e t i n an I n e r t / r e a c t i v e gas glow d i s c h a r g e w i t h the e l e c t r i c a l t r a n s p o r t and  and  o p t i c a l p r o p e r t i e s of A1/A1N g r a n u l a r  m e t a l ( o r cermet) f i l m s produced by t h i s t e c h n i q u e .  E x p e r i m e n t s are  d e s c r i b e d i n w h i c h an A l t a r g e t i s s p u t t e r e d i n Ar/N2 and Ar/C>2 atmospheres.  The  r e l a t i o n s h i p s between c h e m i c a l p r o c e s s e s  o c c u r r i n g on  the t a r g e t s u r f a c e , s u b s t r a t e s u r f a c e , and i n the glow d i s c h a r g e  of a dc  p l a n a r magnetron s p u t t e r i n g system are s t u d i e d f o r the purpose o f c o n t r o l l i n g f i l m composition.  The  p o s i t i v e feedback mechanisms w h i c h  l e a d to the w e l l known t r a n s i t i o n s between bare and covered s u r f a c e s are c o r r e l a t e d w i t h glow d i s c h a r g e  target  characteristics.  are shown t o be i n agreement w i t h a model which assumes two mechanisms f o r t a r g e t coverage:  (1) c h e m i s o r p t i o n  gas s p e c i e s from the s p u t t e r i n g gas; and s p e c i e s from the s p u t t e r i n g c u r r e n t .  These d a t a distinct  of n e u t r a l r e a c t i v e  (2) i o n p l a t i n g of r e a c t i v e gas  T h i s model a l l o w s e s t i m a t i o n of  the s t a b i l i t y of the glow d i s c h a r g e a g a i n s t the p o s i t i v e feedback mechanisms and  i n d i c a t e s under what c i r c u m s t a n c e s  glow d i s c h a r g e w i l l permit surface coverage.  v o l t a g e c o n t r o l of  s u s t a i n e d o p e r a t i o n at a l l degrees o f t a r g e t  W i t h the v o l t a g e c o n t r o l method, a one  correspondence between t a r g e t v o l t a g e and f i l m c o m p o s i t i o n established.  I n a d d i t i o n , a method i s p r e s e n t e d  f i l m composition  the  from o n l y the glow d i s c h a r g e  to  one  is  for calculating  characteristics.  the  - iii  My e x p e r i m e n t s show t h a t v o l t a g e magnetron s p u t t e r i n g  -  c o n t r o l l e d , r e a c t i v e dc, planar  i s i d e a l l y s u i t e d t o the d e p o s i t i o n  cermets of c o n t r o l l e d c o m p o s i t i o n .  X-ray d i f f r a c t i o n ,  of A1/A1N transmission  e l e c t r o n m i c r o s c o p e (TEM), H a l l , and r e s i s t i v i t y v s . temperature d a t a f o r these A1/A1N cermets a r e p r e s e n t e d as a f u n c t i o n of m e t a l volume f r a c t i o n (Xv) and c o r r e l a t e d w i t h t h e glow d i s c h a r g e c h a r a c t e r i s t i c s of the d e p o s i t i o n  process.  M e t a l p r e c i p i t a t e s are seen t o form and,  t h e r e b y , the f i l m p r o p e r t i e s  are i n t e r p r e t e d  i n terms of  granular  composites o f A l and A1N c r y s t a l l i t e s when the A l / N r a t i o becomes greater  than one.  A percolation threshold  i s observed i n t h e  c o n d u c t i v i t y a t a c r i t i c a l volume f r a c t i o n (Xvc) o f 0.72 ± .02.  The  c o n d u c t i v i t y , a, e x h i b i t s power law b e h a v i o r b o t h above and below X v c . Above X v c , a ~ (Xv - X v c ) , w i t h t = 1.75 ± . 1 , i n e x c e l l e n t agreement t  w i t h the t h e o r e t i c a l p r e d i c t i o n of 1.7 f o r a m i x t u r e o f two "normal" c o n d u c t o r s ( i . e . m e t a l l i c o r semiconductor c o n d u c t i o n , but not h o p p i n g or t u n n e l i n g ) . Xv) Xvc,  _ s  Below X v c , c o n d u c t i o n i s v i a hopping and a /** (Xvc -  , w i t h s = 4.3 ± .1. F o r a m i x t u r e of normal c o n d u c t o r s below s i s predicted  t o be 0.7, w h i l e  t h e r e i s no t h e o r e t i c a l p r e d i c t i o n  f o r s when c o n d u c t i o n i s v i a h o p p i n g .  T h i s power law b e h a v i o r o f  hopping c o n d u c t i v i t y w a r r a n t s f u r t h e r t h e o r e t i c a l , as w e l l as experimental, i n v e s t i g a t i o n .  Further,  the temperature b e h a v i o r of t h e  c o n d u c t i v i t y i s c o n s i s t e n t w i t h t h e view t h a t hopping i s from d e f e c t t o d e f e c t w i t h i n the A1N g r a i n s g r a i n hopping.  as opposed t o d i r e c t m e t a l g r a i n t o m e t a l  The temperature b e h a v i o r of the c o n d c u t i v i t y  also  i n d i c a t e s t h a t e l e c t r o n l o c a l i z a t i o n e f f e c t s become i m p o r t a n t f o r Xvc < Xv < 0.8.  - iv -  In s p i t e of the obvious granular nature of these f i l m s , n e i t h e r the e f f e c t i v e medium or M a x w e l l - G a r n e t t t h e o r i e s f o r g r a n u l a r appears adequate i n d e s c r i b i n g t h e i r o p t i c a l p r o p e r t i e s . s t r u c t u r e i n t h e UV o p t i c a l a b s o r p t i o n  Observable  and IR r e f l e c t i v i t y seem t o be  p r o p e r t i e s of A1N and not due t o t h e m i c r o g r a n u l a r A1/A1N c o m p o s i t e .  materials  s t r u c t u r e of the  That o p t i c a l p r o p e r t i e s p r e d i c t e d i n the g r a n u l a r  t h e o r i e s a r e n o t o b s e r v e d , even though the f i l m s a r e g r a n u l a r , i s a t t r i b u t e d t o t h e e f f e c t of a l a r g e number o f s i n g l e and m u l t i p l e atom A l i n c l u s i o n s , w i t h o t h e r than b u l k o p t i c a l p r o p e r t i e s , t h a t a r e not t a k e n i n t o account i n these t h e o r i e s .  - v TABLE OF CONTENTS  Page ABSTRACT  i  TABLE OF CONTENTS  i v  L I S T OF FIGURES  v i i  L I S T OF SYMBOLS  ix  ACKNOWLEDGEMENTS CHAPTER  xii i  I - INTRODUCTION  1  1.1  Sputtering  2  1.2  E l e c t r i c a l T r a n s p o r t and O p t i c a l P r o p e r t i e s of Cermets  9  I.2-a  E l e c t r i c a l T r a n s p o r t P r o p e r t i e s of Cermets  10  1.2- b  O p t i c a l P r o p e r t i e s of Heterogeneous M i x t u r e s  17  1.3  P h y s i c a l P r o p e r t i e s o f A1N and A l  26  1.3- a  A1N  27  I.3-b  Al  28  CHAPTER I I - MECHANISMS AND CONTROL OF THE REACTIVE SPUTTERING PROCESS  30  II. 1  Apparatus  34  II.2  E x p e r i m e n t a l R e s u l t s and D i s c u s s i o n  39  II.2-a II.2-b  The T a r g e t R e a c t i o n P r e d i c t i o n of F i l m C o m p o s i t i o n Characteristics  45  11.2-c  and E x p e r i m e n t a l Method  from Plasma  C a l c u l a t i o n of t h e S p u t t e r i n g Y i e l d  57 66  - vi-  Page CHAPTER I I I - FILM PROPERTIES - EXPERIMENTAL RESULTS AND DISCUSSION 111.1 111.2 CHAPTER  69  E l e c t r i c a l T r a n s p o r t P r o p e r t i e s o f A1/A1N Cermets  69  O p t i c a l P r o p e r t i e s o f A1/A1N Cermets  79  IV - CONCLUSION  IV. 1  Reactive  IV.2  A1/A1N Cermets D e p o s i t e d by V o l t a g e C o n t r o l l e d Reactive  S p u t t e r i n g Mechanisms  Sputtering  96 96  97  IV.2-a  E l e c t r i c a l Transport Properties  97  IV.2-b  Optical Properties  98  BIBLIOGRAPHY  100  APPENDIX ON OPTICAL CALCULATIONS  105  - vii -  LIST OF FIGURES Figure  Page  1  Schematic of s p u t t e r i n g  process  5  2  Schematic of s p u t t e r i n g  chamber  35  3  Al-Ar/N  4  Comparison of v o l t a g e c o n t r o l l e d and power c o n t r o l l e d reactive sputtering discharge c h a r a c t e r i s t i c s  42  Variations i n Al-Ar/N with F F ^ , and S  50  5  2  glow d i s c h a r g e c h a r a c t e r i s t i c s  2  discharge c h a r a c t e r i s t i c s  A r >  6  Variations i n Al-Ar/0 w i t h F , F , and S A r  7  2  discharge c h a r a c t e r i s t i c s 51  Q  V a r i a t i o n of P /P_ w i t h P / I a t 0 = 1 r  t  D e p o s i t i o n r a t e vs A l  9  Variations  N  60  and 1/P„ 2  N  with A l *  p and TCR vs x ( i n AINx)  11  V o l t a g e dependence o f the e f f e c t i v e m e t a l s p u t t e r i n g yield X-ray d i f f r a c t i o n d a t a f o r A1/A1N cermet f i l m s correlated with deposition discharge c h a r a c t e r i s t i c s . . TEM d a t a f o r A1/A1N cermet f i l m s c o r r e l a t e d w i t h deposition discharge c h a r a c t e r i s t i c s R e s i s t i v i t y vs T and InT f o r A1/A1N cermet f i l m s o f v a r i o u s m e t a l volume f r a c t i o n s  13 14 15  62  2  10  12  52  r  8  of P„  40  C o n d u c t i o n a c t i v a t i o n e n e r g i e s f o r A1/A1N cermet films  64  68 70 71 73 75  - viii  -  Figure 16  Page I n v e r s e H a l l c o e f f i c i e n t f o r A1/A1N cermet f i l m s w i t h m e t a l volume f r a c t i o n s near the p e r c o l a t i o n threshold  77  17  C r i t i c a l exponents f o r c o n d u c t i o n i n A1/A1N cermets....  78  18  O p t i c a l a b s o r p t i o n d a t a f o r A1/A1N cermet f i l m s correlated with deposition discharge c h a r a c t e r i s t i c s . . .  80  O p t i c a l a b s o r p t i o n d a t a f o r A1/A1N cermet f i l m s correlated with deposition discharge c h a r a c t e r i s t i c s . . .  81  MGT c a l c u l a t i o n of o p t i c a l a b s o r p t i o n f o r A1/A1N cermets as a f u n c t i o n of A l volume f r a c t i o n  83  MGT c a l c u l a t i o n of o p t i c a l a b s o r p t i o n i n A1/A1N cermets as a f u n c t i o n of A1N r e f r a c t i v e i n d e x  84  EMT c a l c u l a t i o n of o p t i c a l a b s o r p t i o n i n A1/A1N cermets as a f u n c t i o n o f A l volume f r a c t i o n  85  Coated sphere-EMT c a l c u l a t i o n of o p t i c a l a b s o r p t i o n i n A1/A1N cermets as a f u n c t i o n of A l volume f r a c t i o n . .  86  Comparison of o p t i c a l a b s o r p t i o n d a t a f o r a c t u a l A1/A1N cermet f i l m s w i t h coated sphere-EMT calculations  87  EMT c a l c u l a t i o n of r e f l e c t a n c e o f A1/A1N cermets as a f u n c t i o n of A l volume f r a c t i o n  88  Coated sphere-EMT c a l c u l a t i o n of r e f l e c t a n c e o f A1/A1N cermets as a f u n c t i o n of A l volume f r a c t i o n  89  IR r e f l e c t a n c e d a t a f o r A1/A1N cermet f i l m s correlated with deposition discharge c h a r a c t e r i s t i c s . . .  90  19  20 21 22 23 24  25 26 27 28  Optical  c o n s t a n t s o f A1N  108  29  Optical  c o n s t a n t s of A l  109  - ix -  LIST OF SYMBOLS Definition  Used as a r b i t r a r y c o n s t a n t s .  O p t i c a l e m i s s i o n i n t e n s i t y of 3961.5 A l i n e o f n e u t r a l A l atoms. Radius of a p a r t i c l e i n a cermet  material.  Radius of a s p h e r i c a l volume of cermet Energy of a d e f e c t  material.  state.  Photon energy. Fermi E n e r g y . Average e l e c t r i c f i e l d i n s i d e a cermet. E l e c t r o n i c charge. E l e c t r i c f i e l d i n hopping c o n d u c t i o n . Ar f l o w r a t e . N  2  flow rate.  0  2  flow rate.  Fermi-Dirac d i s t r i b u t i o n function. F r a c t i o n of p o s i t i v e i o n s i n s p u t t e r i n g r e a c t i v e gas s p e c i e s . Total sputtering  current  (electronic +  i o n current ionic).  Optical extinction coefficient. Boltzmann's  constant.  G e n e r i c c h e m i c a l symbol f o r s p u t t e r e d m e t a l atom.  that are  - x -  Symbol  Definition  N  Density of states function for defects.  N  Total number of inclusions with dipole moment p.  n  Optical r e f r a c t i v e index.  n  Total number of reactive gas molecules adsorbed on the surface of the sputtering target.  P^ P  r  M  Ar p a r t i a l pressure. No p a r t i a l pressure.  P °2  0  P  Reactive gas p a r t i a l pressure.  r  2  p a r t i a l pressure.  P  Total pressure.  p  Dipole moment of an inclusion i n a cermet material.  Q  For a coated sphere, Q = 1 - coating thickness/total The t o t a l radius includes the coating. Q f o r a coated d i e l e c t r i c (insulating) sphere.  Q  m  Q for a coated metal sphere.  R  Generic chemical symbol for a reactive gas molecule.  R  Optical reflectance.  Rg  H a l l constant.  S  Pumping speed.  S(Ar)  Pumping speed for Ar gas.  S(N2)  Pumping speed f o r N2 gas.  S(02)  Pumping speed for O2 gas.  radius.  - xi -  Symbol  Definition  s  C r i t i c a l exponent f o r c o n d u c t i o n below Xvc.  T  Temperature.  t  Time.  t  C r i t i c a l exponent f o r c o n d u c t i o n above Xvc.  t^  C o a t i n g t h i c k n e s s on coated d i e l e c t r i c  t  C o a t i n g t h i c k n e s s on coated m e t a l  u  C r i t i c a l exponent f o r i n t e r p a r t i c l e s p a c i n g .  V  Cathode v o l t a g e i n s p u t t e r i n g .  W  Cathode power i n s p u t t e r i n g  Xv  Volume f r a c t i o n of m e t a l i n a cermet.  Xvc  C r i t i c a l v a l u e of Xv a t the p e r c o l a t i o n t h r e s h o l d .  x  x i n AINx.  a  P r o d u c t of r e a c t i v e gas impingement r a t e per u n i t P and c o e f f i c i e n t f o r n e u t r a l r e a c t i v e gas c h e m i s o r p t i o n on a sputtering target.  P  Number of N2 m o l e c u l e s g e t t e r e d per A l atom s p u t t e r e d .  Y  Secondary e l e c t r o n e m i s s i o n c o e f f i c i e n t .  6  6A1  e  Ion p l a t i n g s t i c k i n g c o e f f i c i e n t f o r p o s i t i v e r e a c t i v e s p e c i e s i m p i n g i n g on a s p u t t e r i n g t a r g e t .  e  Average d i e l e c t r i c c o n s t a n t of a cermet m a t e r i a l .  sphere.  sphere.  r  the  * = the number of A l atoms s p u t t e r e d per  second. gas  D i e l e c t r i c c o n s t a n t of i n s u l a t i n g m a t e r i a l i n a cermet. e m e^  D i e l e c t r i c c o n s t a n t of m e t a l l i c m a t e r i a l i n a cermet, c  D i e l e c t r i c c o n s t a n t of m a t e r i a l t h a t i s c o a t i n g an sphere i n a cermet.  insulating  - xii -  Symbol E  Definition D i e l e c t r i c c o n s t a n t of m a t e r i a l t h a t i s c o a t i n g a m e t a l l i c sphere i n a cermet.  e^  Average d i e l e c t r i c constant cermet.  of a c o a t e d i n s u l a t i n g sphere i n a  e mcs  Average d i e l e c t r i c constant z cermet.  of a coated m e t a l l i c sphere i n a  n ££  E f f e c t i v e s p u t t e r i n g y i e l d f o r m e t a l atoms.  e  cs  ^eff  =  +  y)'  S p u t t e r i n g y i e l d f o r m e t a l atoms. t]  S p u t t e r i n g y i e l d f o r r e a c t i v e gas  9  Polar angle i n a s p h e r i c a l coordinate  6  F r a c t i o n of the s u r f a c e of a s p u t t e r i n g t a r g e t t h a t i s c o v e r e d w i t h a t a r g e t m a t e r i a l - r e a c t i v e gas compound l a y e r .  \  Photon w a v e l e n g t h .  u  Mobility.  p  Resistivity.  a  Conductivity.  T T  molecules. system.  Time d u r a t i o n of a s p u t t e r i n g c u r r e n t t r a n s i e n t . R  Time r e q u i r e d f o r a p r e s s u r e chamber to be damped out.  t r a n s i e n t i n the  sputtering  $  Electric potential.  AE  AE = E - Ef = the c o n d u c t i o n a c t i v a t i o n energy.  Al  Magnitude of s p u t t e r i n g c u r r e n t t r a n s i e n t .  - xiii -  ACKNOWLEDGEMENTS  I am pleased to thank Dr. R.R. Parsons for the great amounts of time and e f f o r t he has invested i n this project as my supervisor. His guidance was invaluable. I also wish to thank Dr. R. Barrie, N. F o r t i e r , M. Brett, and Dr. J.A. Rostworowski for the many illuminating discussions we have had.  N. F o r t i e r provided valuable assistance with the transport  measurements, Mary Major assisted with the TEM work, and, using Dr. R.R. Haering's profilometer, M. Brett performed many of the f i l m thickness measurements. For f i n a n c i a l support, I wish to thank the Natural Sciences and Engineering Research Council of Canada and the University of B r i t i s h Columbia. To a l l my friends and r e l a t i v e s who encouraged and supported me throughout my studies I give my h e a r t f e l t thanks. repeated  To my father's  question, I would l i k e to answer "Yes, I am f i n a l l y through". Thank you.  - 1 -  CHAPTER 1 INTRODUCTION  Microgranular  m i x t u r e s of m e t a l l i c and i n s u l a t i n g m a t e r i a l s  (cermets o r g r a n u l a r m e t a l s ) a r e c u r r e n t l y of great  i n t e r e s t , both  p r a c t i c a l l y and t h e o r e t i c a l l y . They a r e of p r a c t i c a l i n t e r e s t as s e l e c t i v e s o l a r a b s o r b e r s [1] and temperature s t a b i l i z e d , t h i n f i l m resistors  [ 2 ] , T h e o r e t i c a l l y , they r e p r e s e n t r e a l , macroscopic systems  t h a t may be used t o study t h e c r i t i c a l phenomena a s s o c i a t e d w i t h a p e r c o l a t i o n system near the p e r c o l a t i o n t h r e s h o l d discussed  [2-6],  As w i l l be  s h o r t l y , these p r o p e r t i e s o f i n t e r e s t , b o t h p r a c t i c a l l y and  t h e o r e t i c a l l y , depend c r u c i a l l y upon the m i c r o g e o m e t r i c a l  configuration  of t h e f i l m , and not j u s t upon the o v e r a l l , b u l k c h e m i c a l c o m p o s i t i o n . This  t h e s i s focuses,  i n p a r t , on some of the p h y s i c a l  of A1/A1N cermets r e a c t i v e l y s p u t t e r e d an Ar/N2 atmosphere.  properties  from an A l s p u t t e r i n g t a r g e t i n  However, i n d e v e l o p i n g the f a b r i c a t i o n t e c h n i q u e  some v e r y i n t e r e s t i n g r e s u l t s  c o n c e r n i n g the mechanisms i n v o l v e d i n  r e a c t i v e s p u t t e r i n g were uncovered, and these r e s u l t s seem t o be a t l e a s t as i m p o r t a n t as the p h y s i c a l p r o p e r t i e s  of t h e f i l m s produced.  T h e r e f o r e , i n view of t h e ever i n c r e a s i n g r o l e of r e a c t i v e s p u t t e r i n g i n t h i n f i l m deposition during  the l a s t twenty y e a r s [ 7 - 9 ] , f u l l y  half of  t h i s t r e a t i s e w i l l concern experiments performed t o determine and t o model t h e mechanisms i n v o l v e d i n the r e a c t i v e s p u t t e r i n g p r o c e s s .  Due  t o t h e l a r g e number of i n t e r r e l a t e d parameters i n v o l v e d i n the r e a c t i v e s p u t t e r i n g p r o c e s s , l i t t l e i n the way of g e n e r a l ,  systematic  studies  - 2 -  r e l a t i n g f i l m p r o p e r t i e s or p r o c e s s c o n t r o l t o d e p o s i t i o n parameters been p u b l i s h e d  [7],  Therefore,  has  a study of the mechanisms i n v o l v e d i n  r e a c t i v e s p u t t e r i n g , w i t h the g o a l of d e t e r m i n i n g  some f a i r l y  g u i d e l i n e s f o r c o n t r o l of the d e p o s i t i o n p r o c e s s ,  i s of  universal  considerable  importance. This t h e s i s i s organized  as f o l l o w s .  i n t r o d u c t o r y c h a p t e r w i l l be a r e v i e w o f : s p u t t e r i n g process; of cermets; and Al.  remainder of  I p r e s e n t my  optical  experimental  and  the  properties  o p t i c a l p r o p e r t i e s of A1N  c o n c e r n i n g the mechanisms of r e a c t i v e s p u t t e r i n g . give experimental  this  (1) the p r i n c i p l e s of  (2) the e l e c t r i c a l t r a n s p o r t and  (3) the e l e c t r i c a l and  I n c h a p t e r two,  The  and  theoretical results In chapter three,  data c o n c e r n i n g the e l e c t r i c a l t r a n s p o r t and  I  optical  p r o p e r t i e s of r e a c t i v e l y s p u t t e r e d A1/A1N cermet f i l m s , and an a n a l y s i s of these  1.1  data.  Sputtering " S p u t t t e r i n g " i s a s s o c i a t e d w i t h the impingement of a p a r t i c l e  (ion,  atom, cosmic r a y , e t c . ) on a m a t e r i a l body w i t h the r e s u l t t h a t ,  t h r o u g h momentum t r a n s f e r , some p a r t i c l e s of the m a t e r i a l body are ejected  ("sputtered") [7-14],  The word " s p u t t e r i n g " i s used i n  c o n j u n c t i o n w i t h a l a r g e number of m o d i f i e r s l a r g e number of r e l a t e d p r o c e s s e s .  The  to d e s c r i b e an  equally  m o d i f i e r s are g e n e r a l l y employed  t o i n d i c a t e what type of p a r t i c l e s are c a u s i n g  the s p u t t e r i n g , what  t e c h n i q u e i s used to generate these p a r t i c l e s , and,  i n the case of  c o n t r o l l e d d e p o s i t i o n of t h i n f i l m s , what c o n d i t i o n s e x i s t on s u b s t r a t e upon which the s p u t t e r e d  f l u x lands  [7-14].  the  - 3 -  Ions a r e g e n e r a l l y used t o cause s p u t t e r i n g f o r t h e c o n t r o l l e d d e p o s i t i o n of t h i n f i l m s [13,14],  The two broad c l a s s e s of i o n  s p u t t e r i n g a r e c a l l e d " i o n beam" s p u t t e r i n g and "glow sputtering.  discharge"  I n e i t h e r of these cases the m a t e r i a l t o be s p u t t e r e d ( o r  the t a r g e t ) i s t h i c k enough t h a t the s p u t t e r e d p a r t i c l e s a r e e j e c t e d o n l y from the s u r f a c e t h a t i s under i o n bombardment.  The p a r t i c l e s t h a t  are e j e c t e d a r e g e n e r a l l y atoms o r s m a l l m o l e c u l e s o f t h e t a r g e t m a t e r i a l and "secondary" e l e c t r o n s .  I n the case of I o n beam s p u t t e r i n g ,  a c o l l i m a t e d beam o f i o n s of r a t h e r w e l l d e f i n e d k i n e t i c energy causes the s p u t t e r i n g , and the t e c h n i q u e i s f u r t h e r c a t e g o r i z e d by the method of p r o d u c i n g t h e beam [ 1 3 ] , to be s p u t t e r e d  I n glow d i s c h a r g e  s p u t t e r i n g , the m a t e r i a l  forms the cathode i n a glow d i s c h a r g e  p r i m a r i l y by p o s i t i v e i o n s from t h e glow [ 7 ] ,  and i s bombarded  In this latter  process,  the i n c i d e n t i o n s a r e not c o l l i m a t e d and t h e i r k i n e t i c e n e r g i e s a r e d i s t r i b u t e d ( i n some cases r a t h e r w i d e l y ) from the glow t o the t a r g e t . i s related to: and  due t o c o l l i s i o n s i n t r a n s i t  This d i s t r i b u t i o n i n i n c i d e n t i o n energies  t h e p o t e n t i a l d i f f e r e n c e between the cathode  (target)  the glow; the temperature; the t o t a l and p a r t i a l p r e s s u r e s  gases i n t h e glow d i s c h a r g e  environment; and the c r o s s s e c t i o n f o r  charge t r a n s f e r between t h e " v a r i o u s [7,15],  These glow d i s c h a r g e  by m o d i f i e r s i n d i c a t i n g :  atoms, m o l e c u l e s , and i o n s p r e s e n t  sputter techniques are f u r t h e r  the t a r g e t shape ( p l a n a r ,  b e l t . . . ) ; t h e f r e q u e n c y o f the e l e c t r i c a l d i s c h a r g e e x t e r n a l agent used t o support the glow d i s c h a r g e thermionic  of t h e  described  cylindrical, ( d c , a c , o r r f ) ; any  (magnetic  fields,  e m i t t e r s , t e s l a c o i l s . . . ) ; t h e r e a c t i v i t y of the d i s c h a r g e  - 4 -  gases w i t h r e s p e c t t o t h e t a r g e t m a t e r i a l ( i n e r t o r r e a c t i v e ) ; t h e c o n d i t i o n s e x i s t i n g a t the s u b s t r a t e ( t e m p e r a t u r e ,  s t a t e of motion w i t h  r e s p e c t t o t h e t a r g e t , s u b s t r a t e b i a s , i s t h e r e a glow d i s c h a r g e a t the s u b s t r a t e , and i f s o , a t what f r e q u e n c y ) [8,10-12],  This  seemingly  e n d l e s s a d d i t i o n o f m o d i f y i n g words can l e a d t o some f a i r l y l o n g names. For i n s t a n c e , the e x p e r i m e n t a l  work t o be d i s c u s s e d i n t h i s t h e s i s i s  concerned w i t h " v o l t a g e c o n t r o l l e d , dc, r e a c t i v e , p l a n a r magnetron sputtering".  T h i s name i n d i c a t e s t h a t :  the t a r g e t i s f l a t  (planar); a  magnetic f i e l d i s used t o h e l p c o n f i n e the glow t o a r e g i o n v e r y near the t a r g e t , t o make b e t t e r use o f the i o n i z i n g a b i l i t i e s  of the  secondary e l e c t r o n s and t o c r e a t e t h e i o n s c l o s e t o the t a r g e t where they a r e needed (magnetron); at l e a s t some component i n the gas m i x t u r e w i l l c h e m i c a l l y combine w i t h t h e t a r g e t m a t e r i a l ( r e a c t i v e ) ; the discharge  i s dc ( d c ) ; the e l e c t r i c a l c h a r a c t e r i s t i c s of the glow  discharge are a l t e r e d or maintained  by m o n i t o r i n g and c o n t r o l l i n g t h e  cathode v o l t a g e ( v o l t a g e c o n t r o l l e d ) . Fig.  1 s c h e m a t i c a l l y d e p i c t s the v a r i o u s processes  simultaneously  which  i n s i d e a s p u t t e r i n g chamber w h i l e s p u t t e r i n g a m e t a l  t a r g e t (M) i n t h e presence o f an A r / r e a c t i v e gas (R) m i x t u r e . processes  occur  These  may be b r o a d l y d i v i d e d i n t o t h r e e c a t e g o r i e s a c c o r d i n g t o t h e  p h y s i c a l l o c a t i o n a t w h i c h t h e process  takes p l a c e .  They a r e t a r g e t  r e a c t i o n s , w a l l ( o r s u b s t r a t e ) r e a c t i o n s , and gas r e a c t i o n s . The and  t a r g e t s u r f a c e i s c o n t i n u o u s l y bombarded by e n e r g e t i c i o n s  t h e r m a l n e u t r a l s of the gases p r e s e n t  i n the d i s c h a r g e .  The i o n  Fig.'l " " 5  Schematic d e p i c t i o n o f p r o c e s s e s o c c u r r i n g d u r i n g r e a c t i v e s p u t t e r i n g of a m e t a l t a r g e t (M) i n an A r / R e a c t i v e gas (R) atmosphere.  - 6 -  bombardment can cause s p u t t e r i n g of the t a r g e t s u r f a c e m a t e r i a l and t h e emission  of secondary e l e c t r o n s .  r e a c t i v e gas may c h e m i c a l l y  Further,  the bombarding i o n s of the  bond w i t h the t a r g e t m a t e r i a l and produce a  t a r g e t m a t e r i a l - r e a c t i v e gas compound l a y e r on p a r t s of the t a r g e t surface.  I f n e u t r a l R m o l e c u l e s chemisorb on t h e b u l k t a r g e t m a t e r i a l ,  then t h e f l u x of t h e r m a l n e u t r a l s of R w i l l a l s o c o n t r i b u t e t o t h e formation  o f t h e compound l a y e r .  S i n c e t h e y i e l d of s p u t t e r e d  target  atoms and secondary e l e c t r o n s i s d i f f e r e n t f o r bare metal and compounded targets  [ 8 ] , t h e s e y i e l d s w i l l be h i g h l y dependent on t h e degree of  t a r g e t coverage.  A l s o , the presence of a compound l a y e r on the t a r g e t  s u r f a c e means t h a t the c o n s t i t u e n t s of R w i l l a l s o be s p u t t e r e d target  from t h e  surface. Sputtered  f l u x w i l l condense and r e a c t w i t h t h e t h e r m a l f l u x of R  n e u t r a l s on t h e w a l l s and s u b s t r a t e s  [16-21].  Note t h a t even i f R  m o l e c u l e s do not chemisorb on t h e b u l k t a r g e t m a t e r i a l , t h e condensing f l u x i s l a r g e l y atomic i n n a t u r e [7-8] and i s expected t o be much more r e a c t i v e than t h e b u l k m a t e r i a l .  T h i s compound f o r m a t i o n  on t h e w a l l s  (sometimes c a l l e d g e t t e r i n g ) a l s o s e r v e s t o lower the p a r t i a l of t h e r e a c t i v e gas i n t h e chamber. c o n t r o l l e d by the s p u t t e r e d  pressure  The speed o f t h i s g e t t e r pumping i s  f l u x , w h i c h , i n t u r n , i s c o n t r o l l e d by the  number and energy of i o n s i n c i d e n t on the t a r g e t s u r f a c e as w e l l as t h e degree t o which the t a r g e t s u r f a c e i s covered by a r e a c t i v e  gas-target  m a t e r i a l compound l a y e r . Ar and R a r e a l l o w e d  t o f l o w i n t o the vacuum chamber through a  c o n t r o l l e d l e a k w h i l e they a r e s i m u l t a n e o u s l y  pumped out by m e c h a n i c a l  - 7 -  means (such as a p a r t i a l l y t h r o t t l e d d i f f u s i o n pump). t h i s produces p a r t i a l p r e s s u r e s  I n steady s t a t e ,  of the two gases t h a t a r e determined by  t h e i r i n d i v i d u a l l e a k r a t e s and pumping speeds, p r o v i d e d no glow d i s c h a r g e .  that there i s  I n t h e presence of t h e glow d i s c h a r g e ,  the g e t t e r i n g  a c t i o n o f t h e s p u t t e r e d f l u x on t h e r e a c t i v e gas a c t s as another pumping p o r t i n p a r a l l e l w i t h the d i f f u s i o n pump. e l e c t r o n s emitted  I n the glow r e g i o n , secondary  from t h e t a r g e t h e l p t o s u s t a i n t h e d i s c h a r g e  e l e c t r o n impact I o n i z a t i o n o f the gaseous s p e c i e s p r e s e n t . the glow may a c t as a source o f p o s i t i v e and n e g a t i v e w h i c h serve  through  Therefore,  i o n s o f A r and R  t o d r i v e a v a r i a b l e speed r e a c t i v e gas g e t t e r pump.  The  p o t e n t i a l drop between t h e t a r g e t and t h e glow r e g i o n t h a t i s needed t o maintain  the discharge  w i l l depend on the y i e l d of secondary e l e c t r o n s  from t h e t a r g e t s u r f a c e (more e l e c t r o n s mean a lower v o l t a g e ) .  This  i m p l i e s t h a t t h i s p o t e n t i a l d i f f e r e n c e w i l l depend s t r o n g l y on t h e y i e l d of secondary e l e c t r o n s , w h i c h , i n t u r n , i s l a r g e l y c o n t r o l l e d by t h e degree of t a r g e t coverage.  I n a d d i t i o n , R m o l e c u l e s may d i s s o c i a t e i n t o  i o n s and n e u t r a l s o f t h e i r v a r i o u s c o n s t i t u e n t s .  The p o s i t i v e i o n s i n  the glow w i l l be a c c e l e r a t e d towards the t a r g e t , however, due t o collisions  (mostly  symmetric charge t r a n s f e r r e a c t i o n s [15]) many o f t h e  i o n s t h a t reach t h e cathode have c o n s i d e r a b l y l e s s k i n e t i c energy than e x p e c t e d by merely c o n s i d e r i n g t h e p o t e n t i a l d i f f e r e n c e between t h e cathode and t h e glow d i s c h a r g e The  previous  (cathode f a l l )  d i s c u s s i o n s show t h a t t h e gaseous ambient i s coupled  to. the t a r g e t , w a l l , and glow d i s c h a r g e r e g i o n s a r e a l l coupled longstanding  [7,15].  regions.  Therefore,  these  t o each o t h e r t h r o u g h t h e s p u t t e r i n g gas.  problem i n c o n t r o l l i n g r e a c t i v e l y s p u t t e r e d  film  three A  - 8 -  c o m p o s i t i o n s i s t h a t p o s i t i v e feedback between t h e g e t t e r i n g r a t e a t t h e w a l l and the m e t a l s p u t t e r i n g r a t e c o n s p i r e  t o f o r c e the t a r g e t  t o e i t h e r remain bare m e t a l o r become c o m p l e t e l y layer  [16-21],  surface  covered w i t h a compound  I f the s p u t t e r i n g r a t e i s becoming g r e a t enough t o  uncover some p o r t i o n s of t h e t a r g e t s u r f a c e then t h e s p u t t e r i n g y i e l d increases  from these bare r e g i o n s .  T h i s causes an i n c r e a s e i n t h e  g e t t e r i n g r a t e w h i c h reduces the number of r e a c t i v e gas s p e c i e s a v a i l a b l e to cover the t a r g e t .  T h i s , i n t u r n , a l l o w s the bare spots t o  grow l a r g e r and f u r t h e r i n c r e a s e s  the s p u t t e r i n g y i e l d .  feedback c y c l e q u i c k l y l e a d s t o a c o m p l e t e l y  This p o s i t i v e  bare t a r g e t s u r f a c e .  This  abrupt change i n t h e degree o f s u r f a c e coverage a l s o causes an abrupt change i n the secondary e l e c t r o n e m i s s i o n a b r u p t change i n t h e cathode f a l l .  y i e l d , which r e s u l t s i n an  A l s o , w i t h t h e abrupt i n c r e a s e i n  s p u t t e r i n g y i e l d , an abrupt i n c r e a s e i n s p u t t e r e d  f l u x occurs that i s  accompanied by an abrupt decrease i n r e a c t i v e gas p a r t i a l p r e s s u r e to i n c r e a s e d  gettering.  due  I f one s t a r t s from a bare t a r g e t , the o p p o s i t e  r e a c t i o n , w h i c h l e a d s t o a covered t a r g e t , o c c u r s i f t h e s p u t t e r i n g r a t e becomes t o o low t o keep the e n t i r e s u r f a c e c l e a r e d of the compound layer.  There i s c o n s i d e r a b l e  h y s t e r e s i s observed i n t h e d i s c h a r g e  c h a r a c t e r i s t i c s between these two d i r e c t i o n s [16-21], w i t h the r e s u l t t h a t a gap e x i s t s i n t h e I - V - P operation  of the d i s c h a r g e  films sputtered sputtered  c h a r a c t e r i s t i c s under w h i c h s t a b l e  i s possible.  S i n c e i t has been found t h a t  from a bare t a r g e t are n e a r l y pure m e t a l , w h i l e  from a c o m p l e t e l y  metal-reactive  R  films  covered t a r g e t a r e s t o i c h i o m e t r i c  gas compound [16,20,21], t h i s p o s i t i v e feedback c y c l e i s  - 9 -  seen t o s e v e r e l y r e s t r i c t the a t t a i n a b l e f i l m c o m p o s i t i o n s .  S i n c e the  c o m p o s i t i o n of s p u t t e r e d f i l m s w i l l depend on the r e l a t i v e a r r i v a l r a t e s of s p u t t e r e d atoms and r e a c t i v e gas molecules  at the s u b s t r a t e ,  knowledge of the n a t u r e and s t r e n g t h of the c o u p l i n g between the t a r g e t , gas, and s u b s t r a t e would be v e r y i m p o r t a n t i n any attempt d e p o s i t i o n of t h i n f i l m s .  at c o n t r o l l e d  The n a t u r e of t h i s c o u p l i n g w i l l be e x p l o r e d  i n t h i s t h e s i s through a d e t a i l e d balance a n a l y s i s of the movements of s p u t t e r e d f l u x and r e a c t i v e gas molecules T h i s study w i l l show why  i n the s p u t t e r i n g chamber.  i t i s p o s s i b l e to maintain s t a b l e operating  c o n d i t i o n s at a l l degrees of t a r g e t coverage f o r an A l t a r g e t i n an Ar/N2 atmosphere (and o t h e r m e t a l - r e a c t i v e gas combinations  i n which  r a p i d c h e m i s o r p t i o n of the n e u t r a l r e a c t i v e gas on the b u l k metal does not o c c u r ) , p r o v i d e d t h a t cathode v o l t a g e i s c o n t r o l l e d . at  This  stability  a l l degrees of t a r g e t coverage g i v e s access t o AINx f i l m s f o r a l l x  between zero and one. which x may  In a d d i t i o n , t h i s a n a l y s i s y i e l d s a technique  by  be c a l c u l a t e d from knowledge of the glow d i s c h a r g e  c h a r a c t e r i s t i c s alone.  1.2  E l e c t r i c a l Transport and Optical Properties of Cermets Cermets ( o r g r a n u l a r m e t a l s ) are m i c r o g r a n u l a r m i x t u r e s  i n s u l a t i n g and m e t a l l i c p a r t i c l e s .  T h i s term i s sometimes a p p l i e d t o  s i m i l a r m i x t u r e s of i n s u l a t o r - s e m i c o n d u c t o r or particles.  of  semiconductor-metal  When the volume f r a c t i o n of the m e t a l l i c c o n s t i t u e n t (Xv) i s  near z e r o or one the p r o p e r t i e s of the cermet are c l o s e to those of a pure phase.  However, at i n t e r m e d i a t e v a l u e s of Xv some p r o p e r t i e s  - 10 -  (resistivity, density) while  average  [2,22]  temperature  appear  to  be  intermediate  other  properties  (optical  temperature  dependence  of  fundamentally  different  the  properties  geometric  these  geometry  I.2-a  law  is  law  meant  behaviour that  the is  Xv  in  the  to  be  different  the  A  will  of  the  details  exhibit and  brief  now be  seen  scaling  one  on e i t h e r side  relation.  to  [3,24],  For  more  scaling,  the  reader  and  the  of  depend  theory  only  on  detailed is of  Xvc  of  for  or  (TCR),  pure  of  and  phases,  the  behaviour  arises  that  is  primarily  discussion  of  from  some  of  given.  below  to  Xv  of  Xvc. in  this  The  Xvc.  By  of  The  on  scaling  relation  and  discussions  referred critical  to  the  the  this  -  phenomena  Xvc|  power  and  phase  predict  behaviour  for  that  values  is  law  it  relates  side  the  is  the  called are  sample  behaviour  on p e r c o l a t i o n transitions  of  expected  exponents of  of  electrical  power  other  these  literature  mixtures  law  the  shown  the  for  power  dimensionality on  have  conduction)  expression  exponent  spatial  [24]  case |Xv  than  particular  the  the  higher  studies  some p o w e r  [3,24].  W/AI2O3 c e r m e t s  tunneling  study,  as  side  Xvc The  and  under  vary  of  (a)  hopping  above  to  [23]  Theoretical  (not  both  neighborhood  on  studies  (Xvc).  property  expected  [3]  properties  and  phase  mixture.  resistance  those  [4-6]  pure  conductivity  conductors  conductivity,  exponent  of  threshold  "normal"  power  the  experimental  behaviour  percolation two  either  of  E l e c t r i c a l Transport Properties of Cermets Previous  power  of  to  absorption  resistivity)  from  dependent  coefficient  and theory  [25,26].  - 11 -  When t h e c o n d u c t i v i t i e s o f t h e two phases d i f f e r A1/A1N o r W/AI2O3 cermets normal c o n d u c t i o n i n s t e a d conduction  by as much as i n  does not occur below X v c ,  proceeds v i a t u n n e l i n g between i s o l a t e d m e t a l  p a r t i c l e s and through the i n t e r v e n i n g i n s u l a t o r p a r t i c l e s The  resistivities  than 1 0  1 5  conduction  o f A l and A1N a r e  S2-cm [ 2 9 ] , r e s p e c t i v e l y .  3 x 10  - 6  [2,5,23,27],  Q-cm [28] and g r e a t e r  T h i s added c o m p l i c a t i o n o f t u n n e l i n g  below Xvc has not y e t been t r e a t e d i n t h e c o n t e x t o f a  c r i t i c a l t h e o r y of phase t r a n s i t i o n s , n o r has any e x p e r i m e n t a l for  evidence  c r i t i c a l b e h a v i o u r o f t u n n e l i n g i n t h i s regime been p r e s e n t e d .  method of t h e o r e t i c a l treatment seems s t r a i g h t f o r w a r d enough. s h o u l d e x p r e s s 0, f o r t u n n e l i n g between i s o l a t e d m e t a l i s l a n d s  The  One [30,31],  i n terms of t h e i s l a n d s i z e and i n t e r i s l a n d s e p a r a t i o n , then s u b s t i t u t e the power law r e l a t i o n s f o r t h e s e two d i s t a n c e s i n t o t h e e x p r e s s i o n a.  for  U n f o r t u n a t e l y , w h i l e t h e power law r e l a t i o n f o r t h e m e t a l c l u s t e r  s i z e i s w e l l known [3] t h e r e l a t i o n f o r t h e i n t e r c l u s t e r s p a c i n g i s not.  A measurement o f t h e power law b e h a v i o u r of t u n n e l i n g f o r Xv < X v c  s h o u l d , however, a l l o w t h i s r e l a t i o n t o be determined by i n v e r t i n g t h e expression  f o r the t u n n e l i n g c o n d u c t i v i t y .  Previous  treatments  o f t u n n e l i n g f a r below Xvc, w h i c h were n o t  meant t o d e a l w i t h c r i t i c a l phenomena, i n cermets have p r e d i c t e d [2] and  o b s e r v e d [2,32] l n p <*> 1/VT temperature b e h a v i o u r f o r t h e r e s i s t i v i t y  i n cermet f i l m s w i t h average m e t a l g r a i n s i z e s l e s s than ~ 40 A.  The  e x p l a n a t i o n , however, i n v o l v e d assumptions f o r t h e r e l a t i o n between t h e d i s t r i b u t i o n of g r a i n s i z e s and i n t e r g r a i n s p a c i n g s  that d i d not r e f l e c t  the t r u e s t r u c t u r e o f t h e s e g r a n u l a r m a t e r i a l s [ 6 , 3 3 ] .  In particular,  -  Abeles  et  al.  [2]  granular  metals  electron  is  neighboring both  the  in  and  these  paths  of  the  grain.  This  charging  [6,33]  two  the  always was  a  too 1  a  hopping the  energy  the  the  law,  large  temperature detailed in  have  theory to  just  was  classic this  for  low to  that  the  range  field  to  path  grain  are  change  sizes  size  found  studies  sizes.  which  temperature  Therefore,  order  to  long  to  accomodate  to  be  as  there  follow  over  this  l n p **s 1  intergrain the  that,  grain  the  electrons  in  showed in  as  As  and to  by  resulted  also.  changed  was  macroscopi-  tunneling  predicted  distribution of  spacing  conduction,  sizes.  grain  grain  These  the  and  spacing  the  size  to  of  controversial  dominated  p was  [6,33].  two  a  function  be  behaviour  the  a  intergrain  taken  of  of  be  an on  was  distribution  described,  account  behaviour  contained  done  the  placed  grain  For  optimal  metals,  The  Intergrain  grain  of  to  when  of  conduction  studies  granular been  the  found  and  in  distribution  available  optimal  a path with  of  and  probability.  make  use  broad  size  involved  grain  size.  that  conduction  microscopically  conduction  grain  energy  was  grain  both  very  changed  The [34]  was  energy  the  size,  hopping  metallic  made w e r e ;  temperature  narrow  //T  grain  there  sufficiently  hopping  they  for  charging  isolated  and  assumptions,  recently,  //T  the  caused  distributions 1  that  changed  which  process, More  spacing  "optimal"  temperature  as  to  that  an  the  one  highest  changed  considering  intergrain  -  expression  from  proportional  With  by  an  removed  assumptions  cally;  derived  12  which  spacing  lnp  ^  given  sizes  //T.  was the  the far  lnp  observed. treatment same  idea  of of  variable an  range  optimal  hopping  hopping  given  path.  by  Mott  However,  in  - 13  M o t t ' s t r e a t m e n t the t r a d e o f f was  -  between the e x p o n e n t i a l  dependences  of the hopping f r e q u e n c y on d i s t a n c e between l o c a l i z e d s t a t e s and  the  d i f f e r e n c e i n energy of these s t a t e s (where i t i s assumed t h a t hopping between s t a t e s of e q u a l energy i s f a v o r e d ) . s t a t e s to be a c o n s t a n t More r e c e n t  and  Mott took the d e n s i t y  found l n p ~ 1  t h e o r e t i c a l studies  of  /T.^^  [35,36] have i n d i c a t e d t h a t  the  Coulomb i n t e r a c t i o n between l o c a l i z e d e l e c t r o n s g i v e s r i s e to a "Coulomb gap"  i n the d e n s i t y of s t a t e s near the Fermi l e v e l and  p a r a b o l i c d e n s i t y of s t a t e s near the Fermi l e v e l . density i s incorporated lnp~  1 //T  i n the Mott t h e o r y  behaviour i s obtained,  not  s a t i s f i e d very near t o Xvc,  to i n t e r i s l a n d separation values  of Xv w e l l below  If this  parabolic  f o r v a r i a b l e range h o p p i n g ,  provided  i s s m a l l compared to the hopping l e n g t h  results in a  t h a t the l o c a l i z a t i o n  [36],  length  This l a s t r e s t r i c t i o n i s  or when the r a t i o of m e t a l i s l a n d s i z e  i s l a r g e , but w i l l be expected t o h o l d f o r Xvc.  A l l of these v a r i a b l e range hopping t h e o r i e s p r e d i c t an apparent temperature dependent " a c t i v a t i o n " energy ( i . e . y\rr-henius p l o t s of r e s i s t i v i t y do not y i e l d s t r a i g h t l i n e s ) . of the c o m p e t i t i o n  T h i s i s because of the n a t u r e  between a v a i l a b l e c o n d u c t i o n pathways.  Paths of a  g i v e n p a r t i c l e s i z e or s e p a r a t i o n w i l l have c o n d u c t i o n a c t i v a t i o n energies  t h a t d i f f e r from paths w i t h d i f f e r e n t p a r t i c l e s i z e s or  separations.  The  paths of l e a s t r e s i s t a n c e ( o r o p t i m a l p a t h s ) w i l l  the ones t h a t c a r r y the most c u r r e n t .  Since  the c o m p e t i t i o n  v a r i o u s pathways i s a f f e c t e d by the t e m p e r a t u r e , as the changes the o p t i m a l paths w i l l a l s o change.  be  between the  temperature  S i n c e each c l a s s of  - 14 -  pathways  has  an a c t i v a t i o n  pathways,  the  vary  temperature  with  apparent  energy  that  activation as  the  differs  energy  optimal  for  paths  from  the  the  other  sample  switch  as  with  classes  a whole  of  will  changing  temperature. One  other  has  been  for  Nb/Al 03  presented  2  conduction approach number  treatment  activation  defect  that  of  defect  was  be  via  taken  opposed  to  to  problem,  hopping  Devenyi  Using  [38].  equation, written  a  In  the  hopping directly  showed  e is  statistical the  defect  field. a  to  conduction  as  a  material Nb  that  existed  in  the  defect  across  the  an approach  to  of  the  forbidden in  insulator. presented  approximation  that  the  hopping  to  a  gap.  the  large  Conduction  insulator  as  this et  Boltzmann  conductivityy  His  nonuniform  Croitoru  the  data  the  such  To m o d e l  by  Xvc  temperature.  continuous,  defect  time  found  contained a  below  conductivity  Devenyi  power  excess  from  cermets  regarding  [37]  composites,  vary  in  a l . transport  could  be  as  H(E,T,F)  o~f  where  to  states  relaxation  al.  insulating  due  followed  Croitoru  et  these  energy  states  distribution  hopping  Devenyi  composites.  assumed  of  by  of  At  the  electronic  occupation state this  generalization  function,  energy, point of  charge,  T is  the  optimal  N(E,T,F)  \x i s  carrier  N is  the  Croitoru  f(E,T,F)  the the  density  temperature,  makes path  an  and F  used  (1-1)  mobility, of  assumption  method  dE  defect is  that  by M o t t  the is  f  is  states,  the E  is  electric equivalent  [34],  Abeles  to  -  [2], 1-1  and is  others  sharply  assumed  to  functional  be  peaked only  forms  conductivity  distribution  to  The  at  via  may  due  Devenyi  energy £  [35,36]. a  particular  the  be  of  optimal  that  for  so  the that  integrand conduction  (optimal)  energy.  N,  f  u,  and  of  to  Eqn.  can  be  Various  calculate  the  path.  al.  pointed  then  the  maximum o f  the  solution  by  is  energy  this  used  et  given  -  assumption  states  then  15  out  that the  of  if  f  is  a  integrand  the  Maxwell-Boltzmann  of  following  Eqn.  1-1  occurs  at  an  equation:  o(ln[Nu]) o(E-E  To  explain  vary  as T  their to  data,  some  states-mobility  which  power,  product  showed  Devenyi to  Nf  are  E  and Ef the  density  respectively, level  are  u and  respectively,  experimentally. functional the  form  conduction  yields  the of Uf  state states are  A and  than  activation  N  In  *  u  the  conduction  al.  took  i  l  the  activation  density  L  )  energy  to  of  exp(A[E-E ] ) f  Fermi general  energies and  constants  r e a s o n was gave  energy.  (1-3)  p  f  mobilities  p are  it  f  and  the  No p h y s i c a l other  kT  be  N u ~ where  et  )  the  at  in  that  correct use  the  Fermi  general  given  Making  respectively,  are for  and  and  level at  the  Fermi  determined choosing  temperature of  N  Eqn.  1-3  this behaviour in  Eqn.  1-2  for  - 16 -  1 $-E  f  = (AkTp)  1 _ P  =  AE  (1-4)  and  InAE = l n ( [ A p k ]  1 1-p  ) +  1 1-p  ln(T),  (1-5)  where E i s the o p t i m a l energy w h i c h maximizes the i n t e g r a n d of Eqn. The 1-3,  r e s u l t of t h i s a n a l y s i s , as shown i n Eqn.  1-5,  was  t h a t , given  1-1. Eqn.  the c o n d u c t i o n a c t i v a t i o n energy s h o u l d v a r y as some power ( r e l a t e d  to p) of T.  S i n c e the d e f e c t d e n s i t y w i l l depend s t r o n g l y on the sample  c o m p o s i t i o n , t h i s power of T s h o u l d be d i f f e r e n t f o r each v a l u e of Xv and, t h e r e f o r e , no c h a r a c t e r i s t i c temperature behaviour  should  exist  from sample t o sample. Even though, i n the N b / A l 2 3 samples s t u d i e d by D e v e n y i , n  type of b e h a v i o u r was  observed,  of the Nu p r o d u c t , shown i n Eqn.  this  a p h y s i c a l model f o r the f u n c t i o n a l form 1-3,  would be very d e s i r a b l e .  N e v e r t h e l e s s , the i d e a of a l a r g e number of c o n t i n u o u s l y d e f e c t s t a t e s w i t h i n the f o r b i d d e n gap  distributed  l e a d i n g to a c o n t i n u o u s l y  changing a c t i v a t i o n energy i s c e r t a i n l y v a l i d .  Indeed, i t i s i m p l i c i t  i n a l l of the p r e v i o u s l y mentioned o p t i m a l p a t h approaches t o hopping conduction  [2,34-36].  A l s o , o p t i c a l t r a n s i t i o n s between band t a i l s have  shown the d e n s i t y of s t a t e s i n the c o n d u c t i o n band t a i l s to e x h i b i t e x p o n e n t i a l dependence on E-E^» under c o n s i d e r a t i o n [ 3 9 ] .  an  where E^ i s the energy of the band edge  The more h e a v i l y doped the sample the more  prominent t h e presence o f these e x p o n e n t i a l  t a i l s become.  It is  c e r t a i n l y p o s s i b l e t h a t the m e t a l l i c i m p u r i t i e s w i t h i n the i n s u l a t i n g g r a i n s o f a cermet c o u l d e x h i b i t a s i m i l a r e x p o n e n t i a l with respect  d e n s i t y of s t a t e s  t o t h e i r d i s t r i b u t i o n near the Fermi l e v e l .  I f one has  o n l y r e s i s t a n c e d a t a i t i s not p o s s i b l e , however, t o s e p a r a t e t h e d e n s i t y of s t a t e s and m o b i l i t y c o n t r i b u t i o n s i n Eqn. 1-3. suggests that nonlinear  Devenyi  e f f e c t s a t h i g h f i e l d s may a l l o w f o r such a  separation. For Xv j u s t above Xvc o t h e r i n v e s t i g a t o r s [5,40,41] have observed a m e t a l t o i n s u l a t o r t r a n s i t i o n as a f u n c t i o n of T.  On t h e low T s i d e  of t h i s t r a n s i t i o n , e l e c t r o n l o c a l i z a t i o n e f f e c t s were observed as InT b e h a v i o u r , a n e g a t i v e  m a g n e t o r e s i s t a n c e , and a r e l a t i v e l y  temperature-independent H a l l c o e f f i c i e n t . measurements served  E i t h e r o f these l a s t two  t o determine t h a t t h e p **> InT b e h a v i o u r was due t o  e l e c t r o n l o c a l i z a t i o n and not e l e c t r o n - e l e c t r o n i n t e r a c t i o n .  I.2-b  Optical Properties of Heterogeneous Mixtures There a r e a g r e a t many mean f i e l d type approaches t h a t have been  used t o p r e d i c t the o p t i c a l p r o p e r t i e s of heterogeneous m i x t u r e s o f materials of d i f f e r i n g d i e l e c t r i c properties.  I n f a c t , one r e v i e w  a r t i c l e by Van Beek [42] summarizes 29 d i f f e r e n t methods.  While the  d e t a i l s of these many approaches may d i f f e r c o n s i d e r a b l y ,  i n essence  each i s based on one o f o n l y two d i f f e r e n t fundamental a s s u m p t i o n s : t h a t p a r t i c l e s o f one m a t e r i a l a r e randomly embedded i n an amorphous matrix  of a n o t h e r m a t e r i a l ; o r , a random m i x t u r e of two d i f f e r e n t t y p e s  -  o f p a r t i c l e s i s assumed.  18  -  I n e i t h e r c a s e , a f t e r making one of these two  b a s i c a s s u m p t i o n s , a l o n g w i t h o t h e r l e s s i m p o r t a n t assumptions, an e f f e c t i v e d i e l e c t r i c c o n s t a n t f o r the composite i s d e r i v e d i n terms of the d i e l e c t r i c c o n s t a n t s and volume f r a c t i o n s of the component m a t e r i a l s [42,43].  These c a l c u l a t i o n s are done by a v e r a g i n g over volumes  t h a t are  l a r g e compared w i t h the i n h o m o g e n i t i e s and s m a l l compared w i t h the w a v e l e n g t h of l i g h t i n v o l v e d [42,43].  I n the f i r s t c a s e , the d i e l e c t r i c  c o n s t a n t s of the m a t r i x and embedded m a t e r i a l s appear I n an asymmetric manner i n the d e r i v e d e f f e c t i v e d i e l e c t r i c c o n s t a n t of the c o m p o s i t e , w h i l e o p t i c a l p r o p e r t i e s of both p a r t i c l e s e n t e r s y m m e t r i c a l l y i n the second case.  T h i s i s t o be expected from the symmetries  i n h e r e n t i n the b a s i c assumptions.  (or asymetries)  W h i l e secondary assumptions (such as  the d i s t r i b u t i o n of p a r t i c l e shapes and s i z e s ) l e a d t o q u a n t i t a t i v e d i f f e r e n c e s i n the r e s u l t s , major, and fundamental, q u a l i t a t i v e d i f f e r e n c e s f o l l o w from c h o o s i n g one or the o t h e r of the two b a s i c assumptions mentioned e a r l i e r  [42],  I n a d d i t i o n , each of these  approaches has been g e n e r a l i z e d t o a l l o w f o r m i x t u r e s of more than two m a t e r i a l s [42,43]. At t h i s p o i n t I b r i e f l y p r e s e n t the b a s i c s of t h e s e two fundamental approaches, as w e l l as one g e n e r a l i z a t i o n to more than two materials.  T h i s p r e s e n t a t i o n i s meant t o be u s e f u l i n the a n a l y s i s of  the o p t i c a l p r o p e r t i e s of r e a c t i v e l y s p u t t e r e d t h i n f i l m cermets, and does not even approach a comprehensive e x p o s i t i o n on a l l of the v a r i o u s s u b t l e t i e s t h a t have been i n t r o d u c e d i n the l i t e r a t u r e t o date on the g e n e r a l t o p i c of heterogeneous m i x t u r e s .  -  19  -  Perhaps the s i m p l e s t approach t o an asymmetric t h e o r y i s a g e n e r a l i z a t i o n of a c a l c u l a t i o n of R a y l e i g h ' s f o r a c u b i c a r r a y o f s p h e r e s , of r a d i u s a and d i e l e c t r i c c o n s t a n t e l e c t r i c f i e l d , Eo.  m  I n such an a r r a y , t h e f i e l d  to a f i r s t a p p r o x i m a t i o n , induced  e > i n an e x t e r n a l seen by any sphere i s ,  j u s t Eo because the f i e l d s due t o d i p o l e s  i n o t h e r spheres c a n c e l due t o t h e c u b i c symmetry and h i g h e r  order m u l t i p o l e s are neglected. important increases.  These h i g h e r o r d e r terms become more  as the spheres p a c k i n g d e n s i t y (volume f r a c t i o n , Xv) A s p h e r i c a l p o r t i o n of t h i s a r r a y , o f r a d i u s a , i s then  c e n t e r e d on t h e o r i g i n o f a s p h e r i c a l c o o r d i n a t e system embedded i n a m a t e r i a l of d i e l e c t r i c constant  Then, by making use o f t h e  C l a u s i u s - M o s s o t t i r e l a t i o n f o r p o l a r i z a b l e spheres immersed i n a d i e l e c t r i c medium, f a r away from the a r r a y , at a p o s i t i o n ( r , 9 ) , one may c a l c u l a t e t h e p o t e n t i a l as [ 4 4 ] ,  <t> =  N  m E  m  +  i 2e. i  (1-6)  where r and 6 have the u s u a l meaning i n r e f e r e n c e t o a s p h e r i c a l c o o r d i n a t e system, and N i s t h e t o t a l number of spheres.  Similarly, i f  the s p h e r i c a l s e c t i o n of the c u b i c a r r a y of spheres embedded i n t h e d i e l e c t r i c medium i s assumed t o have an e f f e c t i v e d i e l e c t r i c e, one may a l s o w r i t e t h i s p o t e n t i a l as  constant,  - 20 -  ,3  e - e. i_ N £ + 2E,  H 1  EorcosG  (1-7)  Upon e q u a t i n g Eqns. 1-6 and 1-7 one o b t a i n s  £ -  1  E +  E  E.  2E  = Xv  ~  E.  +  2  m  (1-8)  1  E  m  £ j  i  or  3Xv  E =  £,  1  +  (E  -  E )  m i E + 2 E . - Xv ( E - £. ) m l m l 4  One s h o u l d note t h e asymmetric appearance o f £  (1-9)  m  and  in  Eqns. 1-8 and 1-9, as w e l l as the f a c t t h a t £ d i v e r g e s when EJJ + 2e^ = ^ ( E J J , - E ^ ) .  T h i s d i v e r g e n c e has been l a b e l e d "the  d i e l e c t r i c anomaly" [ 4 ] , and t h i s type o f f e a t u r e i s common t o a l l asymmetric t h e o r i e s . at  E x p r e s s i o n s s i m i l a r t o Eqn. 1-9 have been a r r i v e d  by many o t h e r a u t h o r s  [42, 43] w i t h l e s s r e s t r i c t i v e assumptions  (such as not r e q u i r i n g c u b i c symmetry or s p h e r i c a l p a r t i c l e s ) and more i n v o l v e d mathematics.  I n keeping w i t h the l i t e r a t u r e , I w i l l r e f e r to  asymmetric t h e o r i e s of o p t i c a l p r o p e r t i e s as M a x w e l l - G a r n e t t (MGT).  Theories  T h i s nomenclature a r i s e s because James C l e r k M a x w e l l G a r n e t t was  the f i r s t  t o a r r i v e a t Eqn. 1-9 based on an a n a l y s i s of M a x w e l l ' s  e q u a t i o n s f o r p r o p a g a t i n g e l e c t r o m a g n e t i c waves [ 4 5 ] , whereas o t h e r s , as  - 21  -  I have j u s t o u t l i n e d , had p r e v i o u s l y a r r i v e d at Eqn.  1-9  from s t a t i c  considerations. Symmetric t h e o r i e s are g e n e r a l l y r e f e r r e d to as " E f f e c t i v e Medium Theories"  (EMT), the f i r s t example of which seems to have been put  f o r w a r d by D.A.C. Bruggeman i n 1935 e f f e c t i v e d i e l e t r i c constant,  [46].  Bruggeman sought  the  e, of a randomly d i s p e r s e d m i x t u r e of  t y p e s of p a r t i c l e s , w i t h d i e l e c t r i c c o n s t a n t s r e s p e c t i v e volume f r a c t i o n s Xv and f i e l d w i t h i n the composite i s Eo,  (1-Xv). and  e  and  m  and  with  I f the average e l e c t r i c  i f any  particular particle is  assumed t o be immersed i n a medium of e f f e c t i v e d i e l e c t r i c c o n s t a n t then the induced d i p o l e moment of t h a t p a r t i c l e , say one w i t h constant  e , m  may  be w r i t t e n as  two  e,  dielectric  [4]  3 e - e p = 7— v , Eo 4-n: e + 2e m  (1-10)  m  0  where v i s the volume of the p a r t i c u l a r p a r t i c l e under s c r u t i n y .  Since  t h e s e i n d u c e d d i p o l e s produce d e v i a t i o n s from Eo i n p r o p o r t i o n t o p, sum,  over a l l p a r t i c l e s , of these d e v i a t i o n s  e q u a l z e r o , by d e f i n i t i o n of Eo. 1-10  Therefore,  f o r each type of p a r t i c l e l e a d s  e Xv £ m  m  (or d i p o l e moments) must summation of e q u a t i o n s  like  to  - e ,+ 2E+ (1-Xv) n  the  £. — £ 1  £. + I  2E  = 0  (1-11)  - 22 -  or  e - 7- (A + A *  2  + 8e e.) m i  (1-12)  where  e + £3(1-Xv) - 1^| e m  Note the symmetric r o l e s of e 1-13,  m  and  (1-13)  ±  i n Eqns. 1-11  as w e l l as the l a c k of any d i e l e c t r i c anomaly.  through  T h i s l a c k of a  d i e l e c t r i c anomaly i s common t o a l l symmetric t h e o r i e s .  An EMT  f o r m u l a t i o n t h a t has been seen t o agree more c l o s e l y than o t h e r s t e s t e d , when w e l l d e f i n e d m i x t u r e s of known e, 6^, and  were measured [43]  was  Eqn. approaches.  1-14 has been a r r i v e d at by a t l e a s t two f a i r l y Landau and L i f s h i t z  different  [48] o b t a i n e d i t by; expanding, t o  second o r d e r , the l o c a l d i e l e c t r i c c o n s t a n t , e l e c t r i c f i e l d , and e l e c t r i c displacement  f i e l d s about t h e i r average v a l u e s ; making  s u b s t i t u t i o n s based upon the f a c t t h a t the d i v e r g e n c e of the unaveraged displacement  f i e l d s h o u l d v a n i s h ; t h e n , w i t h t h e h e l p of s e v e r a l v e c t o r  - 23 -  identities,  c a l c u l a t e d the average e l e c t r i c d i s p l a c e m e n t i n the  composite.  Looyenga's [49] approach  to Eqn. 1-14  was  very d i f f e r e n t .  Looyenga assumed t h a t the e f f e c t i v e d i e l e c t r i c c o n s t a n t f o r the m i x t u r e was  the same as f o r another m i x t u r e of the same o v e r a l l c o m p o s i t i o n but  i n w h i c h the d i f f e r e n t types of p a r t i c l e s themselves had volume f r a c t i o n s of the two m a t e r i a l s .  different  Then, to second o r d e r , the  d i e l e c t r i c c o n s t a n t s f o r each type of p a r t i c l e were expanded i n powers of the volume f r a c t i o n s of the p a r t i c l e s about the o v e r a l l c o m p o s i t i o n of the m i x t u r e .  I n the l i m i t of g o i n g t o p a r t i c l e s composed of o n l y one  m a t e r i a l , a second o r d e r d i f f e r e n t i a l e q u a t i o n f o r the e f f e c t i v e d i e l e c t r i c c o n s t a n t as a f u n c t i o n of Xv was s u b j e c t to the boundary c o n d i t i o n s e(o) = symmetry between e  m  and  developed and s o l v e d , and e ( l ) = e . m  as w e l l as the l a c k of any  anomaly i s even more apparent i n Eqn. 1-14  The  dielectric  than i n Eqn. 1-12.  Further,  the more compact f o r m u l a t i o n and t r a n s p a r e n t symmetry of Eqn. 1-14  make  i t e a s i e r to a p p l y i n a c t u a l c a l c u l a t i o n s , p a r t i c u l a r l y when a l l of the d i e l e c t r i c c o n s t a n t s are complex numbers. MGT  has been found t o d e s c r i b e , q u i t e s a t i s f a c t o r i l y , the o p t i c a l  p r o p e r t i e s of m i x t u r e s t h a t were q u i t e o b v i o u s l y p a r t i c l e s of  one  m a t e r i a l embedded i n a m a t r i x of another m a t e r i a l [4,50-54],  Of  p a r t i c u l a r importance t o t h i s work, i t was  found adequate i n d e s c r i b i n g  the o p t i c a l p r o p e r t i e s of c o s p u t t e r e d cermets.  These are cermets  that  were p r e p a r e d by s p u t t e r i n g , s i m u l t a n e o u s l y , from two t a r g e t s (a m e t a l and an i n s u l a t o r ) onto a s i n g l e s u b s t r a t e .  The d i e l e c t r i c anomaly  m a n i f e s t s i t s e l f as a peak i n the o p t i c a l a b s o r p t i o n spectrum of the  -  composite. move  towards  positions are  The  longer  are  and  have  shapes  these  different  in  an  size  effort  particle  anomaly  is  the at  general longer EMT  composites of  found  wavelengths  particles  (or  been  that  composites  [43].  were  properties metal that  may of  of  the  should  shape  heights  in  The  path  is  of  rapidly than  authors sizes  results  as  of  the causing  varied  found  observed  height  of  widths  particle  heights  effects  peak  higher  free  to  peak  and  A number  and  and  the  broaden  mean  much more is  peak  discrepancies.  predicted  Xv  observed,  While  distributions  positions  the  and  values.  electron  and  the  absorption  to  describe a  there  the  with  to  s t i l l  magnitude  the  than  of  dielectric predicted,  predicted,  and  especially  method, either  are  properties  dispersed reported  EMT b e h a v i o u r ,  either well  have  or  EMT  suited  been  introduced EMT  no  optical  mixture cases  of  of of  two  types  sputtered  rather,  these  to  than  mixed.  extending  that  the  randomly  displaying  particularly  in  increased.  widths  particular,  However,  cermets  a particle  size  obviously  of  The  peak  between  is  these  peak  mechanically  be  target.  explain  of  predicted,  predicted  effects  that  is  [8,50-53].  films  One m e t h o d materials  the  -  by MGT,  that  found  were  cosputtered)  the  vanish with  background  has  described  and  In  to  Xv  the  discrepancy  absorption.  as  than  Inclusion  optical  peak  less  lower,  shape.  some  to  were  becomes to  this  from  investigated  conductivity  leave  well  investigations  particle  of  wavelengths  fairly  generally  [54-57]  position  24  MGT  o r MGT to  treating  reactively by  H.C.  consists  more  sputtered  van of  the  two  optical from  de H u l s t a particle  a  [58], of  single assumes  radius  a  - 25 -  and d i e l e c t r i c c o n s t a n t e thickness t  m  (or t  c  i c  ( o r e^) coated w i t h another m a t e r i a l of  m  ) and d i e l e c t r i c c o n s t a n t £  (or £  m c  i c  ).  S i n c e one of these composite p a r t i c l e s i s j u s t a p a r t i c l e of one m a t e r i a l embedded i n a m a t r i x of another m a t e r i a l , the e f f e c t i v e d i e l e c t r i c c o n s t a n t of a coated sphere, e  m c s  o b t a i n e d from Eqn. 1-9, w i t h the f o l l o w i n g  e  e  =>  m  = >  ( o r E ^ g ) . may  be  substitutions  e ( o r e. ) racs ics  e  m  ( o r  e  i  )  (1-15) e. => i  e  ( o r e. ) ic  mc  —i 3  Xv => Q  3  m  =  1  -  mc  _i3  ( o r of =  1  -  'ic  I f , f o r i n s t a n c e , one has a m i x t u r e of coated metal p a r t i c l e s uncoated i n s u l a t i n g p a r t i c l e s , then e  m c s  I s c a l c u l a t e d from Eqn.  w i t h the a p p r o p r i a t e s u b s t i t u t i o n s from Eqns. 1-15. c a l c u l a t e d from e i t h e r Eqn. 1-12 e  m c s  .  I n t h i s way,  p a r t i c l e s may i n enjcg. reported.  or Eqn. 1-14,  and  1-9,  £ i s then  where £  m  i s r e p l a c e d by  a randomly d i s p e r s e d m i x t u r e of two types of  e x h i b i t a d i e l e c t r i c anomaly, due t o a d i e l e c t r i c anomaly  O b s e r v a t i o n s of t h i s type of b e h a v i o u r have not y e t been  - 26 -  It averaging  should  be remembered t h a t these t h e o r i e s a r e based upon  over volumes t h a t a r e l a r g e compared w i t h p a r t i c l e s i z e and  s m a l l compared t o the w a v e l e n g t h o f l i g h t .  A l s o , i f the p a r t i c l e s i z e  i s so s m a l l t h a t b u l k o p t i c a l p r o p e r t i e s no l o n g e r apply t o i t then a l l o w a n c e f o r t h i s e f f e c t must be made. very d i f f i c u l t  T h i s l a t t e r c o r r e c t i o n may be  i f p a r t i c l e s i z e s a r e d i s t r i b u t e d from i s o l a t e d atoms on  up t o c r y s t a l l i t e s w i t h b u l k o p t i c a l p r o p e r t i e s .  1.3  Physical Properties of A1N and A l The  previous  granular metals.  s e c t i o n was concerned w i t h p h y s i c a l p r o p e r t i e s o f  The d i s c u s s i o n f o c u s e d p r i m a r i l y upon those p r o p e r t i e s  t h a t r e s u l t e d from t h e geometry o f t h e m i x t u r e , w i t h t h e p h y s i c a l p r o p e r t i e s of the m i x t u r e ' s m a t e r i a l s b e i n g of secondary i m p o r t a n c e .  Of  c o u r s e , f o r a t l e a s t two r e a s o n s , one must know the p r o p e r t i e s of t h e m i x t u r e ' s m a t e r i a l s when m o d e l l i n g The  the p h y s i c a l p r o p e r t i e s of a cermet.  f i r s t reason i s so t h a t one can i n d e e d know t h a t observed b e h a v i o u r  i s not j u s t the b e h a v i o u r o f one of the m a t e r i a l s p r e s e n t i n the mixture.  The second r e a s o n i s t h a t most of t h e q u a n t i t a t i v e a s p e c t s o f  the v a r i o u s m i x t u r e t h e o r i e s depend on the p h y s i c a l p r o p e r t i e s o f the m a t e r i a l s i n t h e m i x t u r e ( w i t h the c r i t i c a l exponents i n p e r c o l a t i o n theory  being  the e x c e p t i o n ) .  Therefore,  a t t h i s time a b r i e f r e v i e w o f  the p h y s i c a l p r o p e r t i e s o f A1N and A l , t h a t a r e r e l e v a n t t o the experimental  work d i s c u s s e d  i n t h i s t h e s i s , w i l l be p r e s e n t e d .  - 27 -  I.3-a  A1N W h i l e t h e l i t e r a t u r e on A1N i s l e s s e x t e n s i v e than f o r many o t h e r  s e m i c o n d u c t o r s ( S i , Ge, GaAs, ZnO, e t c . ) , a r e a s o n a b l e has been b u i l t up over about t h e l a s t 20 y e a r s  body o f knowledge  [22,29,59-78].  Pure A1N  i s a c o l o r l e s s s o l i d t h a t c r y s t a l i z e s i n t h e hexagonal w u r t z i t e s t r u c t u r e [66]. [66].  A t a t m o s p h e r i c p r e s s u r e , i t . sublimes  a t about 2400°C  A t room temperatures and p r e s s u r e s , i t r e a d i l y o x i d i z e s t o form a  surface l a y e r of  100 A o f amorphous A 1 0 2  3  w i t h i n 24 h.  This  oxide  l a y e r then s e r v e s as a p r o t e c t i v e b a r r i e r a g a i n s t f u r t h e r o x i d a t i o n . T h i s r a p i d o x i d a t i o n ( r o u g h l y t h r e e times  the r a t e of A l metal) leads t o  oxygen b e i n g the main u n i n t e n t i o n a l i m p u r i t y found i n A1N, r e g a r d l e s s o f the method o f p r e p a r a t i o n [ 6 6 ] ,  The tendency towards f o r m i n g  d e f i c i e n t A1N i s a l s o a common problem [ 6 6 ] .  nitrogen  A1N produced by r e a c t i v e  s p u t t e r i n g , under most c o n d i t i o n s , c r y s t a l i z e s w i t h t h e c - a x i s p e r p e n d i c u l a r t o t h e s u b s t r a t e [70,71],  T h i s r e s u l t s i n t h e (002)  peak  b e i n g t h e dominant f e a t u r e i n x-ray d i f f r a c t i o n p a t t e r n s . Pure A1N has a r e s i s t i v i t y i n excess of 1 0  1 5  Q-cm [ 2 9 ] ,  I t has  been doped n-type w i t h S i , w h i l e C, S, and Mg d o p i n g produces p-type conduction A1N  [66],  a r e e x p e c t e d t o produce n-type b e h a v i o u r ,  f o r N [65-73], A1N  N-vacancies or A l i n t e r s t i t i a l s i n n i t r o g e n d e f i c i e n t  The r e p o r t e d d e f e c t c o n d u c t i o n  as s h o u l d 0 s u b s t i t u t i n g a c t i v a t i o n energies f o r  l i e between 0.5 and 5 eV, depending on w h i c h i m p u r i t i e s a r e p r e s e n t ,  w h i l e t h e band gap i s 6.2 eV  [60-66].  O p t i c a l l y , pure A1N e x h i b i t s a d i r e c t band gap o f 6.2 eV. I n cathode luminescence measurements [ 6 2 ] , peaks a t 3.33 and 3.55 eV were  - 28  -  c o r r e l a t e d w i t h n i t r o g e n d e f i c i e n c y , w h i l e peaks at 2.71 were c o r r e l a t e d w i t h oxygen c o n t a m i n a t i o n . broad o p t i c a l a b s o r p t i o n band i n A1N  Pastrnak  method of p r o d u c i n g  A1N  eV  [60].  They  however, t h e i r  ( h i g h v o l t a g e a r c i n g of A l e l e c t r o d e s i n an  atmosphere) i s known t o a l s o produce A1N n i t r o g e n [66].  This technique  of a r c i n g A l e l e c t r o d e s i n N  o p t i c a l a b s o r p t i o n measurements on n i t r o g e n d e f i c i e n t A1N edge s h i f t i n g t o about 4 eV. range o f t h e i r equipment was  [59],  not s u f f i c i e n t to measure l a r g e enough  a l s o measured the d i s p e r s i o n of the A1N  w i t h w a v e l e n g t h , as the band edge was  calculations.  From data limited  not enough t o observe the top of the peak at 4.8  eV,  absorption.  r e f r a c t i v e index  approached.  measurements are g i v e n i n F i g . 28 i n the appendix on  (n)  These  optical  I n the i n f r a r e d , A l N e x h i b i t s a r e s t s t r a h l e n band i n the  w a v e l e n g t h r e g i o n between 11 um and  I.3-b  show the band  I n h i n d s i g h t , i t appears t h a t the dynamic  w h i c h i s on the r a p i d l y r i s i n g t a i l of the d i r e c t gap Pastrnak  their  as w e l l as the p r e s e n t work to be shown l a t e r , t h i s  dynamic range was  2  a l s o seems  2  (they appeared l i m i t e d to t r a n s m i t t a n c e s > 1%).  of P a s t r n a k ,  N  that i s quite d e f i c i e n t i n  l i k e l y t o y i e l d A l i n c l u s i o n s . Others [63,65] have c l a i m e d t h a t  absorptions  eV  et a l . observed a  c e n t e r e d at 4.8  a t t r i b u t e d t h i s broad band to oxygen c o n t a m i n a t i o n ,  and 2.78  15 um  [68,69],  Al A l i s a m e t a l t h a t m e l t s at 659°C and  lattice.  c r y s t a l i z e s i n an  Exposed t o a i r i t w i l l form /v 30 A of amorphous A l 0 3 2  fee on i t ' s  - 29 -  s u r f a c e i n 24 h [ 6 6 ] , w h i c h s e r v e s as a p r o t e c t i v e b a r r i e r a g a i n s t further oxidation. at  metals.  the  of pure A l i s 3.6  x 10  - 6  Q-cm  [28]  room t e m p e r a t u r e , and i t e x h i b i t s p-type b e h a v i o u r i n H a l l  measurements [ 7 9 ] ,  of  The r e s i s t i v i t y  O p t i c a l l y , i t behaves q u a l i t a t i v e l y l i k e most  A d e t a i l e d t a b u l a t i o n of n and k ( t h e r e a l and i m a g i n a r y p a r t s  the r e f r a c t i v e i n d e x , r e s p e c t i v e l y ) f o r A l from the f a r i n f r a r e d t o f a r u l t r a v i o l e t i s p r e s e n t e d by P o w e l l [ 8 0 ] ,  Over the photon energy  range of i n t e r e s t i n t h i s work, P o w e l l ' s d a t a shows the o p t i c a l p r o p e r t i e s of A l t o be smoothly, and s l o w l y , v a r y i n g w i t h photon energy, w i t h the e x c e p t i o n of a peaked s t r u c t u r e i n both n and k near 1.5  eV.  F i g u r e 29, i n the appendix on o p t i c a l c a l c u l a t i o n s , shows P o w e l l ' s d a t a .  - 30 -  CHAPTER I I MECHANISMS AND CONTROL OF THE REACTIVE SPUTTERING PROCESS  P l a n a r magnetron s p u t t e r i n g o f a m e t a l t a r g e t i n a r e a c t i v e gas atmosphere i s a w e l l known and u s e f u l t e c h n i q u e of e i t h e r i n s u l a t i n g o r c o n d u c t i n g  films.  f o r high rate deposition  For most a p p l i c a t i o n s i t i s  d e s i r a b l e t o maximize b o t h the r a t e o f d e p o s i t i o n and the c o n t r o l over f i l m stoichiometry.  A technique  t o achieve  these g o a l s has been  d e v e l o p e d f o r the case o f a dc p l a n a r magnetron w i t h an A l t a r g e t and an Ar/N and  2  s p u t t e r i n g gas m i x t u r e .  The method i s d e s c r i b e d  i n this thesis  i s expected t o be a p p l i c a b l e t o o t h e r systems i n w h i c h the r e a c t i v e  gas does not undergo r a p i d c h e m i s o r p t i o n  on the t a r g e t  surface.  To c o n t r o l f i l m s t o i c h i o m e t r y i t i s n e c e s s a r y t o r e g u l a t e t h e r e l a t i v e r a t e s o f a r r i v a l o f m e t a l atoms and r e a c t i v e gas s p e c i e s a t t h e substrate  [22,67],  The former i s determined by the s p u t t e r i n g r a t e ; t h e  l a t t e r by t h e r e a c t i v e gas p a r t i a l p r e s s u r e  and s t i c k i n g  coefficient.  S i n c e s p u t t e r e d m e t a l d e p o s i t s g e t t e r (combine c h e m i c a l l y w i t h ) r e a c t i v e gas  s p e c i e s on the s u b s t r a t e and on i n n e r s u r f a c e s o f the vacuum  chamber, these two r a t e s are not independent o f each o t h e r .  As a  r e s u l t , one observes a decrease i n the r e a c t i v e gas p a r t i a l p r e s s u r e as the s p u t t e r i n g r a t e i n c r e a s e s .  The method, d e s c r i b e d h e r e , f o r t h e  c o n t r o l o f these two q u a n t i t i e s i n order t o produce a f i l m o f t h e d e s i r e d composition  has been t o use the cathode v o l t a g e t o m o n i t o r t h e  degree t o which the t a r g e t s u r f a c e becomes covered w i t h an i n s u l a t i n g compound o f m e t a l atoms and r e a c t i v e gas s p e c i e s .  A similar  technique  - 31 -  f o r r e a c t i v e s p u t t e r i n g ( a t c o n s t a n t p r e s s u r e ) employed by S c h i l l e r e t a l . has used the t a r g e t v o l t a g e to determine one p a r t i c u l a r s t a t e o f t a r g e t coverage [ 8 1 ] .  I have developed  a model which a l l o w s f o r two  d i s t i n c t mechanisms by which t h i s i n s u l a t i n g l a y e r may form on t h e target surface.  One mechanisms i s c h e m i s o r p t i o n o f t h e n e u t r a l r e a c t i v e  gas s p e c i e s on the t a r g e t s u r f a c e (which can occur w i t h o u t a glow d i s c h a r g e ) ; the o t h e r ; t a r g e t coverage by i o n s and atomic r e a c t i v e gas which i s a c t i v a t e d by the glow d i s c h a r g e . l a t t e r process  "ion p l a t i n g " .  s p e c i e s o f the  I call  T h i s d i f f e r s from the g e n e r a l l y  this accepted  d e f i n i t i o n o f i o n p l a t i n g o n l y i n t h a t I am c o n s i d e r i n g t h e t a r g e t , r a t h e r than t h e s u b s t r a t e , i n t h e p l a t i n g p r o c e s s i n the presence o f 0  2  [8],  S p u t t e r i n g of A l  i s an example o f t h e former mechanism w h i l e  s p u t t e r i n g of A l i n t h e presence o f N  2  represents the l a t t e r .  The model  p r e d i c t s d i f f e r e n c e s between the glow d i s c h a r g e c h a r a c t e r i s t i c s f o r the two mechanisms, which a r e i n agreement w i t h  experiment.  I f one c o u l d smoothly and m o n o t o n i c a l l y i n c r e a s e the s p u t t e r i n g c u r r e n t ( I ) o r power (W), thus i n c r e a s i n g the s p u t t e r i n g r a t e , t o produce a c o r r e s p o n d i n g l y smooth and monotonic decrease i n r e a c t i v e gas p a r t i a l pressure achieved P  r  [22,67].  ( P ) , t h e c o n t r o l o f f i l m c o m p o s i t i o n would be e a s i l y r  A t s u f f i c i e n t l y low v a l u e s of W and h i g h v a l u e s o f  t h e f i l m s would be expected  t o be n e a r l y s t o i c h i o m e t r i c . W i t h  i n c r e a s i n g W, as t h e s p u t t e r i n g r a t e i n c r e a s e d and P  r  decreased  due t o  g e t t e r pumping by t h e s p u t t e r e d m e t a l , t h e f i l m c o m p o s i t i o n would v a r y c o n t i n u o u s l y u n t i l i t was n e a r l y a pure m e t a l a t some h i g h e r v a l u e o f W.  Such a smooth v a r i a t i o n o f P  r  w i t h I o r W does not o c c u r f o r many  -  metal-reactive  gas  that  change  an  varied held  while  the  constant  varied  the  abrupt  combinations  rate  I  The  explanation  or  gettering  formation  of  sputtering  W is  rate an  is  match  target  surface.  target  lowers  occur.  This  is  F  r  an  the  is  found  that  on  the  rate  is P  is  well  W or  into  the  as  follows.  low  r  target  When  the  begins  sputtering  I  known  is  chamber  if  F  is  is  r  surface  so  that  gettering  a bare  form  on p a r t s  rate  from  the  cycle  repeats  itself  two of  deficient  and to  also  b o t h V and P . r  on  the  while  nitrogen TEM). have  low V  films and  Films  occurs,  the  and h i g h  contain  Al  deposited  on  the  pure  metals  of  results  2  side  r  compositions.  also  considerable  Al-Ar/N  V-P  r  transition  the  is  coefficients  in  a  system, of  other  precipitates at  P  is  r  to  target  (V)  with  P  covered  coverage  voltage  hysteresis  For  no  reduced,  for  r  the  the  emission than  produced  intermediate  until  opposite  This  of  target  cathode  The  directions.  A1N, in  covered.  of  can  partially  now much  different  surface  rate  to  value  F  prevent  further  the  low  to  permits  in  At  enough  and  generally  deposited  are  expected  keep  layer  becomes  ranges  gap  are  to  target.  are  to  the  gap  transition  layer  change  stoichiometric  the  if  r  observed  electron  the  diffraction  it  is  secondary  are  x-ray  transition  P  r  the  gap  by  (F )  Since  target  films  gas  rate  covered  operating  of  gettering  the  the  fact,  value  the  observed  in  this  feedback  layers  between  In  With  an a b r u p t  hysteresis  of  reduced  [16,19,20],  a  the  reactive  sufficient  positive  compound  of  interest. in  similar  gettering  for  from  A  insulting  The  increases.  going  flow  metal  covered.  as  of  insulating  rapidly the  observed  -  fixed.  from a  longer  completely  is  [16-21].  and  of  32  points  gap it  this side (as  of seen  within  - 33 -  I have found p r e v i o u s l y [21] t h a t a s i n g l e v a l u e d , monotonic f u n c t i o n a l r e l a t i o n s h i p e x i s t s between V and P  f o r the A l - A r / N  r  system, w h i l e a range e x i s t s where each v a l u e of I corresponds v a l u e s of V or P « r  I was  When the d i s c h a r g e was  2  to three  o p e r a t e d by c o n t r o l l i n g  a b l e to o p e r a t e over the f u l l range of I - V - P  r  V,  combinations.  Thus, I c o u l d operate a t any degree of t a r g e t coverage ( o r f i l m composition) Mo  i n Ar/0  of i n t e r e s t .  Subsequent experiments  w i t h A l , Zn, I n , and  atmospheres r e v e a l e d t h a t v o l t a g e c o n t r o l was  2  not p o s s i b l e  a c r o s s the t r a n s i t i o n between bare and c o m p l e t e l y covered t a r g e t states. was  Also, i n Ar/N  p o s s i b l e w i t h Zn.  atmospheres c o n t r o l was  2  The  not p o s s i b l e w i t h Mo  but  systems t h a t were not c o n t r o l l a b l e were the  ones i n w h i c h r a p i d c h e m i s o r p t i o n of the n e u t r a l d i a t o m i c gaseous s p e c i e s o c c u r s , w h i l e t h i s type of c h e m i s o r p t i o n does not occur i n the others  [82],  T h i s i m p l i e s t h a t the presence  of the glow d i s c h a r g e I s  t o t a l l y r e s p o n s i b l e f o r a c t i v a t i n g the coverage p r o c e s s i n the c a s e , w h i l e i t may  be o n l y p a r t l y r e s p o n s i b l e i n the  E a r l i e r models by H e l l e r  latter  former.  [17] or S h i n o k i [19] have t r e a t e d the  t r a n s i t i o n as d e s c r i b e d above w i t h the o n l y t a r g e t coverage mechanism b e i n g c h e m i s o r p t i o n of r e a c t i v e gas s p e c i e s from the s p u t t e r i n g gas.  In  t h i s work I have i n c l u d e d the i o n i c bombardment mechanism a l s o . F u r t h e r , f o r the A l - A r / N f l u x of N  2  2  system, w i t h the e q u a t i o n s f o r c o n s e r v a t i o n o f  gas f l o w i n g i n t o the chamber, f l o w i n g out through the pumping  p o r t , and f l o w i n g i n t o s p u t t e r d e p o s i t s i t becomes p o s s i b l e to c a l c u l a t e t h e average f i l m c o m p o s i t i o n .  I n t h i s procedure  i t i s not n e c e s s a r y  to  know the system volume i f one knows the a c t u a l g e t t e r i n g r a t e f o r some  - 34  -  s p e c i f i c range of v a l u e s of s p u t t e r r a t e and N F o r t u n a t e l y , the s p u t t e r r a t e - N  2  partial  p a r t i a l pressure  2  pressure.  c h a r a c t e r i s t i c s show a  change of s l o p e when the f i l m s pass from the s t o i c h i o m e t r i c r e g i o n to the n o n - s t o i c h i o m e t r i c r e g i o n . counting  r  One  by  ( v i a o p t i c a l e m i s s i o n measurements) the number of A l atoms  s p u t t e r e d and P.  T h i s procedure i s f a c i l i t a t e d  may  c o u n t i n g the number of N  2  m o l e c u l e s g e t t e r e d by  monitoring  then o b t a i n the average r a t i o of A l / N atoms i n the  film.  I t s h o u l d be noted t h a t knowledge of the r a t i o of A l / N i n the f i l m no i n f o r m a t i o n about the c h e m i c a l  bonding between these  gives  species.  T h e r e f o r e , whether the f i l m c o n s i s t s merely of AINx o r a m i x t u r e  of AINx  and A l must be determined by o t h e r means.  II.1  Apparatus and  Experimental Method  A s c h e m a t i c c r o s s s e c t i o n of the p l a n a r magnetron s p u t t e r i n g chamber i s shown i n F i g . 2.  The  pump w i t h a f r e o n c o l d t r a p .  chamber i s pumped by an o i l d i f f u s i o n  For o p e r a t i o n w h i l e s p u t t e r i n g , the  pumping speed i s r e g u l a t e d by a t h r o t t l i n g v a l v e l o c a t e d between t h e c o l d t r a p and  the d i f f u s i o n pump.  The  15 cm d i a m e t e r t a r g e t of 99.999%  A l i s f i r m l y clamped by a m e t a l r i n g to a water c o o l e d b a c k i n g p l a t e . ground s h i e l d and water c o o l e d anode are p l a c e d i n f r o n t of c o n c e n t r i c t o the t a r g e t .  The  d i s c h a r g e i s powered by a 5  u n f i l t e r e d , f u l l wave r e c t i f i e d , c o n s t a n t (Plasma Therm MDS-5000D, 0-10  and kW,  c u r r e n t , dc power supply  A, 0-1000 V ) .  Operation  i s possible with  the anode e i t h e r f l o a t i n g or grounded to the m e t a l chamber. measured w i t h a c a p a c i t a n c e manometer (MKS  A  Baratron).  Pressure i s  An e l e c t r o m a g n e t  - 35 -  Fig. 2 Mass spectrometer  capacitance manometer  throttle valve  to diffusion pump  Schematic c r o s s s e c t i o n of s p u t t e r i n g  chamber.  - 36  -  i s used t o c o n f i n e the plasma i n the shape of a t o r u s d i r e c t l y i n f r o n t of the t a r g e t , and  thereby  causes the s p u t t e r i n g e r o s i o n of the t a r g e t  t o be a r i n g w i t h o u t e r d i a m e t e r of about 7.5 about 2.5 100C)  cm.  cm and  i n n e r d i a m e t e r of  A d i f f e r e n t i a l l y pumped quadrupole mass spectrometer  i s mounted i n a s i d e arm and m a i n t a i n e d  f o r l e a k d e t e c t i o n , r e s i d u a l gas a n a l y s i s , and  at 1 0  Pa.  - 3  (UTI  I t i s used  i n conduction w i t h  the  c a p a c i t a n c e manometer f o r p a r t i a l p r e s s u r e measurements.  Ar, N ,  gas  (Granville  f l o w s are c o n t r o l l e d through independent l e a k v a l v e s  P h i l l i p s model 203) ( H a s t i n g s H-5  model A l l - 5 ) .  s l i t s of a 3/4  A microprocessor  t h r o u g h a q u a r t z window onto the  m Spex o p t i c a l spectrometer  (model 1702)  system i s used to m o n i t o r ,  r e c o r d , and/or  gas f l o w r a t e s ,  o p t i c a l s p e c t r a , s u b s t r a t e b i a s and  cathode c u r r e n t , power and  to  lines.  c o n t r o l a l l a s p e c t s of the e x p e r i m e n t ; e.g.  The  2  L i g h t from the plasma, seen p e r p e n d i c u l a r  a l l o w m o n i t o r i n g of the plasma e m i s s i o n  p r e s s u r e , mass and  0  and measured by independent mass f l o w meters  t o the t a r g e t s u r f a c e , i s f o c u s s e d entrance  and  2  gas  temperature,  voltage.  s u b s t r a t e h o l d e r - s h u t t e r arrangement accommodates a 5 cm x 5  cm s u b s t r a t e a r e a .  T h i s area can be a s i n g l e s u b s t r a t e or 6 r e c t a n g l e s  of e q u a l s i z e (1.67  cm x 2.5  cm).  The  r o t a t i n g shutter allows f o r  exposure of the e n t i r e s u b s t r a t e a r e a , none o f the s u b s t r a t e a r e a , or any.one of the s m a l l r e c t a n g u l a r areas t o the s p u t t e r e d P r i o r t o any s p u t t e r i n g experiment the chamber was  flux. baked at about  75°C f o r at l e a s t 12 hours f o l l o w e d by 2 t o 4 hours of s p u t t e r c l e a n i n g of the t a r g e t and chamber i n an Ar atmosphere (~ 0.25  Pa) w i t h a cathode  - 37 -  power of about 250 w a t t s . contamination  T h i s s t a r t i n g procedure was used t o minimize  through e x t e n s i v e o u t g a s s i n g , f o l l o w e d by e n c a p s u l a t i o n o f  the i n n e r s u r f a c e s o f t h e chamber w i t h an A l l a y e r .  Further  precautions  a g a i n s t c o n t a m i n a t i o n were e x e r c i s e d a t the end of each experiment i n p r e p a r a t i o n f o r t h e next one. These were t o s p u t t e r f o r about 10 minutes i n an N encapsulate for to  2  atmosphere ( P f l  exchange s u b s t r a t e s .  atmospheric against  ^ ^  a t  l° P w  o w e r  («•* 100 w a t t s ) t o  t h e t a r g e t w i t h a n i t r i d e l a y e r and then t o bake t h e system  s e v e r a l hours i n an N  condensation  2  2  atmosphere b e f o r e b r i e f l y opening t h e chamber  The reason f o r b a k i n g was t o prevent  a f t e r t h e chamber was opened.  The chamber was t a k e n t o  p r e s s u r e w i t h d r y n i t r o g e n gas as a f u r t h e r s a f e g u a r d  condensation. The experiments were o f e s s e n t i a l l y two t y p e s .  I n one, t h e gas  f l o w s and pumping speeds were f i x e d w h i l e the cathode v o l t a g e was incremented  through  t h e range from about 200 t o 500 v o l t s .  I n the  second t y p e , t h e pump speed and A r f l o w were f i x e d , as was e i t h e r cathode power o r c u r r e n t , and t h e r e a c t i v e gas f l o w r a t e was scanned upwards from zero and then back a g a i n . In  t h e e x p e r i m e n t s where v o l t a g e was c o n t r o l l e d , t h e f i r s t  was adjustment o f the pumping speed.  step  T h i s was done by a d m i t t i n g t h e  d e s i r e d f l o w of A r and then a d j u s t i n g t h e d i f f u s i o n pump t h r o t t l e v a l v e to and  obtain the desired pressure.  The r e a c t i v e gas f l o w r a t e was then s e t  the f u r t h e r increase i n pressure recorded.  s t a r t e d and a l l o w e d t o e q u i l i b r a t e  N e x t , t h e d i s c h a r g e was  200 V, - v O . l A ) .  A mapping o f t h e  I-V c h a r a c t e r i s t i c s o f t h e d i s c h a r g e was then performed by i n c r e m e n t i n g  - 38 -  t h e cathode v o l t a g e up t o the d e s i r e d v a l u e i n step s i z e s r a n g i n g from 0.1  to 5 v o l t s .  A l o n g w i t h each I-V p o i n t , a l l o t h e r  experimental  p a r a m e t e r s were r e c o r d e d ( i . e . p r e s s u r e , mass and o p t i c a l s p e c t r a , e l a p s e d t i m e , s u b s t r a t e b i a s and temperature, the I-V c h a r a c t e r i s t i c , the curve was films deposited. monitored  etc.).  After obtaining  r e t r a c e d t o p o i n t s of i n t e r e s t  and  D u r i n g the d e p o s i t i o n , a l l parameters were a g a i n  f o r d r i f t and, i f need be, c o r r e c t e d by the computer so t h a t  f l u c t u a t i o n s were h e l d t o w i t h i n a few t e n t h s of a p e r c e n t . In  the experiments  where cathode c u r r e n t or power was  held  c o n s t a n t a l o n g w i t h Ar f l o w and pumping speed, w h i l e the r e a c t i v e gas f l o w r a t e was  scanned, the f i r s t step was  speed t o a g i v e n Ar f l o w r a t e . to  the d e s i r e d c u r r e n t or power.  The  a g a i n t o a d j u s t the pumping  d i s c h a r g e was  then i g n i t e d and  Then the r e a c t i v e gas f l o w r a t e  set was  scanned up at a r a t e between 1 and 4 SCCM/hour (1 SCCM = 1 s t a n d a r d c u b i c c e n t i m e t e r per minute) and then down a g a i n .  D u r i n g the s c a n , a l l  parameters were r e c o r d e d at i n t e r v a l s of from 30 seconds to s e v e r a l minutes. F i l m t h i c k n e s s e s were measured both o p t i c a l l y  (by comparing  i n t e r f e r e n c e maxima a t two d i f f e r e n t a n g l e s of i n c i d e n c e ) , and w i t h a profilometer.  The  two methods agreed  t o w i t h i n about  10%.  I n v e s t i g a t i o n s of o t h e r p h y s i c a l p r o p e r t i e s of the f i l m s were  conducted  by a v a r i e t y of t e c h n i q u e s , such as s c a n n i n g e l e c t r o n microscopy t r a n s m i s s i o n e l e c t r o n microscopy  (TEM), x - r a y d i f f r a c t i o n ,  IR  r e f l e c t i v i t y , U V - v i s i b l e - n e a r IR a b s o r p t i o n , and c o n d u c t i v i t y measurements.  (SEM),  - 39  II.2  Experimental Results and  -  Discussion  U s i n g the ^ e t h o d s d i s c u s s e d i n the p r e v i o u s s e c t i o n , I the f o l l o w i n g s p u t t e r i n g parameters:  monitored  the t o t a l and p a r t i a l p r e s s u r e s  of  the s p u t t e r i n g gases, up t o t h r e e d i f f e r e n t gas f l o w s i n t o the chamber, the o p t i c a l e m i s s i o n s of the s p e c i e s i n the plasma, and  the  electrical  c h a r a c t e r i s t i c s of the d i s c h a r g e .  The pump speed was  b e g i n n i n g of each experiment.  f l o w s and one of e i t h e r cathode  Gas  c u r r e n t , power, or v o l t a g e are m a i n t a i n e d  s e t a t the  at the d e s i r e d s e t p o i n t s .  T y p i c a l s p u t t e r i n g parameters ( o r d i s c h a r g e c h a r a c t e r i s t i c s ) measured when A l i s s p u t t e r e d i n an A r / N  2  gas m i x t u r e a r e shown i n F i g . 3 f o r the  case when the glow d i s c h a r g e i s m a i n t a i n e d voltage.  Here PJJ  2  i s the N  2  by c o n t r o l l i n g the cathode  p a r t i a l pressure, A l * i  s  the i n t e n s i t y  of the 3961.52 A o p t i c a l e m i s s i o n l i n e of n e u t r a l A l , and I and V r e f e r to  the cathode c u r r e n t and v o l t a g e r e s p e c t i v e l y .  t h e s e d a t a was chamber of 1.00  such t h a t , when no d i s c h a r g e was  The pumping speed f o r present, a flow into  SCCM of Ar r e s u l t e d i n a chamber p r e s s u r e of 0.93  the f u r t h e r a d d i t i o n of 1.50  SCCM of N  2  the  Pa  r a i s e d the p r e s s u r e t o 2.01  and Pa.  I t s h o u l d be noted t h a t the I-V curve of F i g . 3 i s not a dynamic c h a r a c t e r i s t i c but r a t h e r the l o c i of s t a b l e o p e r a t i n g p o i n t s f o r the system. reached  A l l p o i n t s a l o n g the a p p a r e n t l y n e g a t i v e r e s i s t a n c e r e g i o n a r e through p o s i t i v e r e s i s t a n c e s t e p s away from the e q u i l i b r i u m  curve and back a g a i n .  These s t e p s must be much s m a l l e r than the w i d t h  o r h e i g h t of the n e g a t i v e r e s i s t a n c e r e g i o n or o s c i l l a t i o n s w i l l  develop  w i t h the l i k e l i h o o d of the t a r g e t s u r f a c e ending i n one of the extreme s t a t e s of s u r f a c e coverage. parameter i n the experiment  I f I , r a t h e r than V, i s the  controlled  t h e n , f o r i n c r e a s i n g I , upon r e a c h i n g p o i n t  - 40 -  Fig 3  (arbitrary  units)  T y p i c a l glow d i s c h a r g e c h a r a c t e r i s t i c s f o r the A l - A r / N system. are the cathode c u r r e n t and v o l t a g e , r e s p e c t i v e l y , P i s the N 2  N  ?QI! t\ f : i  P  e S S U ^ e ,  I and V  2  °P emission i n t l n s i t y of the j y o l . 5 A l i n e o f n e u t r a l A l atoms i n the d i s c h a r g e . The A r p a r t i a l p r e s s u r e i s 0.93 P a . a  n  d  M  ± S  t h e  t i c a l  - 41 -  C i n F i g . 3 the d i s c h a r g e c h a r a c t e r i s t i c s would s h i f t a b r u p t l y t o those at p o i n t E.  S i m i l a r l y , f o r d e c r e a s i n g I , a s h i f t would o c c u r from p o i n t  D t o p o i n t B. related  The s e t s of p o i n t s (C,E) and (D,B) w i l l be shown t o be  to the t r a n s i t i o n s from covered to bare and bare to covered  target surfaces, respectively. characteristics  P o i n t A r e p r e s e n t s the d i s c h a r g e  i m m e d i a t e l y a f t e r the glow i s i g n i t e d .  I n F i g . 3, no abrupt changes i n the d i s c h a r g e c h a r a c t e r i s t i c s , which are n o r m a l l y a s s o c i a t e d w i t h the t r a n s i t i o n s between bare c o v e r e d t a r g e t s u r f a c e s , are observed.  and  T h e r e f o r e , one does not know  whether a smooth and c o n t i n u o u s t r a v e r s a l through a l l degrees of t a r g e t coverage has o c c u r e d i n F i g . 3. the d i s c h a r g e c h a r a c t e r i s t i c s  To know t h i s one must be a b l e t o r e l a t e  i n the experiments where the abrupt  changes o c c u r to the same parameters control  i s achieved.  i n the experiments where smooth  A l l of the d i s c h a r g e c h a r a c t e r i s t i c s  at one  o p e r a t i n g p o i n t i n one of the experiments must be i d e n t i c a l t o those a t an o p e r a t i n g p o i n t i n the o t h e r experiment  i f the s t a t e of the t a r g e t i s  to be assumed i d e n t i c a l at these two o p e r a t i n g p o i n t s i n the two different  experiments.  U s i n g F i g . 4, I now are  demonstrate  t h a t the p o i n t s C and D of F i g . 3  the p o i n t s where the t a r g e t s u r f a c e i s j u s t b e g i n n i n g t o uncover  has j u s t become c o m p l e t e l y b a r e , r e s p e c t i v e l y .  or  F i g . 4-c shows the  n i t r o g e n p a r t i a l p r e s s u r e ( P ^ ) v e r s u s the n i t r o g e n f l o w r a t e ( F f j ) 2  w i t h the d i s c h a r g e power, W,  h e l d a t 295 w a t t s w i t h 1.00  p r o d u c i n g a chamber p r e s s u r e of 1.00 and from D  1  2  Pa.  SCCM of Ar  The t r a n s i t i o n from C* t o E'  to B' i n F i g . 4-c are w e l l known as t r a n s i t i o n s from c o v e r e d  - 42 -  Fig. 4  .(a)  .5 S C C M  440 vt  r  o  __  x-F  "1.15 S C C M  N  330 295  >i  220  w  /*  *  _  ox  x  I 10  o-F  N z  «1.5 S C C M  1.2 _ " - F N S "  U  5  S  C  C  M  (b)  R  + - Decreasing  (C)  N  2  F  N z  Constant Power ( 2 9 5 W)  o CL Z Q.  .9 .6  7?°'  .3 m ± 150 2 0 0 2 5 0 3 0 0 3 5 0 V  (volts)  1.0 F  N z  1.5  2.0  (SCCM)  Comparison of discharge c h a r a c t e r i s t i c s for the A l - A r / N s y s t e m when v o l t a g e c o n t r o l i s employed (a and b ) , or at c o n s t a n t W w i t h v a r i a b l e F (c). The peaks i n the c u r v e s (a) a r e i d e n t i f i e d as p o i n t s where t h e t a r g e t i s j u s t b e g i n n i n g t o u n c o v e r ( i . e . 6=1) a n d t h e m i n i m a a r e p o i n t s where the t a r g e t i s j u s t becoming bare ( i . e . 0=0). 2  N  2  -  43  -  t o bare and bare t o covered t a r g e t s u r f a c e s , r e s p e c t i v e l y Fig.  [16-21].  4-a shows two W vesus cathode v o l t a g e , V, curves from e x p e r i m e n t s  w i t h i d e n t i c a l pumping speeds and Ar f l o w s as the run of F i g . 4 - c . that FJJ  2  f o r the lower power W-V  curve i s the same as F  t o E ' t r a n s i t i o n of F i g . 4-c w h i l e F J J i s the same as F 295 Fig.  at the D'  N 2  2  N 2  at the  f o r the h i g h e r power W-V  t o B' t r a n s i t i o n .  Note C  curve  Note a l s o t h a t W i s  w a t t s at p o i n t s B,C,D, and E ; the same power as at a l l p o i n t s of 4-c.  F i g s . 4-b and 4-c show t h a t the v a l u e s  p o i n t s B and B',  C and C ,  D and D',  of P J J  and E and E*.  2  are e q u a l f o r  Likewise,  other  •it p l o t s demonstrate the e q u a l i t y of I , V, A l  e t c . f o r the  prime-unprimed p a i r s of o p e r a t i n g p o i n t s i n the two  experiments.  This  i n d i c a t e s t h a t p o i n t C i s the p o i n t at w h i c h the t a r g e t b e g i n s t o u n c o v e r and The  t h a t p o i n t D i s the p o i n t at w h i c h the t a r g e t becomes bare. h y s t e r e s i s i n the experiment of F i g . 4-c i s r e a d i l y  u n d e r s t o o d i n terms of the d i s c h a r g e F i g s . 4-a and 4 - b ) .  c h a r a c t e r i s t i c s of F i g . 3 ( o r  As the t a r g e t s t a r t s t o uncover at p o i n t C  secondary e l e c t r o n e m i s s i o n  the  c o e f f i c i e n t ( y ) s t a r t s to d e c r e a s e r e s u l t i n g  i n a lower t o t a l c u r r e n t , f o r the same v o l t a g e , than i t would have w i t h the h i g h e r y.  As y c o n t i n u e s  to decrease so does I u n t i l the t a r g e t i s  bare at p o i n t D and y i s once a g a i n e s s e n t i a l l y c o n s t a n t . constant  at p o i n t D,  continuously  I begins to increase w i t h V again.  decreases w i t h i n c r e a s i g V f o r a l l values  e x p e r i m e n t s s i m i l a r t o t h a t of F i g . 4 - c , where i n one constant  and F  N 2  With y As w e l l , P J J  of V.  In  case, I or W i s  v a r i e d and i n the o t h e r case 7-^^ i s f i x e d w h i l e  o r W i s v a r i e d , a problem a r i s e s .  2  I  T h i s problem i s t h a t a p o i n t i s  - 44  r e a c h e d ( e i t h e r of p o i n t s C  -  or D' of F i g . 4-c)  when the power s u p p l y i s  t r y i n g to m a i n t a i n a g i v e n v a l u e of I or W but the c o m b i n a t i o n of [V, P^2»  I ] does not b e l o n g t o the l o c i  the system shown i n F i g . 3.  The  values  of s t a b l e o p e r a t i n g p o i n t s of  system i s then f o r c e d t o s h i f t t o an  o p e r a t i n g p o i n t t h a t i s c o n s i s t e n t w i t h the g i v e n I or  W.  Mathematically  f u n c t i o n s of I ;  s t a t e d , V and P  whereas, I and P J J 3.  Therefore,  2  N 2  are not s i n g l e v a l u e d  are s i n g l e v a l u e d  i f one  f u n c t i o n s of V as seen i n F i g .  does not a l t e r the pumping speed or gas  flow  r a t e s , o p e r a t i o n between the p o i n t s C and D r e q u i r e s c o n t r o l over t a r g e t voltage.  I w i l l now  demonstrate t h a t the a b i l i t y t o c o n t r o l the  voltage  t h r o u g h the t r a n s i t i o n r e g i o n i s c r u c i a l l y dependent upon the dominant mechanism of t a r g e t coverage b e i n g Ion p l a t i n g from the c u r r e n t i n s t e a d of c h e m i s o r p t i o n  discharge  of the n e u t r a l r e a c t i v e gas  I n the absence of a d i s c h a r g e , i t i s known t h a t 0 Al metal while N  2  does not  [82,83],  2  species.  chemisorbs on  S i n c e both gases cover A l  s p u t t e r i n g t a r g e t s i n the presence of a glow d i s c h a r g e , i t i s apparent t h a t the d i s c h a r g e  i s t o t a l l y r e s p o n s i b l e f o r the N  may  be o n l y p a r t l y r e s p o n s i b l e f o r the 0  and  compare the d i s c h a r g e  Al  i n an A r / N  2  gas m i x t u r e  2  coverage.  coverage, w h i l e i t  2  Thus, I now  analyze  c h a r a c t e r i s t i c s f o r the r e a c t i v e s p u t t e r i n g of t o those f o r A l i n an A r / 0  atmosphere i n  2  o r d e r t o see the e f f e c t of the d i f f e r e n t mechanisms f o r t a r g e t coverage.  The  changes i n the d i s c h a r g e  systems caused by v a r i a t i o n s i n the gas pumping speed (S) are examined, and  c h a r a c t e r i s t i c s of the f l o w r a t e s ( F J J and F ) 2  the r e s u l t s a n a l y z e d  model f o r the s p u t t e r i n g p r o c e s s which a l l o w s f o r the two mentioned mechanisms f o r t a r g e t coverage.  A r  two and  i n terms of a previously  - 45 -  II.2-a The Target Reaction The molecules  rate  equation  from  the  for  target  surface  dn  n  =  is  g  the  target  and  reactive  B  (  e  the  surface, gas  in  the  discharge of  compound  layer.  covered  the  values  product  of  target  emission atomic first  may b e  emission  written  e  target The  )  9  and P  are,  r  that  the  used  are  Eqn. per  unit  reactive  from  the  target,  coefficient  neutrals order,  has  their  for not  entire  contribution  P  gas  the  gas  target  target  total  of  a  on  parameter the  target  and  9.  surface.  the  bare  when  These represents  e(9)  impinging of  on  gas  the  coefficient  surface,  average  0 is  values,  a(9)  yield  e  ions  values  sticking  species  current,  metal-reactive  their  depend  on  pressure  positive  different  been n e g l e c t e d to  adsorbed  discharge  with  sputtering the  [17-19]:  ( I I - D  the  therefore,  and  gas  I  species,  have  ionic  is  follows  molecules  covered  r  reactive  J^J,  total  will  of  (6)  fraction  the  gas  average  actually  -  e  The  on  a n d y(B)  the  is  I I - l .  for  the  ]  surface,  coefficient  is  )  the  and,  molecules  r  e  parameters  target  rate  (  is  is  that  target in  y  reactive  gas  n (0)  I  t  remaining  +  respectively,  f(P /P ) r  1  reactive  pressure,  surface  of  [  of  entire  are  (  number  current  as  n  reactive  surface,  molecules  t  impingement  neutral  sticking  £  charge,  the  average  for  P  portions  over  +  partial  electronic  fraction  r  total  the  averaged  P  )  is  or  and  P  _JL  where,  absorption  is on  reactive  secondary Target  the the gas  electron coverage  in  Eqn.  I I - l .  coverage  will  also  Since, be  by to  -  proportional for  in  to  the  current  The  first  chemisorption the  second  the  third  In  the  term,  steady  current  dependent  term  of  term,  ion  on  right  reactive  for  plating  ion  Eqn.  of  II-l  f(P /P ) r  B  do  not  Lounsbury  plasmas  has  actually 0.15)  gas  [84],  0.  electrons the  number  will  of  the  small  The  readily in  the  electrons  +  *  M  1  c  r  e  e  in  mechanisms the  the  the  accounts  target  from  for  surface;  discharge  current;  the  target.  r  gas  and  of  manner  to  the  Ar  2  +  the  negative  neutralize  ion  in  on  the  2  work  Ar-02  the  (Po ^t  plasma  ^  ion for  plasma  affinities  through  in  However,  [86]  expected  in  electron  0  2 )  for  present  ions  +  -  where  Nordman  pressures  the  This  form  mechanisms.  Ar  ions  t  species  of  involved  ( I I  = BP /P ,  t  0.15,  form negative  available  on  II-l  accounted  * - i  ^ s  high  plasma.  II-1.  functional  ionization  x  Eqn.  molecules  f(P /P )  partial  decrease  to  ,  different  e  already  Eqn.  with  concentration  p  related  present  [  2  to  gas  and K a r u l k a r  When P o / t  begins  is  the  [85],  of  a particular  other's  that  when  gases.  behavior Either  Aita  present.  independent  each  indicated  concentration  this  affect  side  is  to  expects if  term of  associated  reduces  One  effect  molecules  reactive  analysis  constant,  increases  are  the  required.  a positive  plasma by  is  t  is  continue  their  hand  - f n y - f $  To  -  plating  neutral  sputtering  state,  [8],  ion  the  46  a mixture  which of  both  combination formation  positive  Ar  leads 0  of to  2  and  with  the  reduces  ions  which,  -  therefore, ions. when Ar  leads  t o an increase  I f enough  reactive  the decreasing  species, number  work  constant oxygen  term  target.  2  appear  then  t  current (b+d)  oxygen  Therefore,  dPQ /P ),  that  T  n  increasing  Po / t  is  than  i s  p  2  P  r  o  v  I  have  discharge  a metal  target  i n the oxidized  concentration  of positive  since  extends  1  my d a t a  will  approximate  linearly  decreasing  over  +  ions  data  oxygen  species  such a small  of  propensity  positive  f o r negative  oxygen  concentration  species  the oxide like  t o decrease increase  i n A r  oxygen  2 from  As long  should  +  c  +  ions  +  species.  For  mass [84].  as I  In this  operate the  f o rthe  be v a l i d .  of values  of positive  Further,  for Pg /P , 2  oxygen  species  t  as a  Therefore,  2  i o n formation  decreases  as increases  of P ./P,.. n  (c +  with  o f P_ / P . f o r 0 < P . / P , . < . 1 5 . u t ~ u t ~  as w e l l  f o r low values  from  2  2  this  The  t o t h e g a s , some  (a + bPo /Pt)/(a  expression  range  targets, the  t  [87] and Lounsbury  t h e above  oxygen  i n the discharge  i n positive  regime  function  ions  Is oxidized.  the concentration  added  2  t o be about  of Aita  that  f o r oxide  2  the fractional  i s found  and the  the positive  i s increasing  always  increase  effect  sputtered  has t h e form  that  ratio  and optical  of A r  i s found  the fractional  A  spectrometric  species  ided  being  reached  (a + b P Q / P ) .  no 0  of the positive  function  0 < P /P < 0.15this ~ u2 t ~  work  t h e number  a r e oxygen  2  greater  i f  that,  even w i t h  i n the gas after  this  Regarding  has the form  because,  of positive Ar  i s eventually  offsets  to decrease.  species  the fraction  Po ^t^*  a point  e t a l . [ 8 7 ] h a s shown  (a) arises  species  gas i s added,  begins  of Aita  of positive  i n the concentration  A r atom c o n c e n t r a t i o n  i o n concentration  +  47 -  This  the concentration  theA r ion  mechanism  +  leads  to  - 48 -  f(P  n  U2  /P ) b e i n g g i v e n as (A* - B' P /P ) when P_ /P i s l e s s than 0.15, t 0 t 0 t n  fc  2  2  and f ( P _ / P J b e h a v i n g as (A" + B" P /P ) when P. /P exceeds 0.15, <J2 t U2 t U2 t n  fc  where A', B', A" and B" a r e p o s i t i v e c o n s t a n t s .  My d a t a i n v o l v i n g Ar-02  plasmas i n t h e range o f p a r t i a l t a r g e t coverage always  shows P Q / P 2  t  t o be  l e s s t h a n 0.10, t h e r e f o r e I take f ( P ^ / P ) = (A' - B' P^/P^.). t  I n t h e case o f Ar-N2 plasmas, n e i t h e r N2 n o r N i s a b l e t o form n e g a t i v e i o n s ; t h e r e f o r e the gases a r e expected t o a c t i n d e p e n d e n t l y o f each other w i t h f ( P The  N 2  /P ) = B P /P . t  N 2  t  above-mentioned forms f o r f ( P / P ) l e a d t o the f o l l o w i n g r  t  p r e d i c t i o n s f o r t h e s t e a d y s t a t e p r e s s u r e q u o t i e n t P /P « r  V  for  P  t  =  t A  ' - ^  +  the Ar-02 plasma when P o / t p  +  i s  l  e  s  s  Y<e)l e  t  n  a  N  f o r the A r - N  2  / 2  p t  "  i Hby ~ i fffr  ^2.  11 + Y ( 9 ) 1 6  plasma a t a l l v a l u e s of P / P . N 2  (II-3-a)  0.15; and  n  2  p  t  t  The parameters  <--"> I3  {a, e,  y, and n } w i l l depend on t h e r e a c t i v e g a s - t a r g e t c o m b i n a t i o n under r  study.  T h i s dependence was not e x p l i c i t l y shown i n Eqns. I I - 3 i n o r d e r  to m i n i m i z e the number of symbols. molecules  do not chemisorb  e i t h e r o f Eqns. 3.  I f the n e u t r a l r e a c t i v e gas  on t h e t a r g e t m a t e r i a l , a i s e q u a l t o z e r o i n  I now p r e s e n t d a t a t o compare w i t h these e q u a t i o n s .  - 49 -  F i g s . 5-a t o 5 - i show how independent v a r i a t i o n s o f n i t r o g e n f l o w (F  N 2  ) , argon f l o w ( F ^ ) , o r pump speed ( S ) a f f e c t t h e r  current-voltage (I-V), P N  - v 2  A l i s s p u t t e r e d i n an A r / N t a r g e t and an A r / 0  »  and ( P ^ ^ t ) ^  gas m i x t u r e .  2  c h a r a c t e r i s t i c s when  -  S i m i l a r experiments  f o r an A l  gas m i x t u r e a r e summarized i n F i g s . 6-a t o 6 - i .  2  To  more c l e a r l y p r e s e n t t h e r e l e v a n t d a t a i n F i g s . 6 I have n o t shown t h e t r a n s i t i o n t o a bare t a r g e t s u r f a c e .  Instead, the highest voltage data  p o i n t i n each curve p r e s e n t e d i s t h e l a s t one r e c o r d e d b e f o r e t h e abrupt s h i f t i n the discharge c h a r a c t e r i s t i c s .  T h i s d a t a from t h e bare t a r g e t  d i s c h a r g e would be a t h i g h e r v o l t a g e s than those shown i n F i g s . 6 and a t PQ  values of ^ zero.  2  and  Peaks I n t h e I-V c h a r a c t e r i s t i c s o f t h e N  t h e p o i n t s where t h e abrupt changes occur i n t h e 0  2  2  data  data are  i d e n t i f i e d as t h e p o i n t s where 0 = 1, as e x p l a i n e d i n t h e p r e v i o u s s e c t i o n and d e p i c t e d i n F i g . 4 f o r N .  Because P /P » as g i v e n i n  2  r  Eqns. H - 3 , i s s t r o n g l y dependent on 0 t h r o u g h and  t  t h e parameters { a , e, y,  T| }, I w i l l l i m i t t h e a n a l y s i s t o t h e o p e r a t i n g p o i n t s R  c o r r e s p o n d i n g t o 0 = 1. F i g . 7 shows t h e p l o t s o f P / P t  v s  r  from t h e N Pfl /P 2  t  2  and 0  2  « P^ ' 1  d a t a o f F i g s . 5 and 6.  f  o  r  9  =  1  »  taken  One sees i m m e d i a t e l y  that  i s c o n s t a n t , w i t h i n e x p e r i m e n t a l e r r o r , as p r e d i c t e d by Eqn.  I I - 3 - b w i t h a = 0; i . e . no c h e m i s o r p t i o n o f n e u t r a l r e a c t i v e gas molecules.  Further, o / t p  p  c  i n c r e a s i n g f u n c t i o n o f PQ /^2  non-zero a.  a  ^  n  2  a  s  b e t t e r d e s c r i b e d by a l i n e a r l y  e  p r e d i c t e d by Eqn.  The tendency o f P o / t p  2  higher values of P n / t p  0  v s  *  P  0  2  ^  t  o  II-3-a with a  f l a t t e n out f o r  i s a t t r i b u t e d t o t h e breakdown o f t h e l i n e a r  Fig. 5  V a r i a t i o n o f A l - A r / N d i s c h a r g e c h a r a c t e r i s t i c s w i t h F , F , and S. I n ( a ) - ( c ) , F i s v a r i e d w i t h 1.00 SCCM(Ar) g i v i n g S ( A r = 1.00 SCCM(Ar) p e r 0.76 P a ( A r ) and O-2.00 SCCM(N ), x-1.50 SCCM(N ), and •-1.00 SCCM(N ). I n ( d ) - ( f ) , F i s v a r i e d w i t h 1.50 SCCM(N ) g i v i n g S ( N ) = 1.50 SCCM(N ) p e r 0.84 P a ( N ) and x-1.50 SCCM(Ar), •-1.00 SCCM(Ar), and + -0.50 SCCM(Ar). I n ( g ) - ( i ) , S i s v a r i e d w i t h 1.50 SCCM(Ar) and 1.50 SCCM(N ) and o-S(Ar) = 1.50 SCCM(Ar) p e r 1.48 P a ( A r ) , x-S(Ar) = 1 . 5 0 SCCM(Ar) p e r 1.07 P a ( A r ) , «-S(Ar) = 1 . 5 0 SCCM(Ar) p e r 0.81 P a ( A r ) , and + - S ( A r ) = 1.50 SCCM(Ar) p e r 0.42 P a ( A r ) . 2  A  N  2  N  2  2  2  A r  2  2  2  2  2  - 51 -  Fig 6 2.0  'S  (d)  (a)  (9)  1-5  Q.  E ,.0  2  :  0.5  ff J*  (e)  (b) _ o  .30  %  CL (V)  rf  .20  ~ ***\ +  .10  (c)  CL  :  \ (i)  (f)  —  .20 -  *>  .15  '"  A  \  )I  290  305  o +  1  320  1  1  305  320  V (volts)  V (volts)  ^  o  • °  +  305  *  1  1  320  335  V ( volts)  V a r i a t i o n o f A l - A r / 0 d i s c h a r g e c h a r a c t e r i s t i c s w i t h F , F , and S. I n ( a ) - ( c ) , F i s v a r i e d w i t h 3.00 SCCM(Ar) g i v i n g S ( A r ) = 3.00 SCCM(Ar) p e r 1.13 P a ( A r ) and O-0.90 SCCM(0 ), + -0.60 SCCM(0 ), and •-0.30 SCCM(0 ). I n ( d ) - ( f ) , F i s v a r i e d w i t h 0.60 SCCM(0 ) g i v i n g S ( 0 ) = 0.60 SCCM(0 ) p e r 0.21 P a ( 0 ) and O-6.00 SCCM(Ar), + -5.00 SCCM(Ar), .-4.00 SCCM(Ar), and x-3.00 SCCM(Ar). I n ( g ) - ( i ) , S I s v a r i e d w i t h 3.00 SCCM(Ar) and 0.60 SCCM(0 ) and o-S(Ar) = 3.00 SCCM(Ar) p e r 2.84 P a ( A r ) , + - S ( A r ) = 3.00 SCCM(Ar) p e r 2.06 P a ( A r ) , and «-S(Ar) = 3.00 SCCM(Ar) p e r 1.33 P a ( A r ) . 2  A r  0  Q  2  2  2  A r  2  2  2  2  2  - 52  -  Fig 7  V a r i a t i o n of ( P / P ) w i t h of F i g s . 5 and 6. r  fc  ( P / I ) at the 9 = 1 p o i n t s r  of the  data  - 53 -  relationship for f(P /P ) 0 2  similarities  t  as ^ O o ^ t  n  e  a  r  0.15.  s  Despite the  i n t h e t r a n s i t i o n s between bare and covered t a r g e t s when  s p u t t e r i n g at constant  power or c u r r e n t , i t i s now e v i d e n t  t h a t the  mechanism l e a d i n g t o t a r g e t coverage i s f u n d a m e n t a l l y d i f f e r e n t when s p u t t e r i n g A l i n the presence o f N  2  from t h a t i n v o l v e d w i t h 0  present.  2  From the above a n a l y s i s o f the t a r g e t p r o c e s s e s I conclude t h a t chemisorption  of n e u t r a l r e a c t i v e gas m o l e c u l e s i s an i m p o r t a n t  coverage mechanism when t h e l a t t e r gas i s p r e s e n t , when c o n s i d e r i n g  but i s unimportant  the former.  I now address the q u e s t i o n  o f why o p e r a t i o n  1 and 9 = 0 i s p o s s i b l e f o r the A l - A r / N system.  2  a t p o i n t s between 9 =  system and not f o r the A l - A r / 0  The s t a b i l i t y o f d n / d t , as g i v e n by Eqn. I I - l , w i t h  to f l u c t u a t i o n s i n the discharge (Ar-N  2  c u r r e n t i s examined f o r t h e cases o f no  plasma) and c h e m i s o r p t i o n  (Ar-0  2  plasma).  The  change i n t h e r a t e o f t a r g e t coverage caused by a f l u c t u a t i o n i n the current  ( A l ) i s g i v e n by  dn  oP  2  respect  g  chemisorption  target  5P  n  where, i n the i n t e r e s t o f c l a r i t y , I have d i s c o n t i n u e d  w r i t i n g the  arguments a s s o c i a t e d w i t h t h e v a r i o u s f u n c t i o n s i n Eqn. I I - 4 . I f , p r i o r t o the f l u c t u a t i o n i n d i s c h a r g e  c u r r e n t , the system  [fe-n ] e x i s t e d under steady s t a t e c o n d i t i o n s , then s i n c e -ocP = -TT\—\—by r (l+y)e v i r t u e o f Eqn. I I - 2 , Eqn. I I - 4 may be r e w r i t t e n as r  J  - 54 -  el  U s i n g Eqns. I I - l ,  9f i  (II-5)  I I - 2 and I I - 3 t o g e t h e r w i t h the d a t a  contained  i n F i g s . 5, 6, and 7, one f i n d s t h a t each terra on t h e r i g h t hand s i d e of Eqn.  I I - 5 produced a f r a c t i o n a l change i n d n / d t o f t h e o r d e r o f g  (AI)/I. roughly  I n my system, i n steady s t a t e o p e r a t i n g  conditions, (AI)/I i s  10% a t 360 Hz due t o the n a t u r e o f t h e dc c u r r e n t  u n f i l t e r e d f u l l wave r e c t i f i e d 3-phase). portrays  supply ( i . e .  Note, however, t h a t Eqn. I I - 5  two f u n d a m e n t a l l y d i f f e r e n t mechanisms by which a f l u c t u a t i o n  i n t h e c u r r e n t can cause a change i n the r a t e o f t a r g e t coverage. F i r s t l y , t h e term o c ( P / I ) ( A l ) r e p r e s e n t s r  an immediate change i n b o t h  the r a t e a t which i o n s a r e brought t o the t a r g e t s u r f a c e by the i o n c u r r e n t and t h e r a t e a t which r e a c t i v e gas s p e c i e s a r e r e s p u t t e r e d . T h i s term i s seen t o v a n i s h when a = 0 ( i . e . no  chemisorption).  S e c o n d l y , the o t h e r two terms i n v o l v e s l o w e r changes i n b o t h the chemisorption  and i o n p l a t i n g r a t e s caused by the change i n P > w h i c h r  r e s u l t s from the change i n t h e g e t t e r i n g r a t e t h a t accompanies a change i n the c u r r e n t .  One o f these two terms a l s o v a n i s h e s when a i s z e r o .  T h i s second type o f response i s s l o w e r because o f t h e p r o c e s s e s involved:  the movement of s p u t t e r e d  f l u x t o the g e t t e r i n g s u r f a c e s ; t h e  a c t u a l g e t t e r i n g a t the s u r f a c e ; and the d i f f u s i o n o f t h e p r e s s u r e f l u c t u a t i o n s from the g e t t e r i n g s u r f a c e s back t o the t a r g e t . r e s u l t o f t h e time r e q u i r e d f o r these p r o c e s s e s t o o c c u r ,  As a  changes i n  - 55 -  p r e s s u r e do not f o l l o w the c u r r e n t f l u c t u a t i o n .  I n the l i m i t of the  d u r a t i o n ( T ) of the c u r r e n t t r a n s i e n t b e i n g much l e s s than the time r e q u i r e d f o r the p r e s s u r e t o e q u i l i b r a t e (x )» r  c o n t i n u i t y of f l u x  r e q u i r e s t h a t the magnitude o f the p r e s s u r e response terms of Eqn. I I - 5 be r e d u c e d , by a f a c t o r of o r d e r i/x , v  i n time.  as the response i s spread out  I f t h i s f a c t o r were s m a l l enough, the e f f e c t s of c u r r e n t  i n d u c e d p r e s s u r e t r a n s i e n t s i n Eqn. I I - 5 would be n e g l i g i b l e .  F o r my  system and o p e r a t i n g p r e s s u r e s , a minimum e s t i m a t e of t h i s r e d u c t i o n i s r o u g h l y 100 f o l d .  F o r a minimum e s t i m a t e of -u I c o n s i d e r o n l y t h e  p r o c e s s of the N  p a r t i a l p r e s s u r e t r a n s i e n t d i f f u s i n g from the w a l l  2  r  back t o the t a r g e t . as**.5  T a k i n g the N  cm and**5 x 10** cm/s  time of "'.06 s f o r an N chamber. T  R  Assuming T  R  2  2  mean f r e e p a t h and t h e r m a l v e l o c i t y  [ 8 8 ] , r e s p e c t i v e l y , y i e l d s a mean d i f f u s i o n  m o l e c u l e to t r a v e r s e the 40 cm of the vacuum  t o be s e v e r a l of these d i f f u s i o n times g i v e s  as about a q u a r t e r o f a second.  The time t h a t passes between  a r r i v a l o f some s p u t t e r e d atoms a t a w a l l and t h e i r c o m b i n a t i o n w i t h a r e a c t i v e gas m o l e c u l e may be s i g n i f i c a n t i n the N  2  case.  While N  2  will  not chemlsorb on t h e s u r f a c e of b u l k A l m e t a l i t w i l l r e a c t w i t h A l atoms (as i n the condensing s p u t t e r e d f l u x ) [ 6 6 ] , but the N  2  d i s s o c i a t i o n s t e p i s s t i l l expected t o be much l o n g e r than t h a t f o r 0 dissociation.  T h e r e f o r e , one e x p e c t s *".25s t o be a r e a s o n a b l e l o w e r  limit for T -  W i t h % ~ 1 / 3 6 0 one f i n d s a 90 f o l d r e d u c t i o n .  R  2  From t h i s  a n a l y s i s I c o n c l u d e t h a t the s t a b i l i t y of the d i s c h a r g e c h a r a c t e r i s t i c s s h o u l d be much b e t t e r f o r systems where c h e m i s o r p t i o n of the s p u t t e r i n g gas does not o c c u r than f o r systems where i t c o n t r i b u t e s to  the t a r g e t coverage mechanism.  significantly  I n the regime of p a r t i a l  target  - 56  -  c o v e r a g e , where s m a l l f l u c t u a t i o n s r e s u l t i n p o s i t i v e feedback, t h i s increased s t a b i l i t y  of n o n - c h e m i s o r b i n g systems should be most a p p a r e n t .  I n the case of the A l - A r / N  2  system a = 0 and,  therefore,  expects  o n l y the slow response of the t a r g e t coverage due  induced  fluctuations in P .  The  method of c o n t r o l  e x p l o i t s the s i n g l e v a l u e d r e l a t i o n s h i p between V and section.  to c u r r e n t  I am a b l e t o c o n t r o l the d i s c h a r g e at a l l  r  degrees of t a r g e t coverage i n t h i s system.  previous  one  9 d i s c u s s e d i n the  I c o n t r o l t a r g e t coverage by m o n i t o r i n g  the t a r g e t  v o l t a g e f o r d r i f t away from a s e t p o i n t on the l o c i of s t a b l e o p e r a t i n g p o i n t s f o r the d i s c h a r g e  (as i n F i g . 3) and, when d r i f t i s d e t e c t e d ,  s m a l l changes are made i n the d i s c h a r g e back t o the d e s i r e d v a l u e .  c u r r e n t to b r i n g the  voltage  S i n c e the f a s t f i r s t o r d e r changes i n the  r a t e of t a r g e t coverage v a n i s h , the p o s i t i v e feedback e f f e c t of s m a l l c u r r e n t p u l s e s i s s m a l l and  these  the runaway t r a n s i t i o n between  covered  and bare t a r g e t s t a t e s w i l l take a " l o n g " time to get out of c o n t r o l . W i t h the microcomputer c o n t r o l system, the v o l t a g e i s read about 0.1  s and,  i f d r i f t of more than 0.5  every  v o l t s i s d e t e c t e d , the c u r r e n t i s  changed i n o r d e r to d r i v e the v o l t a g e back to the d e s i r e d v a l u e . time l a g between d e t e c t i o n of d r i f t and l e s s than 0.1 until to  s.  r o u g h l y 0.5  the change i n the c u r r e n t i s  However, a n o t h e r change i n c u r r e n t i s not s has e l a p s e d .  T h i s 0.5  a l l o w the f u l l e f f e c t of the p r e v i o u s  The  about 0.5  R  limit  s i n d i c a t e s that T  of about 0.25  i n order  change t o be r e a l i z e d .  i s about 0.5  If  the p o s i t i v e feedback  f a c t t h a t the n e c e s s a r y  s mentioned e a r l i e r .  initiated  s delay i s necessary  s h o r t e r d e l a y s are used o s c i l l a t i o n s develop and c y c l e runs out of c o n t r o l .  The  d e l a y time i s  s i n s t e a d of the  lower  - 57 -  When c h e m i s o r p t i o n o c c u r s , as i n t h e A l - A r / 0 2 zero and the immediate response  system, a i s n o t  i n the r a t e o f t a r g e t coverage i s t h e  major f a c t o r a f f e c t i n g c o n t r o l o f t h e p r o c e s s .  When d r i f t i s d e t e c t e d  and a c u r r e n t change i s i n i t i a t e d , as d e s c r i b e d above, a second change cannot be made i n a r a t i o n a l way u n t i l another v o l t a g e measurement i s made.  T h i s r e s u l t s i n a minimum d e l a y i n i n i t i a t i n g t h e second change  of a t l e a s t 0.1 s and, e v i d e n t l y , t h i s d e l a y i s t o o l o n g t o prevent t h e p o s i t i v e feedback indicates  from r u n n i n g out o f c o n t r o l .  [83] t h a t t h e monolayer f o r m a t i o n time f o r c h e m i s o r b i n g 0  A l i s on t h e o r d e r o f 1/360 s f o r 0 t h a t I am w o r k i n g a t .  2  2  d i s c h a r g e i n the r e g i o n o f  r a t h e r than a f a s t e r computer c o n t r o l  I t i s w e l l known t h a t 0  monolayer f o r m a t i o n time a t P o '  v  2  chemisorbs on S i ; however t h e P  a  2  the o r d e r of an hour [ 8 9 ] . 2  on  T h e r e f o r e , a h i g h l y f i l t e r e d dc power s u p p l y may  p a r t i a l t a r g e t coverage, algorithm.  2  p a r t i a l p r e s s u r e s i n t h e range  be needed i n o r d e r t o c o n t r o l t h e A l - A r / 0  an A r / 0  I n f a c t , the l i t e r a t u r e  ( s p u t t e r i n g p r e s s u r e s ) i s on  Therefore, voltage control of a S i target i n  atmopsphere s h o u l d be p o s s i b l e .  R e c e n t l y , Steenbeck e t a l .  [90] r e p o r t e d an "N-shaped" I-V c h a r a c t e r i s t i c f o r s p u t t e r i n g i n t h e Si-Ar/0  II.2-b  2  system t h a t i s s i m i l a r t o t h a t i n t h e A l - A r / N  2  system.  Prediction of Film Composition from Plasma C h a r a c t e r i s t i c s F o r most a p p l i c a t i o n s o f t h i n f i l m d e p o s i t i o n an a c c u r a t e  knowledge of f i l m c o m p o s i t i o n d u r i n g f i l m growth i s r e q u i r e d .  I present  a method by which the f i l m c o m p o s i t i o n may be c a l c u l a t e d from t h e s p u t t e r i n g d i s c h a r g e c h a r a c t e r i s t i c s such as those g i v e n i n F i g . 3. The  b a s i s of t h e t e c h n i q u e i s t o use t h e o p t i c a l e m i s s i o n  d a t a t o determine  the f l u x o f m e t a l atoms s p u t t e r e d , and t o o b t a i n the g e t t e r i n g r a t e by monitoring  t h e r e a c t i v e gas p a r t i a l p r e s s u r e .  F o r purposes o f  d e m o n s t r a t i o n I w i l l use d a t a f o r the Al-Ar/N2 system. I assume the r a t e o f r e a c t i o n o f A l w i t h N p r o p o r t i o n a l t o o n l y the A l c o n c e n t r a t i o n when N  2  2  on the s u b s t r a t e i s i s i n extreme  over-abundance, but t h a t t h e r a t e i s p r o p o r t i o n a l t o t h e p r o d u c t o f b o t h reactant  concentrations  when both N  and A l a r e i n l i m i t e d s u p p l y .  2  former c o n d i t i o n means t h a t i n the low V and h i g h P J J discharge  2  The  region of the  c h a r a c t e r i s t i c s , where s t o i c h i o m e t r i c A1N i s d e p o s i t e d , the  g e t t e r i n g r a t e w i l l be p r o p o r t i o n a l t o the s p u t t e r e d A l f l u x o n l y ,  while  the l a t t e r c o n d i t i o n says t h a t t h e g e t t e r i n g r a t e w i l l be p r o p o r t i o n a l t o t h e p r o d u c t o f t h e s p u t t e r e d A l f l u x and P J J discharge  2  i n the region of the  c h a r a c t e r i s t i c s where n i t r o g e n d e f i c i e n t A1N i s d e p o s i t e d .  Based on these two d i f f e r e n t g e t t e r i n g regimes I now p r e s e n t a r a t e equation  a n a l y s i s o f t h e f l o w of N  2  gas i n t o and out o f t h e vacuum  chamber t h a t w i l l a l l o w p r e d i c t i o n o f the A l / N r a t i o i n the s p u t t e r deposits  from d a t a such as i n F i g . 3.  Under steady s t a t e c o n d i t i o n s one  may w r i t e  SP  when N  2  = F„  - ^ (Al flux), forP„  i s i n over-abundance, and  > P*  (II-6-a)  - 59 -  S P  N  " N  " %  F  2  2  ( A 1  f l u x )  >  f  °  when b o t h r e a c t a n t s a r e i n l i m i t e d s u p p l y .  rP  N  < N P  2  ( I I 2  N  2  6  b )  I n these e q u a t i o n s a l l  * * v a r i a b l e s except P ^ and 6 have been p r e v i o u s l y d e f i n e d ; P the N  - "  represents  p a r t i a l p r e s s u r e a t which the g e t t e r i n g b e h a v i o r changes from the  regime of N  2  over-abundance t o the case where both r e a c t a n t s a r e i n  l i m i t e d s u p p l y ; 8 i s t h e c o n s t a n t of p r o p o r t i o n a l i t y which r e l a t e s t h e product P Eqn.  N 2  ( A l f l u x ) t o the g e t t e r i n g r a t e .  I I - 6 - a a r i s e s because two A l atoms a r e r e q u i r e d t o g e t t e r one N  molecule  2  P h y s i c a l l y , SPJJ  out o f t h e chamber through the pumping p o r t ; F J J  d e l i b e r a t e l y l e t i n t o the chamber through i n Eqn. I I - 6 - a o r 8 P J J N  2  2  t o form two A1N m o l e c u l a r u n i t s i n the s t o i c h i o m e t r i c A1N  r e g i o n of the discharge c h a r a c t e r i s t i c s . of N  The f a c t o r of 1/2 i n  2  2  i s the flow  I s the N  2  the l e a k v a l v e ; 1/2(Al  flow flux)  ( l f l u x ) i n Eqn. I I - 6 - b ) r e p r e s e n t t h e f l o w o f A  2  into sputtered deposits.  Note t h a t , i n Eqn. I I - 6 - b , -  J l — gives the N  P P  2  average,  over a l l g e t t e r i n g s u r f a c e s , o f the r a t i o o f A l / N atoms i n t h e  s p u t t e r e d d e p o s i t s when P„ N i s o f c e n t r a l importance  *  2  < P„ N  ( o r 2BP„ N  = x i n AINx). 2  i n the determination of f i l m  One now needs t o determine characteristics.  2  Therefore, 8 ' r  composition.  the A l f l u x i n terms of the d i s c h a r g e  I take t h e number o f A l atoms s p u t t e r e d per second t o  be d i r e c t l y p r o p o r t i o n a l t o t h e i n t e n s i t y of o p t i c a l e m i s s i o n from n e u t r a l A l atoms i n the glow d i s c h a r g e .  T h i s assumption i s j u s t i f i e d by •k  *  F i g . 8, which i s a p l o t o f the d e p o s i t i o n r a t e v e r s u s A l , where A l i s t h e i n t e n s i t y of the 3961.52A o p t i c a l e m i s s i o n l i n e o f n e u t r a l A l  - 60 -  Fig. 8  V a r i a t i o n of f i l m t h i c k n e s s d e p o s i t i o n r a t e w i t h A l * from d a t a of F i g . 3. I n r e f e r e n c e t o F i g . 3, x-between p o i n t s A and C, •-between p o i n t s C and D, + - a t p o i n t D, and o-betwen p o i n t s D and E.  - 61  from the d a t a of F i g . 3.  The  -  t r a n s i t i o n from one  l i n e a r dependence to  a n o t h e r i n F i g . 8 i s accounted f o r by the change i n d e n s i t y as composition  changes from A1N  gm/cc and 2.7  gm/cc f o r A1N  w r i t e ( A l f l u x ) = 6A1 constant  to A l .  I have assumed d e n s i t i e s of  and A l , r e s p e c t i v e l y [ 6 6 ] ,  I therefore  of p r o p o r t i o n a l i t y which r e l a t e s the i n t e n s i t y of the  I I - 6 - a and Eqn.  3.26  over the e n t i r e o p e r a t i n g range, where 6 i s a  l i n e t o the s p u t t e r e d f l u x from the t a r g e t . Eqn.  the  II-6-b  T h i s a l l o w s one  emission  to r e w r i t e  as  F P  N  2  N  2  ~ If  = -f~  A 1  *'  f  °  r  P  N  > %  2  ( I I  - " 7  a )  and  P  F  ^- + = ^ A 1 * , for P N N ' F  2  2  S i n c e S i s known, 6 may p l o t of P  N 2  M  < P* 2  (II-7-b)  N  be determined t h r o u g h Eqn.  I I - 7 - a from a  v s . A l * i n the r e g i o n between A and C of F i g . 3.  Once 6 1  has been d e t e r m i n e d , p may  *  be determined from the s l o p e of a -=— N  vs. A l  2  p l o t i n the r e g i o n a f t e r p o i n t D. a s s o c i a t e d w i t h Eqn.  I I - 7 - a i s g i v e n i n F i g . 9-a w h i l e F i g . 9-b  be used i n c o n j u n c t i o n w i t h Eqn. The  For the d a t a of F i g . 3 the p l o t  v a l u e of pP^  should  II-7-b.  c a l cc uullaatteedd at p o i n t Du or of FJ?ig. i g . 3J i s about *  i n d i c a t i n g the r a t i o of A l / N i n the f i l m i s about 2.  Point D i s also  V a r i a t i o n s of P F i g . 3.  N  (a) and 1/P  (b) w i t h A l * from the d a t a of  N 2  - 63 -  the p o i n t where f i l m c o n d u c t i v i t y begins  to r i s e q u i t e r a p i d l y i n  c o n c e r t w i t h a r a p i d i n c r e a s e i n the number of A l p r e c i p i t a t e s . shows room temperature r e s i s t i v i t y  F i g . 10  (p) and temperature c o e f f i c i e n t of  r e s i s t a n c e (TCR) as a f u n c t i o n of x i n AINx f i l m s d e p o s i t e d a l o n g t h e I-V c h a r a c t e r i s t i c of F i g . 3, where x i s c a l c u l a t e d by the method j u s t discussed.  The volume f r a c t i o n of A l i n the samples (Xv) i s a l s o shown,  where Xv was c a l c u l a t e d by assuming t h a t a l l A l i n excess of what i s needed t o form s t o i c h i o m e t r i c A1N from the i n c o r p o r a t e d N Al precipitates.  2  i s present  as  S i n c e no attempt was made t o account f o r c r o s s d o p i n g  between A l and A1N phases, these v a l u e s f o r Xv a r e o n l y upper l i m i t s . Of c o u r s e , the A l p e r c i p l t a t e s a r e expected t o c o n t a i n n i t r o g e n i m p u r i t i e s , w h i l e the A1N c r y s t a l s w i l l c o n t a i n excess A l .  Also  i n c l u d e d i s s i m i l a r data of I t o h and Misawa [22] f o r r e a c t i v e , r f s p u t t e r e d AINx f i l m s , where x was o b t a i n e d from e l e c t r o n m i c r o p r o b e analysis.  One sees t h a t the agreement between the two s e t s of d a t a i s  e x c e l l e n t f o r the low r e s i s t i v i t y f i l m s (more m e t a l l i c ) , but t h a t my f i l m s show a p e r c o l a t i o n t h r e s h o l d a t a much lower v a l u e of x ( h i g h e r Xv) than I t o h ' s .  I b e l i e v e t h i s d i f f e r e n c e a r i s e s , i n p a r t because  I t o h ' s d e p o s i t i o n r a t e i s much h i g h e r than mine (^ x 4) and i n p a r t because h i s f i l m s a r e much t h i c k e r than mine (> 3500 A as compared w i t h < 1400 A f o r my  samples).  I e x p l a i n t h i s i n terms of the A l - N  2  r e a c t i o n mechanism w h i c h  t a k e s p l a c e on the s u b s t r a t e ( I observe no A1N e m i s s i o n l i n e s i n the glow d i s c h a r g e  [91]).  q u i c k l y than the A l - N  The A l - A l r e a c t i o n i s e x p e c t e d t o proceed more 2  r e a c t i o n due t o the N  2  d i s s o c i a t i o n step of t h e  - 64 -  Fig.10 Volume fraction of A l ( X ) I.0 .88 .76 .65.54 .44 .35 25 J 7 .08 0 v  I0  C  T  i  X  r  (a)  lo-'h E u I  C3 10" fit to d a t a of Itoh ,°ef al. (  (b)  + 2000 o o Q_ Q_  -20001-  ^ (i) fit t o d a t a o f Itoh, et al.  or o  Sample Geometry  \- - 4 0 0 0  -6000 I  .2  i  l  I  .4 .6 X in AIN„  I  I  .8  L  V a r i a t i o n s of p (a) and TCR (b) w i t h x, x-my d a t a where x i s c a l c u l a t e d from the data of F i g . 9 and Eqns. I I - 7 - a and I I - 7 - b , the s o l i d l i n e i s a f i t t o d a t a of I t o h and Misawa where x was measured by e l e c t r o n microprobe a n a l y s i s .  - 65  latter.  Therefore,  -  h i g h a b s o l u t e A l s p u t t e r r a t e s should  i n n i t r o g e n doped A l i f t h e r e i s not s u f f i c i e n t time f o r d i s s o c i a t i o n , r e a c t i o n w i t h A l , and implies that higher and  s m a l l e r and  s p u t t e r r a t e may  formation  N  l e s s p r e v a l e n t A1N  crystals.  F u r t h e r , i n c r e a s i n g the A l  j u s t l e a d to i n c r e a s i n g l y d i r t y ( n i t r o g e n doped) A l i f From f i l m s d e p o s i t e d  in  c h a r a c t e r i s t i c s there i s evidence  c r y s t a l s i z e w i t h i n c r e a s i n g A l r a t e from x - r a y  diffraction studies.  At c o n s t a n t  the i n s u l a t i n g s i d e of Xvc,  Xv I have a l s o o b s e r v e d , f o r f i l m s on  t h a t p i s constant  for thicknesses  <~ 2000 A, but d e c r e a s e s r a p i d l y (by ^ x 5) f o r t h i c k n e s s e s  4000 A.  This  a b s o l u t e A l s p u t t e r r a t e s l e a d to more A l i n c l u s i o n s  the s t o i c h i o m e t r i c r e g i o n of the I-V  <-> 2000 A and  2  of c r y s t a l l i n e A1N.  enough time f o r the r e a c t i o n i s not a l l o w e d .  f o r s m a l l e r A1N  r e s u l t merely  4000 A, and becomes c o n s t a n t  I b e l i e v e t h i s e f f e c t may  l e s s than  between  again f o r thicknesses  be due  over  to the s e n s i t i v i t y of  hopping mechanism t o the d i m e n s i o n a l i t y of the f i l m .  I f the  film  t h i c k n e s s i s not many m e t a l l i c g r a i n s i z e s t h i c k the hopping may 2- d i m e n s i o n a l  [92].  3- d i m e n s i o n a l  f o r normal c o n d u c t i o n p r o c e s s e s and  the  be  For the e s s e n t i a l l y m e t a l l i c samples the sample i s g r a i n s i z e should  not  be a major f a c t o r a f f e c t i n g p i n a m e t a l l i c m a t r i x , e s p e c i a l l y when the m e t a l i s very impure i n each case. r e a s o n a b l e t o assume t h a t my  For these reasons I t h i n k i t i s  deduced c o m p o s i t i o n s are c o r r e c t even a f t e r  the p o i n t where the p v s . x p l o t d e p a r t s from I t o h ' s I am now c o m p o s i t i o n and  i n a p o s i t i o n t o d i s c u s s how deposition rate.  one may  data. obtain a given  I have observed t h a t f i l m s  film  deposited  on the low V s i d e of the I-V maximum, as i n F i g . 3, appear t o be  - 66 -  s t o i c h i o m e t r i c A1N w h i l e x i n AINx s t e a d i l y decreases w i t h i n c r e a s i n g V on the h i g h V s i d e o f the peak.  F u r t h e r , i f v a r i a t i o n s i n pump speed o r  gas f l o w a r e i n t r o d u c e d , as i n F i g s . 5, e q u i v a l e n t o p e r a t i n g p o i n t s a l o n g d i f f e r e n t c h a r a c t e r i s t i c s ( i . e . A, B, C e t c . as i n F i g . 3) appear to y i e l d i d e n t i c a l f i l m c o m p o s i t i o n s as w e l l as c a l c u l a t e d v a l u e s o f (8 N ^ P  2  t  n  a  t  agree t o w i t h i n 10%. T h e r e f o r e , i n c r e a s i n g t h e N  2  flow  r a t e w i l l i n c r e a s e t h e d i s c h a r g e power (and t h e r e f o r e s p u t t e r i n g r a t e ) for  e q u i v a l e n t p o i n t s a l o n g the I-V c u r v e , w h i l e the p o s i t i o n a l o n g t h e  c h a r a c t e r i s t i c may be used t o p r e d i c t the c o m p o s i t i o n .  11.2-c  Calculation of the Sputtering Y i e l d I f one equates the s t a n d a r d e x p r e s s i o n f o r c a l c u l a t i n g t h e  s p u t t e r e d f l u x from t h e s p u t t e r i n g c u r r e n t [19] t o 6A1  o f Eqn. I I - 7 ,  the r e s u l t i n g e x p r e s s i o n i s  [I  where  +  Y  (9)]e =  6  M  ( I I  "  i s the s p u t t e r i n g y i e l d i n A l atoms p e r i n c i d e n t i o n , y i s  t h e e f f e c t i v e secondary  e l e c t r o n emission c o e f f i c i e n t f o r the t a r g e t , e  i s the e l e c t r o n i c charge, and I i s the d i s c h a r g e c u r r e n t .  I t follows  from Eqn. I I - 8 t h a t a p l o t o f e 6 A l / I vs V w i l l g i v e t h e v o l t a g e dependence o f r\ ff e  used.  8 )  f o r t h e p a r t i c u l a r t a r g e t and gas c o m p o s i t i o n  Where t h e e f f e c t i v e s p u t t e r i n g y i e l d  ( n / ( l + y)) m  has been  - 67 -  labeled  T )  e  f f  The d a t a o f F i g . 3 has been used t o make such a p l o t  which i s presented  as F i g . 11.  I n t h e h i g h V and low P^  2  r e g i o n one might expect t h e e f f e c t i v e  s p u t t e r i n g y i e l d t o approach t h e v a l u e s r e c o r d e d  i n the l i t e r a t u r e f o r  normal i n c i d e n c e s p u t t e r i n g y i e l d s of A l i n an A r atmosphere. v a l u e s i n F i g . 11 a r e l e s s than h a l f t h e a c c e p t e d 40%).  values  These  [93] (about  I n a d d i t i o n , the data of F i g . 11 was o b t a i n e d from a new t a r g e t  and as t h e t a r g e t i s used more, c a u s i n g the e r o s i o n channel  t o deepen,  the e f f e c t i v e s p u t t e r i n g y i e l d can r i s e t o about 60% of the accepted v a l u e f o r t h i s geometry.  The r i s e i s a t t r i b u t e d t o i n c r e a s e d s p u t t e r i n g  at o b l i q u e i n c i d e n c e as t h e e r o s i o n channel  deepens [ 9 4 ] ,  There a r e s e v e r a l mechanisms t h a t c o u l d s e r v e t o lower from t h e a c c e p t e d  values.  The i o n e n e r g i e s may be lower than  g i v e n by the cathode v o l t a g e drop because of c o l l i s i o n s the i o n c u r r e n t i s s t i l l N Ar.  2  s p e c i e s w i t h a lower  A l s o , w h i l e t h e t a r g e t appears bare and P  N 2  [15],  i) ff e  those Some o f  sputtering yield  than  i s v e r y low, t h e N  2  t h a t i s p r e s e n t may s t i l l be k e e p i n g y h i g h . I n any event, Eqn. I I - 8 and F i g . 11 s h o u l d g i v e a good i n d i c a t i o n o f t h e r e l a t i v e magnitudes o f t h e e f f e c t i v e s p u t t e r i n g y i e l d s f o r v a r i o u s degrees of t a r g e t coverage.  - 68 -  Fia11 I  (amps) —  —  r°  The v o l t a g e dependence of the e f f e c t i v e s p u t t e r i n g y i e l d . «-I from F i g . 3 and o — n f f c a l c u l a t e d from Eqn. I I - 8 and the d a t a of F i g . 3. e  CHAPTER I I I FILM PROPERTIES - EXPERIMENTAL RESULTS AND DISCUSSION  At t h i s p o i n t I w i l l p r e s e n t  e l e c t r i c a l t r a n s p o r t and o p t i c a l  d a t a from measurements made on A1/A1N cermets produced by v o l t a g e c o n t r o l l e d , r e a c t i v e , d c , p l a n a r magnetron s p u t t e r i n g of an A l t a r g e t i n an A r / N  2  atmosphere, as d e s c r i b e d i n t h e p r e v i o u s s e c t i o n .  d a t a w i l l be p r e s e n t e d  Much o f t h e  g r a p h i c a l l y a l o n g w i t h an i n s e t of t h e d e p o s i t i o n  glow d i s c h a r g e I-V c h a r a c t e r i s t i c (as i n F i g . 3) i n o r d e r t h a t , i n t h e end,  an i n t u i t i v e f e e l i n g may be developed f o r the r e l a t i o n s h i p between  f i l m p r o p e r t i e s and d e p o s i t i o n c o n d i t i o n s .  III.l  E l e c t r i c a l Transport Properties of A1/A1N Cermets . As d i s c u s s e d e a r l i e r , F i g . 10 and t h e t e x t of pages 63 and 64  shows r e s i s t i v i t y (p) and temperature c o e f f i c i e n t of r e s i s t a n c e (TCR) d a t a t h a t demonstrates t h a t the method of c a l c u l a t i n g f i l m from the glow d i s c h a r g e  c h a r a c t e r i s t i c s does work.  compositions  X-ray d i f f r a c t i o n  measurements o f AINx f i l m s a r e c o r r e l a t e d w i t h t h e d e p o s i t i o n I-V c h a r a c t e r i s t i c i n F i g . 12, w h i l e F i g . 13 shows t r a n s m i s s i o n e l e c t r o n m i c r o s c o p e (TEM) d a t a c o r r e l a t e d i n l i k e manner.  One sees the A1N  c r y s t a l s becoming s m a l l e r and fewer f o r i n c r e a s i n g V, w h i l e the A l c r y s t a l s become l a r g e r and more p r e v a l e n t . A1N  I n p a r t i c u l a r , one sees; t h e  c r y s t a l s i z e t o be r o u g h l y 300 A f o r f i l m s d e p o s i t e d  on t h e low V  s i d e o f t h e I-V maximum (the s t o i c h i o m e t r i c r e g i o n ) ; between the I-V maximum and minimum the A1N c r y s t a l s i z e d e c r e a s e s s t e a d i l y t o about 150 A w h i l e more and more A l i n c l u s i o n s appear w i t h d i a m e t e r s l e s s than  Fig. 12  2 6 (DEGREES)  X - r a y d i f f r a c t i o n d a t a f o r f i l m s d e p o s i t e d at the p o s i t i o n s the i n s e t I-V c u r v e .  indicated  -  71  -  Fig 13  TEM f o r curve.  f i l m s deposited at the p o s i t i o n s i n d i c a t e d The f i l m s a r e a b o u t 1500 A t h i c k .  on t h e  inset  I-V  - 72 -  50 A; j u s t p a s t the I-V minimum an abrupt d e c r e a s e , o c c u r s i n the A1N  to about 50  c r y s t a l s i z e ; a f t e r the abrupt drop i n A1N  A,  crystal  s i z e , w i t h i n c r e a s i n g V the A l c r y s t a l s i z e grows s t e a d i l y l a r g e r w h i l e the A1N  s i z e grows s t e a d i l y s m a l l e r .  A l s o , i n t h i s l a s t r e g i o n , one  w i l l n o t i c e the tendency of the A l i n c l u s i o n s t o form l a r g e s i n g l e p a r t i c l e s i n s t e a d of l a b y r i n t h i a n i n t e r c o n n e c t i o n s of s m a l l e r p a r t i c l e s , and t h a t , even a t v e r y h i g h volume f r a c t i o n s of A l , the tendency i s to form A1N  b a r r i e r s between the A l i n c l u s i o n s .  b a r r i e r s has been a t t r i b u t e d  To t h i s tendency to form  [2] the f a c t t h a t cermet f i l m s  invariably  e x h i b i t an Xvc t h a t i s h i g h e r than t h e o r y p r e d i c t s f o r a random p e r c o l a t i o n network (Xvc = .33 i n t h e o r y f o r 3-dimensions [ 3 ] ) . b a r r i e r f o r m a t i o n i s undoubtedly  This  a thermodynamic e f f e c t r e l a t e d t o the  s u r f a c e t e n s i o n of the d i f f e r e n t i n c l u s i o n s , and s e r v e s to remove the randomness from the system.  However, t h e o r e t i c a l s t u d i e s have shown  [59,96] t h a t a c o r r e l a t e d p e r c o l a t i o n system l i k e t h i s may  have a much  h i g h e r v a l u e f o r Xvc, but the c r i t i c a l exponents s h o u l d remain unchanged. In F i g . 14 i s shown n o r m a l i z e d p v s . T data f o r f o u r samples t h a t are r e p r e s e n t a t i v e of the t h r e e types of b e h a v i o r seen near Xvc.  For  Xv  > .8 the b e h a v i o r i s t y p i c a l of an impure metal w i t h p d e c r e a s i n g l i n e a r l y w i t h T t o some lower l i m i t .  For .72 < Xv < .8, p  decreases  w i t h T at h i g h T, reaches a minimum, and then i n c r e a s e s w i t h d e c r e a s i n g T from the minimum. d e c r e a s i n g T, p ^  I n t h i s r e g i o n where p i s i n c r e a s i n g w i t h  InT and  the temperature  moves to h i g h e r T as Xv i s reduced. temperature  b e h a v i o r of p ± m  n  at which the minimum o c c u r s  T h i s p ~ InT b e h a v i o r and  i s c h a r a c t e r i s t i c of e l e c t r o n  the  - 73 -  Fig. 14  0>  N o r m a l i z e d p v s . T (a) and v s . InT (b) f o r samples near Xvc. (Xv, Pmin' Pmax^» r e s i s t i v i t i e s i n ^.Q-cm, f o r each sample a r e : squares - (.66, 840, 9 8 4 ) , s o l i d c i r c l e s - (.75, 299.0, 292.5), open c i r c l e s - (.79, 128.3, 128.7), and t r i a n g l e s - (.84, 41.6, 52.8).  - 74 -  l o c a l i z a t i o n i n a cermet j u s t above Xvc magnetoresistance temperature)  [5,40,41],  (Detailed  and H a l l c o e f f i c i e n t measurements (as a f u n c t i o n of  are p r e s e n t l y b e i n g performed  samples e x h i b i t i n g p ~  by Normand F o r t i e r on  the  InT b e h a v i o r i n o r d e r t o d i f f e r e n t i a t e between  e l e c t r o n l o c a l i z a t i o n or e l e c t r o n - e l e c t r o n i n t e r a c t i o n e f f e c t s . )  For  Xv < .72, p i s i n c r e a s i n g w i t h d e c r e a s i n g T w i t h no w e l l known temperature  dependence, and d e f i n i t e l y not as l n p  1//T  seen w i t h s m a l l e r g r a i n s i z e s and lower v a l u e s f o r Xvc  as o t h e r s have [2,32],  U s i n g the method of Denvenyi et a l . [ 3 7 ] , d i s c u s s e d e a r l i e r , I have made I n - I n p l o t s of a c t i v a t i o n energy v e r s u s T f o r samples j u s t below Xv  .72 and found t h a t , i n d e e d , the a c t i v a t i o n energy v a r i e s as  some power of T.  The a c t i v a t i o n e n e r g i e s are found by t a k i n g the s l o p e  at many p o i n t s a l o n g a l n p v s . 1/T  plot.  F i g . 15 i s a t y p i c a l example  of t h i s p r o c e d u r e , and the power of T i s seen to v a r y from sample to sample a l s o , i n accordance The view  w i t h Devenyi's  model.  [37] t h a t a v e r y l a r g e number of d e f e c t s t a t e s e x i s t s i n  t h e i n s u l a t i n g g r a i n s , due to excess A l , seems e x t r e m e l y l i k e l y when one c o n s i d e r s the way j u s t below X v ^ the A1N  i n which these f i l m s grow.  .72 the N /A1 2  I n the c o m p o s i t i o n range  a r r i v a l r a t e a t the s u b s t r a t e i s v e r y  low,  c r y s t a l s i z e i s e x t r e m e l y s m a l l ( l e s s than ^ 50 A ) , the A l  i s l a n d s a r e becoming v e r y l a r g e and p r e v a l e n t , and t h e r e i s not y e t a c o n t i n u o u s m e t a l l i c pathway a c r o s s the sample. a l a r g e amount of A l atoms d i s p e r s e d i n the A1N,  One,  t h e r e f o r e , expects  and t h a t c o n d u c t i o n  does not proceed v i a a c o n t i n u o u s m e t a l l i c c h a n n e l .  The  island  sizes  - 75 -  Fig. 15 >• o UJ  UJ o I—  | o <  2.0  3.0 4.0 5.0 In ( T E M P E R A T U R E )  6.0  (k)  UJ  c  or—'  .02 .04 .06 .08 (TEMPERATURE)"  .10  1  (k")  l n - l n p l o t s of c o n d u c t i o n a c t i v a t i o n e n e r g i e s v s . T (a) and I n p v s . 1/T at Xv = .66 ( b ) . The d a t a ( s q u a r e s ) i n (b) was used to c a l c u l a t e the d a t a ( t r i a n g l e s ) i n ( a ) , then the s l o p e and i n t e r c e p t i n (a) were used to f i n d A and p, as i n Eqn. 1-5. The s o l i d l i n e i n (b) i s c a l c u l a t e d from Eqn. 1-5, w i t h the A and p v a l u e s from ( a ) .  - 76 -  ( e s t i m a t e d from the x - r a y and TEM  d a t a of F i g s . 12 and 13) i n d i c a t e the  t y p i c a l c h a r g i n g e n e r g i e s f o r the m e t a l i s l a n d s t o be of the o r d e r of .leV  a t Xv = .65.  T h e r e f o r e , i t i s u n l i k e l y t h a t many of these  are charged below 300 K.  The  islands  c o n d u c t i o n mechanism i s then l i k e l y to be  hopping between i s o l a t e d d e f e c t s .  However, the p h y s i c a l n a t u r e of these  f i l l e d and u n f i l l e d d e f e c t s t a t e s i s not i m m e d i a t e l y  apparent.  As Xv = .72 i s c r o s s e d from the i n s u l a t i n g t o the m e t a l l i c s i d e one observes  (see F i g . 16) the c a r r i e r type i n room temperature  measurements to change from n t o p. w h i l e A l i s p-type are a l s o expected  [79],  Hopping s h o u l d y i e l d n-type  While e i t h e r A l i n t e r s t i t i a l s  to produce n-type c o n d u c t i o n i n A1N  the d a t a of F i g s . 12 through 15 i n d i c a t e t h a t hopping more l i k e l y mechanism i n t h i s case.  The  or  [97]  N-vacancies  through  doping,  c o n d u c t i o n i s the  c o m p o s i t i o n ranges f o r the  InT b e h a v i o r and the changing H a l l s i g n coupled w i t h TCR, changing  Hall  s i g n a t Xv = .72 s t r o n g l y i n d i c a t e s t h a t Xvc =  p~  i n F i g . 10, .72.  U s i n g the c o n d u c t i v i t i e s e x t r a p o l a t e d t o T = 0 K t o f i t a to a power law form, b o t h above and below Xvc, w i t h Xvc as a f r e e parameter gave a best f i t of Xvc = .72 ± .02. w i t h the v a l u e from the TCR, Fig. .72.  T h i s v a l u e i s i n good agreement  H a l l , and p ~ InT d a t a d i s c u s s e d e a r l i e r .  17 shows l o g ( a ) v s . Xv and l o g ( a ) v s . l o g |Xvc - Xv| w i t h Xvc Above Xvc one f i n d s a ~ (Xv - X v c )  t  w i t h t = 1.75  ± .1, i n  e x c e l l e n t agreement w i t h the t h e o r e t i c a l v a l u e [3] of 1.7. one f i n d s a ~  (Xv - X v c )  - S  w i t h s = 4.3  ± .1.  not agree w i t h the t h e o r e t i c a l v a l u e of 0.7 c o n d u c t o r s and, of c o u r s e , t h i s i s due tunneling.  =  Below Xvc  T h i s l a s t exponent does  f o r a m i x t u r e of normal  to the c o n d u c t i o n mechanism b e i n g  - 77 -  Fig 16  - 3 - 2 - 1 0 1 2 O I I I I II I I I I  X < 0)  • 00 —  o  I n v e r s e H a l l c o n s t a n t v s . Xv f o r f i l m s d e p o s i t e d near Xv = Xvc =  .72.  Fig. 17 Log ( C O N D U C T I V I T Y ) Vs V O L U M E F R A C T I O N (experimental)  Log ( C O N D U C T I V I T Y ) V s V O L U M E F R A C T I O N (theoretical) (a)  a  z> o z o o  av-cr /X -X ) I  vc  v  o .5  V O L U M E FRACTION  .6  .7  .8  .9  I.0  VOLUME FRACTION  Log(CONDUCTIVITY)Vs Log | X - X | 5.0r (c) V C  V  EXPERIMENTAL)  >-  4.0-  >  = a  o o  -  o> o  I  E  <-> 3.0h 3  2J0|I.O -2.0  J — •I.5 Log  -I.0 |X -X | V C  -0.5  V  (a) The t h e o r e t i c a l form f o r l n ( a ) v s . Xv, w i t h t h e s c a l i n g r e l a t i o n s shown f o r a 3 - d i m e n s i o n a l m i x t u r e of "normal" c o n d u c t o r s . (b) l n ( a) v s . Xv from d a t a from f i l m s d e p o s i t e d near Xv = Xvc = .72. ( c ) l n ( a ) v s . I n Xvc - X v l f o r d a t a i n ( b ) . As d e p i c t e d i n ( a ) , from ( c ) one o b t a i n s t h e c r i t i c a l exponents t = 1.75 ± .1 and s = 4.3 ± .1. The d i s c r e p a n c y between t h e observed and p r e d i c t e d v a l u e s of s a r i s e s because, f o r the d a t a , c o n d u c t i o n proceeds v i a hopping.  - 79 -  I f one adopts Neugebauer's f o r m u l a  o ~  R —  2  f o r t u n n e l i n g [30]  -e exp(-aR) e x p ( ^ " ) 2  (III-l)  r  where R i s t h e p a r t i c l e s e p a r a t i o n and r i s t h e p a r t i c l e s i z e , then i n the l i m i t of b o t h (aR) and ( e / k T r ) b e i n g s m a l l one f i n d s t h a t R ~ (Xvc 2  - X v ) with u u  .9.  r has been t a k e n t o v a r y as (Xvc - X v )  - 1  ^  5  with  6 = .4 [ 3 ] , Of c o u r s e , i n h o p p i n g from d e f e c t t o d e f e c t t h e p a r t i c l e s i z e may not be as b i g a f a c t o r i n the t u n n e l i n g p r o c e s s conduction  III.2  and t h e h o p p i n g  may o n l y depend on t h e i n t e r d e f e c t s p a c i n g s .  O p t i c a l Properties of A1/A1N Cermets The o p t i c a l a b s o r p t i o n of A1/A1N f i l m s , d e p o s i t e d a t v a r i o u s  p o s i t i o n s a l o n g the I-V c h a r a c t e r i s t i c of F i g . 3, was measured. shows t h e p r o d u c t  of f i l m t h i c k n e s s (d) and o p t i c a l  F i g . 18  absorption  c o e f f i c i e n t ( a ) v s . w a v e l e n g t h f o r f i l m s of t h i c k n e s s e s between 4000 A and 7000 A.  Taking  account of f i l m t h i c k n e s s e s , F i g . 19 shows /a v s .  photon energy f o r the same f i l m s as i n F i g . 18.  On t h e h i g h v o l t a g e  s i d e of t h e I-V minimum the f i l m s t u r n from c l e a r , t o y e l l o w brown, t o dark brown, t o b l a c k , and f i n a l l y s i l v e r y F i g . 18.  ( l i k e A l m e t a l ) by f i l m #8 of  The a b s o r p t i o n peak a t 4.8 eV i n F i g . 18 and 19 i s i d e n t i c a l  i n p o s i t i o n and appearance t o t h a t observed by P a s t r n a k d e s c r i b e d i n the i n t r o d u c t i o n . P a s t r n a k  concluded  peak was due t o oxygen i m p u r i t i e s i n t h e f i l m .  e t a l . [ 6 0 ] , as  that t h i s  absorption  T h i s c o n c l u s i o n was  - 80  -  Fig. 18  P r o d u c t of f i l m t h i c k n e s s (d) and o p t i c a l a b s o r p t i o n c o e f f i c i e n t v s . w a v e l e n g t h f o r f i l m s d e p o s i t e d at the p o s i t i o n s shown i n the I-V c u r v e .  (a) inset  - 81 -  Fig. 19  0  1  2  3 4 5 E(eV)  /a v s . E f o r the f i l m s shown i n F i g .  18.  6  7  - 82  -  based upon d i f f u s e r e f l e c t a n c e measurements on crushed prepared  A1N  by h i g h v o l t a g e a r c i n g of A l e l e c t r o d e s i n an N  crystals atmosphere,  2  where the g e n e r a l background r e f l e c t a n c e ( a f t e r c r u s h i n g ) and 4.8  eV  a b s o r p t i o n i n t e n s i t y ( b e f o r e c r u s h i n g ) seemed c o r r e l a t e d w i t h oxygen content  i n the powdered samples ( a f t e r c r u s h i n g ) .  g r a n u l a r n a t u r e of the f i l m s of F i g s . 18 and a r c d i s c h a r g e method of making A1N  I n view of the known  19, and  the f a c t t h a t  the  i s known t o produce v a r y i n g degrees  of n i t r o g e n d e f i c i e n c y [66] (and p o s s i b l y A l i n c l u s i o n s ) , the a r i s e s as t o whether the a b s o r p t i o n at 4.8  eV c o u l d be due  question  t o some form  of the d i e l e c t r i c anomaly, a s s o c i a t e d w i t h g r a n u l a r m a t e r i a l s , as d e s c r i b e d i n the i n t r o d u c t i o n . In o r d e r t o determine whether or not the 4.8  eV a b s o r p t i o n i s due  t o the g r a n u l a r n a t u r e of the f i l m s , c a l c u l a t i o n s , based upon the EMT,  and  coated  sphere a p p r o x i m a t i o n s  cermets were performed and 27.  presented  e a r l i e r , f o r A1/A1N  the r e s u l t s are d i s p l a y e d i n F i g s . 20  For these c a l c u l a t i o n s : the A l o p t i c a l c o n s t a n t s  were used [ 8 0 ] ; the r e f r a c t i v e i n d e x data of P a s t r n a k d i s p e r s i o n , was  g i v e n by  o b t a i n e d from o p t i c a l a b s o r p t i o n measurements on A1N characteristics.  through Powell  [59], i n c l u d i n g  used; and the e x t i n c t i o n c o e f f i c i e n t f o r A1N  s t o i c h i o m e t r i c p o r t i o n of the I-V  MGT,  was  d e p o s i t e d i n the D e t a i l s of  these  c a l c u l a t i o n s are g i v e n i n the appendix on o p t i c a l c a l c u l a t i o n s . F i g . 20 shows the r e s u l t of the MGT  calculation.  The  p o s i t i o n of  the d i e l e c t r i c anomaly i s seen t o s h i f t a p p r e c i a b l y w i t h Xv, whereas the data of P a s t r n a k position.  and of F i g s . 18 and  19 i n d i c a t e s a c o n s t a n t  peak  S i n c e I r e n e and Z i r i n s k y [65] r e p o r t e d a l o w e r i n g of  r e f r a c t i v e i n d e x i n A1N  w i t h A l enrichment ( t o ^  1.7) , F i g . 21 shows the  - 83 -  Fig. 20  /a v s . E c a l c u l a t e d i n the MGT a p p r o x i m a t i o n f o r A1/A1N composites v a r i o u s v a l u e s of Xv. See Eqn. 1-9 and the appendix on o p t i c a l calculations.  at  - 84 -  Fi g. 21  E(eV)  /a v s . E c a l c u l a t e d i n the MGT a p p r o x i m a t i o n f o r A1/A1N composites Xv = .10, but at v a r i o u s v a l u e s of A1N r e f r a c t i v e i n d e x . See Eqn. and the appendix on o p t i c a l c a l c u l a t i o n s .  at 1-9  - 85 -  Fig. 22  O O o  E(eV)  /a v s . E c a l c u l a t e d I n the EMT a p p r o x i m a t i o n f o r A1/A1N composites v a r i o u s v a l u e s of Xv. See Eqn. 1-14 and the appendix on o p t i c a l calculations.  at  - 86 -  Fig. 23  /a v s . E c a l c u l a t e d I n the coated sphere-EMT a p p r o x i m a t i o n f o r A1/A1N composites at v a r i o u s v a l u e s of Xv. See Eqns. 1-14 and 1-15 and the appendix on o p t i c a l c a l c u l a t i o n s .  - 87 -  Fig. 24  Comparison of /a v s . E data of F i g . 19 (a) w i t h c a l c u l a t i o n s , from F i g . 23 (b) i n the coated sphere-EMT a p p r o x i m a t i o n .  - 88  -  Fig. 25  R e f l e c t a n c e v s . E c a l c u l a t e d i n the EMT a p p r o x i m a t i o n f o r A1/A1N composites at v a r i o u s v a l u e s of Xv. See Eqn. 1-14 and the appendix on optical calculations.  - 89 -  Fig 26 CO  C\J -  01  PARAMETERS FOR THE COATED Al S P H E R E S ARE THE SAME AS I N FIG.23  Q  0  3.5 E(eV)  7  R e f l e c t a n c e v s . E c a l c u l a t e d i n the c o a t e d sphere-EMT a p p r o x i m a t i o n f o r A1/A1N composites at v a r i o u s v a l u e s o f Xv. The c o a t i n g parameters a r e the same as those used i n F i g . 23. See Eqns. 1-14 and 1-15 and t h e appendix on o p t i c a l c a l c u l a t i o n s .  - 90 -  Fig. 27 240  V (VOLTS) 340 440 I-V DEPOSITION CHARACTERISTICS FOR FILMS 0 TO ©  Al MIRROR QUARTZ SUBSTRATES  Ld _J  <  : J 3 U L K - A I N  O  <  LU  Al M I R R O R  z H  Q:  O  5  >  6  7 8 10 14 2 0 (MICRONS)  50  I n f r a r e d r e f l e c t a n c e data f o r : f i l m s deposited at the p o s i t i o n s i n d i c a t e d i n the i n s e t I-V c u r v e ; b u l k AIN; and the s u b s t r a t e s used f o r the d e p o s i t e d f i l m s .  -  e f f e c t , i n the MGT reasonable  -  91  c a l c u l a t i o n , of changing n.  t o assume t h a t the s h i f t  I t does not seem  ( t o lower e n e r g i e s ) i n peak p o s i t i o n  w i t h i n c r e a s i n g Xv c o u l d be e x a c t l y c a n c e l l e d o u t , f o r a l l Xv, by the shift  ( t o h i g h e r e n e r g i e s ) i n peak p o s i t i o n as n d e c r e a s e s w i t h  i n c r e a s i n g Xv, e s p e c i a l l y s i n c e such a low i n d e x i s r e q u i r e d , even a t Xv ~ 0, t o s h i f t the peak t o 4.8 eV. d i e l e c t r i c anomaly as the source  Therefore,  one must r u l e out the MGT  of the 4.8 eV a b s o r p t i o n .  F i g . 22 r e v e a l s the r e s u l t s of the EMT c a l c u l a t i o n f o r A1/A1N cermets.  No a b s o r p t i o n peak i s o b s e r v e d , and the g e n e r a l background  l e v e l of a b s o r p t i o n i s seen to i n c r e a s e w i t h Xv.  Therefore,  one must  a l s o r u l e out the EMT model as an e x p l a n a t i o n of the 4.8 eV a b s o r p t i o n . F i g . 23 i s based on coated A l spheres I n an EMT a p p r o x i m a t i o n f o r A1/A1N cermets.  The c o a t i n g m a t e r i a l was taken t o have a r e f r a c t i v e  i n d e x of 1.6 and an e x t i n c t i o n c o e f f i c i e n t v a r y i n g as t h a t of A1N, but a t f i v e times the i n t e n s i t y .  The v a l u e of Q ( i . e . 1 - c o a t i n g  t h i c k n e s s / i n c l u s i o n r a d i u s ) was taken as 0.2. are seen t o resemble t h e e x p e r i m e n t a l absorption i n t e n s i t y , quite w e l l .  The r e s u l t s of F i g . 23  r e s u l t s , a s i d e from a b s o l u t e  However, the assumption of c o n s t a n t  Q  = 0.2, r e g a r d l e s s o f Xv, means t h a t as Xv and i n c l u s i o n s i z e change the f r a c t i o n o f the i n c l u s i o n r a d i u s t h a t i s the c o a t i n g m a t e r i a l remains constant  a t 0.8.  T h i s may or may not be a r e a s o n a b l e  assumption.  The  c o a t i n g of i n c l u s i o n s h a s , i n the p a s t , been a t t r i b u t e d to thermodynamic e f f e c t s , such as s u r f a c e t e n s i o n [ 2 ] , and used t o e x p l a i n the r a i s i n g of the p e r c o l a t i o n t h r e s h o l d i n c o s p u t t e r e d  granular metals.  I n these  A1/A1N f i l m s , c o n d e n s i n g A l atoms cease growing as c r y s t a l l i n e A l a t  - 92 -  some p a r t i c u l a r c r y s t a l s i z e .  According  t o the x - r a y and TEM d a t a of  F i g s . 12 and 13, t h i s s i z e i s dependent on the r e l a t i v e a r r i v a l r a t e s o f Al  and N  2  a t the s u b s t r a t e .  l i k e l y , important for  The a b s o l u t e a r r i v a l r a t e s a r e , most  i n t h i s respect  t h e growing A1N c r y s t a l s .  as w e l l .  A similar situation  obtains  I t i s p o s s i b l e t h a t the " b r i d g e " between  the two types o f p a r t i c l e s i s an amorphous, m e t a l e n r i c h e d A1N c o a t i n g , and t h a t t h e t h i c k n e s s i s r e l a t e d t o t h e i n c i d e n t f l u x o f condensing atoms and i s i n some way p r o p o r t i o n a l t o the p a r t i c l e s i z e s f o r some thermodynamic reason.  The v a l u e s o f Q, n, and k f o r the c o a t i n g  m a t e r i a l used i n the c a l c u l a t i o n would then r e p r e s e n t t h i s " b r i d g e " o f amorphous m a t e r i a l . the coated one  average v a l u e s f o r  F i g . 24 compares the r e s u l t s of  sphere c a l c u l a t i o n of F i g . 23 w i t h the data o f F i g . 19, and  sees good q u a l i t a t i v e agreement.  to support t h e assumption o f c o n s t a n t approximation  However, w i t h o u t Q, t h i s coated  f u r t h e r evidence  sphere-EMT  can o n l y be thought o f as a p o s s i b i l i t y , perhaps o n l y a  remote p o s s i b i l i t y , f o r the d e s c r i p t i o n of t h e o r i g i n of t h e 4.8 eV a b s o r p t i o n band.  The remoteness o f t h i s p o s s i b i l i t y becomes even more  apparent when one c o n s i d e r s  t h a t Q i s ac t u a l l y X v  1 / 3  i n an MGT  c a l c u l a t i o n f o r a s i n g l e sphere and, t h e r e f o r e , s m a l l changes i n Q w i l l produce n o t i c e a b l e s h i f t s i n the peak p o s i t i o n , as i n F i g . 20. seems r e a s o n a b l e  Since i t  t h a t Q s h o u l d be r e l a t e d t o b o t h the a b s o l u t e and  r e l a t i v e c o n d e n s a t i o n r a t e s f o r A l and N2 a t the s u b s t r a t e , i t seems u n l i k e l y that Pastrnak's technique  a r c discharge  and the r e a c t i v e s p u t t e r i n g  o f t h i s work would produce the same Q and, t h e r e f o r e , the same  peak p o s i t i o n .  - 93  -  Oxygen i m p u r i t i e s do not seem t o be a l i k e l y o r i g i n f o r the eV a b s o r p t i o n e i t h e r .  I n t h i s work, the base p r e s s u r e s  t h r o t t l i n g the d i f f u s i o n pump were l e s s than 10 Pa a f t e r t h r o t t l i n g . the I-V  These base p r e s s u r e s  c h a r a c t e r i s t i c the f i l m was  i n c o r p o r a t i o n should m a n i f e s t a t 4.8  4.8  before  Pa, and  l e s s than 10  are independent of where on  deposited.  Therefore,  oxygen  i t s e l f i n a l l f i l m s i n an a b s o r p t i o n peak  eV.  Measurements on f i l m s d e p o s i t e d i n the s t o i c h i o m e t r i c r e g i o n  of the I-V  c h a r a c t e r i s t i c s w i t h t h i c k n e s s e s v a r y i n g from 300 A to 50,000  A have shown no e v i d e n c e of e i t h e r browning or an a b s o r p t i o n band at  4.8  eV. The at 4.8  f i l m s of t h i s work w h i c h d i s p l a y an o p t i c a l a b s o r p t i o n band  eV are a l l A1/A1N cermets where the AIN  excess A l atoms and/or N-vacancies and nitrogen.  I t seems l i k e l y  i s most l i k e l y doped w i t h  the A l i s most l i k e l y doped w i t h  that Pastrnak's  samples have, at l e a s t ,  e x c e s s A l and/or N - v a c a n c i e s i n an AIN m a t r i x l i t y of A l i n c l u s i o n s can not be r u l e d out.  [ 6 6 ] , w h i l e the  A l s o , N o r e i k a et a l . p e r -  formed a b s o r p t i o n measurements on dark brown, r f , r e a c t i v e l y AIN  films  [63] and o b t a i n e d  possibi-  sputtered  r e s u l t s s i m i l a r to f i l m #8 of F i g s . 18  and  19, but observed no A l l i n e s i n e l e c t r o n d i f f r a c t i o n p a t t e r n s . Therefore,  i t seems p o s s i b l e t h a t e i t h e r N - v a c a n c i e s or i n c l u d e d A l  atoms g i v e r i s e t o the o p t i c a l a b s o r p t i o n band at 4.8 I f the a b s o r p t i o n band at 4.8 AIN  eV i s due  eV i n AIN.  to some d e f e c t s t a t e i n  (such as N - v a c a n c i e s or A l i n t e r s t i t i a l s ) , the EMT  theory  d e s c r i b e the o p t i c a l p r o p e r t i e s of the g r a n u l a r f i l m s , and band s h o u l d be superimposed upon i t .  should  the 4.8  eV  I n f r a r e d r e f l e c t a n c e measurements  - 94 -  on t h e s e A1/A1N cermets do not support t h i s s u p p o s i t i o n v e r y w e l l . F i g s . 25 and 26 are r e f l e c t a n c e v s . E (photon energy) curves i n the EMT  and coated sphere-EMT a p p r o x i m a t i o n s , r e s p e c t i v e l y , f o r  A1/A1N cermets.  The  c o a t e d sphere-EMT c a l c u l a t i o n s show the IR  r e f l e c t i v i t y of A1/A1N cermets the EMT with  calculated  t o be i d e n t i c a l to t h a t of A1N,  c a l c u l a t i o n shows the r e f l e c t i v i t y to i n c r e a s e f a i r l y  whereas rapidly  Xv. A c t u a l IR r e f l e c t a n c e d a t a , as a f u n c t i o n of d e p o s i t i o n I-V  c h a r a c t e r i s t i c s , f o r A1/A1N cermet f i l m s , between 4000 A and 7000 A t h i c k , a r e p r e s e n t e d i n F i g . 27.  The v a r i o u s peaks p r e s e n t i n t h e s e  d a t a can be a t t r i b u t e d t o the q u a r t z s u b s t r a t e or the A1N bands.  Assuming these peaks to be superimposed  upon the  reststrahlen reflectivities  c a l c u l a t e d f o r g r a n u l a r A1/A1N c o m p o s i t e s , one s e e s , i n t h e s e d a t a , the IR r e f l e c t i v i t y of the cermets  to be v e r y c l o s e to t h a t of the pure  w i t h much of the d i f f e r e n c e accounted  f o r by d i f f e r i n g i n t e r f e r e n c e  maxima f o r f i l m s of d i f f e r i n g t h i c k n e s s . The a p p r o x i m a t i o n seems t o f i t a p p r o x i m a t i o n does.  A1N,  coated sphere-EMT  these d a t a much c l o s e r than the  EMT  However, i f the coated sphere-EMT a p p r o x i m a t i o n  d e s c r i b e s the o p t i c a l b e h a v i o r of these f i l m s , a d i e l e c t r i c anomaly would be e x p e c t e d i n the o p t i c a l a b s o r p t i o n , and the p r e v i o u s d i s c u s s i o n s i n d i c a t e d t h a t no d i e l e c t r i c anomaly i s observed.  Since i t  i s common t h a t a b s o l u t e magnitudes of a b s o r p t i o n are not w e l l p r e d i c t e d by these g r a n u l a r t h e o r i e s [ 5 4 , 5 7 ] , i t may EMT-like.  be t h a t the f i l m s are  However, the d i f f e r e n c e between the observed and p r e d i c t e d  l e v e l s of a b s o r p t i o n are much g r e a t e r (by a / 1 0 ) than the observed  - 95 -  d i f f e r e n c e s r e p o r t e d t o date [4,50-54].  The c o m p l e x i t y o f the  m i c r o s t r u c t u r e o f these f i l m s , however, may not be a d e q u a t e l y for  accounted  i n any of the r e l a t i v e l y s i m p l e t h e o r i e s I have d i s c u s s e d i n t h i s  work, s i n c e t h e r e a r e , u n d o u b t e d l y , a g r e a t many s i n g l e and m u l t i p l e atom i n c l u s i o n s w i t h o p t i c a l p r o p e r t i e s f a r d i f f e r e n t than b u l k A l . model w h i c h , more r e a l i s t i c a l l y ,  A  i n c o r p o r a t e s the t r u e m i c r o s t r u c t u r e o f  these f i l m s i s , most l i k e l y , needed t o a c c u r a t e l y d e s c r i b e d the o p t i c a l p r o p e r t i e s of these  films.  W h i l e the a b s o r p t i o n a t 4.8 eV i s most l i k e l y due t o e i t h e r excess A l atoms o r N - v a c a n c i e s i n AIN, the coated approximation possibility.  sphere-EMT  f o r g r a n u l a r A1/A1N composites remains a remote  - 96 -  CHAPTER IV CONCLUSION  IV.1  Reactive Sputtering Mechanisms T h i s work has shown t h a t two s e p a r a t e mechanisms a r e a t work i n  c o v e r i n g a s p u t t e r i n g t a r g e t w i t h a r e a c t i v e gas compound l a y e r : chemisorption  o f r e a c t i v e gas n e u t r a l s from t h e s p u t t e r i n g gas and i o n  p l a t i n g o f r e a c t i v e gas s p e c i e s from t h e s p u t t e r i n g i o n c u r r e n t .  The  degree t o w h i c h e i t h e r mechanism c o n t r i b u t e s t o t a r g e t coverage w i l l depend on t h e p a r t i c u l a r t a r g e t - r e a c t i v e gas c o m b i n a t i o n However, s i n c e t h e c h e m i s o r p t i o n  under  study.  r a t e s o f most common gasses on most  m e t a l s a r e known [ 8 2 ] , one s h o u l d be a b l e t o p r e d i c t , i n advance, w h i c h mechanism w i l l  dominate.  When i o n p l a t i n g i s the dominant t a r g e t coverage mechanism, v o l t a g e c o n t r o l o f t h e glow d i s c h a r g e w i l l permit a l l degrees o f t a r g e t coverage.  stable operation at  Under these c i r c u m s t a n c e s ,  s p u t t e r e d f l u x t o r e a c t i v e gas m o l e c u l e s i m p i n g i n g be a s i n g l e v a l u e d f u n c t i o n of t h e t a r g e t v o l t a g e . determines the f i l m composition  the r a t i o o f  on t h e s u b s t r a t e Since t h i s  [22,67], v o l t a g e c o n t r o l a l l o w s  ratio film  composition  c o n t r o l when i o n p l a t i n g i s the dominant t a r g e t coverage  mechanism.  S i n c e thermodynamic c o n s i d e r a t i o n s should d i c t a t e a  s o l u b i l i t y l i m i t f o r any p a r t i c u l a r d e f e c t i n a c h e m i c a l  will  system, when  the s p u t t e r e d f i l m becomes t o o d e f i c i e n t i n t h e r e a c t i v e gas c o n s t i t u e n t p r e c i p i t a t e s o f t h e s p u t t e r e d m a t e r i a l s h o u l d appear i n t h e f i l m . Therefore, voltage c o n t r o l i n r e a c t i v e s p u t t e r i n g I s w e l l s u i t e d to the  - 97 -  c o n t r o l l e d c o m p o s i t i o n d e p o s i t i o n of t h i n f i l m cermets from a s i n g l e t a r g e t when t a r g e t coverage  IV.2  i s dominated by the i o n p l a t i n g mechanism.  A1/A1N Cermets Deposited by Voltage Controlled Reactive Sputtering  IV.2-a  E l e c t r i c a l Transport Properties The volume f r a c t i o n (Xv) of A l i n c l u s i o n s i n A1/A1N cermets  was  found to be r e a d i l y c o n t r o l l a b l e through r e g u l a t i o n of the t a r g e t v o l t a g e i n the manner d i s c u s s e d i n Chapter I I . At the p r e c o l a t i o n t h r e s h o l d the temperature zero.  c o e f f i c i e n t of r e s i s t a n c e (TCR) was  T h e r e f o r e , the t e c h n i q u e s of Chapter  I I have a v e r y p r a c t i c a l  a p p l i c a t i o n i n the c o n t r o l l e d c o m p o s i t i o n d e p o s i t i o n of stabilized thin film resistors.  seen to be  temperature  The g r a n u l a r n a t u r e of t h e s e  c o u p l e d w i t h the h i g h l y c o n t r o l l a b l e Xv, a l s o makes these  films,  techniques  w e l l s u i t e d to the study of e l e c t r o n l o c a l i z a t i o n e f f e c t s as w e l l as the c r i t i c a l phenomena a s s o c i a t e d w i t h p e r c o l a t i o n systems near p e r c o l a t i o n threshold (Xvc). Xvc)  Above Xvc, i t was  the  found t h a t a  (Xv -  w i t h t = 1.75  ± .1, i n e x c e l l e n t agreement w i t h the t h e o r e t i c a l  p r e d i c t i o n ( o f 1.7)  f o r a 3 - d i m e n s i o n a l m i x t u r e of normal c o n d u c t o r s .  fc  Below Xvc, c o n d u c t i o n appears to be v i a hopping  from d e f e c t to d e f e c t  w i t h i n the AIN g r a i n s and a ^ (Xvc - X v ) ~ , w i t h s = 4.3 s  m i x t u r e s of normal c o n d u c t o r s , s i s p r e d i c t e d to be 0.7. p r e d i c t i o n s f o r s e x i s t , at p r e s e n t , when hopping  i s the  ± .1. No  For  theoretical  conduction  mechanism because the d i v e r g e n c e of the i n t e r p a r t i c l e ( o r i n t e r d e f e c t )  - 98  spacing,  as the p e r c o l a t i o n t h r e s h o l d  -  i s approached, i s not known.  T h e r e f o r e , t h i s method of cermet f a b r i c a t i o n , w h i c h f a v o r s t h i s h o p p i n g c o n d u c t i o n mechanism below Xvc, may  defect  be v e r y u s e f u l i n v e r i f y i n g  f u t u r e p r e d i c t i o n s of the power law b e h a v i o u r of the i n t e r p a r t i c l e s p a c i n g i n p e r c o l a t i o n systems.  The  rather tortuously  l a b y r i n t h i a n c o n d u c t i o n pathways i n a system near the threshold  are p r e d i c t e d  w i t h i n the l a b y r i n t h .  interconnected percolation  [5,40,41] to g i v e r i s e to e l e c t r o n  localization  A g a i n , the p r e c i s e c o n t r o l over Xv makes the  f a b r i c a t i o n methods of t h i s t h e s i s i d e a l l y s u i t e d to the study of these phenomena.  Towards t h i s end,  Normand F o r t i e r i s p r e s e n t l y  an i n depth study of p e r c o l a t i o n and t h i n f i l m s sputtered  IV.2-b  undertaking  electron l o c a l i z a t i n effects i n  by the t e c h n i q u e s of t h i s Ph.D.  t h e s i s study.  Optical Properties I t appears t h a t the o p t i c a l a b s o r p t i o n  f o r .5 < Xv < .7 i n my N - v a c a n c i e s i n AIN  band observed at 4.8  f i l m s , i s more l i k e l y due  than to the g r a n u l a r  s u g g e s t e d , oxygen c o n t a m i n a t i o n . anomaly" i n the o p t i c a l a b s o r p t i o n  The  to excess A l or  geometry o r , as P a s t r n a k  l a c k of any  eV,  observed  seems to r u l e out  has  "dielectric  the MGT  or c o a t e d  sphere-EMT a p p r o x i m a t i o n s f o r d e s c r i b i n g the o p t i c a l p r o p e r t i e s of A1/A1N cermets of t h i s work.  However, the e x t r e m e l y l a r g e  difference,  i n magnitude, between the observed and EMT-predicted o p t i c a l seems to a l s o r u l e out the EMT  approximation.  the  absorption  T h i s l a c k of agreement  p r o b a b l y a r i s e s because n e i t h e r of these t h r e e t h e o r i e s i s equipped t o d e a l w i t h a d i s t r i b u t i o n of i n c l u s i o n s i z e s r a n g i n g c o n t i n u o u s l y  from  - 99 -  s i n g l e atoms t o c r y s t a l l i t e s w i t h b u l k o p t i c a l p r o p e r t i e s .  A  d i s t r i b u t i o n i n A l i n c l u s i o n s i z e s l i k e t h i s i s almost c e r t a i n l y p r e s e n t i n the f i l m s d i s c u s s e d i n t h i s work. been g e n e r a l i z e d  Both the EMT and MGT  t o any number o f types of i n c l u s i o n s  of these g e n e r a l i z a t i o n s  theories  [43,55-57],  have One  may a p p l y i f the s i n g l e , d o u b l e , t r i p l e , e t c .  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M.H. Cohen, J . J o r t n e r , and I . Webman, Phys. Rev. B, J^7_, 4555 (1978).  97.  L. Friedman,  p. 356,  E. S t e i n b e i s s , and K.D. U f e r t , T h i n S o l i d F i l m s , 92_,  J . Non-Cryst.  Solids,  329 (1971).  -  105  -  APPENDIX ON OPTICAL CALCULATIONS  In  t h i s appendix,  the s t e p s i n v o l v e d i n c a l c u l a t i n g  a b s o r p t i o n c o e f f i c i e n t s ( a ) and r e f l e c t i v i t i e s 1-9, 1-14, o r 1-15 w i l l be d e t a i l e d .  optical  (R) from any o f Eqns.  T h i s procedure may be s u b d i v i d e d  i n t o t h e f o l l o w i n g f o u r (4) s t e p s : 1.  Standard t e c h n i q u e s a r e used t o o b t a i n the r e a l and i m a g i n a r y p a r t s o f the d i e l e c t r i c c o n s t a n t s o f t h e c o n s t i t u t e n t m a t e r i a l s of a g r a n u l a r composite  from data on t h e i r  r e f r a c t i v e i n d i c i e s (n) and e x t i n c t i o n c o e f f i c i e n t s ( k ) . 2.  The r e a l and i m a g i n a r y p a r t s o f t h e d i e l e c t r i c c o n s t a n t s o f the m i x t u r e components ( c a l c u l a t e d i n s t e p 1) a r e s u b s t i t u t e d i n t o e i t h e r Eqn. 1-9 o r Eqn. 1-14 t o o b t a i n t h e e f f e c t i v e v a l u e s f o r t h e r e a l and i m a g i n a r y p a r t s o f the d i e l e c t r i c c o n s t a n t ( e ) o f the m i x t u r e o f the two m a t e r i a l s .  3.  U s i n g s t a n d a r d t e c h n i q u e s , the m i x t u r e ' s e f f e c t i v e n and k v a l u e s a r e c a l c u l a t e d from the r e a l and i m a g i n a r y p a r t s o f e (obtained i n step 2 ) .  4.  a and R a r e then c a l c u l a t e d , by s t a n d a r d t e c h n i q u e s , from t h e n and k v a l u e s from s t e p 3.  Mathematical  d e t a i l s o f t h i s method, and the s t a n d a r d t e c h n i q u e s ,  will  now be p r e s e n t e d . The f o l l o w i n g e x p r e s s i o n s a r e some s t a n d a r d formulas  [39] w h i c h  i n t e r r e l a t e many o f the o p t i c a l c o n s t a n t s o f a s i n g l e m a t e r i a l .  - 106  e  + je  x  -  = |e| e x p ( j 6 ) - |e|(cos9 + j s i n G ) ,  2  , 2 . 2vl/2 = (e + e ) , x  tan  n  2  2  (e /e ).  1  2  1  2 + k ,  2nk  1/2[(E  1/2  [(E  [<n - D  + £  2  2  2  +  2  + e )  1 / 2  2  -  ^1  6 l  ]  + k ]/[(n + l ) + 2  2  k ] 2  4*k/X  i n Eqns. A - l t h r o u g h A-5 dielectric  constant  the r e a l p a r t of E  are d e f i n e d as  follows  -  -  107  &2  = the i m a g i n a r y p a r t of e  j  =  n  = the r e f r a c t i v e  index  k  = the e x t i n c t i o n  coefficient  R  = the r e f l e c t i v i t y  a  = the a b s o r p t i o n c o e f f i c i e n t  X  = the wavelength  of l i g h t  The d i e l e c t r i c c o n s t a n t of AIN i s o b t a i n e d from the n and k d a t a o f F i g . 28 and Eqns. A-2 and A - l . F o r use i n Eqns. 1-9, 1-14, and 1-15 the d i e l e c t r i c c o n s t a n t of AIN i s w r i t t e n as  £  i  =  £  il  +  e  i2  =  | i | *P^ i)» e  e  e  A _ 6  where the c o n v e n t i o n s of Eqns. A - l a r e f o l l o w e d and the s u b s c r i p t i stands f o r i n s u l a t o r .  S i m i l a r l y , F i g . 29 and Eqns. A-2 and A - l a r e used  t o w r i t e the d i e l e c t r i c c o n s t a n t of A l as  e  m  =  £  ml  +  J m2 = | m| *P^ J> £  e  e  Q  '  A  7  where the s u b s c r i p t m stands f o r m e t a l . Eqns. A-6 and A-7 may now be used w i t h e i t h e r of Eqns. 1-9 o r 1-14 t o c a l c u l a t e e f o r a g r a n u l a r m i x t u r e of A l and AIN.  The d e t a i l s  of t h i s procedure f o r the MGT, EMT, and c o a t e d sphere a p p r o x i m a t i o n s f o r g r a n u l a r m a t e r i a l s w i l l now be d i s c u s s e d .  -  108  -  Fig. 28  .275  .1375 -  O p t i c a l c o n s t a n t s f o r A1N. The r e f r a c t i v e i n d i c e s (n) a r e from d a t a of P a s t r n a k et a l . [ 5 9 ] , w h i l e the e x t i n c t i o n c o e f f i c i e n t s (k) were c a l c u l a t e d from my o p t i c a l a b s o r p t i o n d a t a f o r s t o i c h i o m e t r i c A l n f i l m s .  - 109  -  Fig. 29  The  o p t i c a l c o n s t a n t s of A l from the data of P o w e l l [ 8 0 ] ,  -  The MGT  -  110  Approximation  S u b s t i t u t i o n of Eqns. A-6 and A-7 i n t o Eqn. 1-9 p e r m i t s , e x t e n s i v e rearrangement, e t o be w r i t t e n as  e = (A + j B ) / ( C + J D ) ,  where  A = 2Xv(R  -  + R  x  + 2R ,  B = 2Xv(I^ - I ) + I  I  + 2I ,  x  2  C  D  =  X  =  v  X  (  v  e  i l -  i2  (  e  e  il ml  £  m l  )  - Sn2>  +  +  e  e  l  p  _  2  e  e  2 _ i l  e  m2  i2 m2' e  2 e  i2  2  m l  and  R  2  +  +  2  2 e  e  i l '  i2>  - Ill  X  l  =  e  I  2  =  2  i 2 ml e  £  i l  e  l  e  il  e  A-8-h  m2'  i2  The r e s u l t s of Eqns. A-8 a l l o w  e  +  -  A-8-i  and  t o  D e  w r i t t e n as  = (AC + B D ) / ( C  2  - D )  A-9-a  = (BC - A D ) / ( C  2  - D)  A-9-b  2  and  e  2  2  E q u a t i o n s A-9 may then be used i n c o n c e r t w i t h Eqns. A-3, A-4, and A-5 t o c a l c u l a t e t h e o p t i c a l p r o p e r t i e s of an A1/A1N cermet i n t h e MGT  approximation.  The EMT Approximation  S u b s t i t u t i o n of Eqns. A-6 and A-7 i n t o eqn. 1-14 y i e l d s  e = j e| e x p ( j 9) = [(1 - Xv) { j e j e x p ( j 9 . ) }  1 / 3  + Xv { | e j e x p ( j 9  f f l  )}  1 / 3  ] . 3  A-10  - 112 -  S i n c e ( e x p ( j 9 ) } ^ ^ has t h r e e (3) s o l u t i o n s i t i s apparent t h a t Eqn.  A-10 has more than one s o l u t i o n .  However, o n l y one o f t h e  s o l u t i o n s t o Eqn. A-10 s a t i s f i e s the p h y s i c a l requirement  of b e i n g  symmetric w i t h r e s p e c t t o the r o l e s of the two types of p a r t i c l e s . T h e r e f o r e , the symmetric s o l u t i o n i s used, and i t i s w r i t t e n as f o l l o w s :  e - (1 - X v ) | e . |  exp(j9 ) + X v ^ e J  3  + 3Xv(l - X v ) l e . | 2  |  + 3Xv  2  exp(j9 )  1  e | m|  2 / 3  11  (1 - Xv) | e |  |  1 / 3  ±  m  e x p { i ( 2 9 . + 9 )/3} l m '  1 / 3  r i J  e m  |  2 / 3  exp{j(9  + 2QJ/3.}.  i  A-ll  U s i n g the i d e n t i t y e x p ( j 9 ) = cos9 + j s i n 9 i n Eqn. A - l l a l l o w s t h e r e a l and i m a g i n a r y p a r t s of e t o be w r i t t e n as e = (1 - v ) | e | c o s C j g ^ + v | e | x  3  x  3  i  m  + 3Xv(l - X v ) | e J [ 11 2  + 3Xv  2  |e | I m|  2 / 3  (1 - Xv) | e |  1 / 3  ±  1 / 3  |e |  cos(j9 ) m  cos ( j (20, + 9 )/3} I m 2 / 3  m  c o s { j ( 9 + 20 )/3}. 1  m  A-12-a  and e = (1 - X v ) I e . I s i n ( j 9,) + X v I e I s i n ( j 9 ) |i| i I m| m 3  3  + 3Xv(l - X v ) | e J I iI 2  + 3Xv  Z  |e | | m|  2 / 3  (1 - Xv) | e j | i|  1  /  3  1 / 3  |e I m  1  sin{j(29  2/3  i  4  + 9 )/3} m  s i n l j ( 9 , + 29 )/3}. i m l J  J  A-12-b  - 113 -  Eqns. A-12 may be used i n c o n c e r t w i t h Eqns. A-3, A-4, and A-5 t o c a l c u l a t e the o p t i c a l p r o p e r t i e s of an A1/A1N cermet i n the EMT approximation.  The Coated Sphere Approximation  The coated sphere a p p r o x i m a t i o n i s used i n c o n j u n c t i o n w i t h e i t h e r t h e MGT o r EMT a p p r o x i m a t i o n s .  The o n l y m o d i f i c a t i o n b e i n g t h a t ,  i n Eqns. A-9 o r A-12, e i t h e r o r both of the e f f e c t i v e  or e  ra  are replaced w i t h  d i e l e c t r i c c o n s t a n t f o r a sphere of t h e o r i g i n a l m a t e r i a l  (1 o r m) t h a t i s coated w i t h a l a y e r of a n o t h e r m a t e r i a l .  The  effective  d i e l e c t r i c c o n s t a n t f o r such a sphere i s c a l c u l a t e d i n the MGT a p p r o x i m a t i o n where the c o a t i n g m a t e r i a l i s taken as the amorphous d i e l e c t r i c m a t r i x t h a t t h e o r i g i n a l sphere i s embedded i n . W i t h t h e effective uncoated  d i e l e c t r i c c o n s t a n t s f o r coated spheres i n p l a c e of t h e sphere d i e l e c t r i c c o n s t a n t s , a random d i s t r i b u t i o n o f two types  of coated spheres i s t r e a t e d i n t h e EMT a p p r o x i m a t i o n (Eqns. 1-14 and A - 1 2 ) , w h i l e a random d i s t r i b u t i o n of one type o f coated sphere i n an amorphous m a t r i x of another m a t e r i a l I s t r e a t e d i n the MGT approximation  (Eqns. 1-9 and A - 9 ) .  embedded  

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