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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 Techology, 1975 M.Sc, Wayne State 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 i n THE FACULTY OF GRADUATE STUDIES Department of Physics We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1984 © John David A f f i n i t o , 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 ABSTRACT This t h e s i s deals 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 metal target i n an I n e r t / r e a c t i v e gas glow discharge and 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 o p t i c a l p r o p e r t i e s of A1/A1N granul a r metal (or cermet) f i l m s produced by t h i s technique. Experiments are described i n which an A l target i s sputtered i n Ar/N2 and Ar/C>2 atmospheres. The r e l a t i o n s h i p s between chemical processes o c c u r r i n g on the target s u r f a c e , substrate surface, and i n the glow discharge of a dc planar magnetron s p u t t e r i n g system are studied f o r the purpose of 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 which lead to the w e l l known t r a n s i t i o n s between bare and covered target surfaces are c o r r e l a t e d w i t h glow discharge c h a r a c t e r i s t i c s . These data are shown to be i n agreement w i t h a model which assumes two d i s t i n c t mechanisms f o r target coverage: (1) chemisorption of n e u t r a l r e a c t i v e gas species from the s p u t t e r i n g gas; and (2) i o n p l a t i n g of r e a c t i v e gas species from the s p u t t e r i n g c u r r e n t . This model allows e s t i m a t i o n of the s t a b i l i t y of the glow discharge against the p o s i t i v e feedback mechanisms and i n d i c a t e s under what circumstances voltage c o n t r o l of the glow discharge w i l l permit sustained operation at a l l degrees of target surface coverage. With the voltage c o n t r o l method, a one to one correspondence between target voltage and f i l m composition i s e s t a b l i s h e d . In a d d i t i o n , a method i s presented f o r c a l c u l a t i n g the f i l m composition from only the glow discharge c h a r a c t e r i s t i c s . - i i i -My experiments show that voltage c o n t r o l l e d , r e a c t i v e dc, planar magnetron s p u t t e r i n g i s i d e a l l y s u i t e d to the d e p o s i t i o n of A1/A1N cermets of c o n t r o l l e d composition. X-ray d i f f r a c t i o n , transmission e l e c t r o n microscope (TEM), H a l l , and r e s i s t i v i t y vs. temperature data f o r these A1/A1N cermets are presented as a f u n c t i o n of metal 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 the glow discharge 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. Metal p r e c i p i t a t e s are seen to form and, thereby, 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 of A l and A1N c r y s t a l l i t e s when the Al/N r a t i o becomes greater than one. A p e r c o l a t i o n threshold i s observed i n the c o n d u c t i v i t y at a c r i t i c a l volume f r a c t i o n (Xvc) of 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 behavior both above and below Xvc. Above Xvc, 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 p r e d i c t i o n of 1.7 f o r a mixture of two "normal" conductors ( i . e . m e t a l l i c or semiconductor conduction, but not hopping or t u n n e l i n g ) . Below Xvc, conduction i s v i a hopping and a /** (Xvc -X v ) _ s , w i t h s = 4.3 ± .1. For a mixture of normal conductors below Xvc, s i s p r e d i c t e d to be 0.7, while there 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 conduction i s v i a hopping. This power law behavior of hopping c o n d u c t i v i t y warrants 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 . F u r t h e r , the temperature behavior of the 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 the view that hopping i s from defect to defect w i t h i n the A1N grains as opposed to d i r e c t metal g r a i n to metal g r a i n hopping. The temperature behavior of the c o n d c u t i v i t y a l s o i n d i c a t e s that 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 important f o r Xvc < Xv < 0.8. - i v -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 Maxwell-Garnett t h e o r i e s f o r granular m a t e r i a l s 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 . Observable s t r u c t u r e i n the UV o p t i c a l absorption and IR r e f l e c t i v i t y seem to be p r o p e r t i e s of A1N and not due to the microgranular s t r u c t u r e of the A1/A1N composite. 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 granular t h e o r i e s are not observed, even though the f i l m s are granular, i s a t t r i b u t e d to the e f f e c t of a large number of 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 other than bulk o p t i c a l p r o p e r t i e s , that are not taken i n t o account i n these t h e o r i e s . - v -TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS v LIST OF FIGURES v i i LIST OF SYMBOLS i x ACKNOWLEDGEMENTS x i i i CHAPTER I - INTRODUCTION 1 1.1 S p u t t e r i n g 2 1.2 E l e c t r i c a l Transport 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 Transport 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 Mixtures 17 1.3 P h y s i c a l P r o p e r t i e s of A1N and A l 26 1.3- a A1N 27 I.3-b A l 28 CHAPTER II - MECHANISMS AND CONTROL OF THE REACTIVE SPUTTERING PROCESS 30 I I . 1 Apparatus and Experimental Method 34 II . 2 Experimental R e s u l t s and D i s c u s s i o n 39 II. 2 - a The Target Reaction 45 II.2-b P r e d i c t i o n of F i l m Composition from Plasma C h a r a c t e r i s t i c s 57 11.2-c C a l c u l a t i o n of the S p u t t e r i n g Y i e l d 66 - v i -Page CHAPTER III - FILM PROPERTIES - EXPERIMENTAL RESULTS AND DISCUSSION 69 111.1 E l e c t r i c a l Transport P r o p e r t i e s of A1/A1N Cermets 69 111.2 O p t i c a l P r o p e r t i e s of A1/A1N Cermets 79 CHAPTER IV - CONCLUSION 96 IV. 1 Reactive S p u t t e r i n g Mechanisms 96 IV.2 A1/A1N Cermets Deposited by Voltage C o n t r o l l e d Reactive S p u t t e r i n g 97 IV.2-a E l e c t r i c a l Transport P r o p e r t i e s 97 IV.2-b O p t i c a l P r o p e r t i e s 98 BIBLIOGRAPHY 100 APPENDIX ON OPTICAL CALCULATIONS 105 - v i i -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 A l - A r / N 2 glow discharge c h a r a c t e r i s t i c s 40 4 Comparison of voltage c o n t r o l l e d and power c o n t r o l l e d r e a c t i v e s p u t t e r i n g discharge c h a r a c t e r i s t i c s 42 5 V a r i a t i o n s i n A l - A r / N 2 discharge c h a r a c t e r i s t i c s w i t h F A r > F ^ , and S 50 6 V a r i a t i o n s i n A l - A r / 0 2 discharge c h a r a c t e r i s t i c s w i t h F A r , F Q , and S 51 7 V a r i a t i o n of P /P_ w i t h P /I at 0 = 1 52 r t r 8 D e p o s i t i o n ra t e vs A l 60 9 V a r i a t i o n s of P„ and 1/P„ w i t h A l * 62 N 2 N 2 10 p and TCR vs x ( i n AINx) 64 11 Voltage dependence of the e f f e c t i v e metal s p u t t e r i n g y i e l d 68 12 X-ray d i f f r a c t i o n data 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 d e p o s i t i o n discharge c h a r a c t e r i s t i c s . . 70 13 TEM data 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 d e p o s i t i o n discharge c h a r a c t e r i s t i c s 71 14 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 of var i o u s metal volume f r a c t i o n s 73 15 Conduction a c t i v a t i o n energies f o r A1/A1N cermet f i l m s 75 - v i i i -Figure Page 16 Inverse 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 metal volume f r a c t i o n s near the p e r c o l a t i o n t h r e s h o l d 77 17 C r i t i c a l exponents f o r conduction i n A1/A1N cermets.... 78 18 O p t i c a l a b s o r p t i o n data 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 d e p o s i t i o n discharge c h a r a c t e r i s t i c s . . . 80 19 O p t i c a l absorption data 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 d e p o s i t i o n discharge c h a r a c t e r i s t i c s . . . 81 20 MGT c a l c u l a t i o n of o p t i c a l a bsorption 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 21 MGT c a l c u l a t i o n of o p t i c a l absorption 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 index 84 22 EMT c a l c u l a t i o n of o p t i c a l a bsorption 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 85 23 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 24 Comparison of o p t i c a l a bsorption data f o r a c t u a l A1/A1N cermet f i l m s w i t h coated sphere-EMT c a l c u l a t i o n s 87 25 EMT c a l c u l a t i o n of r e f l e c t a n c e of 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 26 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 of 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 27 IR r e f l e c t a n c e data 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 d e p o s i t i o n discharge c h a r a c t e r i s t i c s . . . 90 28 O p t i c a l constants of A1N 108 29 O p t i c a l constants of A l 109 - i x -LIST OF SYMBOLS D e f i n i t i o n Used as a r b i t r a r y constants. O p t i c a l emission i n t e n s i t y of 3961.5 A l i n e of 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 m a t e r i a l . Radius of a s p h e r i c a l volume of cermet m a t e r i a l . Energy of a defect s t a t e . Photon energy. Fermi Energy. 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 conduction. Ar flow r a t e . N 2 flow r a t e . 0 2 flow r a t e . Fermi-Dirac d i s t r i b u t i o n f u n c t i o n . F r a c t i o n of p o s i t i v e ions i n s p u t t e r i n g i o n current that are r e a c t i v e gas species. T o t a l s p u t t e r i n g current ( e l e c t r o n i c + i o n i c ) . O p t i c a l e x t i n c t i o n c o e f f i c i e n t . Boltzmann's constant. Generic chemical symbol f o r sputtered metal atom. - x -Symbol Definition N Density of states function for defects. N Total number of inclusions with dipole moment p. n Optical refractive index. n Total number of reactive gas molecules adsorbed on the surface of the sputtering target. P^r Ar partial pressure. P M No partial pressure. P 0 2 partial pressure. °2 P r Reactive gas partial pressure. P Total pressure. p Dipole moment of an inclusion in a cermet material. Q For a coated sphere, Q = 1 - coating thickness/total radius. The total radius includes the coating. Q for a coated dielectric (insulating) sphere. Q m Q for a coated metal sphere. R Generic chemical symbol for a reactive gas molecule. R Optical reflectance. Rg Hall constant. S Pumping speed. S(Ar) Pumping speed for Ar gas. S(N2) Pumping speed for N2 gas. S(02) Pumping speed for O2 gas. - x i -Symbol D e f i n i t i o n s C r i t i c a l exponent f o r conduction below Xvc. T Temperature. t Time. t C r i t i c a l exponent f o r conduction above Xvc. t ^ Coating thickness on coated d i e l e c t r i c sphere. t Coating thickness on coated metal sphere. 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 spacing. V Cathode voltage 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 metal i n a cermet. Xvc C r i t i c a l value of Xv at 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 Product of r e a c t i v e gas impingement rate per u n i t P r and the 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 chemisorption on a s p u t t e r i n g t a r g e t . P Number of N2 molecules gettered per A l atom sputtered. Y Secondary e l e c t r o n emission c o e f f i c i e n t . * 6 6A1 = the number of A l atoms sputtered per second. 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 gas species impinging 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 constant of a cermet m a t e r i a l . D i e l e c t r i c constant of i n s u l a t i n g m a t e r i a l i n a cermet. e D i e l e c t r i c constant of m e t a l l i c m a t e r i a l i n a cermet, m e^ c D i e l e c t r i c constant of m a t e r i a l that i s c o a t i n g an i n s u l a t i n g sphere i n a cermet. - x i i -Symbol D e f i n i t i o n E D i e l e c t r i c constant of m a t e r i a l that i s coating a m e t a l l i c sphere i n a cermet. e^ c s Average d i e l e c t r i c constant of a coated i n s u l a t i n g sphere i n a cermet. e Average d i e l e c t r i c constant of a coated m e t a l l i c sphere i n a mcs z cermet. n 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 f o r metal atoms. ^ e f f = + y)' S p u t t e r i n g y i e l d f o r metal 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 molecules. 9 P o l a r angle i n a s p h e r i c a l coordinate system. 6 F r a c t i o n of the surface of a s p u t t e r i n g target that i s covered 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 wavelength. u M o b i l i t y . p R e s i s t i v i t y . a C o n d u c t i v i t y . T Time d u r a t i o n of a s p u t t e r i n g current t r a n s i e n t . T R Time re q u i r e d f o r a pressure t r a n s i e n t i n the s p u t t e r i n g chamber to be damped out. $ E l e c t r i c p o t e n t i a l . AE AE = E - Ef = the conduction a c t i v a t i o n energy. A l Magnitude of s p u t t e r i n g current t r a n s i e n t . - x i i i -ACKNOWLEDGEMENTS I am pleased to thank Dr. R.R. Parsons for the great amounts of time and effort he has invested in this project as my supervisor. His guidance was invaluable. I also wish to thank Dr. R. Barrie, N. Fortier, M. Brett, and Dr. J.A. Rostworowski for the many illuminating discussions we have had. N. Fortier 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 film thickness measurements. For financial support, I wish to thank the Natural Sciences and Engineering Research Council of Canada and the University of British Columbia. To a l l my friends and relatives who encouraged and supported me throughout my studies I give my heartfelt thanks. To my father's repeated question, I would like to answer "Yes, I am fin a l l y through". Thank you. - 1 -CHAPTER 1 INTRODUCTION Microgranular mixtures 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 or granular metals) are 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 are 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 absorbers [1] and temperature s t a b i l i z e d , t h i n f i l m r e s i s t o r s [ 2 ] , T h e o r e t i c a l l y , they represent r e a l , macroscopic systems that may be used to study the c r i t i c a l phenomena as 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 threshold [2-6], As w i l l be discussed s h o r t l y , these p r o p e r t i e s of 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 , depend c r u c i a l l y upon the microgeometrical c o n f i g u r a t i o n of the f i l m , and not j u s t upon the o v e r a l l , bulk chemical composition. 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 p r o p e r t i e s of A1/A1N cermets r e a c t i v e l y sputtered from an A l s p u t t e r i n g target i n an Ar/N2 atmosphere. However, i n developing the f a b r i c a t i o n technique some very i n t e r e s t i n g r e s u l t s concerning 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 to be at l e a s t as important as the 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 produced. Therefore, i n view of the 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 d e p o s i t i o n during the l a s t twenty years [7-9], f u l l y h a l f of t h i s t r e a t i s e w i l l concern experiments performed to determine and to model the mechanisms inv 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 process. Due to the large number of i n t e r r e l a t e d parameters in 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 process, l i t t l e i n the way of general, 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 process c o n t r o l to d e p o s i t i o n parameters has been published [ 7 ] , Therefore, a study of the mechanisms inv 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 goal of determining some f a i r l y u n i v e r s a l 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 process, i s of considerable importance. This t h e s i s i s organized as f o l l o w s . The remainder of t h i s i n t r o d u c t o r y chapter w i l l be a review of: (1) the p r i n c i p l e s of the s p u t t e r i n g process; (2) the e l e c t r i c a l transport and o p t i c a l p r o p e r t i e s of cermets; and (3) the e l e c t r i c a l and o p t i c a l p r o p e r t i e s of A1N and A l . In chapter two, I present my experimental and t h e o r e t i c a l r e s u l t s concerning the mechanisms of r e a c t i v e s p u t t e r i n g . In chapter three, I give experimental data concerning the e l e c t r i c a l transport and 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 sputtered A1/A1N cermet f i l m s , and an a n a l y s i s of these data. 1.1 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 ( i o n , atom, cosmic ray, etc.) on a m a t e r i a l body with the r e s u l t t h a t , through 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 conjunction w i t h a l a r g e number of m o d i f i e r s to describe an e q u a l l y l a r g e number of r e l a t e d processes. The m o d i f i e r s are g e n e r a l l y employed to i n d i c a t e what type of p a r t i c l e s are causing the s p u t t e r i n g , what technique 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 con d i t i o n s e x i s t on the substrate upon which the sputtered f l u x lands [7-14]. - 3 -Ions are g e n e r a l l y used to cause s p u t t e r i n g f o r the 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 classes of i o n s p u t t e r i n g are c a l l e d "ion beam" s p u t t e r i n g and "glow discharge" s p u t t e r i n g . In e i t h e r of these cases the m a t e r i a l to be sputtered (or the t a r g e t ) i s t h i c k enough that the sputtered p a r t i c l e s are ejected only from the surface that i s under i on bombardment. The p a r t i c l e s that are e j e c t e d are g e n e r a l l y atoms or small molecules of the target m a t e r i a l and "secondary" e l e c t r o n s . In the case of Ion beam s p u t t e r i n g , a c o l l i m a t e d beam of ions of rat h e r w e l l defined k i n e t i c energy causes the s p u t t e r i n g , and the technique i s f u r t h e r categorized by the method of producing the beam [13], In glow discharge s p u t t e r i n g , the m a t e r i a l to be sputtered forms the cathode i n a glow discharge and i s bombarded p r i m a r i l y by p o s i t i v e ions from the glow [7] , In t h i s l a t t e r process, the i n c i d e n t ions are not c o l l i m a t e d and t h e i r k i n e t i c energies are d i s t r i b u t e d ( i n some cases rather widely) due to c o l l i s i o n s i n t r a n s i t from the glow to the t a r g e 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 i s r e l a t e d t o : the p o t e n t i a l d i f f e r e n c e between the cathode ( t a r g e t ) and the glow; the temperature; the t o t a l and p a r t i a l pressures of the gases i n the glow discharge environment; and the cross s e c t i o n f o r charge t r a n s f e r between the"various atoms, molecules, and ions present [7,15], These glow discharge s p u t t e r techniques are f u r t h e r described by m o d i f i e r s i n d i c a t i n g : the target shape (plan a r , c y l i n d r i c a l , b e l t . . . ) ; the frequency of the e l e c t r i c a l discharge (dc, ac, or r f ) ; any e x t e r n a l agent used to support the glow discharge (magnetic f i e l d s , thermionic e m i t t e r s , t e s l a c o i l s . . . ) ; the r e a c t i v i t y of the discharge - 4 -gases w i t h respect to the target m a t e r i a l ( i n e r t or r e a c t i v e ) ; the co n d i t i o n s e x i s t i n g at the substrate (temperature, s t a t e of motion w i t h respect to the t a r g e t , substrate b i a s , i s there a glow discharge at the su b s t r a t e , and i f so, at what frequency) [8,10-12], This seemingly endless a d d i t i o n of modifying words can lead to some f a i r l y long names. For i n s t a n c e , the experimental work to be discussed i n t h i s t h e s i s i s concerned w i t h "voltage c o n t r o l l e d , dc, r e a c t i v e , planar magnetron s p u t t e r i n g " . This name i n d i c a t e s that: the target i s f l a t ( p l a n a r ) ; a magnetic f i e l d i s used to help confine the glow to a region very near the t a r g e t , to make b e t t e r use of 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 to create the ions close to the target where they are needed (magnetron); at l e a s t some component i n the gas mixture w i l l c hemically combine w i t h the target m a t e r i a l ( r e a c t i v e ) ; the discharge i s dc (dc); 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 monitoring and c o n t r o l l i n g the cathode voltage (voltage c o n t r o l l e d ) . F i g . 1 s c h e m a t i c a l l y d e p i c t s the various processes which occur simultaneously i n s i d e a s p u t t e r i n g chamber while s p u t t e r i n g a metal ta r g e t (M) i n the presence of an A r / r e a c t i v e gas (R) mixture. These processes may be broadly d i v i d e d i n t o three categories according to the p h y s i c a l l o c a t i o n at which the process takes place. They are target r e a c t i o n s , w a l l (or substrate) r e a c t i o n s , and gas r e a c t i o n s . The target surface i s continuously bombarded by energetic ions and thermal n e u t r a l s of the gases present i n the discharge. The i o n Fig.'l "5" Schematic d e p i c t i o n of processes o c c u r r i n g during r e a c t i v e s p u t t e r i n g of a metal target (M) i n an Ar/Reactive gas (R) atmosphere. - 6 -bombardment can cause s p u t t e r i n g of the target surface m a t e r i a l and the emission of secondary e l e c t r o n s . Further, the bombarding ions of the r e a c t i v e gas may chemically bond w i t h the target m a t e r i a l and produce a target m a t e r i a l - r e a c t i v e gas compound l a y e r on parts of the target s u r f a c e . I f n e u t r a l R molecules chemisorb on the bulk target m a t e r i a l , then the f l u x of thermal 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 to the formation of the compound l a y e r . Since the y i e l d of sputtered 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 ta r g e t s [ 8 ] , these y i e l d s w i l l be h i g h l y dependent on the degree of target coverage. A l s o , the presence of a compound l a y e r on the ta r g e t surface means that the c o n s t i t u e n t s of R w i l l a l s o be sputtered from the target surface. Sputtered f l u x w i l l condense and react w i t h the thermal f l u x of R n e u t r a l s on the w a l l s and substrates [16-21]. Note that even i f R molecules do not chemisorb on the bulk target m a t e r i a l , the condensing f l u x i s l a r g e l y atomic i n nature [7-8] and i s expected to be much more r e a c t i v e than the bulk m a t e r i a l . This compound formation on the 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 serves to lower the p a r t i a l pressure of the r e a c t i v e gas i n the chamber. The speed of t h i s g e t t e r pumping i s c o n t r o l l e d by the sputtered f l u x , which, i n t u r n , i s c o n t r o l l e d by the number and energy of ions i n c i d e n t on the target surface as w e l l as the degree to which the target surface 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 are allowed to flow i n t o the vacuum chamber through a c o n t r o l l e d leak while they are simultaneously pumped out by mechanical - 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). In steady s t a t e , t h i s produces p a r t i a l pressures of the two gases that are determined by t h e i r i n d i v i d u a l leak rates and pumping speeds, provided that there i s no glow discharge. In the presence of the glow discharge, the g e t t e r i n g a c t i o n of the sputtered f l u x on the r e a c t i v e gas acts as another pumping port 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. In the glow region, secondary e l e c t r o n s emitted from the target help to s u s t a i n the discharge through e l e c t r o n impact I o n i z a t i o n of the gaseous species present. Therefore, the glow may act as a source of p o s i t i v e and negative ions of Ar and R which serve to 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 the target and the glow region that i s needed to 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 the target surface (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 that 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 the y i e l d of secondary e l e c t r o n s , which, 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 the degree of target coverage. In a d d i t i o n , R molecules may d i s s o c i a t e i n t o ions and n e u t r a l s of t h e i r various c o n s t i t u e n t s . The p o s i t i v e ions i n the glow w i l l be ac c e l e r a t e d towards the t a r g e t , however, due to c o l l i s i o n s (mostly symmetric charge t r a n s f e r r e a c t i o n s [15]) many of the ions that reach the cathode have considerably l e s s k i n e t i c energy than expected by merely c o n s i d e r i n g the p o t e n t i a l d i f f e r e n c e between the cathode and the glow discharge (cathode f a l l ) [7,15]. The previous d i s c u s s i o n s show that the gaseous ambient i s coupled to. the t a r g e t , w a l l , and glow discharge regions. Therefore, these three regions are a l l coupled to each other through the s p u t t e r i n g gas. A longstanding problem i n c o n t r o l l i n g r e a c t i v e l y sputtered f i l m - 8 -compositions i s that p o s i t i v e feedback between the g e t t e r i n g r a t e at the w a l l and the metal s p u t t e r i n g rate conspire to force the target surface to e i t h e r remain bare metal or become completely covered w i t h a compound l a y e r [16-21], I f the s p u t t e r i n g rate i s becoming great enough to uncover some po r t i o n s of the target surface then the s p u t t e r i n g y i e l d increases from these bare regions. This causes an increase i n the g e t t e r i n g r a t e which reduces the number of r e a c t i v e gas species 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 , allows the bare spots to grow l a r g e r and f u r t h e r increases the s p u t t e r i n g y i e l d . This p o s i t i v e feedback c y c l e q u i c k l y leads to a completely bare target surface. This abrupt change i n the degree of surface coverage a l s o causes an abrupt change i n the secondary e l e c t r o n emission y i e l d , which r e s u l t s i n an abrupt change i n the cathode f a l l . A l s o , w i t h the abrupt increase i n s p u t t e r i n g y i e l d , an abrupt increase i n sputtered 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 pressure due to increased g e t t e r i n g . I f one s t a r t s from a bare t a r g e t , the opposite r e a c t i o n , which leads to a covered t a r g e t , occurs i f the s p u t t e r i n g r a t e becomes too low to keep the e n t i r e surface c l e a r e d of the compound l a y e r . There i s considerable h y s t e r e s i s observed i n the discharge 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], with the r e s u l t that a gap e x i s t s i n the I-V-P R c h a r a c t e r i s t i c s under which s t a b l e o p e r a t i o n of the discharge i s p o s s i b l e . Since i t has been found that f i l m s sputtered from a bare target are ne a r l y pure metal, while f i l m s sputtered from a completely covered target are s t o i c h i o m e t r i c m e t a l - r e a c t i v e 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 to severely r e s t r i c t the a t t a i n a b l e f i l m compositions. Since the composition of sputtered 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 sputtered 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 nature and strength of the coupling between the t a r g e t , gas, and substrate would be very important i n any attempt at 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 . The nature of t h i s coupling w i l l be explored 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 sputtered f l u x and r e a c t i v e gas molecules i n the s p u t t e r i n g chamber. This study w i l l show why 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 target coverage f o r an A l target i n an Ar/N2 atmosphere (and other m e t a l - r e a c t i v e gas combinations i n which r a p i d chemisorption of the n e u t r a l r e a c t i v e gas on the bulk metal does not o c c u r ) , provided that cathode voltage i s c o n t r o l l e d . This s t a b i l i t y at a l l degrees of target coverage gives access to AINx f i l m s f o r a l l x between zero and one. 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 which x may be c a l c u l a t e d from knowledge of the glow discharge 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 (or granular metals) are microgranular mixtures of 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 . This term i s sometimes a p p l i e d to s i m i l a r mixtures of insulator-semiconductor or semiconductor-metal p a r t i c l e s . 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 zero 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 intermediate values of Xv some p r o p e r t i e s - 10 -( r e s i s t i v i t y , a v e r a g e t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t a n c e ( T C R ) , a n d d e n s i t y ) [ 2 , 2 2 ] a p p e a r t o be i n t e r m e d i a t e t o t h o s e o f t h e p u r e p h a s e s , w h i l e o t h e r p r o p e r t i e s ( o p t i c a l a b s o r p t i o n a n d d e t a i l s o f t h e t e m p e r a t u r e d e p e n d e n c e o f r e s i s t i v i t y ) [ 4 - 6 ] e x h i b i t b e h a v i o u r t h a t i s f u n d a m e n t a l l y d i f f e r e n t f r o m e i t h e r p u r e p h a s e a n d a r i s e s p r i m a r i l y f r o m t h e g e o m e t r i c p r o p e r t i e s o f t h e m i x t u r e . A b r i e f d i s c u s s i o n o f some o f t h e s e g e o m e t r y d e p e n d e n t p r o p e r t i e s w i l l now be g i v e n . I.2-a E l e c t r i c a l Transport Properties of Cermets P r e v i o u s e x p e r i m e n t a l s t u d i e s [ 2 3 ] o f W/AI2O3 c e r m e t s h a v e s h o w n p o w e r l a w b e h a v i o u r o f c o n d u c t i v i t y ( a ) f o r X v h i g h e r t h a n t h e p e r c o l a t i o n t h r e s h o l d ( X v c ) . T h e o r e t i c a l s t u d i e s [ 2 4 ] f o r m i x t u r e s o f two " n o r m a l " c o n d u c t o r s ( n o t h o p p i n g o r t u n n e l i n g c o n d u c t i o n ) p r e d i c t p o w e r l a w b e h a v i o u r b o t h a b o v e a n d b e l o w X v c . B y p o w e r l a w b e h a v i o u r i t i s m e a n t t h a t t h e p r o p e r t y u n d e r s t u d y , i n t h i s c a s e t h e e l e c t r i c a l c o n d u c t i v i t y , i s s e e n t o v a r y a s some p o w e r o f | X v - X v c | f o r v a l u e s o f X v i n t h e n e i g h b o r h o o d o f X v c [ 3 , 2 4 ] . T h e p a r t i c u l a r p o w e r i s e x p e c t e d t o be d i f f e r e n t o n e i t h e r s i d e o f X v c . T h e e x p r e s s i o n t h a t r e l a t e s t h e e x p o n e n t o n o n e s i d e o f X v c t o t h e e x p o n e n t o n t h e o t h e r s i d e i s c a l l e d t h e s c a l i n g r e l a t i o n . T h e s c a l i n g r e l a t i o n a n d t h e s e e x p o n e n t s a r e e x p e c t e d t o d e p e n d o n l y o n t h e s p a t i a l d i m e n s i o n a l i t y o f t h e s a m p l e [ 3 , 2 4 ] , F o r mo re d e t a i l e d d i s c u s s i o n s o n t h i s p o w e r l a w b e h a v i o u r a n d s c a l i n g , t h e r e a d e r i s r e f e r r e d t o t h e l i t e r a t u r e o n p e r c o l a t i o n t h e o r y [ 3 ] a n d t h e t h e o r y o f c r i t i c a l p h e n o m e n a a n d p h a s e t r a n s i t i o n s [ 2 5 , 2 6 ] . - 11 -When the c o n d u c t i v i t i e s of the two phases d i f f e r by as much as i n A1/A1N or W/AI2O3 cermets normal conduction does not occur below Xvc, in s t e a d conduction proceeds v i a t u n n e l i n g between i s o l a t e d metal 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 [2,5,23,27], The r e s i s t i v i t i e s of A l and A1N are 3 x 1 0 - 6 Q-cm [28] and greater than 1 0 1 5 S2-cm [29], r e s p e c t i v e l y . This added com p l i c a t i o n of t u n n e l i n g conduction below Xvc has not yet been t r e a t e d i n the context of a c r i t i c a l theory of phase t r a n s i t i o n s , nor has any experimental evidence f o r c r i t i c a l behaviour of tunneling i n t h i s regime been presented. The 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. One should express 0, f o r t u n n e l i n g between i s o l a t e d metal i s l a n d s [30,31], i n terms of the 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 these two distances i n t o the expression f o r a. U n f o r t u n a t e l y , while the power law r e l a t i o n f o r the metal c l u s t e r s i z e i s w e l l known [3] the r e l a t i o n f o r the i n t e r c l u s t e r spacing i s not. A measurement of the power law behaviour of tu n n e l i n g f o r Xv < Xvc should, however, allow t h i s r e l a t i o n to be determined by i n v e r t i n g the expression f o r the tu n n e l i n g c o n d u c t i v i t y . Previous treatments of tun n e l i n g f a r below Xvc, which were not meant to deal 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 observed [2,32] lnp <*> 1/VT temperature behaviour f o r the r e s i s t i v i t y i n cermet f i l m s w i t h average metal g r a i n s i z e s l e s s than ~ 40 A. The ex p l a n a t i o n , however, i n v o l v e d assumptions f o r the r e l a t i o n between the 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 spacings that d i d not r e f l e c t the true s t r u c t u r e of these granular m a t e r i a l s [6,33]. In p a r t i c u l a r , - 12 -A b e l e s e t a l . [ 2 ] d e r i v e d a n e x p r e s s i o n f o r h o p p i n g c o n d u c t i o n i n g r a n u l a r m e t a l s b y c o n s i d e r i n g t h e c h a r g i n g e n e r g y i n v o l v e d when a n e l e c t r o n i s r e m o v e d f r o m one i s o l a t e d m e t a l l i c g r a i n a n d p l a c e d o n a n e i g h b o r i n g g r a i n . T h i s c h a r g i n g e n e r g y was f o u n d t o be a f u n c t i o n o f b o t h t h e i n t e r g r a i n s p a c i n g a n d t h e g r a i n s i z e . T h e t w o c o n t r o v e r s i a l a s s u m p t i o n s [ 6 , 3 3 ] t h a t t h e y made w e r e ; t h a t t h e i n t e r g r a i n s p a c i n g wa s p r o p o r t i o n a l t o t h e g r a i n s i z e , b o t h m i c r o s c o p i c a l l y a n d m a c r o s c o p i -c a l l y ; a n d t h a t t h e r e was a v e r y b r o a d d i s t r i b u t i o n o f g r a i n s i z e s . W i t h t h e s e t w o a s s u m p t i o n s , c o n d u c t i o n wa s t a k e n t o be d o m i n a t e d b y p a t h s o f a n " o p t i m a l " g r a i n s i z e a n d I n t e r g r a i n s p a c i n g w h i c h r e s u l t e d i n t h e h i g h e s t h o p p i n g p r o b a b i l i t y . F o r l o w f i e l d c o n d u c t i o n , a s t h e t e m p e r a t u r e c h a n g e d t h e e n e r g y a v a i l a b l e t o t h e t u n n e l i n g e l e c t r o n s c h a n g e d w h i c h c a u s e d t h e o p t i m a l g r a i n s i z e t o c h a n g e a l s o . T h e r e f o r e , a s t h e t e m p e r a t u r e c h a n g e d t h e c o n d u c t i o n p a t h c h a n g e d i n o r d e r t o a l w a y s make u s e o f a p a t h w i t h o p t i m a l g r a i n s i z e s . A s l o n g a s t h e r e was a s u f f i c i e n t l y l a r g e d i s t r i b u t i o n o f g r a i n s i z e s t o a c c o m o d a t e t h i s p r o c e s s , t h e t e m p e r a t u r e b e h a v i o u r o f p was p r e d i c t e d t o be l n p **s 1 / / T . M o r e r e c e n t l y , d e t a i l e d s t u d i e s o f t h e g r a i n s i z e a n d i n t e r g r a i n s p a c i n g d i s t r i b u t i o n s i n g r a n u l a r m e t a l s , t h a t a r e f o u n d t o f o l l o w t h e l n p ^ 1 / / T l a w , h a v e b e e n d o n e [ 6 , 3 3 ] . T h e s e s t u d i e s s h o w e d t h a t , g i v e n t h e h o p p i n g t h e o r y j u s t d e s c r i b e d , t h e d i s t r i b u t i o n i n g r a i n s i z e s wa s f a r t o o n a r r o w t o a c c o u n t f o r t h e r a n g e o f t e m p e r a t u r e o v e r w h i c h t h e l n p 1 / / T b e h a v i o u r was o b s e r v e d . T h e c l a s s i c t r e a t m e n t o f v a r i a b l e r a n g e h o p p i n g g i v e n b y M o t t [ 3 4 ] c o n t a i n e d t h i s same i d e a o f a n o p t i m a l h o p p i n g p a t h . H o w e v e r , i n - 13 -Mott's treatment the trade o f f was between the exponential dependences of the hopping frequency on distance between l o c a l i z e d states and the d i f f e r e n c e i n energy of these states (where i t i s assumed that hopping between st a t e s of equal energy i s favored). Mott took the density of s t a t e s to be a constant and found lnp ~ 1 /T.^^ More recent t h e o r e t i c a l studies [35,36] have i n d i c a t e d that 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 gives 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 r e s u l t s i n a 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 . I f t h i s p a r a b o l i c d e n s i t y i s incorporated i n the Mott theory f o r v a r i a b l e range hopping, l n p ~ 1 //T behaviour i s obtained, provided that the l o c a l i z a t i o n length i s small compared to the hopping length [36], This l a s t r e s t r i c t i o n i s not s a t i s f i e d very near to Xvc, or when the r a t i o of metal i s l a n d s i z e to i n t e r i s l a n d separation i s l a r g e , but w i l l be expected to hold f o r values of Xv w e l l below 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 ) . This i s because of the nature of the competition between a v a i l a b l e conduction pathways. Paths of a given p a r t i c l e s i z e or separation w i l l have conduction a c t i v a t i o n energies that 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 s e p a r a t i o n s . The paths of l e a s t r e s i s t a n c e (or optimal paths) w i l l be the ones that carry the most current. Since the competition between the various pathways i s a f f e c t e d by the temperature, as the temperature changes the optimal paths w i l l a l s o change. Since each c l a s s of - 14 -p a t h w a y s h a s a n a c t i v a t i o n e n e r g y t h a t d i f f e r s f r o m t h e o t h e r c l a s s e s o f p a t h w a y s , t h e a p p a r e n t a c t i v a t i o n e n e r g y f o r t h e s a m p l e a s a w h o l e w i l l v a r y w i t h t e m p e r a t u r e a s t h e o p t i m a l p a t h s s w i t c h w i t h c h a n g i n g t e m p e r a t u r e . One o t h e r t r e a t m e n t o f h o p p i n g c o n d u c t i o n i n c e r m e t s b e l o w X v c h a s b e e n p r e s e n t e d b y D e v e n y i e t a l . [37] r e g a r d i n g c o n d u c t i v i t y d a t a f o r N b / A l 2 0 3 c o m p o s i t e s . I n t h e s e c o m p o s i t e s , D e v e n y i f o u n d t h e 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 y t o v a r y a s a p o w e r o f t h e t e m p e r a t u r e . H i s a p p r o a c h a s s u m e d t h a t t h e i n s u l a t i n g m a t e r i a l c o n t a i n e d s u c h a l a r g e n u m b e r o f d e f e c t s t a t e s due t o e x c e s s Nb t h a t a c o n t i n u o u s , n o n u n i f o r m d i s t r i b u t i o n o f d e f e c t s t a t e s e x i s t e d i n t h e f o r b i d d e n g a p . C o n d u c t i o n was t a k e n t o b e v i a h o p p i n g f r o m d e f e c t t o d e f e c t i n t h e i n s u l a t o r a s o p p o s e d t o h o p p i n g d i r e c t l y a c r o s s t h e i n s u l a t o r . To m o d e l t h i s p r o b l e m , D e v e n y i f o l l o w e d a n a p p r o a c h p r e s e n t e d b y C r o i t o r u e t a l . [38]. U s i n g a r e l a x a t i o n t i m e a p p r o x i m a t i o n t o t h e B o l t z m a n n t r a n s p o r t e q u a t i o n , C r o i t o r u s h o w e d t h a t t h e h o p p i n g c o n d u c t i v i t y y c o u l d be w r i t t e n a s o~f H ( E , T , F ) f ( E , T , F ) N ( E , T , F ) dE (1-1) w h e r e e i s t h e e l e c t r o n i c c h a r g e , \x i s t h e c a r r i e r m o b i l i t y , f i s t h e s t a t i s t i c a l o c c u p a t i o n f u n c t i o n , N i s t h e d e n s i t y o f d e f e c t s t a t e s , E i s t h e d e f e c t s t a t e e n e r g y , T i s t h e t e m p e r a t u r e , a n d F i s t h e e l e c t r i c f i e l d . A t t h i s p o i n t C r o i t o r u m a k e s a n a s s u m p t i o n t h a t i s e q u i v a l e n t t o a g e n e r a l i z a t i o n o f t h e o p t i m a l p a t h m e t h o d u s e d b y M o t t [34], A b e l e s - 15 -[ 2 ] , a n d o t h e r s [ 3 5 , 3 6 ] . T h e a s s u m p t i o n i s t h a t t h e i n t e g r a n d o f E q n . 1 -1 i s s h a r p l y p e a k e d a t a p a r t i c u l a r e n e r g y s o t h a t c o n d u c t i o n c a n b e a s s u m e d t o be o n l y v i a s t a t e s o f t h i s ( o p t i m a l ) e n e r g y . V a r i o u s f u n c t i o n a l f o r m s may t h e n be u s e d f o r N , u , a n d f t o c a l c u l a t e t h e c o n d u c t i v i t y d u e t o t h e o p t i m a l p a t h . D e v e n y i e t a l . p o i n t e d o u t t h a t i f f i s a M a x w e l l - B o l t z m a n n d i s t r i b u t i o n t h e n t h e max imum o f t h e i n t e g r a n d o f E q n . 1 -1 o c c u r s a t a n e n e r g y £ g i v e n b y t h e s o l u t i o n o f t h e f o l l o w i n g e q u a t i o n : o ( l n [ N u ] ) o ( E - E ) k T * u L ) T o e x p l a i n t h e i r d a t a , w h i c h s h o w e d t h e 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 y t o v a r y a s T t o some p o w e r , D e v e n y i e t a l . t o o k t h e d e n s i t y o f s t a t e s - m o b i l i t y p r o d u c t t o be N u ~ N f l i f e x p ( A [ E - E f ] p ) ( 1 - 3 ) w h e r e E a n d E f a r e t h e s t a t e a n d F e r m i e n e r g i e s r e s p e c t i v e l y , N a n d N f a r e t h e d e n s i t y o f s t a t e s I n g e n e r a l a n d a t t h e F e r m i l e v e l r e s p e c t i v e l y , u a n d U f a r e t h e m o b i l i t i e s i n g e n e r a l a n d a t t h e F e r m i l e v e l r e s p e c t i v e l y , A a n d p a r e c o n s t a n t s t h a t a r e d e t e r m i n e d e x p e r i m e n t a l l y . No p h y s i c a l r e a s o n was g i v e n f o r c h o o s i n g t h i s f u n c t i o n a l f o r m o t h e r t h a n i t g a v e t h e c o r r e c t t e m p e r a t u r e b e h a v i o u r f o r t h e 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 y . M a k i n g u s e o f E q n . 1 - 3 i n E q n . 1 - 2 y i e l d s - 16 -1 $-E f = ( A k T p ) 1 _ P = AE (1-4) and 1 InAE = ln([Apk] 1-p ) + 1 l n ( T ) , (1-5) 1-p where E i s the optimal energy which maximizes the integrand of Eqn. 1-1. The 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 Eqn. 1-3, the conduction a c t i v a t i o n energy should vary as some power ( r e l a t e d to p) of T. Since the defect d e n s i t y w i l l depend s t r o n g l y on the sample composition, t h i s power of T should be d i f f e r e n t f o r each value 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 e x i s t from sample to sample. Even though, i n the Nb/Al2 n3 samples studied by Devenyi, t h i s type of behaviour was observed, 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 of the Nu product, shown i n Eqn. 1-3, would be very d e s i r a b l e . Nevertheless, the idea of a l a r g e number of continuously d i s t r i b u t e d defect s t a t e s w i t h i n the forbidden gap l e a d i n g to a continuously 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 optimal path approaches to 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 conduction band t a i l s to e x h i b i t an e x p o n e n t i a l dependence on E-E^» where E^ i s the energy of the band edge under c o n s i d e r a t i o n [39]. The more h e a v i l y doped the sample the more prominent the presence of these exponential t a i l s become. I t i s c e r t a i n l y p o s s i b l e that 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 of a cermet could e x h i b i t a s i m i l a r exponential d e n s i t y of st a t e s w i t h respect to 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 only r e s i s t a n c e data i t i s not p o s s i b l e , however, to separate the dens i t y of st 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. Devenyi suggests that n o n l i n e a r e f f e c t s at high f i e l d s may a l l o w f o r such a sep a r a t i o n . For Xv j u s t above Xvc other i n v e s t i g a t o r s [5,40,41] have observed a metal to 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 the low T side 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 behaviour, a negative magnetoresistance, 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 . E i t h e r of these l a s t two measurements served to determine that the p **> InT behaviour 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 are a great many mean f i e l d type approaches that have been used to 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 mixtures of m a t e r i a l s of d i f f e r i n g d i e l e c t r i c p r o p e r t i e s . In f a c t , one review 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 of only two d i f f e r e n t fundamental assumptions: that p a r t i c l e s of one m a t e r i a l are randomly embedded i n an amorphous matrix of another m a t e r i a l ; or, a random mixture of two d i f f e r e n t types - 18 -of p a r t i c l e s i s assumed. In e i t h e r case, a f t e r making one of these two b a s i c assumptions, along with other l e s s important assumptions, an e f f e c t i v e d i e l e c t r i c constant f o r the composite i s derived i n terms of the d i e l e c t r i c constants 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 averaging over volumes that are large compared with the inhomogenities and small compared with the wavelength of l i g h t i n v o l v e d [42,43]. In the f i r s t case, the d i e l e c t r i c constants of the matrix and embedded m a t e r i a l s appear In an asymmetric manner i n the derived e f f e c t i v e d i e l e c t r i c constant of the composite, while 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 enter symmetrically i n the second case. This i s to be expected from the symmetries (or asymetries) inherent i n the b a s i c assumptions. While 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 ) lead to 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 choosing one or the other of the two b a s i c assumptions mentioned e a r l i e r [42], In 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 to a l l o w f o r mixtures of more than two m a t e r i a l s [42,43]. At t h i s point I b r i e f l y present the b a s i c s of these 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 m a t e r i a l s . This p r e s e n t a t i o n i s meant to 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 sputtered 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 various s u b t l e t i e s that have been introduced i n the l i t e r a t u r e to date on the general t o p i c of heterogeneous mixtures. - 19 -Perhaps the simplest approach to an asymmetric theory 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 Rayleigh's f o r a cubic array of spheres, of radius a and d i e l e c t r i c constant em> i n an e x t e r n a l e l e c t r i c f i e l d , Eo. In such an array, the f i e l d seen by any sphere i s , to a f i r s t approximation, j u s t Eo because the f i e l d s due to d i p o l e s induced i n other spheres cancel due to the cubic symmetry and higher order m u l t i p o l e s are neglected. These higher order terms become more important as the spheres packing d e n s i t y (volume f r a c t i o n , Xv) i n c r e a s e s . 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 , of radius a , i s then centered on the o r i g i n of a s p h e r i c a l coordinate 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 of the 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 array, at a p o s i t i o n ( r , 9 ) , one may c a l c u l a t e the p o t e n t i a l as [44], where r and 6 have the usual meaning i n reference to a s p h e r i c a l coordinate system, and N i s the t o t a l number of spheres. S i m i l a r l y , i f the s p h e r i c a l s e c t i o n of the cubic array of spheres embedded i n the d i e l e c t r i c medium i s assumed to have an e f f e c t i v e d i e l e c t r i c constant, 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 <t> = N m i E + 2e. m i (1-6) - 20 -N e - e. i _ £ + 2E, ,3 H 1 EorcosG (1-7) Upon equating Eqns. 1-6 and 1-7 one obtains £ - E. E ~ E. 1 = Xv m 1 E + 2E E + 2 £ j m i (1-8) or E = £, 1 + 3Xv (E - E 4 ) m i E + 2 E . - Xv ( E - £. ) m l m l (1-9) One should note the asymmetric appearance of £ m and i n Eqns. 1-8 and 1-9, as w e l l as the f a c t that £ diverges when EJJ + 2e^ = ^( E J J , - E ^ ) . This divergence 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 of feature i s common to a l l asymmetric t h e o r i e s . Expressions s i m i l a r to Eqn. 1-9 have been a r r i v e d at by many other authors [42, 43] with 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 cubic symmetry or s p h e r i c a l p a r t i c l e s ) and more in v o l v e d mathematics. In 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 Maxwell-Garnett Theories (MGT). This nomenclature a r i s e s because James Cl e r k Maxwell Garnett was the f i r s t to a r r i v e at Eqn. 1-9 based on an a n a l y s i s of Maxwell's equations f o r propagating electromagnetic waves [45], whereas others, 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 c o n s i d e r a t i o n s . 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 forward by D.A.C. Bruggeman i n 1935 [46]. Bruggeman sought the e f f e c t i v e d i e l e t r i c constant, e, of a randomly dispersed mixture of two types of p a r t i c l e s , w i t h d i e l e c t r i c constants e m and and w i t h r e s p e c t i v e volume f r a c t i o n s Xv and (1-Xv). I f the average e l e c t r i c f i e l d w i t h i n the composite i s Eo, and i f any p a r t i c u l a r p a r t i c l e i s assumed to 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 constant e, then the induced d i p o l e moment of that p a r t i c l e , say one w i t h d i e l e c t r i c constant e m, may be w r i t t e n as [4] 3 e - e p = 7— v m , 0 Eo (1-10) 4-n: e + 2e m 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 these induced 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 to p, the 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 (or d i p o l e moments) must equal zero, by d e f i n i t i o n of Eo. Therefore, summation of equations l i k e 1-10 f o r each type of p a r t i c l e leads to e - e £. — £ Xv m , n + (1-Xv) 1 £ + 2E m £. + 2E I = 0 (1-11) - 22 -or e - 7- (A + A 2 + 8e e.) * m i (1-12) where e + m £3(1-Xv) - 1^| e ± (1-13) Note the symmetric r o l e s of e m and i n Eqns. 1-11 through 1-13, as w e l l as the l a c k of any d i e l e c t r i c anomaly. This l a c k of a d i e l e c t r i c anomaly i s common to a l l symmetric t h e o r i e s . An EMT fo r m u l a t i o n that has been seen to agree more c l o s e l y than others t e s t e d , Eqn. 1-14 has been a r r i v e d at by at l e a s t two f a i r l y d i f f e r e n t approaches. Landau and L i f s h i t z [48] obtained i t by; expanding, to second order, the l o c a l d i e l e c t r i c constant, 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 values; making s u b s t i t u t i o n s based upon the f a c t that the divergence of the unaveraged displacement f i e l d should vanish; then, w i t h the help of s e v e r a l vector when w e l l defined mixtures of known e, 6^, and were measured [43] was - 23 -i d e n t i t i e s , c a l c u l a t e d the average e l e c t r i c displacement 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 that the e f f e c t i v e d i e l e c t r i c constant f o r the mixture was the same as f o r another mixture of the same o v e r a l l composition but i n which the d i f f e r e n t types of p a r t i c l e s themselves had d i f f e r e n t volume f r a c t i o n s of the two m a t e r i a l s . Then, to second order, the d i e l e c t r i c constants 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 composition of the mixture. In the l i m i t of going to p a r t i c l e s composed of only one m a t e r i a l , a second order d i f f e r e n t i a l equation f o r the e f f e c t i v e d i e l e c t r i c constant as a f u n c t i o n of Xv was developed and solved, subject to the boundary c o n d i t i o n s e(o) = and e ( l ) = e m. The symmetry between e m and as w e l l as the l a c k of any d i e l e c t r i c anomaly i s even more apparent i n Eqn. 1-14 than i n Eqn. 1-12. F u r t h e r , the more compact f o r m u l a t i o n and transparent symmetry of Eqn. 1-14 make i t e a s i e r to apply 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 constants are complex numbers. MGT has been found to 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 mixtures that were quite obviously p a r t i c l e s of one m a t e r i a l embedded i n a matrix 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 to 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 cosputtered cermets. These are cermets that were prepared by s p u t t e r i n g , simultaneously, from two t a r g e t s (a metal 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 manifests i t s e l f as a peak i n the o p t i c a l absorption spectrum of the - 24 -c o m p o s i t e . T h e p o s i t i o n o f t h i s p e a k i s p r e d i c t e d , a n d o b s e r v e d , t o move t o w a r d s l o n g e r w a v e l e n g t h s a s X v i s i n c r e a s e d . W h i l e t h e p e a k p o s i t i o n s a r e f a i r l y w e l l d e s c r i b e d b y MGT, t h e p e a k h e i g h t s a n d w i d t h s a r e g e n e r a l l y d i f f e r e n t f r o m t h e p r e d i c t e d v a l u e s . A n u m b e r o f a u t h o r s [ 5 4 - 5 7 ] h a v e i n v e s t i g a t e d t h e e f f e c t s o f d i s t r i b u t i o n s i n p a r t i c l e s i z e s a n d s h a p e s i n a n e f f o r t t o e x p l a i n t h e s e d i s c r e p a n c i e s . T h e r e s u l t s o f t h e s e i n v e s t i g a t i o n s w e r e t h a t p e a k w i d t h s s h o u l d b r o a d e n a s t h e p a r t i c l e s i z e b e c o m e s l e s s t h a n t h e e l e c t r o n mean f r e e p a t h c a u s i n g t h e c o n d u c t i v i t y t o l o w e r , a n d t h a t p e a k p o s i t i o n s a n d h e i g h t s v a r i e d w i t h p a r t i c l e s h a p e . I n c l u s i o n o f s i z e a n d s h a p e e f f e c t s i s f o u n d t o s t i l l l e a v e some d i s c r e p a n c y b e t w e e n t h e p r e d i c t e d a n d o b s e r v e d m a g n i t u d e o f o p t i c a l a b s o r p t i o n . I n p a r t i c u l a r , t h e p e a k h e i g h t o f t h e d i e l e c t r i c a n o m a l y i s f o u n d t o v a n i s h w i t h X v much m o r e r a p i d l y t h a n p r e d i c t e d , a n d t h e g e n e r a l b a c k g r o u n d a b s o r p t i o n i s h i g h e r t h a n p r e d i c t e d , e s p e c i a l l y a t l o n g e r w a v e l e n g t h s [ 8 , 5 0 - 5 3 ] . EMT h a s b e e n f o u n d t o d e s c r i b e t h e o p t i c a l p r o p e r t i e s o f c o m p o s i t e s t h a t w e r e o b v i o u s l y a r a n d o m l y d i s p e r s e d m i x t u r e o f two t y p e s o f p a r t i c l e s [ 4 3 ] . H o w e v e r , t h e r e a r e n o r e p o r t e d c a s e s o f s p u t t e r e d ( o r c o s p u t t e r e d ) f i l m s d i s p l a y i n g EMT b e h a v i o u r , r a t h e r , t h e s e c o m p o s i t e s w e r e m e c h a n i c a l l y m i x e d . One m e t h o d o f e x t e n d i n g e i t h e r EMT o r MGT t o m o r e t h a n t w o m a t e r i a l s may be p a r t i c u l a r l y w e l l s u i t e d t o t r e a t i n g t h e o p t i c a l p r o p e r t i e s o f c e r m e t s t h a t h a v e b e e n r e a c t i v e l y s p u t t e r e d f r o m a s i n g l e m e t a l t a r g e t . T h e m e t h o d , i n t r o d u c e d b y H . C . v a n de H u l s t [ 5 8 ] , a s s u m e s t h a t a p a r t i c l e i n e i t h e r EMT o r MGT c o n s i s t s o f a p a r t i c l e o f r a d i u s a - 25 -and d i e l e c t r i c constant e m (or e^) coated w i t h another m a t e r i a l of th i c k n e s s t m c (or t i c ) and d i e l e c t r i c constant £ m c (or £ i c ) . Since 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 matrix 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 constant of a coated sphere, e m c s (or E ^ g ) . may be obtained from Eqn. 1-9, w i t h the f o l l o w i n g s u b s t i t u t i o n s e => e (or e. ) racs i c s em = > em ( o r e i ) (1-15) e. => e (or e. ) i mc i c Xv => Q3 = m — i 3 1 - mc (or of = _i3 1 -' i c I f , f o r i n s t a n c e , one has a mixture of coated metal p a r t i c l e s and 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 Is c a l c u l a t e d from Eqn. 1-9, w i t h the appropriate s u b s t i t u t i o n s from Eqns. 1-15. £ i s then c a l c u l a t e d from e i t h e r Eqn. 1-12 or Eqn. 1-14, where £ m i s replaced by e m c s . In t h i s way, a randomly dispersed mixture of two types of p a r t i c l e s may e x h i b i t a d i e l e c t r i c anomaly, due to a d i e l e c t r i c anomaly i n enjcg. Observations of t h i s type of behaviour have not yet been reported. - 26 -I t should be remembered that these t h e o r i e s are based upon averaging over volumes that are large compared with p a r t i c l e s i z e and small compared to the wavelength of 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 small that bulk o p t i c a l p r o p e r t i e s no longer apply to i t then allowance f o r t h i s e f f e c t must be made. This l a t t e r c o r r e c t i o n may be very d i f f i c u l t i f p a r t i c l e s i z e s are d i s t r i b u t e d from i s o l a t e d atoms on up to c r y s t a l l i t e s w i t h bulk 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 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 of granular metals. The d i s c u s s i o n focused p r i m a r i l y upon those p r o p e r t i e s that r e s u l t e d from the geometry of the mixture, w i t h the p h y s i c a l p r o p e r t i e s of the mixture's m a t e r i a l s being of secondary importance. Of course, f o r at l e a s t two reasons, one must know the p r o p e r t i e s of the mixture's m a t e r i a l s when modelling the p h y s i c a l p r o p e r t i e s of a cermet. The f i r s t reason i s so that one can indeed know that observed behaviour i s not j u s t the behaviour of one of the m a t e r i a l s present i n the mixture. The second reason i s that most of the q u a n t i t a t i v e aspects of the various mixture 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 of the m a t e r i a l s i n the mixture (with 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 exc e p t i o n ) . Therefore, at t h i s time a b r i e f review of the p h y s i c a l p r o p e r t i e s of A1N and A l , that are relevant to the experimental work discussed i n t h i s t h e s i s , w i l l be presented. - 27 -I.3-a A1N While the l i t e r a t u r e on A1N i s l e s s extensive than f o r many other semiconductors ( S i , Ge, GaAs, ZnO, e t c . ) , a reasonable body of knowledge has been b u i l t up over about the l a s t 20 years [22,29,59-78]. Pure A1N i s a c o l o r l e s s s o l i d that c r y s t a l i z e s i n the hexagonal w u r t z i t e s t r u c t u r e [66]. At atmospheric pressure, i t . sublimes at about 2400°C [66]. At room temperatures and pressures, i t r e a d i l y o x i d i z e s to form a surface l a y e r of 100 A of amorphous A 1 2 0 3 w i t h i n 24 h. This oxide l a y e r then serves as a p r o t e c t i v e b a r r i e r against f u r t h e r o x i d a t i o n . This r a p i d o x i d a t i o n (roughly three times the r a t e of A l metal) leads to oxygen being the main u n i n t e n t i o n a l impurity found i n A1N, regardless of the method of pr e p a r a t i o n [66], The tendency towards forming n i t r o g e n d e f i c i e n t A1N i s als o a common problem [66]. 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 the c-axis perpendicular to the substrate [70,71], This r e s u l t s i n the (002) peak being the dominant fea 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 [29], I t has been doped n-type w i t h S i , while C, S, and Mg doping produces p-type conduction [66], N-vacancies or A l i n t e r s t i t i a l s i n ni t r o g e n d e f i c i e n t A1N are expected to produce n-type behaviour, as should 0 s u b s t i t u t i n g f o r N [65-73], The reported defect conduction a c t i v a t i o n energies f o r A1N l i e between 0.5 and 5 eV, depending on which i m p u r i t i e s are present, w h i l e the 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 of 6.2 eV. In cathode luminescence measurements [62], peaks at 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 , while peaks at 2.71 and 2.78 eV were c o r r e l a t e d with oxygen contamination. Pastrnak et a l . observed a broad o p t i c a l a bsorption band i n A1N centered at 4.8 eV [60]. They a t t r i b u t e d t h i s broad band to oxygen contamination, however, t h e i r method of producing A1N (high voltage a r c i n g of A l e l e c t r o d e s i n an N 2 atmosphere) i s known to a l s o produce A1N that i s q u i t e d e f i c i e n t i n 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 2 a l s o seems l i k e l y to y i e l d A l i n c l u s i o n s . Others [63,65] have claimed that t h e i r o p t i c a l absorption measurements on n i t r o g e n d e f i c i e n t A1N show the band edge s h i f t i n g to about 4 eV. In h i n d s i g h t , i t appears that the dynamic range of t h e i r equipment was not s u f f i c i e n t to measure l a r g e enough absorptions (they appeared l i m i t e d to transmittances > 1%). From data of Pastrnak, as w e l l as the present work to be shown l a t e r , t h i s l i m i t e d dynamic range was not enough to observe the top of the peak at 4.8 eV, which 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 absorption. Pastrnak a l s o measured the d i s p e r s i o n of the A1N r e f r a c t i v e index (n) [59], w i t h wavelength, as the band edge was approached. These measurements are given i n F i g . 28 i n the appendix on o p t i c a l c a l c u l a t i o n s . In the i n f r a r e d , AlN 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 wavelength region between 11 um and 15 um [68,69], I.3-b Al A l i s a metal that melts at 659°C and c r y s t a l i z e s i n an fee l a t t i c e . Exposed to a i r i t w i l l form /v 30 A of amorphous A l 2 0 3 on i t ' s - 29 -surface i n 24 h [66], which serves as a p r o t e c t i v e b a r r i e r against f u r t h e r o x i d a t i o n . The r e s i s t i v i t y of pure A l i s 3.6 x 1 0 - 6 Q-cm [28] at room temperature, and i t e x h i b i t s p-type behaviour i n H a l l measurements [79], 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 metals. A d e t a i l e d t a b u l a t i o n of n and k (the r e a l and imaginary parts of the r e f r a c t i v e index, 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 to the f a r u l t r a v i o l e t i s presented by Powell [80], Over the photon energy range of i n t e r e s t i n t h i s work, Powell's data shows the o p t i c a l p r o p e r t i e s of A l to 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 exception of a peaked s t r u c t u r e i n both n and k near 1.5 eV. Figure 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 Powell's data. - 30 -CHAPTER II MECHANISMS AND CONTROL OF THE REACTIVE SPUTTERING PROCESS Planar magnetron s p u t t e r i n g of a metal target 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 technique f o r high rate d e p o s i t i o n of e i t h e r i n s u l a t i n g or conducting f i l m s . 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 to maximize both the rate of d e p o s i t i o n and the c o n t r o l over f i l m s t o i c h i o m e t r y . A technique to achieve these goals has been developed f o r the case of a dc planar magnetron w i t h an A l t a r g e t and an Ar/N 2 s p u t t e r i n g gas mixture. The method i s described i n t h i s t h e s i s and i s expected to be a p p l i c a b l e to other systems i n which the r e a c t i v e gas does not undergo r a p i d chemisorption on the target 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 necessary to regulate the r e l a t i v e rates of a r r i v a l of metal atoms and r e a c t i v e gas species at the subst r a t e [22,67], The former i s determined by the s p u t t e r i n g r a t e ; the l a t t e r by the r e a c t i v e gas p a r t i a l pressure and s t i c k i n g c o e f f i c i e n t . Since sputtered metal deposits g e t t e r (combine chemically with) r e a c t i v e gas species on the substrate and on inner surfaces of the vacuum chamber, these two rates are not independent of each other. 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 pressure 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, described here, f o r the c o n t r o l of these two q u a n t i t i e s i n order to produce a f i l m of the de s i r e d composition has been to use the cathode voltage to monitor the degree to which the target surface becomes covered with an i n s u l a t i n g compound of metal atoms and r e a c t i v e gas species. A s i m i l a r technique - 31 -f o r r e a c t i v e s p u t t e r i n g (at constant pressure) employed by S c h i l l e r et a l . has used the target voltage to determine one p a r t i c u l a r s t a t e of ta r g e t coverage [81]. I have developed a model which allows 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 the ta r g e t s u rface. One mechanisms i s chemisorption of the n e u t r a l r e a c t i v e gas species on the target surface (which can occur without a glow d i s c h a r g e ) ; the other; target coverage by ions and atomic species of the r e a c t i v e gas which i s a c t i v a t e d by the glow discharge. I c a l l t h i s l a t t e r process "ion p l a t i n g " . This d i f f e r s from the g e n e r a l l y accepted d e f i n i t i o n of i o n p l a t i n g only i n that I am c o n s i d e r i n g the t a r g e t , r a t h e r than the s u b s t r a t e , i n the p l a t i n g process [ 8 ] , S p u t t e r i n g of A l i n the presence of 0 2 i s an example of the former mechanism w h i l e s p u t t e r i n g of A l i n the presence of 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 discharge c h a r a c t e r i s t i c s f o r the two mechanisms, which are i n agreement w i t h experiment. I f one could smoothly and monotonically increase the s p u t t e r i n g current ( I ) or 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 , to produce a correspondingly smooth and monotonic decrease i n r e a c t i v e gas p a r t i a l pressure ( P r ) , the c o n t r o l of f i l m composition would be e a s i l y achieved [22,67]. At s u f f i c i e n t l y low values of W and high values of P r the f i l m s would be expected to be n e a r l y s t o i c h i o m e t r i c . With i n c r e a s i n g W, as the s p u t t e r i n g rate increased and P r decreased due to g e t t e r pumping by the sputtered metal, the f i l m composition would vary continuously u n t i l i t was nearly a pure metal at some higher value of W. Such a smooth v a r i a t i o n of P r w i t h I or W does not occur f o r many - 32 -m e t a l - r e a c t i v e g a s c o m b i n a t i o n s o f i n t e r e s t . I n f a c t , i t i s w e l l k n o w n t h a t a n a b r u p t c h a n g e i s o b s e r v e d i n t h e v a l u e o f P r i f W o r I i s v a r i e d w h i l e t h e r a t e o f f l o w o f r e a c t i v e g a s ( F r ) i n t o t h e c h a m b e r i s h e l d c o n s t a n t [ 1 6 - 2 1 ] . A s i m i l a r t r a n s i t i o n i s o b s e r v e d i f F r i s v a r i e d a n d I o r W i s f i x e d . T h e e x p l a n a t i o n o f t h i s t r a n s i t i o n i s a s f o l l o w s . A t l o w F r t h e g e t t e r i n g r a t e i s s u f f i c i e n t t o k e e p P r l o w e n o u g h t o p r e v e n t f o r m a t i o n o f a n i n s u l a t i n g l a y e r o n t h e t a r g e t s u r f a c e s o t h a t s p u t t e r i n g i s f r o m a m e t a l t a r g e t . When t h e g e t t e r i n g r a t e c a n n o l o n g e r m a t c h F r a n i n s u l t i n g l a y e r b e g i n s t o f o r m o n p a r t s o f t h e t a r g e t s u r f a c e . T h e r e d u c e d s p u t t e r i n g r a t e f r o m t h e p a r t i a l l y c o v e r e d t a r g e t l o w e r s t h e g e t t e r i n g r a t e a n d p e r m i t s f u r t h e r t a r g e t c o v e r a g e t o o c c u r . T h i s p o s i t i v e f e e d b a c k c y c l e r e p e a t s i t s e l f u n t i l t h e t a r g e t i s c o m p l e t e l y c o v e r e d . W i t h t h e g e t t e r i n g r a t e now much r e d u c e d , P r r a p i d l y i n c r e a s e s . S i n c e t h e s e c o n d a r y 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 s f o r t h e c o m p o u n d l a y e r s a r e g e n e r a l l y d i f f e r e n t t h a n f o r t h e p u r e m e t a l s [ 1 6 , 1 9 , 2 0 ] , a n a b r u p t c h a n g e i n t h e v a l u e o f c a t h o d e v o l t a g e ( V ) i s a l s o o b s e r v e d a s t h e t a r g e t b e c o m e s c o v e r e d . T h e o p p o s i t e t r a n s i t i o n o f g o i n g f r o m a c o v e r e d t o a b a r e s u r f a c e a l s o o c c u r s , w i t h c o n s i d e r a b l e h y s t e r e s i s b e t w e e n t h e two d i r e c t i o n s . T h i s h y s t e r e s i s r e s u l t s i n a g a p i n t h e o p e r a t i n g r a n g e s o f b o t h V a n d P r . F o r t h e A l - A r / N 2 s y s t e m , i t i s f o u n d t h a t f i l m s d e p o s i t e d o n t h e l o w V a n d h i g h P r s i d e o f t h i s g a p a r e s t o i c h i o m e t r i c A 1 N , w h i l e f i l m s p r o d u c e d o n t h e o t h e r s i d e o f t h e g ap a r e d e f i c i e n t i n n i t r o g e n a n d c o n t a i n A l p r e c i p i t a t e s ( a s s e e n b y x - r a y d i f f r a c t i o n a n d T E M ) . F i l m s d e p o s i t e d a t V - P r p o i n t s w i t h i n t h e g a p a r e e x p e c t e d t o h a v e i n t e r m e d i a t e c o m p o s i t i o n s . - 33 -I have found p r e v i o u s l y [21] that a s i n g l e valued, 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 r f o r the A l - A r / N 2 system, while a range e x i s t s where each value of I corresponds to three values of V or Pr« When the discharge was operated by c o n t r o l l i n g V, I was able to operate over the f u l l range of I-V-P r combinations. Thus, I could operate at any degree of t a r g e t coverage (or f i l m composition) of i n t e r e s t . Subsequent experiments w i t h A l , Zn, I n , and Mo i n A r / 0 2 atmospheres revealed that voltage c o n t r o l was not p o s s i b l e across the t r a n s i t i o n between bare and completely covered target s t a t e s . A l s o , i n Ar/N 2 atmospheres c o n t r o l was not p o s s i b l e w i t h Mo but was p o s s i b l e w i t h Zn. The systems that were not c o n t r o l l a b l e were the ones i n which r a p i d chemisorption of the n e u t r a l diatomic gaseous species occurs, while t h i s type of chemisorption does not occur i n the others [82], This i m p l i e s that the presence of the glow discharge Is 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 process i n the l a t t e r case, while i t may be only p a r t l y r esponsible i n the former. E a r l i e r models by H e l l e r [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 described above w i t h the only target coverage mechanism being chemisorption of r e a c t i v e gas species from the s p u t t e r i n g gas. I n t h i s work I have in c l u d e d the i o n i c bombardment mechanism a l s o . Further, f o r the A l - A r / N 2 system, with the equations f o r conservation of f l u x of N 2 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 deposits i t becomes p o s s i b l e to c a l c u l a t e the average f i l m composition. In t h i s procedure i t i s not necessary 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 rate f o r some - 34 -s p e c i f i c range of values of sputter rate and N 2 p a r t i a l pressure. F o r t u n a t e l y , the sputter r a t e - N 2 p a r t i a l pressure c h a r a c t e r i s t i c s show a change of slope when the f i l m s pass from the s t o i c h i o m e t r i c region to the n o n - s t o i c h i o m e t r i c region. This procedure i s f a c i l i t a t e d by counting ( v i a o p t i c a l emission measurements) the number of A l atoms sputtered and counting the number of N 2 molecules gettered by monitoring P r. One may then obtain the average r a t i o of Al/N atoms i n the f i l m . I t should be noted that knowledge of the r a t i o of Al/N i n the f i l m gives no i n f o r m a t i o n about the chemical bonding between these species. Therefore, whether the f i l m c o n s i s t s merely of AINx or a mixture of AINx and A l must be determined by other means. II . 1 Apparatus and Experimental Method A schematic cross s e c t i o n of the planar magnetron s p u t t e r i n g chamber i s shown i n F i g . 2. The chamber i s pumped by an o i l d i f f u s i o n pump w i t h a freon c o l d t r a p . For operation while s p u t t e r i n g , the pumping speed i s regulated by a t h r o t t l i n g valve l o c a t e d between the c o l d trap and the d i f f u s i o n pump. The 15 cm diameter target of 99.999% A l i s f i r m l y clamped by a metal r i n g to a water cooled backing p l a t e . A ground s h i e l d and water cooled anode are placed i n f r o n t of and c o n c e n t r i c to the t a r g e t . The discharge i s powered by a 5 kW, u n f i l t e r e d , f u l l wave r e c t i f i e d , constant c u r r e n t , dc power supply (Plasma Therm MDS-5000D, 0-10 A, 0-1000 V). Operation i s p o s s i b l e w i t h the anode e i t h e r f l o a t i n g or grounded to the metal chamber. Pressure i s measured w i t h a capacitance manometer (MKS B a r a t r o n ) . An electromagnet - 35 -Fig. 2 Mass spectrometer capacitance manometer throttle valve to diffusion pump Schematic cross s e c t i o n of s p u t t e r i n g chamber. - 36 -i s used to confine the plasma i n the shape of a torus 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 to be a r i n g w i t h outer diameter of about 7.5 cm and inner diameter of about 2.5 cm. A d i f f e r e n t i a l l y pumped quadrupole mass spectrometer (UTI 100C) i s mounted i n a side arm and maintained at 1 0 - 3 Pa. I t i s used f o r leak 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 i n conduction w i t h the capacitance manometer f o r p a r t i a l pressure measurements. Ar, N 2, and 0 2 gas flows are c o n t r o l l e d through independent leak valves ( G r a n v i l l e P h i l l i p s model 203) and measured by independent mass flow meters (Hastings H-5 model A l l - 5 ) . L i g h t from the plasma, seen perpendicular to the target surface, i s focussed through a quartz window onto the entrance s l i t s of a 3/4 m Spex o p t i c a l spectrometer (model 1702) to a l l o w monitoring of the plasma emission l i n e s . A microprocessor system i s used to monitor, record, and/or c o n t r o l a l l aspects of the experiment; e.g. gas flow r a t e s , gas pressure, mass and o p t i c a l s p e c t r a , substrate bias and temperature, cathode c u r r e n t , power and v o l t a g e . The substrate 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 area. This area can be a s i n g l e substrate or 6 rectangles of equal 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 substrate area, none of the substrate area, or any.one of the small r e c t a n g u l a r areas to the sputtered f l u x . P r i o r to any s p u t t e r i n g experiment the chamber was baked at about 75°C f o r at l e a s t 12 hours followed by 2 to 4 hours of sputter 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 watts. This s t a r t i n g procedure was used to minimize contamination through extensive outgassing, followed by encapsulation of the i n n e r surfaces of the chamber with an A l l a y e r . Further precautions against contamination were e x e r c i s e d at the end of each experiment i n pr e p a r a t i o n f o r the next one. These were to sput t e r f o r about 10 minutes i n an N 2 atmosphere ( P f l 2 ^ ^ a t l ° w P o w e r («•* 100 watts) to encapsulate the target w i t h a n i t r i d e l a y e r and then to bake the system f o r s e v e r a l hours i n an N 2 atmosphere before b r i e f l y opening the chamber to exchange s u b s t r a t e s . The reason f o r baking was to prevent condensation a f t e r the chamber was opened. The chamber was taken to atmospheric pressure w i t h dry ni t r o g e n gas as a f u r t h e r safeguard against condensation. The experiments were of e s s e n t i a l l y two types. In one, the gas flows and pumping speeds were f i x e d while the cathode voltage was incremented through the range from about 200 to 500 v o l t s . In the second type, the pump speed and Ar flow were f i x e d , as was e i t h e r cathode power or c u r r e n t , and the r e a c t i v e gas flow r a t e was scanned upwards from zero and then back again. In the experiments where voltage was c o n t r o l l e d , the f i r s t step was adjustment of the pumping speed. This was done by admitting the de s i r e d flow of Ar and then a d j u s t i n g the d i f f u s i o n pump t h r o t t l e valve to o b t a i n the de s i r e d pressure. The r e a c t i v e gas flow rate was then set and the f u r t h e r increase i n pressure recorded. Next, the discharge was s t a r t e d and allowed to e q u i l i b r a t e 200 V, -vO.l A). A mapping of the I-V c h a r a c t e r i s t i c s of the discharge was then performed by incrementing - 38 -the cathode voltage up to the d e s i r e d value i n step s i z e s ranging from 0.1 to 5 v o l t s . Along w i t h each I-V p o i n t , a l l other experimental parameters were recorded ( i . e . pressure, mass and o p t i c a l s p e c t r a , elapsed time, substrate bias and temperature, e t c . ) . A f t e r o b t a i n i n g the I-V c h a r a c t e r i s t i c , the curve was r e t r a c e d to points of i n t e r e s t and f i l m s deposited. During the d e p o s i t i o n , a l l parameters were again monitored f o r d r i f t and, i f need be, co r r e c t e d by the computer so that f l u c t u a t i o n s were held to w i t h i n a few tenths of a percent. In the experiments where cathode current or power was held constant along w i t h Ar flow and pumping speed, while 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 again to adjust the pumping speed to a given Ar flow r a t e . The discharge was then i g n i t e d and set to the d e s i r e d current or power. Then the r e a c t i v e gas flow r a t e was scanned up at a rate between 1 and 4 SCCM/hour (1 SCCM = 1 standard cubic centimeter per minute) and then down again. During the scan, a l l parameters were recorded 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 thicknesses 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 at two d i f f e r e n t angles of i n c i d e n c e ) , and w i t h a p r o f i l o m e t e r . The two methods agreed to w i t h i n about 10%. I n v e s t i g a t i o n s of other 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 techniques, such as scanning e l e c t r o n microscopy (SEM), tr a n s m i s s i o n e l e c t r o n microscopy (TEM), x-ray 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 absorption, and c o n d u c t i v i t y measurements. - 39 -II.2 Experimental Results and Discussion Using the ^ethods discussed i n the previous s e c t i o n , I monitored the f o l l o w i n g s p u t t e r i n g parameters: the t o t a l and p a r t i a l pressures of the s p u t t e r i n g gases, up to three d i f f e r e n t gas flows i n t o the chamber, the o p t i c a l emissions of the species i n the plasma, and 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 discharge. The pump speed was set at the beginning of each experiment. Gas flows and one of e i t h e r cathode c u r r e n t , power, or voltage are maintained 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 (or discharge c h a r a c t e r i s t i c s ) measured when A l i s sputtered i n an Ar/N 2 gas mixture are shown i n F i g . 3 f o r the case when the glow discharge i s maintained by c o n t r o l l i n g the cathode v o l t a g e . Here PJJ 2 i s the N 2 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 emission 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 current and voltage r e s p e c t i v e l y . The pumping speed f o r these data was such t h a t , when no discharge was present, a flow i n t o the chamber of 1.00 SCCM of Ar r e s u l t e d i n a chamber pressure of 0.93 Pa and the f u r t h e r a d d i t i o n of 1.50 SCCM of N 2 r a i s e d the pressure to 2.01 Pa. I t should be noted that 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 operating points f o r the system. A l l points along the apparently negative r e s i s t a n c e region are reached through p o s i t i v e r e s i s t a n c e steps away from the e q u i l i b r i u m curve and back again. These steps must be much smaller than the width or height of the negative r e s i s t a n c e region or o s c i l l a t i o n s w i l l develop wit h the l i k e l i h o o d of the target surface ending i n one of the extreme s t a t e s of surface coverage. I f I , rather than V, i s the c o n t r o l l e d parameter i n the experiment then, f o r i n c r e a s i n g I , upon reaching point - 40 -Fig 3 ( a r b i t r a r y u n i t s ) T y p i c a l glow discharge c h a r a c t e r i s t i c s f o r the A l - A r / N 2 system. I and V are the cathode current and v o l t a g e , r e s p e c t i v e l y , P N i s the N 2 ?QI ! : i t \ P f e S S U ^ e , a n d M ± S t h e ° P t i c a l emission i n t l n s i t y of the j y o l . 5 A l i n e of n e u t r a l A l atoms i n the discharge. The Ar p a r t i a l pressure i s 0.93 Pa. - 41 -C i n F i g . 3 the discharge c h a r a c t e r i s t i c s would s h i f t a bruptly to those at point E. S i m i l a r l y , f o r decreasing I , a s h i f t would occur from point D to point B. The sets of points (C,E) and (D,B) w i l l be shown to be r e l a t e d to the t r a n s i t i o n s from covered to bare and bare to 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 . P o i n t A represents the discharge c h a r a c t e r i s t i c s immediately a f t e r the glow i s i g n i t e d . In F i g . 3, no abrupt changes i n the discharge c h a r a c t e r i s t i c s , which are normally associated with the t r a n s i t i o n s between bare and covered t a r g e t s u r f a c e s , are observed. Therefore, one does not know whether a smooth and continuous t r a v e r s a l through a l l degrees of t a r g e t coverage has occured i n F i g . 3. To know t h i s one must be able to r e l a t e the discharge c h a r a c t e r i s t i c s i n the experiments where the abrupt changes occur to the same parameters i n the experiments where smooth c o n t r o l i s achieved. A l l of the discharge 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 point i n one of the experiments must be i d e n t i c a l to those at an operating point i n the other experiment i f the s t a t e of the target i s to be assumed i d e n t i c a l at these two operating p o i n t s i n the two d i f f e r e n t experiments. Using F i g . 4, I now demonstrate that the p o i n t s C and D of F i g . 3 are the p o i n t s where the target surface i s j u s t beginning to uncover or has j u s t become completely bare, r e s p e c t i v e l y . F i g . 4-c shows the n i t r o g e n p a r t i a l pressure ( P ^ 2 ) versus the n i t r o g e n flow ra t e ( F f j 2 ) w i t h the discharge power, W, held at 295 watts w i t h 1.00 SCCM of Ar producing a chamber pressure of 1.00 Pa. The t r a n s i t i o n from C* to E' and from D1 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 covered - 42 -Fig. 4 4 4 0 vt __ _ r 3 3 0 o w 220 I 10 1.2 .9 .6 .3 o CL Z Q . .5 SCCM .(a) x - F N "1.15 SCCM ox * /* 2 9 5 > i x o - F N z «1.5 SCCM _ "-FNS " U 5 S C C M (b) R N 2 + - Decreasing F N z Constant Power (295 W) (C) m ± 7 ? ° ' 150 200 250 300 350 V (volts) 1.0 1.5 F N z ( S C C M ) 2.0 C o m p a r i s o n o f 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 t h e A l - A r / N 2 s y s t e m when v o l t a g e c o n t r o l i s e m p l o y e d ( a a n d b ) , o r a t c o n s t a n t W w i t h v a r i a b l e F N 2 ( c ) . T h e p e a k s i n t h e c u r v e s ( a ) a r e i d e n t i f i e d a s p o i n t s w h e r e 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 w h e r e t h e t a r g e t i s j u s t b e c o m i n g b a r e ( i . e . 0 = 0 ) . - 43 -t o bare and bare to covered target s u r f a c e s , r e s p e c t i v e l y [ 1 6 - 2 1 ] . F i g . 4-a shows two W vesus cathode v o l t a g e , V, curves from experiments w i t h i d e n t i c a l pumping speeds and Ar flows as the run of F i g . 4-c. Note that F J J 2 f o r the lower power W-V curve i s the same as F N 2 at the C to E ' t r a n s i t i o n of F i g . 4-c while F J J 2 f o r the higher power W-V curve i s the same as F N 2 at the D' to B' t r a n s i t i o n . Note a l s o that W i s 2 9 5 watts 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 F i g . 4-c. F i g s . 4-b and 4-c show that the values of P J J 2 are equal f o r p o i n t s B and B', C and C , D and D', and E and E*. L i k e w i s e , 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 operating p o i n t s i n the two experiments. This i n d i c a t e s that point C i s the point at which the target begins to uncover and that point D i s the point at which the target becomes bare. The 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 understood i n terms of the discharge c h a r a c t e r i s t i c s of F i g . 3 (or F i g s . 4-a and 4-b). As the target s t a r t s to uncover at point C the secondary e l e c t r o n emission c o e f f i c i e n t (y) s t a r t s to decrease 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 higher y. As y continues to decrease so does I u n t i l the target i s bare at point D and y i s once again e s s e n t i a l l y constant. With y constant at point D, I begins to increase w i t h V again. As w e l l , P J J 2 continuously decreases w i t h i n c r e a s i g V f o r a l l values of V. In experiments s i m i l a r to that of F i g . 4-c, where i n one case, I or W i s constant and F N 2 v a r i e d and i n the other case 7-^^ i s f i x e d while I or W i s v a r i e d , a problem a r i s e s . This problem i s that a point i s - 44 -reached ( 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 supply i s t r y i n g to maintain a given value of I or W but the combination of values [V, P^2» I] does not belong to the l o c i of s t a b l e operating points of the system shown i n F i g . 3. The system i s then forced to s h i f t to an operating point that i s c o n s i s t e n t w i t h the given I or W. Mathematically s t a t e d , V and P N 2 are not s i n g l e valued f u n c t i o n s of I ; whereas, I and P J J 2 are s i n g l e valued f u n c t i o n s of V as seen i n F i g . 3. Therefore, i f one does not a l t e r the pumping speed or gas flow r a t e s , operation between the points C and D r e q u i r e s c o n t r o l over target v o l t a g e . I w i l l now demonstrate that the a b i l i t y to c o n t r o l the voltage through the t r a n s i t i o n region i s c r u c i a l l y dependent upon the dominant mechanism of target coverage being Ion p l a t i n g from the discharge current i n s t e a d of chemisorption of the n e u t r a l r e a c t i v e gas species. In the absence of a discharge, i t i s known that 0 2 chemisorbs on A l metal while N 2 does not [82,83], Since 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 discharge, i t i s apparent that the discharge 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 2 coverage, while i t may be only p a r t l y r e s p o n s i b l e f o r the 0 2 coverage. Thus, I now analyze and compare the discharge 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 A l i n an Ar/N 2 gas mixture to those f o r A l i n an A r / 0 2 atmosphere i n order to see the e f f e c t of the d i f f e r e n t mechanisms f o r target coverage. The changes i n the discharge c h a r a c t e r i s t i c s of the two systems caused by v a r i a t i o n s i n the gas flow rates (FJJ 2 and F A r ) and pumping speed (S) are examined, and the r e s u l t s analyzed i n terms of a model f o r the s p u t t e r i n g process which allows f o r the two p r e v i o u s l y mentioned mechanisms f o r target coverage. - 45 -II.2-a The Target Reaction T h e r a t e e q u a t i o n f o r a b s o r p t i o n a n d e m i s s i o n o f r e a c t i v e g a s m o l e c u l e s f r o m t h e t a r g e t s u r f a c e may b e w r i t t e n a s f o l l o w s [ 1 7 - 1 9 ] : d n P n ( 6 ) I _ J L = B ( e ) P r + £ e ( 9 ) [ 1 + y ( e ) ] e - J ^ J , ( I I - D w h e r e , n g i s t h e t o t a l n u m b e r o f r e a c t i v e g a s m o l e c u l e s a d s o r b e d on t h e t a r g e t s u r f a c e , P t a n d P r a r e , r e s p e c t i v e l y , t h e t o t a l p r e s s u r e a n d r e a c t i v e g a s p a r t i a l p r e s s u r e , I i s t h e t o t a l d i s c h a r g e c u r r e n t , e i s t h e e l e c t r o n i c c h a r g e , f ( P r / P t ) i s t h e f r a c t i o n o f p o s i t i v e i o n s i n t h e d i s c h a r g e c u r r e n t t h a t a r e r e a c t i v e g a s s p e c i e s , a n d 0 i s t h e f r a c t i o n o f t h e t a r g e t s u r f a c e t h a t i s c o v e r e d w i t h a m e t a l - r e a c t i v e g a s c o m p o u n d l a y e r . T h e r e m a i n i n g p a r a m e t e r s h a v e d i f f e r e n t v a l u e s o n b a r e o r c o v e r e d p o r t i o n s o f t h e t a r g e t a n d , t h e r e f o r e , t h e i r v a l u e s , w h e n a v e r a g e d o v e r t h e e n t i r e t a r g e t s u r f a c e , w i l l d e p e n d o n 9 . T h e s e a v e r a g e v a l u e s a r e u s e d i n E q n . I I - l . T h e p a r a m e t e r a ( 9 ) r e p r e s e n t s t h e p r o d u c t o f i m p i n g e m e n t r a t e p e r u n i t P r a n d t h e s t i c k i n g 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 g a s m o l e c u l e s o n t h e t a r g e t s u r f a c e , e ( 9 ) i s t h e s t i c k i n g c o e f f i c i e n t f o r r e a c t i v e g a s i o n i c s p e c i e s i m p i n g i n g o n t h e t a r g e t s u r f a c e , n r ( 0 ) i s t h e a v e r a g e s p u t t e r i n g y i e l d o f r e a c t i v e g a s m o l e c u l e s f r o m t h e t a r g e t , a n d y(B) i s t h e a v e r a g e s e c o n d a r y 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 f o r t h e e n t i r e t a r g e t s u r f a c e . T a r g e t c o v e r a g e b y a t o m i c n e u t r a l s h a s n o t a c t u a l l y b e e n n e g l e c t e d i n E q n . I I - l . S i n c e , t o f i r s t o r d e r , t h e i r c o n t r i b u t i o n t o t a r g e t c o v e r a g e w i l l a l s o be - 46 -p r o p o r t i o n a l t o t h e i o n c u r r e n t [ 8 ] , t h e i r e f f e c t i s a l r e a d y a c c o u n t e d f o r i n t h e c u r r e n t d e p e n d e n t i o n p l a t i n g t e r m o f E q n . I I - 1 . T h e f i r s t t e r m o n t h e r i g h t h a n d s i d e o f E q n . I I - l a c c o u n t s f o r 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 g a s m o l e c u l e s o n t h e t a r g e t s u r f a c e ; t h e s e c o n d t e r m , f o r i o n p l a t i n g a s s o c i a t e d w i t h t h e d i s c h a r g e c u r r e n t ; t h e t h i r d t e r m , s p u t t e r i n g o f r e a c t i v e g a s m o l e c u l e s f r o m t h e t a r g e t . I n s t e a d y s t a t e , E q n . I I - l r e d u c e s t o - f n y - f $ [ , + * M 1 * - i ( I I - 2 ) T o c o n t i n u e t h e a n a l y s i s a p a r t i c u l a r f u n c t i o n a l f o r m f o r f ( P r / P t ) i s r e q u i r e d . One e x p e c t s f ( P r / P t ) = B P r / P t , w h e r e B i s a p o s i t i v e c o n s t a n t , i f t h e d i f f e r e n t g a s s p e c i e s p r e s e n t i n t h e p l a s m a do n o t a f f e c t e a c h o t h e r ' s i o n i z a t i o n m e c h a n i s m s . H o w e v e r , w o r k b y L o u n s b u r y [ 8 4 ] , A i t a [ 8 5 ] , a n d K a r u l k a r a n d N o r d m a n [ 8 6 ] o n A r - 0 2 p l a s m a s h a s i n d i c a t e d t h a t t h e c o n c e n t r a t i o n o f A r + i o n s i n t h e p l a s m a a c t u a l l y i n c r e a s e s w h e n s m a l l p a r t i a l p r e s s u r e s o f 0 2 ( P o 2 ^ t ^ 0 . 1 5 ) a r e p r e s e n t . When Po 2 / p t e x c e e ^ s 0 . 1 5 , t h e A r + i o n c o n c e n t r a t i o n b e g i n s t o d e c r e a s e i n t h e m a n n e r e x p e c t e d f o r a m i x t u r e o f i n d e p e n d e n t g a s e s . T h e m e c h a n i s m s i n v o l v e d i n t h e p l a s m a w h i c h l e a d s t o t h i s b e h a v i o r i s r e l a t e d t o t h e h i g h e l e c t r o n a f f i n i t i e s o f b o t h 0 2 a n d 0 . E i t h e r w i l l r e a d i l y f o r m n e g a t i v e i o n s t h r o u g h c o m b i n a t i o n w i t h t h e e l e c t r o n s p r e s e n t i n t h e p l a s m a . T h i s n e g a t i v e i o n f o r m a t i o n r e d u c e s t h e n u m b e r o f e l e c t r o n s a v a i l a b l e t o n e u t r a l i z e p o s i t i v e A r i o n s w h i c h , - 47 -t h e r e f o r e , l e a d s t o a n i n c r e a s e i n t h e c o n c e n t r a t i o n o f p o s i t i v e A r i o n s . I f e n o u g h r e a c t i v e g a s i s a d d e d , a p o i n t i s e v e n t u a l l y r e a c h e d w h e n t h e d e c r e a s i n g A r a t o m c o n c e n t r a t i o n o f f s e t s t h i s e f f e c t a n d t h e A r + i o n c o n c e n t r a t i o n b e g i n s t o d e c r e a s e . R e g a r d i n g t h e p o s i t i v e o x y g e n s p e c i e s , w o r k o f A i t a e t a l . [ 8 7 ] h a s shown t h a t , f o r o x i d e t a r g e t s , t h e n u m b e r o f p o s i t i v e o x y g e n s p e c i e s h a s t h e f o r m ( a + b P Q 2 / P t ) . T h e c o n s t a n t t e r m ( a ) a r i s e s b e c a u s e , e v e n w i t h no 0 2 a d d e d t o t h e g a s , some o x y g e n s p e c i e s a p p e a r i n t h e g a s a f t e r b e i n g s p u t t e r e d f r o m t h e o x i d e t a r g e t . T h e r e f o r e , i f t h e n u m b e r o f A r + i o n s i s i n c r e a s i n g l i k e ( c + d P Q 2 / P t ) , t h e n t h e f r a c t i o n o f t h e p o s i t i v e i o n s i n t h e d i s c h a r g e c u r r e n t t h a t a r e o x y g e n s p e c i e s h a s t h e f o r m ( a + bPo 2 / P t ) / ( a + c + ( b + d ) Po 2^t^* T n i s f u n c t i o n i s f o u n d a l w a y s t o d e c r e a s e w i t h i n c r e a s i n g Po 2 / p t P r o v i d e d t h a t t h e f r a c t i o n a l i n c r e a s e i n A r + i o n s i s g r e a t e r t h a n t h e f r a c t i o n a l i n c r e a s e i n p o s i t i v e o x y g e n s p e c i e s . F o r 0 < P A / P < 0 . 1 5 t h i s r a t i o i s f o u n d t o be a b o u t 2 f r o m m a s s ~ u 2 t ~ s p e c t r o m e t r i c a n d o p t i c a l d a t a o f A i t a [ 8 7 ] a n d L o u n s b u r y [ 8 4 ] . I n t h i s w o r k I h a v e a m e t a l t a r g e t t h a t I s o x i d i z e d . A s l o n g a s I o p e r a t e t h e d i s c h a r g e i n t h e o x i d i z e d r e g i m e t h e a b o v e e x p r e s s i o n f o r t h e c o n c e n t r a t i o n o f p o s i t i v e o x y g e n s p e c i e s s h o u l d b e v a l i d . F u r t h e r , s i n c e my d a t a e x t e n d s o v e r s u c h a s m a l l r a n g e o f v a l u e s f o r P g 2 / P t , 1 w i l l a p p r o x i m a t e t h e c o n c e n t r a t i o n o f p o s i t i v e o x y g e n s p e c i e s a s a l i n e a r l y d e c r e a s i n g f u n c t i o n o f P_ / P . f o r 0 < P . / P , . < . 1 5 . T h e r e f o r e , u 2 t ~ u 2 t ~ t h i s p r o p e n s i t y f o r n e g a t i v e i o n f o r m a t i o n d e c r e a s e s t h e c o n c e n t r a t i o n o f p o s i t i v e o x y g e n s p e c i e s a s w e l l a s i n c r e a s e s t h e A r + i o n c o n c e n t r a t i o n f o r l o w v a l u e s o f P n . / P , . . T h i s m e c h a n i s m l e a d s t o - 48 -f ( P n /P ) being given as (A* - B' P n /P ) when P_ /Pfc i s l e s s than 0.15, U 2 t 0 2 t 0 2 t and f ( P _ / P J behaving as (A" + B" P n /P ) when P. /Pfc exceeds 0.15, <J2 t U 2 t U 2 t where A', B', A" and B" are p o s i t i v e constants. My data i n v o l v i n g Ar-02 plasmas i n the range of p a r t i a l target coverage shows PQ 2/P t to be always l e s s than 0.10, t h e r e f o r e I take f ( P ^ / P t ) = (A' - B' P^/P^.). In the case of Ar-N2 plasmas, n e i t h e r N2 nor N i s able to form negative ions; therefore the gases are expected to act independently of each other w i t h f ( P N 2 / P t ) = B P N 2 / P t . The above-mentioned forms f o r f ( P r / P t ) l e a d to the f o l l o w i n g p r e d i c t i o n s f o r the steady s t a t e pressure quotient P r/P t« V P t = t A ' - ^ + + Y<e)l e ^ 2 . (II - 3 - a ) f o r the Ar-02 plasma when P o 2 / p t i s l e s s t n a n 0.15; and p N 2 / p t " i Hby ~ i fffr 11 + Y ( 9 ) 1 6 <I-3-"> f o r the Ar-N 2 plasma at a l l values of P N 2 / P t . The parameters {a, e, y, and n r} w i l l depend on the r e a c t i v e gas-target combination under study. This dependence was not e x p l i c i t l y shown i n Eqns. I I - 3 i n order to minimize the number of symbols. I f the n e u t r a l r e a c t i v e gas molecules do not chemisorb on the target m a t e r i a l , a i s equal to zero i n e i t h e r of Eqns. 3. I now present data to compare w i t h these equations. - 49 -F i g s . 5-a to 5 - i show how independent v a r i a t i o n s of n i t r o g e n flow ( F N 2 ) , argon flow ( F ^ r ) , or pump speed (S) a f f e c t the cu r r e n t - v o l t a g e ( I - V ) , P N 2 - v » and ( P ^ ^ t ) - ^ c h a r a c t e r i s t i c s when A l i s sputtered i n an A r / N 2 gas mixture. S i m i l a r experiments f o r an A l target and an A r / 0 2 gas mixture are summarized i n F i g s . 6-a to 6 - i . To more c l e a r l y present the relevant data i n F i g s . 6 I have not shown the t r a n s i t i o n to a bare target surface. Instead, the highest voltage data point i n each curve presented i s the l a s t one recorded before the 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 . This data from the bare t a r g e t discharge would be at higher voltages than those shown i n F i g s . 6 and at P Q 2 values of ^  zero. Peaks In the I-V c h a r a c t e r i s t i c s of the N 2 data and the p o i n t s where the abrupt changes occur i n the 0 2 data are i d e n t i f i e d as the points where 0 = 1, as explained i n the previous s e c t i o n and depicted i n F i g . 4 f o r N 2 . Because P r/P t» as given i n Eqns. H-3, i s s t r o n g l y dependent on 0 through the parameters {a, e, y, and T|R}, I w i l l l i m i t the a n a l y s i s to the operating p o i n t s corresponding to 0 = 1. F i g . 7 shows the p l o t s of P r/Pt v s « P ^ 1 ' f o r 9 = 1» taken from the N 2 and 0 2 data of F i g s . 5 and 6. One sees immediately that P f l 2 / P t i s constant, w i t h i n experimental e r r o r , as p r e d i c t e d by Eqn. II-3-b w i t h a = 0; i . e . no chemisorption of n e u t r a l r e a c t i v e gas molecules. F u r t h e r , p o 2 / p t c a n ^ e b e t t e r described by a l i n e a r l y i n c r e a s i n g f u n c t i o n of PQ2/^- a s p r e d i c t e d by Eqn. I I - 3 - a w i t h a non-zero a. The tendency of P o 2 / p t v s * P 0 2 ^ t o f l a t t e n out f o r higher values of P n 0 / p t i s a t t r i b u t e d to the breakdown of the l i n e a r Fig. 5 V a r i a t i o n of A l - A r / N 2 discharge c h a r a c t e r i s t i c s w i t h F A , F N , and S. I n ( a ) - ( c ) , F N 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 2 = 1.00 SCCM(Ar) per 0.76 Pa(Ar) and O-2.00 SCCM(N 2), x-1.50 SCCM(N 2), and •-1.00 SCCM(N 2). In ( d ) - ( f ) , F A r i s v a r i e d w i t h 1.50 SCCM(N 2) g i v i n g S(N 2) = 1.50 SCCM(N 2) per 0.84 Pa(N 2) and x-1.50 SCCM(Ar), •-1.00 SCCM(Ar), and + -0.50 SCCM(Ar). In ( g ) - ( i ) , S i s v a r i e d w i t h 1.50 SCCM(Ar) and 1.50 SCCM(N 2) and o-S(Ar) = 1.50 SCCM(Ar) per 1.48 Pa(A r ) , x-S(Ar) =1.50 SCCM(Ar) per 1.07 Pa ( A r ) , «-S(Ar) =1.50 SCCM(Ar) per 0.81 Pa(A r ) , and + -S(Ar) = 1.50 SCCM(Ar) per 0.42 Pa(Ar). - 51 -Fig 6 2.0 'S 1-5 Q. E 2 ,.0 0.5 _ .30 o CL .20 (V) rf .10 .20 - .15 CL (a) (d) : ff J * (9) (b) ~+***\ (e) - % *> : \ (c) — ' " A ) - \ I 1 (f) o + 1 1 (i) ^ o • ° + * 1 1 290 305 320 V (volts) 3 0 5 320 V (volts) 3 0 5 320 335 V ( volts) V a r i a t i o n of A l - A r / 0 2 discharge c h a r a c t e r i s t i c s w i t h F A r , F 0 , and S. In ( a ) - ( c ) , F Q i s v a r i e d w i t h 3.00 SCCM(Ar) g i v i n g S(Ar) = 3.00 SCCM(Ar) per 1.13 Pa(Ar) and O-0.90 SCCM(0 2), + -0.60 SCCM(0 2), and •-0.30 SCCM(0 2). In ( d ) - ( f ) , F A r i s v a r i e d w i t h 0.60 SCCM(0 2) g i v i n g S ( 0 2 ) = 0.60 SCCM(0 2) per 0.21 P a ( 0 2 ) and O-6.00 SCCM(Ar), + -5.00 SCCM(Ar), .-4.00 SCCM(Ar), and x-3.00 SCCM(Ar). In ( g ) - ( i ) , S Is v a r i e d w i t h 3.00 SCCM(Ar) and 0.60 SCCM(0 2) and o-S(Ar) = 3.00 SCCM(Ar) per 2.84 Pa(A r ) , + - S(Ar) = 3.00 SCCM(Ar) per 2.06 Pa(Ar), and «-S(Ar) = 3.00 SCCM(Ar) per 1.33 Pa(Ar). - 52 -Fig 7 V a r i a t i o n of (P r/P f c) w i t h ( P r / I ) at the 9 = 1 points of the data of F i g s . 5 and 6. - 53 -r e l a t i o n s h i p f o r f ( P 0 2 / P t ) as ^Oo^t n e a r s 0.15. Despite the s i m i l a r i t i e s i n the t r a n s i t i o n s between bare and covered ta r g e t s when s p u t t e r i n g at constant power or curr e n t , i t i s now evident that the mechanism l e a d i n g to target coverage i s fundamentally 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 of N 2 from that i n v o l v e d w i t h 0 2 present. From the above a n a l y s i s of the target processes I conclude that chemisorption of n e u t r a l r e a c t i v e gas molecules i s an important target coverage mechanism when the l a t t e r gas i s present, but i s unimportant when c o n s i d e r i n g the former. I now address the question of why operation at points between 9 = 1 and 9 = 0 i s p o s s i b l e f o r the A l - A r / N 2 system and not f o r the A l - A r / 0 2 system. The s t a b i l i t y of dn g/dt, as given by Eqn. I I - l , w i t h respect to f l u c t u a t i o n s i n the discharge current i s examined f o r the cases of no chemisorption (Ar-N 2 plasma) and chemisorption ( A r - 0 2 plasma). The change i n the r a t e of target coverage caused by a f l u c t u a t i o n i n the current ( A l ) i s given by dn oP 5P n where, i n the i n t e r e s t of c l a r i t y , I have discontinued w r i t i n g the arguments a s s o c i a t e d w i t h the various f u n c t i o n s i n Eqn. I I - 4 . I f , p r i o r to the f l u c t u a t i o n i n discharge c u r r e n t , the system [ f e - n r ] 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 since -ocP = -TT\—\—by r (l+y)e J v i r t u e of Eqn. I I - 2 , Eqn. II-4 may be r e w r i t t e n as - 54 -e l 9f i ( I I - 5 ) Using Eqns. I I - l , I I - 2 and II - 3 together w i t h the data contained i n F i g s . 5, 6, and 7, one f i n d s that each terra on the r i g h t hand side of Eqn. I I - 5 produced a f r a c t i o n a l change i n dn g/dt of the order of ( A I ) / I . In my system, i n steady s t a t e operating c o n d i t i o n s , ( A I ) / I i s roughly 10% at 360 Hz due to the nature of the dc current supply ( i . e . 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). Note, however, that Eqn. I I - 5 portrays two fundamentally 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 the current can cause a change i n the rate of target coverage. F i r s t l y , the term oc(P r/I)(Al) represents an immediate change i n both the r a t e at which ions are brought to the target surface by the i o n current and the rate at which r e a c t i v e gas species are res p u t t e r e d . This term i s seen to vanish when a = 0 ( i . e . no chemisorption). Secondly, the other two terms i n v o l v e slower changes i n both the chemisorption and i o n p l a t i n g rates caused by the change i n Pr> which r e s u l t s from the change i n the g e t t e r i n g rate that accompanies a change i n the cu r r e n t . One of these two terms a l s o vanishes when a i s zero. This second type of response i s slower because of the processes i n v o l v e d : the movement of sputtered f l u x to the g e t t e r i n g surfaces; the a c t u a l g e t t e r i n g at the surface; and the d i f f u s i o n of the pressure f l u c t u a t i o n s from the g e t t e r i n g surfaces back to the t a r g e t . As a r e s u l t of the time required f o r these processes to occur, changes i n - 55 -pressure do not f o l l o w the current f l u c t u a t i o n . In the l i m i t of the d u r a t i o n (T) of the current t r a n s i e n t being much l e s s than the time r e q u i r e d f o r the pressure to e q u i l i b r a t e (xr)» c o n t i n u i t y of f l u x r e q u i r e s that the magnitude of the pressure response terms of Eqn. I I - 5 be reduced, by a f a c t o r of order i/xv, as the response i s spread out i n time. I f t h i s f a c t o r were small enough, the e f f e c t s of current induced pressure 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 . For my system and operating pressures, a minimum estimate of t h i s r e d u c t i o n i s roughly 100 f o l d . For a minimum estimate of -ur I consider only the process of the N 2 p a r t i a l pressure t r a n s i e n t d i f f u s i n g from the w a l l back to the t a r g e t . Taking the N 2 mean free path and thermal v e l o c i t y as**.5 cm and**5 x 10** cm/s [88], 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 time of "'.06 s f o r an N 2 molecule to tr a v e r s e the 40 cm of the vacuum chamber. Assuming T R to be s e v e r a l of these d i f f u s i o n times gives T R as about a quarter of a second. The time that passes between a r r i v a l of some sputtered atoms at a w a l l and t h e i r combination w i t h a r e a c t i v e gas molecule may be s i g n i f i c a n t i n the N 2 case. While N 2 w i l l not chemlsorb on the surface of bulk A l metal i t w i l l react w i t h A l atoms (as i n the condensing sputtered f l u x ) [66], but the N 2 d i s s o c i a t i o n step i s s t i l l expected to be much longer than that f o r 0 2 d i s s o c i a t i o n . Therefore, one expects *".25s to be a reasonable lower l i m i t f o r T R- With %~1/360 one f i n d s a 90 f o l d r e d u c t i o n . From t h i s a n a l y s i s I conclude that the s t a b i l i t y of the discharge c h a r a c t e r i s t i c s should be much b e t t e r f o r systems where chemisorption of the s p u t t e r i n g gas does not occur than f o r systems where i t c o n t r i b u t e s s i g n i f i c a n t l y to the target coverage mechanism. In the regime of p a r t i a l t a rget - 56 -coverage, where small 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 non-chemisorbing systems should be most apparent. In the case of the A l - A r / N 2 system a = 0 and, t h e r e f o r e , one expects only the slow response of the target coverage due to current induced f l u c t u a t i o n s i n P r. I am able to c o n t r o l the discharge at a l l degrees of target coverage i n t h i s system. 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 valued r e l a t i o n s h i p between V and 9 discussed i n the previous s e c t i o n . I c o n t r o l target coverage by monitoring the target voltage 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 operating p o i n t s f o r the discharge (as i n F i g . 3) and, when d r i f t i s detected, small changes are made i n the discharge current to b r i n g the voltage back to the d e s i r e d value. Since the f a s t f i r s t order changes i n the r a t e of target coverage vanish, the p o s i t i v e feedback e f f e c t of these small current pulses i s small and the runaway t r a n s i t i o n between covered and bare target s t a t e s w i l l take a "long" time to get out of c o n t r o l . With the microcomputer c o n t r o l system, the voltage i s read about every 0.1 s and, i f d r i f t of more than 0.5 v o l t s i s detected, the current i s changed i n order to d r i v e the voltage back to the d e s i r e d value. The time l a g between d e t e c t i o n of d r i f t and the change i n the current i s l e s s than 0.1 s. However, another change i n current i s not i n i t i a t e d u n t i l roughly 0.5 s has elapsed. This 0.5 s delay i s necessary i n order to allow the f u l l e f f e c t of the previous change to be r e a l i z e d . I f s h o r t e r delays are used o s c i l l a t i o n s develop and the p o s i t i v e feedback c y c l e runs out of c o n t r o l . The f a c t that the necessary delay time i s about 0.5 s i n d i c a t e s that T R i s about 0.5 s i n s t e a d of the lower l i m i t of about 0.25 s mentioned e a r l i e r . - 57 -When chemisorption occurs, as i n the Al-Ar/02 system, a i s not zero and the immediate response i n the rate of target coverage i s the major f a c t o r a f f e c t i n g c o n t r o l of the process. When d r i f t i s detected and a current change i s i n i t i a t e d , as described 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 voltage measurement i s made. This r e s u l t s i n a minimum delay i n i n i t i a t i n g the second change of at l e a s t 0.1 s and, e v i d e n t l y , t h i s delay i s too long to prevent the p o s i t i v e feedback from running out of c o n t r o l . In f a c t , the l i t e r a t u r e i n d i c a t e s [83] that the monolayer formation time f o r chemisorbing 0 2 on A l i s on the order of 1/360 s f o r 0 2 p a r t i a l pressures i n the range that I am working at. Therefore, a h i g h l y f i l t e r e d dc power supply may be needed i n order to c o n t r o l the A l - A r / 0 2 discharge i n the region of p a r t i a l t a rget coverage, rather than a f a s t e r computer c o n t r o l a l g o r i t h m . I t i s w e l l known that 0 2 chemisorbs on S i ; however the monolayer formation time at P o 2 ' v P a ( s p u t t e r i n g pressures) i s on the order of an hour [89]. Therefore, voltage c o n t r o l of a S i target i n an A r / 0 2 atmopsphere should be p o s s i b l e . Recently, Steenbeck et a l . [90] reported 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 the S i - A r / 0 2 system that i s s i m i l a r to that i n the A l - A r / N 2 system. II.2-b Prediction of Film Composition from Plasma Characteristics For most a p p l i c a t i o n s of t h i n f i l m d e p o s i t i o n an accurate knowledge of f i l m composition during f i l m growth i s re q u i r e d . I present a method by which the f i l m composition may be c a l c u l a t e d from the s p u t t e r i n g discharge c h a r a c t e r i s t i c s such as those given i n F i g . 3. The b a s i s of the technique i s to use the o p t i c a l emission data to determine the f l u x of metal atoms sputtered, and to obtain the g e t t e r i n g rate by monitoring the r e a c t i v e gas p a r t i a l pressure. For purposes of demonstration I w i l l use data f o r the Al-Ar/N2 system. I assume the rate of r e a c t i o n of A l w i t h N 2 on the substrate i s p r o p o r t i o n a l to only the A l concentration when N 2 i s i n extreme over-abundance, but that the r a t e i s p r o p o r t i o n a l to the product of both reactant concentrations when both N 2 and A l are i n l i m i t e d supply. The former c o n d i t i o n means that i n the low V and high P J J 2 region of the discharge 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 deposited, the g e t t e r i n g rate w i l l be p r o p o r t i o n a l to the sputtered A l f l u x only, w h i l e the l a t t e r c o n d i t i o n says that the g e t t e r i n g rate w i l l be p r o p o r t i o n a l to the product of the sputtered A l f l u x and P J J 2 i n the region of the discharge 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 deposited. 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 present a r a t e equation a n a l y s i s of the flow of N 2 gas i n t o and out of the vacuum chamber that w i l l a l l o w p r e d i c t i o n of the Al/N r a t i o i n the s p u t t e r deposits from data 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 = F„ - ^  ( A l f l u x ) , f o r P„ > P* (II-6-a) when N 2 i s i n over-abundance, and - 59 -S P N 2 " F N 2 " % ( A 1 f l u x ) > f ° r P N 2 < P N 2 ( I I - 6 " b ) when both r e a c t a n t s are i n l i m i t e d supply. In these equations 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 defined; P N represents the N 2 p a r t i a l pressure at which the g e t t e r i n g behavior changes from the regime of N 2 over-abundance to the case where both reactants are i n l i m i t e d supply; 8 i s the constant 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 product P N 2 ( A l f l u x ) to the g e t t e r i n g r a t e . The f a c t o r of 1/2 i n Eqn. I I - 6 - a a r i s e s because two A l atoms are required to g e t t e r one N 2 molecule to form two A1N molecular u n i t s i n the s t o i c h i o m e t r i c A1N region of the discharge c h a r a c t e r i s t i c s . P h y s i c a l l y , S P J J 2 i s the flow of N 2 out of the chamber through the pumping p o r t ; F J J 2 Is the N 2 flow d e l i b e r a t e l y l e t i n t o the chamber through the leak valve; 1/2(Al f l u x ) i n Eqn. I I - 6 - a or 8PJJ 2 ( A l f l u x ) i n Eqn. II-6-b) represent the flow of N 2 i n t o sputtered d e p o s i t s . Note t h a t , i n Eqn. II- 6 - b , - J l — gives the P P N 2 average, over a l l g e t t e r i n g s u r f a c e s , of the r a t i o of Al/N atoms i n the * sputtered deposits when P„ < P„ (or 2BP„ = x i n AINx). Therefore, 8 N 2 N 2 N 2 ' r i s of c e n t r a l importance i n the determination of f i l m composition. One now needs to determine the A l f l u x i n terms of the discharge c h a r a c t e r i s t i c s . I take the number of A l atoms sputtered per second to be d i r e c t l y p r o p o r t i o n a l to the i n t e n s i t y of o p t i c a l emission from n e u t r a l A l atoms i n the glow discharge. This 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 of the d e p o s i t i o n rate versus A l , where A l i s the i n t e n s i t y of the 3961.52A o p t i c a l emission l i n e of 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 thickness d e p o s i t i o n r a t e w i t h A l * from data of F i g . 3. I n reference to F i g . 3, x-between points A and C, •-between p o i n t s C and D, + - at point D, and o-betwen points D and E. - 61 -from the data 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 another i n F i g . 8 i s accounted f o r by the change i n density as the composition changes from A1N to A l . I have assumed d e n s i t i e s of 3.26 gm/cc and 2.7 gm/cc f o r A1N and A l , r e s p e c t i v e l y [66], I t h e r e f o r e w r i t e ( A l f l u x ) = 6A1 over the e n t i r e operating range, where 6 i s a constant 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 emission l i n e to the sputtered f l u x from the t a r g e t . This allows one to r e w r i t e Eqn. I I - 6 - a and Eqn. II-6-b as F P N 2 = -f~ ~ If A 1 * ' f ° r P N 2 > % ( I I - 7 " a ) and ^ - + = ^ A 1 * , f o r P M < P* (II-7-b) P N 2 F N 2 F N 2 ' N 2 Since S i s known, 6 may be determined through Eqn. I I - 7 - a from a p l o t of P N 2 vs. A l * i n the region between A and C of F i g . 3. Once 6 1 * has been determined, p may be determined from the slope of a -=— vs. A l N 2 p l o t i n the region a f t e r point D. For the data of F i g . 3 the p l o t a s s o c i a t e d w i t h Eqn. II-7-a i s given i n F i g . 9-a while F i g . 9-b should be used i n conjunction w i t h Eqn. II-7-b. c a l c u l a t e d at point u or J?ig. J i s about * i n d i c a t i n g the r a t i o of Al/N i n the f i l m i s about 2. P o i n t D i s a l s o The value of pP^ a t e d D f F i 3V a r i a t i o n s of P N (a) and 1/P N (b) with A l * from the data of F i g . 3. 2 - 63 -the point 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 concert w i t h a r a p i d increase i n the number of A l p r e c i p i t a t e s . F i g . 10 shows room temperature 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) as a f u n c t i o n of x i n AINx f i l m s deposited along the 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 that a l l A l i n excess of what i s needed to form s t o i c h i o m e t r i c A1N from the incorporated N 2 i s present as A l p r e c i p i t a t e s . Since no attempt was made to account f o r cross doping between A l and A1N phases, these values f o r Xv are only upper l i m i t s . Of course, the A l p e r c i p l t a t e s are expected to conta i n n i t r o g e n i m p u r i t i e s , w h i le the A1N c r y s t a l s w i l l c ontain excess A l . A l s o 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 sputtered AINx f i l m s , where x was obtained from e l e c t r o n microprobe a n a l y s i s . One sees that the agreement between the two sets of data 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 that my f i l m s show a p e r c o l a t i o n threshold at a much lower value of x (higher 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 part because Itoh's d e p o s i t i o n r a t e i s much higher than mine (^ x 4) and i n part because h i s f i l m s are 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 which takes place on the substrate ( I observe no A1N emission l i n e s i n the glow discharge [91]). The A l - A l r e a c t i o n i s expected to proceed more q u i c k l y than the A l - N 2 r e a c t i o n due to the N 2 d i s s o c i a t i o n step of the - 64 -Fig.10 V o l u m e f r a c t i o n o f A l ( X v ) I.0 .88 .76 . 6 5 . 5 4 .44 .35 25 J 7 .08 0 I 0 C l o - ' h E u I C3 10" + 2 0 0 0 o o Q _ Q_ or o \-- 2 0 0 0 1 -- 4 0 0 0 - 6 0 0 0 T X i r (a) fit to d a t a o f Itoh (,°ef al. ( b ) ^ (i) fit t o d a t a o f I t o h , et al. S a m p l e G e o m e t r y I i l I I I L .2 .4 .6 X i n A I N „ .8 V a r i a t i o n s of p (a) and TCR (b) w i t h x, x-my data where x i s c a l c u l a t e d from the data of F i g . 9 and Eqns. II - 7 - a and II-7-b, the s o l i d l i n e i s a f i t to data 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 -l a t t e r . Therefore, high absolute A l s p u t t e r r a t e s should r e s u l t merely i n n i t r o g e n doped A l i f there i s not s u f f i c i e n t time f o r N 2 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 formation of c r y s t a l l i n e A1N. This i m p l i e s that higher absolute A l sputter rates lead to more A l i n c l u s i o n s and smaller and l e s s prevalent A1N c r y s t a l s . F u r t h e r , i n c r e a s i n g the A l s p u t t e r rate may j u s t lead 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 enough time f o r the r e a c t i o n i s not allowed. From f i l m s deposited i n the s t o i c h i o m e t r i c region of the I-V c h a r a c t e r i s t i c s there i s evidence f o r smaller A1N 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-ray d i f f r a c t i o n s t u d i e s . At constant Xv I have a l s o observed, f o r f i l m s on the i n s u l a t i n g side of Xvc, that p i s constant f o r thicknesses l e s s than <~ 2000 A, but decreases r a p i d l y (by ^ x 5) f o r thicknesses between <-> 2000 A and 4000 A, and becomes constant again f o r thicknesses over 4000 A. I b e l i e v e t h i s e f f e c t may be due to the s e n s i t i v i t y of the hopping mechanism to the d i m e n s i o n a l i t y of the f i l m . I f the f i l m t h ickness 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 be 2- dimensional [92]. 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 3- dimensional f o r normal conduction processes and 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 matrix, e s p e c i a l l y when the metal i s very impure i n each case. For these reasons I think i t i s reasonable to assume that my deduced compositions are c o r r e c t even a f t e r the point where the p vs. x p l o t departs from Itoh's data. I am now i n a p o s i t i o n to discuss how one may o b t a i n a given f i l m composition and d e p o s i t i o n r a t e . I have observed that f i l m s deposited on the low V side of the I-V maximum, as i n F i g . 3, appear to be - 66 -s t o i c h i o m e t r i c A1N while 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 high V side of the peak. Further, i f v a r i a t i o n s i n pump speed or gas flow are introduced, as i n F i g s . 5, equivalent operating points along 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 et 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 compositions as w e l l as c a l c u l a t e d values of (8 P N 2 ^ t n a t agree to w i t h i n 10%. Therefore, i n c r e a s i n g the N 2 flow r a t e w i l l i ncrease the discharge power (and ther e f o r e s p u t t e r i n g r a t e ) f o r equivalent points along the I-V curve, while the p o s i t i o n along the c h a r a c t e r i s t i c may be used to p r e d i c t the composition. 11.2-c Calculation of the Sputtering Yield I f one equates the standard expression f o r c a l c u l a t i n g the sputtered f l u x from the s p u t t e r i n g current [19] to 6A1 of Eqn. I I - 7 , the r e s u l t i n g expression i s [I + Y ( 9 ) ] e = 6 M ( I I " 8 ) where i s the s p u t t e r i n g y i e l d i n A l atoms per i n c i d e n t i o n , y i s the 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 discharge c u r r e n t . I t f o l l o w s from Eqn. I I - 8 that a p l o t of e6Al / I vs V w i l l give the voltage dependence of r\eff f o r the p a r t i c u l a r target and gas composition used. Where 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 ( n m / ( l + y)) has been - 67 -l a b e l e d T ) e f f The data of F i g . 3 has been used to make such a p l o t which i s presented as F i g . 11. In the high V and low P^ 2 region one might expect 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 to approach the values recorded i n the l i t e r a t u r e f o r normal incidence s p u t t e r i n g y i e l d s of A l i n an Ar atmosphere. These values i n F i g . 11 are l e s s than h a l f the accepted values [93] (about 40%). In a d d i t i o n , the data of F i g . 11 was obtained from a new t a r g e t and as the t a r g e t i s used more, causing the er o s i o n channel to 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 to about 60% of the accepted value 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 to increased s p u t t e r i n g at oblique incidence as the eros i o n channel deepens [94], There are s e v e r a l mechanisms that could serve to lower i)eff from the accepted values. The i o n energies may be lower than those given by the cathode voltage drop because of c o l l i s i o n s [15], Some of the i o n current i s s t i l l N 2 species w i t h a lower s p u t t e r i n g y i e l d than Ar. A l s o , w h i l e the target appears bare and P N 2 i s very low, the N 2 that i s present may s t i l l be keeping y high. In any event, Eqn. II-8 and F i g . 11 should give a good i n d i c a t i o n of the r e l a t i v e magnitudes 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 s f o r various degrees of target coverage. - 68 -Fia11 I ( a m p s ) — — r° The voltage 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 e f f c a l c u l a t e d from Eqn. I I - 8 and the data of F i g . 3. CHAPTER III FILM PROPERTIES - EXPERIMENTAL RESULTS AND DISCUSSION At t h i s p o i n t I w i l l present e l e c t r i c a l transport and o p t i c a l data from measurements made on A1/A1N cermets produced by voltage c o n t r o l l e d , r e a c t i v e , dc, planar magnetron s p u t t e r i n g of an A l target i n an Ar/N 2 atmosphere, as described i n the previous s e c t i o n . Much of the data w i l l be presented g r a p h i c a l l y along w i t h an i n s e t of the d e p o s i t i o n glow discharge 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 order t h a t , i n the 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 . I I I . l E l e c t r i c a l Transport Properties of A1/A1N Cermets . As discussed e a r l i e r , F i g . 10 and the te 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) data that demonstrates that the method of c a l c u l a t i n g f i l m compositions from the glow discharge c h a r a c t e r i s t i c s does work. X-ray d i f f r a c t i o n measurements of AINx f i l m s are c o r r e l a t e d w i t h the 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, while F i g . 13 shows trans m i s s i o n e l e c t r o n microscope (TEM) data 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 smaller and fewer f o r i n c r e a s i n g V, while the A l c r y s t a l s become l a r g e r and more prevalent. In p a r t i c u l a r , one sees; the A1N c r y s t a l s i z e to be roughly 300 A f o r f i l m s deposited on the low V side of the 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 decreases s t e a d i l y to 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 diameters l e s s than Fig. 12 2 6 ( D E G R E E S ) X-ray d i f f r a c t i o n 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 the i n s e t I-V curve. - 71 -Fig 13 TEM f o r f i l m s d e p o s i t e d a t t h e p o s i t i o n s i n d i c a t e d o n t h e i n s e t I - V c u r v e . The f i l m s a r e a b o u t 1500 A t h i c k . - 72 -50 A; j u s t past the I-V minimum an abrupt decrease, to about 50 A, occurs i n the A1N c r y s t a l s i z e ; a f t e r the abrupt drop i n A1N 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 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 while 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 gion, 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 to 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 smaller p a r t i c l e s , and t h a t , even at very high 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 . To t h i s tendency to form b a r r i e r s has been a t t r i b u t e d [2] the f a c t that cermet f i l m s i n v a r i a b l y e x h i b i t an Xvc that i s higher than theory 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 theory f o r 3-dimensions [ 3 ] ) . This b a r r i e r formation i s undoubtedly a thermodynamic e f f e c t r e l a t e d to the surface 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 serves to remove the randomness from the system. However, t h e o r e t i c a l s tudies have shown [59,96] that 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 higher value f o r Xvc, but the c r i t i c a l exponents should remain unchanged. In F i g . 14 i s shown normalized p vs. T data f o r four samples that are r e p r e s e n t a t i v e of the three types of behavior seen near Xvc. For Xv > .8 the behavior i s t y p i c a l of an impure metal w i t h p decreasing l i n e a r l y w i t h T to some lower l i m i t . For .72 < Xv < .8, p decreases w i t h T at high T, reaches a minimum, and then increases w i t h decreasing T from the minimum. In t h i s region where p i s i n c r e a s i n g w i t h decreasing T, p ^ InT and the temperature at which the minimum occurs moves to higher T as Xv i s reduced. This p ~ InT behavior and the temperature behavior of pm±n 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 - 73 -Fig. 14 0> Normalized p vs. T (a) and vs. 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 are: squares - (.66, 840, 984), 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 [5,40,41], ( D e t a i l e d magnetoresistance 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 temperature) are p r e s e n t l y being performed by Normand F o r t i e r on the samples e x h i b i t i n g p ~ InT behavior i n order to 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 decreasing 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 lnp 1//T as others have seen w i t h smaller g r a i n s i z e s and lower values f o r Xvc [2,32], Using the method of Denvenyi et a l . [37], discussed e a r l i e r , I have made In-In p l o t s of a c t i v a t i o n energy versus T f o r samples j u s t below Xv .72 and found t h a t , indeed, 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 energies are found by t a k i n g the slope at many points along a lnp vs. 1/T p l o t . F i g . 15 i s a t y p i c a l example of t h i s procedure, and the power of T i s seen to vary from sample to sample a l s o , i n accordance w i t h Devenyi's model. The view [37] that a very large number of defect s t a t e s e x i s t s i n the i n s u l a t i n g g r a i n s , due to excess A l , seems extremely l i k e l y when one considers the way i n which these f i l m s grow. In the composition range j u s t below X v ^ .72 the N 2/A1 a r r i v a l r a t e at the substrate i s very low, the A1N c r y s t a l s i z e i s extremely small ( l e s s than ^ 50 A), the A l i s l a n d s are becoming very large and p r e v a l e n t , and there i s not yet a continuous m e t a l l i c pathway across the sample. One, t h e r e f o r e , expects a l a r g e amount of A l atoms dispersed i n the A1N, and that conduction does not proceed v i a a continuous m e t a l l i c channel. The i s l a n d s i z e s - 75 -Fig. 15 >• o UJ UJ o I— | o < UJ c o r — ' 2.0 3.0 4.0 5.0 In ( T E M P E R A T U R E ) (k ) 6.0 .02 .04 .06 .08 ( T E M P E R A T U R E ) " 1 (k") .10 l n - l n p l o t s of conduction a c t i v a t i o n energies vs. T (a) and In p vs. 1/T at Xv = .66 ( b ) . The data (squares) i n (b) was used to c a l c u l a t e the data ( t r i a n g l e s ) i n ( a ) , then the slope 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 values from ( a ) . - 76 -(estimated from the x-ray and TEM data of F i g s . 12 and 13) i n d i c a t e the t y p i c a l charging energies f o r the metal i s l a n d s to be of the order of .leV at Xv = .65. Therefore, i t i s u n l i k e l y that many of these i s l a n d s are charged below 300 K. The conduction 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 nature of these f i l l e d and u n f i l l e d defect s t a t e s i s not immediately apparent. As Xv = .72 i s crossed from the i n s u l a t i n g to the m e t a l l i c side one observes (see F i g . 16) the c a r r i e r type i n room temperature H a l l measurements to change from n to p. Hopping should y i e l d n-type [97] while A l i s p-type [79], While e i t h e r A l i n t e r s t i t i a l s or N-vacancies are a l s o expected to produce n-type conduction i n A1N through doping, the data of F i g s . 12 through 15 i n d i c a t e that hopping conduction i s the more l i k e l y mechanism i n t h i s case. The composition ranges f o r the p ~ InT behavior and the changing H a l l s i g n coupled w i t h TCR, i n F i g . 10, changing s i g n at Xv = .72 s t r o n g l y i n d i c a t e s that Xvc = .72. Using 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 to T = 0 K to f i t a to a power law form, both 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. This value i s i n good agreement w i t h the value from the TCR, H a l l , and p ~ InT data discussed e a r l i e r . F i g . 17 shows l o g ( a ) vs. Xv and l o g ( a ) vs. l o g |Xvc - Xv| w i t h Xvc = .72. 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 value [3] of 1.7. Below Xvc one f i n d s a ~ (Xv - X v c ) - S w i t h s = 4.3 ± .1. This l a s t exponent does not agree w i t h the t h e o r e t i c a l value of 0.7 f o r a mixture of normal conductors and, of course, t h i s i s due to the conduction mechanism being t u n n e l i n g . - 77 -Fig 16 - 3 - 2 - 1 0 1 2 O X < 0) 00 o I I I I I I I I I I • — Inverse H a l l constant vs. Xv f o r f i l m s deposited near Xv = Xvc = .72. Fig. 17 Log (CONDUCTIVITY) Vs VOLUME FRACTION (theoretical) a z> o z o o o (a) av-cr I/X v c-X v) VOLUME FRACTION Log (CONDUCTIVITY) Vs VOLUME FRACTION (experimental) .5 .6 .7 .8 .9 VOLUME FRACTION I.0 Log(CONDUCTIVITY)Vs Log | X V C - X V | EXPERIMENTAL) 5.0r >-> 4.0-= E I a <-> 3.0h o 3 o - 2J0|-o> o (c) I.O -2.0 •I.5 -I.0 Log | X V C-X V| J — -0.5 (a) The t h e o r e t i c a l form f o r l n ( a ) vs. Xv, w i t h the s c a l i n g r e l a t i o n s shown f o r a 3-dimensional mixture of "normal" conductors. (b) l n ( a) vs. Xv from data from f i l m s deposited near Xv = Xvc = .72. (c) l n ( a ) vs. In Xvc - Xvl f o r data i n (b) . As depicted i n ( a ) , from (c) one obtains the c r i t i c a l exponents t = 1.75 ± .1 and s = 4.3 ± .1. The discrepancy between the observed and p r e d i c t e d values of s a r i s e s because, f o r the data, conduction proceeds v i a hopping. - 79 -I f one adopts Neugebauer's formula f o r t u n n e l i n g [30] R 2 - e 2 o ~ — exp(-aR) exp(^ r") ( I I I - l ) where R i s the p a r t i c l e s e paration and r i s the p a r t i c l e s i z e , then i n the l i m i t of both (aR) and (e 2/kTr) being small one f i n d s that R ~ (Xvc - X v ) u w i t h u .9. r has been taken to vary as (Xvc - X v ) - 1 ^ 5 w i t h 6 = .4 [ 3 ] , Of course, i n hopping from defect to defect the 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 process and the hopping conduction may only depend on the i n t e r d e f e c t spacings. III.2 Optical Properties of A1/A1N Cermets The o p t i c a l a bsorption of A1/A1N f i l m s , deposited at various p o s i t i o n s along the I-V c h a r a c t e r i s t i c of F i g . 3, was measured. F i g . 18 shows the product of f i l m t h i c k n e s s (d) and o p t i c a l absorption c o e f f i c i e n t (a) vs. wavelength f o r f i l m s of thicknesses 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 vs. photon energy f o r the same f i l m s as i n F i g . 18. On the high voltage side of the I-V minimum the f i l m s t u r n from c l e a r , to yellow brown, to dark brown, to black, and f i n a l l y s i l v e r y ( l i k e A l metal) by f i l m #8 of F i g . 18. The absorption peak at 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 to that observed by Pastrnak et a l . [60], as described i n the i n t r o d u c t i o n . Pastrnak concluded that t h i s a bsorption peak was due to oxygen i m p u r i t i e s i n the f i l m . This conclusion was - 80 -Fig. 18 Product of f i l m t hickness (d) and o p t i c a l absorption c o e f f i c i e n t (a) vs. wavelength f o r f i l m s deposited at the p o s i t i o n s shown i n the i n s e t I-V curve. - 81 -Fig. 19 0 1 2 3 4 5 6 7 E(eV) /a vs. E f o r the f i l m s shown i n F i g . 18. - 82 -based upon d i f f u s e r e f l e c t a n c e measurements on crushed A1N c r y s t a l s prepared by high voltage a r c i n g of A l e l e c t r o d e s i n an N 2 atmosphere, where the general background r e f l e c t a n c e ( a f t e r crushing) and 4.8 eV absorption i n t e n s i t y (before crushing) 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 ) . In view of the known granular nature of the f i l m s of F i g s . 18 and 19, and the f a c t that the a r c discharge method of making A1N i s known to 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 question a r i s e s as to whether the absorption at 4.8 eV could be due to some form of the d i e l e c t r i c anomaly, as s o c i a t e d w i t h granular m a t e r i a l s , as described i n the i n t r o d u c t i o n . In order to determine whether or not the 4.8 eV absorption i s due to the granular nature of the f i l m s , c a l c u l a t i o n s , based upon the MGT, EMT, and coated sphere approximations presented e a r l i e r , f o r A1/A1N cermets were performed and 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 through 27. For these c a l c u l a t i o n s : the A l o p t i c a l constants given by Powell were used [80]; the r e f r a c t i v e index data of Pastrnak [59], i n c l u d i n g d i s p e r s i o n , was 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 was obtained from o p t i c a l absorption measurements on A1N deposited i n the 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 c h a r a c t e r i s t i c s . D e t a i l s of these c a l c u l a t i o n s are given 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 c a l c u l a t i o n . 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 to s h i f t a p preciably w i t h Xv, whereas the data of Pastrnak and of F i g s . 18 and 19 i n d i c a t e s a constant peak p o s i t i o n . Since Irene and Z i r i n s k y [65] reported a lowering of r e f r a c t i v e index i n A1N w i t h A l enrichment (to ^ 1.7) , F i g . 21 shows the - 83 -Fig. 20 /a vs. E c a l c u l a t e d i n the MGT approximation f o r A1/A1N composites at v a r i o u s values of Xv. See Eqn. 1-9 and the appendix on o p t i c a l c a l c u l a t i o n s . - 84 -Fi g. 21 E(eV) /a vs. E c a l c u l a t e d i n the MGT approximation f o r A1/A1N composites at Xv = .10, but at various values of A1N r e f r a c t i v e index. See Eqn. 1-9 and the appendix on o p t i c a l c a l c u l a t i o n s . - 85 -Fig. 22 O O o E(eV) /a vs. E c a l c u l a t e d In the EMT approximation f o r A1/A1N composites at v a r i o u s values of Xv. See Eqn. 1-14 and the appendix on o p t i c a l c a l c u l a t i o n s . - 86 -Fig. 23 /a vs. E c a l c u l a t e d In the coated sphere-EMT approximation f o r A1/A1N composites at various values 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 vs. E data of F i g . 19 (a) with c a l c u l a t i o n s , from F i g . 23 (b) i n the coated sphere-EMT approximation. - 88 -Fig. 25 Reflectance vs. E c a l c u l a t e d i n the EMT approximation f o r A1/A1N composites at various values of Xv. See Eqn. 1-14 and the appendix on o p t i c a l c a l c u l a t i o n s . - 89 -Fig 26 CO C\J -01 Q PARAMETERS FOR THE COATED Al SPHERES ARE THE SAME AS I N FIG.23 0 3.5 E(eV) 7 R e f l e c t a n c e vs. E c a l c u l a t e d i n the coated sphere-EMT approximation f o r A1/A1N composites at various values of Xv. The coating parameters are the same as those used i n F i g . 23. 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 . - 90 -Fig. 27 V (VOLTS) 240 340 440 Ld _J < < L U z H Q: O Al MIRROR QUARTZ SUBSTRATES : J 3 U L K - A I N O Al MIRROR I-V DEPOSITION CHARACTERISTICS FOR FILMS 0 TO © 5 6 7 8 10 14 20 50 > (MICRONS) 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 curve; bulk AIN; and the substrates used f o r the deposited f i l m s . - 91 -e f f e c t , i n the MGT c a l c u l a t i o n , of changing n. I t does not seem reasonable to assume that the s h i f t (to lower energies) 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 could be e x a c t l y c a n c e l l e d out, f o r a l l Xv, by the s h i f t (to higher energies) i n peak p o s i t i o n as n decreases 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 since such a low index i s r e q u i r e d , even at Xv ~ 0, to s h i f t the peak to 4.8 eV. Therefore, one must r u l e out the MGT d i e l e c t r i c anomaly as the source of the 4.8 eV absorption. F i g . 22 re 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 absorption peak i s observed, and the general background l e v e l of absorption i s seen to increase w i t h Xv. Therefore, one must a l s o r u l e out the EMT model as an explanation of the 4.8 eV absorption. F i g . 23 i s based on coated A l spheres In an EMT approximation f o r A1/A1N cermets. The coating m a t e r i a l was taken to have a r e f r a c t i v e index 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 arying as that of A1N, but at f i v e times the i n t e n s i t y . The value of Q ( i . e . 1 - coating 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. The r e s u l t s of F i g . 23 are seen to resemble the experimental r e s u l t s , aside from absolute absorption i n t e n s i t y , q u i t e w e l l . However, the assumption of constant Q = 0.2, regardless of Xv, means that 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 of the i n c l u s i o n radius that i s the coating m a t e r i a l remains constant at 0.8. This may or may not be a reasonable assumption. The coating of i n c l u s i o n s has, i n the past, been a t t r i b u t e d to thermodynamic e f f e c t s , such as surface t e n s i o n [ 2 ] , and used to 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 cosputtered granular metals. In these A1/A1N f i l m s , condensing A l atoms cease growing as c r y s t a l l i n e A l at - 92 -some p a r t i c u l a r c r y s t a l s i z e . According to the x-ray and TEM data 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 rates of A l and N 2 at the substrate. The absolute a r r i v a l r a t e s are, most l i k e l y , important i n t h i s respect as w e l l . A s i m i l a r s i t u a t i o n obtains f o r the growing A1N c r y s t a l s . I t i s p o s s i b l e that the "bridge" between the two types of p a r t i c l e s i s an amorphous, metal enriched A1N c o a t i n g , and that the thickness i s r e l a t e d to the i n c i d e n t f l u x of condensing atoms and i s i n some way p r o p o r t i o n a l to the p a r t i c l e s i z e s f o r some thermodynamic reason. The values of Q, n, and k f o r the coating 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 represent average values f o r t h i s "bridge" of amorphous m a t e r i a l . F i g . 24 compares the r e s u l t s of the coated sphere c a l c u l a t i o n of F i g . 23 with the data of F i g . 19, and one sees good q u a l i t a t i v e agreement. However, without f u r t h e r evidence to support the assumption of constant Q, t h i s coated sphere-EMT approximation can only be thought of as a p o s s i b i l i t y , perhaps only 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 the o r i g i n of the 4.8 eV absorption band. The remoteness of t h i s p o s s i b i l i t y becomes even more apparent when one considers that 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 , small 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. Since i t seems reasonable that Q should be r e l a t e d to both the absolute and r e l a t i v e condensation r a t e s f o r A l and N2 at the su b s t r a t e , i t seems u n l i k e l y that Pastrnak's arc discharge and the r e a c t i v e s p u t t e r i n g technique of 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 to be a l i k e l y o r i g i n f o r the 4.8 eV absorption e i t h e r . In t h i s work, the base pressures before 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, and l e s s than 10 Pa a f t e r t h r o t t l i n g . These base pressures are independent of where on the I-V c h a r a c t e r i s t i c the f i l m was deposited. Therefore, oxygen i n c o r p o r a t i o n should manifest i t s e l f i n a l l f i l m s i n an absorption peak at 4.8 eV. Measurements on f i l m s deposited i n the s t o i c h i o m e t r i c region of the I-V c h a r a c t e r i s t i c s w i t h thicknesses v a r y i n g from 300 A to 50,000 A have shown no evidence of e i t h e r browning or an absorption band at 4.8 eV. The f i l m s of t h i s work which d i s p l a y an o p t i c a l a bsorption band at 4.8 eV are a l l A1/A1N cermets where the AIN i s most l i k e l y doped w i t h excess A l atoms and/or N-vacancies and the A l i s most l i k e l y doped w i t h n i t r o g e n . I t seems l i k e l y that Pastrnak's samples have, at l e a s t , excess A l and/or N-vacancies i n an AIN matrix [66], while the p o s s i b i -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. A l s o , Noreika et a l . per-formed absorption measurements on dark brown, r f , r e a c t i v e l y sputtered AIN f i l m s [63] and obtained 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 that e i t h e r N-vacancies or included A l atoms give r i s e to the o p t i c a l absorption band at 4.8 eV i n AIN. I f the absorption band at 4.8 eV i s due to some defect s t a t e i n AIN (such as N-vacancies or A l i n t e r s t i t i a l s ) , the EMT theory should describe the o p t i c a l p r o p e r t i e s of the granular f i l m s , and the 4.8 eV band should be superimposed upon i t . I n f r a r e d r e f l e c t a n c e measurements - 94 -on these A1/A1N cermets do not support t h i s s u p p o s i t i o n very w e l l . F i g s . 25 and 26 are r e f l e c t a n c e vs. E (photon energy) curves c a l c u l a t e d i n the EMT and coated sphere-EMT approximations, r e s p e c t i v e l y , f o r A1/A1N cermets. The coated 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 to be i d e n t i c a l to that of A1N, whereas the EMT 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 increase f a i r l y r a p i d l y w i t h Xv. A c t u a l IR r e f l e c t a n c e data, 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 , are presented i n F i g . 27. The various peaks present i n these data can be a t t r i b u t e d to the quartz substrate or the A1N r e s t s t r a h l e n bands. Assuming these peaks to be superimposed upon the r e f l e c t i v i t i e s c a l c u l a t e d f o r granular A1/A1N composites, one sees, i n these data, the IR r e f l e c t i v i t y of the cermets to be very c l o s e to that of the pure A1N, 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 coated sphere-EMT approximation seems to f i t these data much c l o s e r than the EMT approximation does. However, i f the coated sphere-EMT approximation describes the o p t i c a l behavior of these f i l m s , a d i e l e c t r i c anomaly would be expected i n the o p t i c a l a b s o r p tion, and the previous d i s c u s s i o n s i n d i c a t e d that no d i e l e c t r i c anomaly i s observed. Since i t i s common that absolute magnitudes of absorption are not w e l l p r e d i c t e d by these granular t h e o r i e s [54,57], i t may be that the f i l m s are EMT-like. 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 absorption are much greater (by a / 1 0 ) than the observed - 95 -d i f f e r e n c e s reported to date [4,50-54]. The complexity of the m i c r o s t r u c t u r e of these f i l m s , however, may not be adequately accounted f o r i n any of the r e l a t i v e l y simple t h e o r i e s I have discussed i n t h i s work, since there are, undoubtedly, a great 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 bulk A l . A model which, more r e a l i s t i c a l l y , i ncorporates the true m i c r o s t r u c t u r e of these f i l m s i s , most l i k e l y , needed to a c c u r a t e l y described the o p t i c a l p r o p e r t i e s of these f i l m s . While the absorption at 4.8 eV i s most l i k e l y due to e i t h e r excess A l atoms or N-vacancies i n AIN, the coated sphere-EMT approximation f o r granular A1/A1N composites remains a remote p o s s i b i l i t y . - 96 -CHAPTER IV CONCLUSION IV.1 Reactive Sputtering Mechanisms This work has shown that two separate mechanisms are at work i n covering a s p u t t e r i n g target w i t h a r e a c t i v e gas compound l a y e r : chemisorption of r e a c t i v e gas n e u t r a l s from the s p u t t e r i n g gas and i o n p l a t i n g of r e a c t i v e gas species from the s p u t t e r i n g i o n cur r e n t . The degree to which e i t h e r mechanism c o n t r i b u t e s to target coverage w i l l depend on the 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 combination under study. However, since the chemisorption rates of most common gasses on most metals are known [82], one should be able to p r e d i c t , i n advance, which mechanism w i l l dominate. When i o n p l a t i n g i s the dominant target coverage mechanism, vol t a g e c o n t r o l of the glow discharge w i l l permit s t a b l e operation at a l l degrees of target coverage. Under these circumstances, the r a t i o of sputtered f l u x to r e a c t i v e gas molecules impinging on the substrate w i l l be a s i n g l e valued f u n c t i o n of the target v o l t a g e . Since t h i s r a t i o determines the f i l m composition [22,67], voltage c o n t r o l allows f i l m composition c o n t r o l when i o n p l a t i n g i s the dominant target coverage mechanism. Since thermodynamic co 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 defect i n a chemical system, when the sputtered f i l m becomes too d e f i c i e n t i n the r e a c t i v e gas co n s t i t u e n t p r e c i p i t a t e s of the sputtered m a t e r i a l should appear i n the 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 Is w e l l s u i t e d to the - 97 -c o n t r o l l e d composition 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 target coverage i s dominated by the i o n p l a t i n g mechanism. IV.2 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 voltage i n the manner discussed 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 c o e f f i c i e n t of r e s i s t a n c e (TCR) was seen to be zero. Therefore, the techniques of Chapter I I have a very 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 composition d e p o s i t i o n of temperature s t a b i l i z e d t h i n f i l m r e s i s t o r s . The granular nature of these f i l m s , coupled 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 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 as 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 the p e r c o l a t i o n t h r e s h o l d (Xvc). Above Xvc, i t was found that a (Xv -Xvc) f c 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 (of 1.7) f o r a 3-dimensional mixture of normal conductors. Below Xvc, conduction appears to be v i a hopping from defect to defect w i t h i n the AIN grains and a ^ (Xvc - X v ) ~ s , w i t h s = 4.3 ± .1. For mixtures of normal conductors, s i s p r e d i c t e d to be 0.7. No t h e o r e t i c a l p r e d i c t i o n s f o r s e x i s t , at present, when hopping i s the conduction mechanism because the divergence of the i n t e r p a r t i c l e (or 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 threshold i s approached, i s not known. Therefore, t h i s method of cermet f a b r i c a t i o n , which favors t h i s defect hopping conduction mechanism below Xvc, may be very 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 behaviour of the i n t e r p a r t i c l e spacing i n p e r c o l a t i o n systems. The r a t h e r t o r t u o u s l y interconnected l a b y r i n t h i a n conduction pathways i n a system near the p e r c o l a t i o n t h r e s h o l d are p r e d i c t e d [5,40,41] to give r i s e to e l e c t r o n l o c a l i z a t i o n w i t h i n the l a b y r i n t h . Again, 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 undertaking an i n depth study of p e r c o l a t i o n and e l e c t r o n l o c a l i z a t i n e f f e c t s i n t h i n f i l m s sputtered by the techniques of t h i s Ph.D. t h e s i s study. IV.2-b Optical Properties I t appears that the o p t i c a l absorption band observed at 4.8 eV, f o r .5 < Xv < .7 i n my f i l m s , i s more l i k e l y due to excess A l or N-vacancies i n AIN than to the granular geometry or, as Pastrnak has suggested, oxygen contamination. The l a c k of any observed " d i e l e c t r i c anomaly" i n the o p t i c a l absorption seems to r u l e out the MGT or coated sphere-EMT approximations 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 the A1/A1N cermets of t h i s work. However, the extremely large d i f f e r e n c e , i n magnitude, between the observed and EMT-predicted o p t i c a l absorption seems to a l s o r u l e out the EMT approximation. This l a c k of agreement probably a r i s e s because n e i t h e r of these three t h e o r i e s i s equipped to deal 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 ranging continuously from - 99 -s i n g l e atoms to c r y s t a l l i t e s w i t h bulk 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 present i n the f i l m s discussed i n t h i s work. 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B, 11, 2885 (1975). 96. M.H. Cohen, J . J o r t n e r , and I. Webman, Phys. Rev. B, J^ 7_, 4555 (1978). 97. L. Friedman, J . Non-Cryst. S o l i d s , 329 (1971). - 105 -APPENDIX ON OPTICAL CALCULATIONS In t h i s appendix, the steps i n v o l v e d i n c a l c u l a t i n g 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 s (a) and r e f l e c t i v i t i e s (R) from any of Eqns. 1-9, 1-14, or 1-15 w i l l be d e t a i l e d . This procedure may be subdivided i n t o the f o l l o w i n g four (4) steps: 1. Standard techniques are used to ob t a i n the r e a l and imaginary p a r t s of the d i e l e c t r i c constants of the c o n s t i t u t e n t m a t e r i a l s of a granular 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 imaginary parts of the d i e l e c t r i c constants of the mixture components ( c a l c u l a t e d i n step 1) are s u b s t i t u t e d i n t o e i t h e r Eqn. 1-9 or Eqn. 1-14 to obtain the e f f e c t i v e values f o r the r e a l and imaginary parts of the d i e l e c t r i c constant (e) of the mixture of the two m a t e r i a l s . 3. Using standard techniques, the mixture's e f f e c t i v e n and k values are c a l c u l a t e d from the r e a l and imaginary parts of e (obtained i n step 2). 4. a and R are then c a l c u l a t e d , by standard techniques, from the n and k values from step 3. Mathematical d e t a i l s of t h i s method, and the standard techniques, w i l l now be presented. The f o l l o w i n g expressions are some standard formulas [39] which i n t e r r e l a t e many of the o p t i c a l constants of a s i n g l e m a t e r i a l . - 106 -e x + j e 2 = |e| exp(j6) - |e|(cos9 + j s i n G ) , , 2 . 2vl/2 = ( e x + e 2) , tan 1 ( e 2 / e 1 ) . 2 2 n + k , 2nk 1/2[(E 2 + £ 2 + ^ 1 1/2 [ ( E 2 + e 2 ) 1 / 2 - 6 l ] [<n - D 2 + k 2 ] / [ ( n + l ) 2 + k 2 ] 4*k/X i n Eqns. A - l through A-5 are defined as f o l l o w s d i e l e c t r i c constant the r e a l part of E - 107 -&2 = the imaginary part 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 c o e f f i c i e n t R = the r e f l e c t i v i t y a = the absorption 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 constant of AIN i s obtained from the n and k data of F i g . 28 and Eqns. A-2 and A - l . For use i n Eqns. 1-9, 1-14, and 1-15 the d i e l e c t r i c constant of AIN i s w r i t t e n as £ i = £ i l + e i 2 = | e i | e*P^ ei)» A _ 6 where the conventions of Eqns. A - l are followed 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 are used to w r i t e the d i e l e c t r i c constant of A l as em = £ml + J £m2 = | em| e*P^QJ> A'7 where the s u b s c r i p t m stands f o r metal. Eqns. A-6 and A-7 may now be used w i t h e i t h e r of Eqns. 1-9 or 1-14 to c a l c u l a t e e f o r a granular mixture 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 coated sphere approximations f o r granular m a t e r i a l s w i l l now be discussed. - 108 -Fig. 28 .275 .1375 -O p t i c a l constants f o r A1N. The r e f r a c t i v e i n d i c e s (n) are from data of Pastrnak et a l . [59], while 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 absorption data 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 constants of A l from the data of Powell [80], - 110 -The MGT 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 permits, extensive rearrangement, e to be w r i t t e n as e = (A + jB ) / ( C + JD), where and A = 2Xv(R x - + R x + 2R 2, B = 2Xv(I^ - I 2 ) + II + 2 I 2 , C = X v ( e i l - £ m l ) + e m l + 2 e i l ' D = X v ( e i 2 - Sn2> + em2 + 2 e i 2 > R l e i l e m l e i 2 e m 2 ' p _ 2 _ 2 2 e i l e i 2 - I l l -X l = e i 2 eml + e i l em2' A-8-h I 2 = 2 £ i l e i 2 A - 8 - i The r e s u l t s of Eqns. A-8 allow and t o D e w r i t t e n as el = (AC + BD)/(C 2 - D 2) A-9-a and e 2 = (BC - AD)/(C 2 - D 2) A-9-b Equations A-9 may then be used i n concert w i t h Eqns. A-3, A-4, and A-5 to 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 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| exp(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 -Since ( e x p ( j 9 ) } ^ ^ has three (3) s o l u t i o n s i t i s apparent that Eqn. A-10 has more than one s o l u t i o n . However, only one of the s o l u t i o n s to Eqn. A-10 s a t i s f i e s the p h y s i c a l requirement of being symmetric w i t h respect to the r o l e s of the two types of p a r t i c l e s . Therefore, 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 - Xv) 3 | e . | e x p ( j 9 1 ) + X v ^ e J e x p ( j 9 m ) + 3Xv(l - X v ) 2 l e . | 2 / 3 e | 1 / 3 exp{i(29. + 9 )/3} | 11 m| r i J l m ' + 3Xv 2 (1 - Xv) | e ± | 1 / 3 | e m | 2 / 3 e x p { j ( 9 i + 2QJ/3.}. A - l l Using the i d e n t i t y exp(j9) = cos9 + j s i n 9 i n Eqn. A - l l allows the r e a l and imaginary parts of e to be w r i t t e n as e = (1 - x v ) 3 | e i | c o s C j g ^ + x v 3 | e m | c o s ( j 9 m ) + 3Xv(l - X v ) 2 | e J 2 / 3 |e | 1 / 3 cos (j (20, + 9 )/3} [ 11 I m| I m + 3Xv 2 (1 - Xv) | e ± | 1 / 3 | e m | 2 / 3 c o s { j ( 9 1 + 20 m)/3}. A-12-a and e = (1 - Xv) 3Ie. I s i n ( j 9,) + X v 3 I e I s i n ( j 9 ) | i | i I m| m + 3Xv(l - X v ) 2 | e J 2 / 3 |e | 1 / 3 s i n { j ( 2 9 4 + 9 )/3} I i I | m| i m + 3Xv Z (1 - Xv) | e j 1 / 3 |e 1 s i n l j ( 9 , + 29 )/3}. A-12-b | i| I m l J i m J 2/3 - 113 -Eqns. A-12 may be used i n concert w i t h Eqns. A-3, A-4, and A-5 to 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 approximation i s used i n conjunction w i t h e i t h e r the MGT or EMT approximations. The only m o d i f i c a t i o n being t h a t , i n Eqns. A-9 or A-12, e i t h e r or both of or e r a are replaced w i t h the e f f e c t i v e d i e l e c t r i c constant f o r a sphere of the o r i g i n a l m a t e r i a l (1 or m) that i s coated w i t h a l a y e r 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 constant f o r such a sphere i s c a l c u l a t e d i n the MGT approximation where the coating m a t e r i a l i s taken as the amorphous d i e l e c t r i c matrix that the o r i g i n a l sphere i s embedded i n . With the e f f e c t i v e d i e l e c t r i c constants f o r coated spheres i n place of the uncoated sphere d i e l e c t r i c constants, a random d i s t r i b u t i o n of two types of coated spheres i s t r e a t e d i n the EMT approximation (Eqns. 1-14 and A-12), while a random d i s t r i b u t i o n of one type of coated sphere embedded i n an amorphous matrix of another m a t e r i a l Is t r e a t e d i n the MGT approximation (Eqns. 1-9 and A-9). 

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