Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Preparation of thin insulating films by plasma anodization Olive, Graham 1969

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1970_A7 O45.pdf [ 3.53MB ]
Metadata
JSON: 831-1.0101999.json
JSON-LD: 831-1.0101999-ld.json
RDF/XML (Pretty): 831-1.0101999-rdf.xml
RDF/JSON: 831-1.0101999-rdf.json
Turtle: 831-1.0101999-turtle.txt
N-Triples: 831-1.0101999-rdf-ntriples.txt
Original Record: 831-1.0101999-source.json
Full Text
831-1.0101999-fulltext.txt
Citation
831-1.0101999.ris

Full Text

PREPARATION OF THIN INSULATING FILMS BY PLASMA ANODIZATION by GRAHAM OLIVE B.Sc. Brunei U n i v e r s i t y , 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept t h i s t h e s i s as conforming to the required standard Research Supervisor # Members of the Committee Act i n g Head of the Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA December, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date g y W . V u ^ ABSTRACT The plasma anodization of p o l y c r y s t a l l i n e niobium samples has been undertaken using a d.c. glow discharge i n oxygen. The apparatus used, which has f a c i l i t i e s f o r i n s i t u e l l i p s o m e t r y measurements and sample temperature c o n t r o l , i s described. Anodizations were c a r r i e d out at various constant current d e n s i t i e s up to 1 . 5 mA cm , and Langmuir probes were used to estimate the v o l t drop across the oxide during growth. The e l l i p s o m e t r y measurements y i e l d oxide thickness and r e f r a c -t i v e index, and i n d i c a t e that the f i l m s have a two-layer s t r u c t u r e . Ionic currents are c a l c u l a t e d from growth rates using Faraday's Law. Ionic current and oxide f i e l d s trength data are analyzed and compared w i t h published s o l u t i o n anodiz-a t i o n r e s u l t s on the basis of the c l a s s i c a l model of i o n i c conduction at high f i e l d strengths. The p e r m i t t i v i t y and l o s s f a c t o r of the oxide f i l m s are deduced from bridge measurements on c a p a c i t o r s t r u c t u r e s produced by d e p o s i t i n g counterelectrodes on the oxide surface. The i n t r o d u c t i o n of water i n t o the d i s -charge was i n v e s t i g a t e d , and found to a f f e c t the oxide growth r a t e . i TABLE OF CONTENTS -D ABSTRACT i TABLE OF CONTENTS i i LIST OF ILLUSTRATIONS i i ACKNOWLEDGEMENT v 1. INTRODUCTION 1 2 . BACKGROUND AND THEORY 3 3. D . C . DISCHARGE EXPERIMENTS 9 3-1 Apparatus 9 3.2 Exper imenta l Procedure i 14 3 .2 .1 Thickness Determinat ion 18 3 .2 .2 Oxide F i e l d S t rength Determinat ion 20 (1) I n t e g r a l F i e l d 20 (2) D i f f e r e n t i a l F i e l d . 20 ' 3 . 2 .3 Ion ic Current Determinat ion 21 3 .2 .4 R e l a t i v e P e r m i t t i v i t y and Loss Fac tor 22 3.3 Resu l t s 22 3-3.1 E l l i p s o m e t r y 23 3 .3 .2 Oxide F i e l d S t rength Es t ima t ions 26 3 .3 .3 P e r m i t t i v i t y and Less Fac to r 38 3 .3 .4 The I n t r o d u c t i o n of Water to the D i s c h a r g e . . . 4 2 4. DISCUSSION 48 5. CONCLUSION 52 APPENDIX I C l a s s i c a l Theory of I o n i c Conduction i n S o l i d s at High F i e l d Strengths 54 APPENDIX I I E l l i p s o m e t r i c Method of Measuring Thickness and R e f r a c t i v e Index of Thin F i lms Grown on R e f l e c t -i n g Surfaces 56 APPENDIX I I I . Measurements u s ing Plasma Probes 61 APPENDIX IV Langmuir Probe Theory f o r Plane Probe i n the Absence of Negat ive Ions 64 REFERENCES 68 i i LIST OF ILLUSTRATIONS Figure Page 1 A n o d i z a t i o n arrangement 2 2 The d . c . glow discharge 5 3 Schematic of d ischarge c e l l and e l l i p s o m e t e r 10 4 Schematic of vacuum system 13 5 Discharge and a n o d i z i n g current c i r c u i t s 15 6 Vol tage measuring c i r c u i t 15 7 Capacitance br idge bas i c c i r c u i t 19 o 8 E l l i p s o m e t r y r e s u l t s f o r sample 1 at 0Q = 65 , \ = 5461A..24 o 0 9 E l l i p s o m e t r y r e s u l t s f o r sample 2 at 0 q = 65 , \ = 5461A..25 10 T y p i c a l v a r i a t i o n of sample p o t e n t i a l w i th respect to a f l o a t i n g probe dur ing a format ion 30 11 ' T a f e l ' p l o t f o r sample 2 . . . 31 12 ' T a f e l ' p l o t f o r sample 3 33 13- Composite ' T a f e l ' p l o t w i t h data from samples 1, 2 and 3-«34 14. T y p i c a l c o r r e c t i o n p l o t f o r 0.5 mA formations on sample I . 3 6 15. T y p i c a l c o r r e c t i o n p l o t f o r 1 mA formations on sample 3 - • • 3 7 16. C i r c u i t used to ob ta in sample and probe cu r r en t -vo l t age c h a r a c t e r i s t i c s 39 17. C h a r a c t e r i s t i c of a tantalum wi re probe 40 2 18. C h a r a c t e r i s t i c of a niobium sample, area ~ 1 cm 41 19. System used to feed oxygen/water mixture to d i scharge c e l l 44 20. R . G . A . output scan t y p i c a l of dry oxygen formations 45 21. R . G . A . output scan du r ing format ion 3 on sample 3 45 22. R . G . A . output scans f o r format ion 4 on sample 3 46 i i i "Figure Page 23. R.G-.A. output scan d u r i n g f o r m a t i o n 6 on sample 3 47 24. Supposed p o t e n t i a l energy of i o n v e r s u s d i s t a n c e •with and w i t h o u t an a p p l i e d f i e l d 55 25. Computed e l l i p s o m e t r y curve f o r s i n g l e f i l m (N^ = 2.25) on n i o b i u m (N = 3.6 - J3-6) a t 0q = 65° and X o = 5461 A 58 26. Two l a y e r model 59 27. I d e a l c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of a Langmuir probe 66 i v ACKNOWLEDGEMENT The a u t h o r wishes t o expr e s s h i s g r a t i t u d e f o r the encouragement and guidance r e c e i v e d from Dr. L. Young t h r o u g h -out t h i s i n v e s t i g a t i o n . The a u t h o r i s a l s o i n d e b t e d t o Dr. D.L. P u l f r e y f o r h i s c o n s i d e r a b l e h e l p and f o r r e a d i n g the m a n u s c r i p t , t o Mr. C.J. D e l l ' O c a f o r guidance i n u s i n g h i s computer programs, and t o b o t h f o r many v a l u a b l e d i s c u s s i o n s . G r a t e f u l acknowledgement i s made of the t e c h n i c a l a s s i s t a n c e r e c e i v e d from Messrs. J . Stuber and A. MacKenzie, and the a u t h o r a l s o thanks h i s w i f e f o r her p a t i e n c e , Messrs. N. Taneja, T. Tucker and G. Yan f o r p r o o f r e a d i n g , and Mrs. V. A l e x a n d e r f o r t y p i n g the t h e s i s . The a u t h o r i s g r a t e f u l f o r the f i n a n c i a l s u p p o r t r e c e i v e d from the Defence R e s e a r c h Board and the U.S. A i r Force ( c o n t r a c t 7 0 C 3 - 6 7 - 3 ) , and the N a t i o n a l Research C o u n c i l ( o p e r a t i n g g r a n t NRCA-3392 and a p o s t • g r a d u a t e s c h o l a r s h i p ) . v 1 1. INTRODUCTION In recent years t h i n d i e l e c t r i c f i l m s have found wide a p p l i c a t i o n i n the m i c r o e l e c t r o n i c device f i e l d s , p a r t i c u l a r l y s i l i c o n d i o x i d e f i l m s i n s i l i c o n a c t i v e device technology and tantalum pentoxide f i l m s i n passive t h i n f i l m m i c r o c i r c u i t r y . The accumulation of knowledge on systems c o n t a i n i n g these f i l m s has l e d to a d e t a i l e d understanding of t h e i r p r o p e r t i e s , inherent l i m i t a t i o n s and problems associated w i t h production methods. The disadvantages have prompted studies of other d i e l e c t r i c s and new methods of p r e p a r a t i o n , p a r t i c u l a r l y those which would allow automated production of i n t e g r a t e d devices i n a m u l t i s t a t i o n vacuum system. Plasma a n o d i z a t i o n i s one such technique f o r the formation of d i e l e c t r i c f i l m s from metals or semiconductors which should s a t i s f y the above requirement. The p r i n c i p l e of the tech-nique i s s i m i l a r to that of a n o d i z a t i o n i n an aqueous e l e c t r o l y t e , namely the m a t e r i a l - t o be anodized i s exposed to a medium con t a i n -i n g i o n i z e d reactant species and biased p o s i t i v e l y with respect to t h i s medium, which i s a gaseous plasma i n the case of plasma ano d i z a t i o n - see f i g . 1. This process allows the growth of f i l m s which are s o l u b l e i n the usual a n o d i z a t i o n e l e c t r o l y t e s , and i t s r e l a t i v e l y low temperature o f f e r s considerable advantages over thermal o x i d a t i o n i n a c t i v e device f a b r i c a t i o n . Being a vacuum technique i t i s compatible w i t h other t h i n f i l m technology processes, and promises e a s i e r c o n t r o l over contamination than e i t h e r wet anodization or thermal o x i d a t i o n . The plasma anodization process has been i n v e s t i g a t e d since 1962, but the mechanisms involved are s t i l l l i t t l e 2 METAL (ANODE) OXIDE ELECTROLYTE SOLUTION OR OXYGEN PLASMA CA THODE F i g . 1 Anodization arrangement understood. The p r i m a r y aim of the work d e s c r i b e d i n t h i s t h e s i s was to c l a r i f y the n a t u r e of the growth mechanisms; i n a d d i t i o n i t was hoiJed t o i n v e s t i g a t e the c a p a b i l i t i e s of d i f f e r e n t plasma a n o d i z a t i o n t e c h n i q u e s as methods of p r o d u c i n g t h i n d i e l e c t r i c f i l m s f o r t h e m i c r o e l e c t r o n i c s t e c h n o l o g y . For the f i r s t problem, the growth of a n o d i c oxide f i l m s on n i o b i u m i n a d.c. low p r e s s u r e oxygen glow d i s c h a r g e was i n v e s t i g a t e d . Towards t h e second problem the d e s i g n and i n i t i a l c o n s t r u c t i o n of improved systems, one employing r . f . e x c i t a t i o n , the o t h e r a t h e r m i o n i c cathode d.c. d i s c h a r g e , has been commenced. 2. BACKGROUND AND THEORY Many s t u d i e s of the plasma a n o d i z a t i o n p r o c e s s have u t i l i z e d the f a m i l i a r and e a s i l y produced d.c. low p r e s s u r e glow d i s c h a r g e i n oxygen"'" ^ but gaseous plasmas can be produced by 7 8 9 v a r i o u s means, and r . f . and microwave ' e x c i t a t i o n of 0^ plasmas have a l s o .been used. The range of m e t a l s and s e m i c o n d u c t o r s which have been a n o d i z e d by t h i s method i n c l u d e s A l , Ta, Cr, Sb, B i , Be, Ge, S i , T i , Z r , L a - T i and GaAs, and the t e c h n i q u e has a l r e a d y been a p p l i e d to the f a b r i c a t i o n of t h i n f i l m c a p a c i t o r s and b o t h s i l i c o n and t h i n f i l m CdSe E.E.T.'s w i t h a n o d i c aluminum o x i d e 1 4- A -u 10,11 i n s u l a t e d g a t e s . ' These i n v e s t i g a t i o n s , some of which a r e r e f e r r e d to i n 1? more d e t a i l i n a r e c e n t r e v i e w paper ~ , e s t a b l i s h e d the g e n e r a l l y low c u r r e n t e f f i c i e n c y of plasma a n o d i z a t i o n compared w i t h wet anodiza.tio.n, but a d e t a i l e d t h e o r y of the mechanism of a n o d i c growth i n plasmas has not been f o r m u l a t e d y e t . By analogy w i t h wet a n o d i z a t i o n , i t might be argued that both oxide growth processes proceed by v i r t u e of the same fundamental mechanism -the f i e l d a s s i s t e d migration of p o s i t i v e l y charged metal and/or n e g a t i v e l y charged oxygen ions through the otherwise o x i d a t i o n -i n h i b i t i n g oxide f i l m , i . e . , i o n i c conduction at high f i e l d 12 strengths. However, the f a c t that high growth r a t e s can be •5 9 achieved i n some dense plasmas ' i n s p i t e of the low current e f f i c i e n c i e s suggests that the concentration of some e x c i t e d species at the o x i d e - e l e c t r o l y t e i n t e r f a c e may be the c o n t r o l l i n g f a c t o r , e s p e c i a l l y since growth r a t e s of the same high order were obtained without b i a s i n g the sample w i t h respect to the plasma. The d e n s i t y d i s t r i b u t i o n s of the various species of i o n i z e d oxygen i n a d.c. glow discharge cannot be pr e d i c t e d w i t h c e r t a i n t y , since they depend markedly on the presence of v a r i o u s i m p u r i t i e s . Negatively charged oxygen ions are p a r t i c u l a r l y d i f f i c u l t to detect since they have no c l e a r l y i d e n t i f i a b l e 13 emission spectrum, although i t i s known that the e l e c t r o n attachment process by which they can be created has a maximum c r o s s - s e c t i o n f o r e l e c t r o n s of energy 6.5 ev, and t h i s may be taken i n t o c o n s i d e r a t i o n when s e l e c t i n g the region of the d i s -charge to be used as the source of i o n i z e d reactant species. The.main regions of the d.c. cold cathode discharge, as shown i n f i g . 2, are the Crookes dark space, the negative glow, the Faraday dark space, and the p o s i t i v e column. Electrons are emitted from the cathode mainly by p o s i t i v e i o n bombardment ."^ The e l e c t r o n s form a negative space charge close to the cathode s u r f a c e , but are then ac c e l e r a t e d by the e l e c t r i c f i e l d , and some bf them cause excitation of gas molecules, g i v i n g r i s e to the cathode glow. The high density of incoming p o s i t i v e ions r e s u l t s i n a l a r g e net p o s i t i v e space charge extending through the Crookes dark space and electrons are accelerated s u f f i c i e n t l y by the associated voltage "gradient such that they produce intense i o n i z a t i o n and hence m u l t i p l i c a t i o n . Beyond the end of the Crookes dark space, the e l e c t r o n d e n s i t y increases so much that the net space charge becomes negative, the f i e l d r e v e r s i n g and remaining s m a l l . Thus i n t h i s next re g i o n the e l e c t r o n s do not a c c e l e r a t e but l o s e t h e i r energy by ' " c o l l i s i o n i o n i z a t i o n and e x c i t a t i o n , g i v i n g the negative glow. As the e l e c t r o n s are slowed down the negative space charge reaches a maximum, the e x c i t a t i o n f a l l s o f f and the Faraday dark space begins. The e l e c t r o n d e n s i t y decreases by recombination and d i f f u s i o n i n the dark space u n t i l the space charge becomes zero again and the f i e l d r i s e s to a constant small value, a c c e l e r a t i n g the e l e c t r o n s once more and producing the p o s i t i v e column. The f i e l d i n the l a t t e r assumes a value, t y p i c a l l y of the order of 1 vcm \ j u s t s u f f i c i e n t to maintain along the l e n g t h of the column the degree of i o n i z a t i o n r e quired to carry the d i s -charge current. The r e s u l t i n g column of i o n i z e d gas con-s t i t u t e s a plasma, as does the negative glow r e g i o n , but the net space charge i s smaller i n the p o s i t i v e column, i . e . the concentrations of p o s i t i v e ions and e l e c t r o n s are more nea r l y equal. A survey of previous plasma an o d i z a t i o n experiments 7 does not y i e l d conc lus ive evidence of an optimum r e g i o n of the d ischarge f o r a n o d i z a t i o n . The absence of growth on samples biased n e g a t i v e l y w i t h respect to the adjacent glow discharge r e g i o n may i n d i c a t e that some form of n e g a t i v e l y charged oxygen ion. i s important i n the growth process . I f t h i s i s so , however, i t appears tha t t h i s charged species i s not abundantly a v a i l a b l e i n the r e l a t i v e l y weakly i o n i z e d plasma of a c o l d cathode d . c . glow d i scha rge , w i t h which only very slow growth r a t e s , of the o order of 2 A / m i n , have been recorded . 15 15 Accord ing to F r a n c i s , e l e c t r o n d e n s i t i e s of 10 cm ' are not uncommon i n h igh frequency d ischarges (by v i r t u e of the reduced l o s se s to w a l l s or e l e c t r o d e s ) . This i s a f a c t o r of 10 h igher than i n the d . c . d i scha rge , and the assoc ia ted increase i n degree of i o n i z a t i o n of the ga.s would be expected to produce increased anodizs . t ion r a t e s p a r t i c u l a r l y i f the lower breakdown f i e l d , fo r a . c . breakdown resul ted, i n more e l ec t rons of the lower energies appropr ia te f o r e l e c t r o n attachment. Operat ing at the h igher pressures p o s s i b l e w i t h h . f . d ischarges should a l s o inc rease the negat ive i o n y i e l d of the attachment p rocess . o Growth ra tes as h igh as 6,000 A / h r have been, repor ted for the a n o d i z a t i o n of s i l i c o n i n plasmas e x c i t e d by a 2.45 kMHz m i c r o -9 wave genera tor . Another advantage of h igh frequency induced plasmas i s the absence of i n t e r n a l d i s c h a r g e - s u s t a i n i n g e l e c t r o d e s , which can be a. major source of f i l m contaminat ion by s p u t t e r i n g . Except fo r r e s u l t s on h . f . plasma a n o d i z a t i o n of Si-i n d i c a t i n g a d i f f u s i o n c o n t r o l l e d process*"', pub l i shed data p e r t a i n i n g to growth mechanisms has l a r g e l y been confined tc the 'anodization constant 1 or inverse e l e c t r i c f i e l d , i . e . f i n a l t hickness d i v i d e d by f i n a l v oltage. In any i n v e s t i g a t i o n of the growth mechanisms involved i n plasma an o d i z a t i o n , measurement of oxide thickness i s obviously of prime importance, and i t i s h i g h l y d e s i r a b l e to obtain data on i o n i c currents as functions of f i e l d i n the oxide during growth,' w i t h temperature as parameter, to t e s t f o r an i o n i c conduction mechanism s i m i l a r to that observed during the wet a n o d i z a t i o n process - see A-ppendix I. The i o n i c current can be c a l c u l a t e d from Faraday's Law i f the time rate of increase i n oxide thickness i s known. C a l c u l a t i o n of the f i e l d i n the oxide r e q u i r e s knowledge of the r e l a t i v e p o t e n t i a l s of the metal/ oxide and oxide/plasma i n t e r f a c e s . In p a r t i c u l a r , c o n s i d e r a t i o n should be given to the f o l l o w i n g : (1) Preparation of the substrate surface. (2) Pressure and p u r i t y of the gas or gas mixture to be i o n i z e d . (3) Ion and e l e c t r o n d e n s i t y and energy d i s t r i b u t i o n s i n the plasma. (4) Plasma s t a b i l i t y and conditions to be held constant during growth. (5) Contamination by s p u t t e r i n g from electrodes and/or w a l l s . fThe presence of water vapour i n the o x i d i z i n g ambient i s known to increase the thermal o x i d a t i o n rate of s i l i c o n . v „ 17 Experience w i t h wet anodization ha.s shown that i n c o r p o r a t i o n of i m p u r i t i e s during oxide growth can have a s i g n i f i c a n t e f f e c t on f i l m p r o p e r t i e s , and i n plasma anodization major discrepancies i n f i l m thickness can be produced by contamination w i t h m a t e r i a l sputtered from electrodes.6 9 (6) Substrate temperature measurement and c o n t r o l . (7) Measurement and c o n t r o l of anodizing current, and substrate p o t e n t i a l with respect to the plasma. (S) Measurement of oxide t h i c k n e s s . O p t i c a l methods are p a r t i c u l a r l y u s e f u l f o r determin-i n g the thickness of t h i n f i l m s , and the technique of e l l i p s o m e t r y 18—20 has been a p p l i e d e x t e n s i v e l y to anodic f i l m s as i t enables both thickness and r e f r a c t i v e index*to be determined. In p r i n c i p l e the method Involves having e l l i p t i c a l l y p o l a r i z e d l i g h t i n c i d e n t at a known oblique angle on the f i l m , grown on a r e f l e c t -i n g substrate surface, and determining the q u a n t i t i e s and A which are measures of the r e l a t i v e changes i n amplitude and phase r e s p e c t i v e l y which occur when the l i g h t i s r e f l e c t e d . These changes are r e l a t e d to the o p t i c a l constants of the f i l m and surface, f i l m t h i c k n e s s , angle of incidence, and wavelength. More d e t a i l s are given i n Appendix I I . 3. D.C. DISCHARGE EXPERIMENTS 5.1 Apparatus The d.c. glow discharge equipment used i n t h i s study had been designed to provide substrate temperature c o n t r o l and allow e l l i p s o m e t r y measurements to be made on plasma-anodized f i l m s i n s i t u i n the plasma producing apparatus. R e f e r r i n g to f i g . 3» the sample substrate (S) i s secured to a water cooled W R o H TS P>LAMP X FIL TER COLLIMATOR XPOLARIZER Xo.W PLATE h-ySULJUULs ) y ANALYZER 7"EL E SCOPE PHOTOMULTIPL/ER F i g . 3 Schematic of discharge c e l l and e l l i p s o m e t e r H o s t a i n l e s s s t e e l holder (H) w i t h a glass-enclosed thermistor (T) i n a recess j u s t beneath the sample to obtain a measure of the sample temperature. The l a t t e r i s c o n t r o l l e d by c o n t r o l l i n g the temperature of a b a l l a s t water volume. The substrate holder i s suspended i n a 5 c m diameter c y l i n d r i c a l Pyre>: discharge tube which i s provided with o p t i c a l l y f l a t windows ( 0 ) near the sub-s t r a t e holder and can be p o s i t i o n e d between the arms of a Gaertner model L 1 1 9 e l l i p s o m e t e r . The substrate surface i s nominally perpendicular to the tube a x i s and'can be t i l t e d by a feedthrough u n i t to f a c i l i t a t e alignment on the e l l i p s o m e t e r a x i s . L i g h t o of wavelength 5 4 6 1 A f i l t e r e d from a mercury arc lamp i s mechan-i c a l l y chopped at 1 4 7 0 Hz before e n t e r i n g the e l l i p s o m e t e r c o l l i m a t o r . The c c l l i m a t e d beam i s i n c i d e n t on the sample surface at an angle of 6 5 ° and the r e f l e c t e d l i g h t transmitted by the analyzer i s detected by an RCA type 9 3 1 A p h o t o m u l t i p l i e r tube, the s i g n a l from which i s fed to a tuned a m p l i f i e r (G.R. 1 2 3 2 A ) . The discharge i s struck between 9 9 . 9 9 9 % pure A l d i s c s (R), t h i s metal being chosen because of i t s low s p u t t e r i n g y i e l d when protected by i t s oxide. Movement of the electrodes i n the discbarge tube u s i n g e x t e r n a l magnets a c t i n g on a s o f t i r o n l u g i s f a c i l i t a t e d by h e l i c a l wound e l e c t r i c a l leads (¥), so that the desired region of the discharge may be l o c a t e d around the sample. The cathode i s of the inverse brush geometry having a c l o s e l y spaced uniform array of holes d r i l l e d i n t o i t s surface. This design gives b e t t e r s t a b i l i t y by e l i m i n a t i n g i l l - d e f i n e d mobile 'hot-spots', and increased current d e n s i t y by v i r t u e of the l a r g e surface area at a g r a z i n g angle to the incoming ions which cause secondary e l e c t r o n emission. " E l e c t r i c a l connection to the sample i s made by spot welding a glas s i n s u l a t e d lead to a tab on the sample. E l e c t r i c a l probes, i n s u l a t e d by glass except f o r t h e i r t i p s , can also be i n s e r t e d i n t o the d i s -charge tube i n the v i c i n i t y of the sample to gain information on l o c a l f l o a t i n g p o t e n t i a l s , e l e c t r o n d e n s i t i e s and tempera-tures . The oxygen gas u s e d + has a nominal p u r i t y of 99-999% and i s admitted to the system through a leak valve which can be servo operated - see f i g . 4. The system can be operated i n the dynamic flow mode, wit h c o n t i n u a l pumping by a s o r p t i o n pump to reduce the b u i l d up i n the ga.s of i m p u r i t i e s l i b e r a t e d from the w a l l s by energetic species i n the discharge. Gaseous contamin-a t i o n can be detected w i t h a QUAD 150A Residual Gas Analyzer provided w i t h i t s own i o n pump ( f i g . 4), and o p t i c a l emission spectroscopy u s i n g a J a r r e l Ash monochromator and p h o t o m u l t i p l i e r can be employed to i d e n t i f y the presence of various molecular and i o n i c species. Automa.tic c o n t r o l of the oxygen pressure to - 1% of the set value may be achieved by a G r a n v i l l e - P h i l l i p s capacitance manometer and associated c o n t r o l u n i t which operates the leak v a l v e . Pressure c o n t r o l to t h i s tolerance i s necessary as changes of 10 mtorr around 1 t o r r have been recorded by 2 Langmuir probes to change the plasma f l o a t i n g p o t e n t i a l by 1.5 v o l t s . I t may be more relev a n t to hold t h i s l a t t e r property of ^ F l o a t i n g or w a l l p o t e n t i a l i s defined as the p o t e n t i a l of a probe l o c a t e d i n the region i n question when the probe i s i s o l a t e d , i . e . drawing zero net current. +Matheson Research Grade. CAPACITOR MANOMETER SORPTION PUMP FROM OXYGEN FEED SYSTEM ELLIPSOMETER AXIS DISCHARGE ELECTRODE F i g . 4 Schematic of vacuum system 14 the discharge (measured near the sample) constant during an anod i z a t i o n , r a t h e r than the pressure as i n d i c a t e d by an e l e c t r o -mechanical instrument. In l a t e r experiments, a thermocouple gauge was al s o used as a check on the capacitance manometer. Copper gaskets are used at a l l j o i n t s and the e n t i r e system can be baked to around 400°C. Pumping with the s o r p t i o n pump followed by a d i f f e r e n t i a l i o n pump and baking at 100°C -9 has enabled base pressures b e t t e r than 1 x 10 t o r r to be achieved. The main e l e c t r i c a l discharge c i r c u i t i s shown i n f i g . 5 together w i t h the c i r c u i t i n c o r p o r a t i n g an e l e c t r o n i c constant current generator (Northeast S c i e n t i f i c model RI 233) which i s used to bias the sample f o r constant current anodiza-t i o n . To monitor sample and probe p o t e n t i a l s , two i s o l a t e d high input impedance electrometers ( K e i t h l e y model 602) with appropriate back-off voltage supplies are used to generate inputs to a chart recorder (Moseley model 7100 BM) as shown i n f i g . 6. 3.2 Experimental Procedure The samples used i n t h i s work were cut from a c o l d -r o l l e d 0.050 i n . t h i c k sheet of c a p a c i t o r grade p o l y c r y s t a l l i n e niobium, supplied by Fans t e e l . The sample dimensions were 3/8 i n . square, w i t h a l / l 6 i n . wide p r o t r u d i n g stub f o r welding an e l e c t r i c a l connection. The surface to be anodized was f i r s t mechanically abraded on emery papers to 4/0 grade, and then 4kv VARIABLE SUPPLY 180 KJX A A A -/ CATHODE ' t N 5juf SAMPLE ANODE 1 c \ \ 777777 CONSTANT CURRENT GENERATOR 15 F i g . 5 Discharge and anodizing current c i r c u i t s SAMPLE PROBE i i-^ T O CONSTANT CURRENT GENERATOR + 40 v VARIABLE SUPPLY EL'R VOLTME TER \ 1 — 1 \ V. 1 ' / / y + 1kv VARIABLE SUPPLY EL }R 'VOLTMETER 7/J in CHART RECORDER F i g . 6 Voltage measuring c i r c u i t •X-e l e c t r o p o l i s h e d to g ive good o p t i c a l r e f l e c t i v i t y . For samples 1 and 2, a p o l i s h i n g s o l u t i o n of' 8 par t s 48% HF, 92 par t s 96% H^SO^ was used (wi th a c e l l vo l t age of ~12 v o l t s ) fo r about 30 m i n s . , but w i t h sample 3, an a l t e r n a t i v e mixture of 18 par ts 48% HF, 34 par t s 96% H 2 S0^ and 48 par t s l a c t i c a c i d used f o r 22 only 15 minutes gave b e t t e r r e f l e c t i v i t y . The e l e c t r o p o l i s h i n g was fo l lowed by a r i n s e i n d i s t i l l e d water , and i n the case of sample 3, a 10 second e tch i n 48% HF fo l lowed by another d i s - -t i l l e d water r i n s e . Mounting of the p o l i s h e d sample cn the wa te r -coo led ho lde r was accomplished by us ing a s m a l l drop of U l t e k h igh vacuum epoxy r e s i n a.nd a very t h i n wafer of mica sheet to e l e c t r i c a l l y i n s u l a t e the sample from the h o l d e r . The mounted sample was then p o s i t i o n e d on the e l l i p s o m e t e r a x i s i n the d i s -charge tube w i t h one or more probes of tantalum or tungsten wi re l o c a t e d c lose to but not touch ing the surface under exam-i n a t i o n , the l a t t e r f a c i n g the anode (otherwise m a t e r i a l sput te red from the cathode could contaminate the growing f i l m ^ ) . The sample surface was then a l i g n e d on the e l l i p s o m e t e r a x i s , and the system pumped by f i r s t the s o r p t i o n pump and then the d i f f e r e n t i a l i o n pump u n t i l a base pressure of around 10 t o r r was ob ta ined . This could be improved by bak ing i f d e s i r e d . At t h i s stage e l l i p s o m e t e r readings were taken w i t h the sub-s t r a t e i n i t s a s - p o l i s h e d c o n d i t i o n , i . e . w i t h an i n i t i a l oxide *Sing le c r y s t a l niobium, i s known to g ive b e t t e r o p t i c a l r e f l e c t -i v i t y on e l e c t r o p o l i s h i n g . S ing le c r y s t a l m a t e r i a l was not r e c e i v e d i n time f o r these s t u d i e s , but w i l l be used i n fu ture work. !7 o l a y e r a few tens of A t h i c k . The thickness of t h i s i n i t i a l f i l m of oxide may be deduced from the computed f i t to the f ina l e l l i p s o m e t e r curve - see s e c t i o n 3-3-1-The pumping f u n c t i o n was then returned to the s o r p t i o n pump i n order to Gperate i n the dynamic flow mode at a constant-pressure around 60 mTorr by c o n t i n u a l l y l e a k i n g oxygen through the s e r v o - c o n t r o l l e d valve.. ( A l t e r n a t i v e pressure c o n t r o l by manual operation of both the servo valve and the s i m i l a r l e a k valve at the s o r p t i o n pump proved to be quite f e a s i b l e , and was given preference f o r specimens 2 & 3 since i t enabled f i n e c o n t r o l over a probe f l o a t i n g p o t e n t i a l w i t h respect to the anode). With de s i r e d pressure e s t a b l i s h e d , the discharge was stru c k and i t s current adjusted, u s u a l l y to 10mA. A l l samples were l o c a t e d near the cathode end of the negative glow. When the l a t t e r was s t a b l e w i t h reasonable noise l e v e l as i n d i c a t e d by probe voltage s i g n a l s and wit h the substrate holder temper-ature c o n t r o l l e d (at 30°C t 1°C) by the water c i r c u l a t i o n , the constant current supply was connected to the sample and the plasma an o d i z a t i o n c a r r i e d out f o r a s u i t a b l e time. The p o t e n t i a l d i f f e r e n c e between the substrate and an adjacent f l o a t i n g probe, and the p o t e n t i a l of the probe with respect to the anode, were monitored on the chart recorder p r i o r t o , throughout and j u s t a f t e r the anodic formation. R.G.A. scans were obtained at s u i t a b l e times to assess any changes i n gas c o n s t i t u e n t s . In general, substrates were subjected to a s e r i e s of successive oxide formations at various t o t a l current l e v e l s i n 18 the range 0.1mA to 1.5mA i n order to obtain data on anodization at s e v e r a l d i f f e r e n t oxide f i e l d strengths and i o n i c current d e n s i t i e s . Sets of e l l i p s o m e t e r readings were taken i n s i t u between each formation, the system being maintained under vacuum. Measurements were made i n a l l four zones to minimize e r r o r s due to p o l a r i z a t i o n of the l i g h t by the c e l l windows. A f t e r s u f f i c i e n t points had been obtained, and the des i r e d thickness reached, the substrate was removed from the c e l l and e l l i p s o m e t e r readings taken over the oxide surface i n a i r . The sample was then t r a n s f e r r e d to a vacuum d e p o s i t i o n apparatus (Veeco 400), i n which an array of gold counterelectrodes approximately 0.68 mm o i n diameter,1000A t h i c k was evaporated through a metal mask onto the oxide surface f o r subsequent capacitance and d i e l e c t r i c l o s s measurements. These were th r e e - t e r m i n a l measurements, made usin g a G-.R. bridge model 1615A and tuned detector operating at 1 kHz i n the c i r c u i t shown i n f i g . 7. The amplitude of the bridge generator s i g n a l was 100 mv peak to peak, and the bridge accuracy was - 0.01% f o r capacitance measurements at 1 kHz and + 0.1% f o r l o s s f a c t o r . 3.2.1. Thickness Determination The parameters W and A obtained from each set of e l l i p -someter readings were p l o t t e d against each other, and a 23 s p e c i a l l y designed computer program was used to f i t a curve to these experimental points on the basis of a t h e o r e t i c a l model of the growing f i l m by v a r y i n g model parameters such as the 19 F i g . 7 Capacitance bridge basic c i r c u i t 20 oxide r e f r a c t i v e index. This program a l s o computed the t h i c k -ness of the f i l m appropriate to each </M p a i r , i . e . the t h i c k -ness at the end of each formation. 5.2.2. Oxide F i e l d Strength Determination (1) I n t e g r a l F i e l d The i n t e g r a l oxide f i e l d i s defined as the e l e c t r o -s t a t i c ' p o t e n t i a l d i f f e r e n c e across the oxide between two points j u s t i n s i d e the oxide surfaces, V :, d i v i d e d by the t o t a l oxide thickness D. ox J Since i n the present experiments e l l i p s o m e t r y measurements can only be made w i t h the discharge o f f , the steady s t a t e i n t e g r a l f i e l d i s only a c c e s s i b l e at the end of a formation (and at the beginning i f voltage measurements are e x t r a -polated through the i n i t i a l t r a n s i e n t ) . (2) D i f f e r e n t i a l F i e l d . The d i f f e r e n t i a l f i e l d i s defined as dV /dD ox' and i s estimated by the incremental f i e l d AV /AD, where AV i s the change i n V during a formation ox to ox b and AD i s the increase i n oxide t h i c k n e s s . The c e n t r a l problem of o b t a i n i n g a value f o r V i s ^ to ox s i m i l a r to the wet anod i z a t i o n case i n that the measured p o t e n t i a l d i f f e r e n c e s include changes in-p o t e n t i a l at the various i n t e r f a c e s i n the metal-o x i d e - i o n i z e d medium-auxiliary electrode system. Some t h e o r e t i c a l c o n siderations appropriate to 21 the use of plasma probes i n estimating V are ^ to ox discussed i n Appendix I I I . 3.2.3- Ionic Current Determination From Faraday's law, an i o n i c current of I amps f l o w i n g f o r t seconds would provide I t / F gm-equivalents of oxygen f o r oxide formation where F = 96,500 coulombs. In forming NbgO^, of Mol. wt. M, I t / F gm-equivalents of oxygen w i l l combine to produce MIt/lOF gms of oxide, which i f 2 -3 deposited over an area A cm wit h d e n s i t y p g cm w i l l have a thickness D = Mtl/lOFpA cm. Thus a uniform increase i n thickness dD i n time dt w i l l be produced by an i o n i c current d e n s i t y J.= lOFp dD amps cm 1 M dt Hence the e l l i p s o m e t r y readings before and -after a constant current formation of known d u r a t i o n can be used w i t h an assumed value of oxide d e n s i t y (4-74 g cm as determined on OA solution-anodized Nb o0 c f i l m s ) to c a l c u l a t e the i o n i c current 2 5 den s i t y f o r that formation. Using the exposed specimen area to c a l c u l a t e the i o n i c current and expressing t h i s as a percentage of the t o t a l ( i o n i c + e l e c t r o n i c ) current gives the current e f f i c i e n c y of the process. 3.2.4. R e l a t i v e P e r m i t t i v i t y and Loss Factor 22 The three terminal connections used w i t h the G-.R. transformer capacitance bridge e l i m i n a t e d capacitances between the leads ( i n c l u d i n g probes and electrodes) to ground. The bridge measurements gave readings of the s e r i e s equivalent capacitance C and the l o s s f a c t o r t a n S = coC R where the l o s s ^ s s s angle S i s defined as S = (90° - 0), 0 being the phase angle between the current and the a p p l i e d v o l t a g e , and R i s the s e r i e s equivalent r e s i s t a n c e of the - niobium - oxide - gold electrode s t r u c t u r e . Each of these s t r u c t u r e s was taken to be a p a r a l l e l - p l a t e c a p a c i t o r of area A equal to that of the i n d i v i d u a l gold electrode s.s determined from t r a v e l l i n g micro-scope measurements of diameter. Values of r e l a t i v e p e r m i t t i v i t y e were then computed from C = e e A/D where the oxide thickness r o r D i s obtained from the appropriate i n - a i r e l l i p s o m e t r y compu-t a t i o n . 3.3 Results The f i l m s formed by plasma anodization of niobium i n o an oxygen d.c. glow discharge to thicknesses of about 800 A were found to be e l e c t r i c a l l y i n s u l a t i n g and were presumed, to be amorphous. S p e c i f i c r e s u l t s were as f o l l o w s . 23 5 .5 .1 E l l i p s o m e t r y The yj, A va lues obtained from i n _ s i t u e l l i p s o m e t r y measurements made between formations at va r i ous cur-rents on samples 1 and 2 (discharge cur ren t = 10 mA, pressure 60 mTorr) are p l o t t e d i n f i g s . 8 and 9. The exper imenta l po in t s were f i t t e d w e l l i f the computer program assumed a model w i t h two non-absorbing l a y e r s of ox ide , growing at somewhat d i f f e r e n t r a t e s , the outer l a y e r hav ing a lower r e f r a c t i v e index than the l a y e r adjacent to the me ta l . The curve i n f i g . 8 was computed u s i n g o p t i c a l constants of n^ = 3-60, k^ = 3.60 fo r the niobium subs t ra te (N^ = n^ - j k ^ ) , JNL-, = 2.37 fo r the inner oxide l a y e r , N-^  = 2.15 fo r the outer oxide l a y e r , and assuming that the outer f i l m composed 40% of the t o t a l oxide t h i c k n e s s , the r a t i o ' of the growth r a t e s of the l a y e r s be ing cons tant . The f i t of the data to the computed curve gave a s tandard d e v i a t i o n of l e s s than 0 . 4 7 ° i n A a n d - 0 . 1 2 ° i n V ; « The continuous curve i n f i g . 9 was computed u s i n g the same metal cons tan ts , 2.38 and 2.12 fo r the inne r and outer l a y e r r e f r a c t i v e i n d i c e s , and w i t h the outer l a y e r 47.5% of the t o t a l t h i c k n e s s . Data from a t h i r d sample a l so , f e l l c lose to t h i s l i n e . The dashed curve i s a p o r t i o n of one of the c l o s e s t f i t s obtained when a s i n g l e absorb ing f i l m model (n^ = 2=17, k^ = 0 . 0 4 ) was used. The above constants of the niobium subs t ra te and a l s o the r e f r a c t i v e index of the inner A quar tz p l a t e was f i t t e d behind sample 2 i n an attempt to screen the e f f ec t of the c o o l i n g tubes and improve oxide u n i f o r m i t y over the sample surface - see end of t h i s s e c t i o n . 360 300 240 A 180 120 60 0 20 24 O = EXPERIMEN TA L PO/N TS MODEL USED TO COMPUTE CURVE O J o N,=2.15yN2=2.37 Dj = 0-4 (Dj + POLISHED SURFACE INCREASING THICKNESS 40 60 80 F i g . 8 E l l i p s o m e t r y r e s u l t s f o r sample 1 a t 65°, \ o 5461 A 360 300 240 WO 120 60 0 20 25 ° o= EXPERIMENTAL POINTS MODEL USED TO COMPUTE SOLID CURVE: Nj=2.12, N? = 2.38 D7 = 0.475 (D.j + D2) MODEL USED TO COMPUTE DASHED CURVE ! ^ M S - POLISHED SURFACE \ nj = 2-17 ' kj = o.04 INCREASING. THICKNESS 40 670 80 F i g . 9 E l l i p s o m e t r y r e s u l t s f o r sample 2 at 0 - 65°, \=546l A 26 oxide l a y e r which enable the model to f i t the r e s u l t s were taken 19 from previous work on anodic oxides grown i n s o l u t i o n on niobium. I n t e r p r e t a t i o n of the e l l i p s o m e t r y data on the basis of the above model y i e l d e d computed values of the thickness of the o r i g i n a l oxide on each sample, and the thicknesses of the oxide l a y e r s at the end of each formation. The mean growth r a t e s , i o n i c current d e n s i t i e s and current e f f i c i e n c i e s could then be c a l c u -l a t e d . The r e s u l t s are c o l l e c t e d i n Tables 1 and 2, together with estimates of the f i e l d strength i n the oxide r e f e r r e d to i n the next s e c t i o n . I t can be seen that the current e f f i c i e n c y i s ge n e r a l l y l a r g e r f o r a l a r g e r t o t a l current, but always decreases f o r successive formations at the same t o t a l current. E l l i p s o m e t r y measurements made at d i f f e r e n t p o s i t i o n s over the sample surface a f t e r removal from the discharge c e l l i n d i c a t e d the f i l m s to be somewhat non-uniform i n t h i c k n e s s , u s u a l l y being about 10% t h i c k e r at the top than at the bottom of the sample. This may have been caused by the l o c a t i o n of the s t e e l water c o o l i n g pipes, which we:re not c o a x i a l w i t h the discharge tube but entered the l a t t e r r a d i a l l y from above. 3-3.2 Oxide F i e l d Strength Estimations During each a n o d i z a t i o n the p o t e n t i a l of the sample w i t h respect to a nearby f l o a t i n g probe, (V - V„ ) in c r e a s e s , g e n e r a l l y s x ]p. uniformly w i t h time a f t e r an i n i t i a l t r a n s i e n t , as The i n i t i a l oxide i s tr e a t e d as a double l a y e r i n t h i s com-pu t a t i o n , but the r e s u l t i s s t i l l v a l i d since f o r very t h i n f i l m s the method i s r e l a t i v e l y i n s e n s i t i v e to oxide r e f r a c t i v e index - see Appendix I I . 27 Formation Order T o t a l Sample Current Mean Growth Rate Estimt" I n t e g r a l i ted F i e l d D i f f e r e n t i a l I o n i c Current Dens i ty Current E f f i c -i ency mA 0 -1 Amin i n 6 " I 10 vcm 10 vcm 10~ 6 Acm~ 2 1 0.5 0.88 3.5 4.5 2.5 0.51 2 0.5 0.68 3.8 6.0 2.0 0.39 3 0.5 0.66 4.7 5.8 1.9 0.38 4 0.5 •0 .60 4.6 5.6 1.7 0.34 5 1.0 1.1 5.0 ' 4.5 ' 3.3 0.33 6 1.5 1.6 4.4 3.5 4.6 0.31 7 0.3 0.18 4.0 15 0.53 0.18 8 0.1 0.041 3-1 2.4 0.12 0.12 9 0.5 0.67 4.2 3.7 1.9 0.38 10 0.5 0.63 4.2 8.3 1.8 0.36 11 1.0 1.9 4.2 2.9 5.4 0.54 12 1.0 1.2 4.2 3.2 3-5 0.35 Table 1 - Current., and F i e l d data f o r sample 1 28 Formation T o t a l Mean Est imated F i e l d I o n i c Current Order Sample Growth I n t e g r a l D i f f e r e n t i a l Current E f f i c -Current Rate Dens i ty iency mA 0 -1 Amin i n 6 -1 10 vcm m 6 " I 10 vcm 1 0 _ 6 A c m ~ 2 % 1 0.5 0.67 5.1 4.6 1.9 0.38 2 1.0 2.6 5.4 3-3 7.3 0.73 3 1.5 3-4 4.9 3.3 9.9 0.66 4 1.5 2.3 4.7 3.0 6.6 0.44 5 0.3 0.15 3.5 2.7 0.44 0.15 6 0.4 0.28 4.2 10.0 0.80 0.20 7 0.5 0.55 4.4 6.1 1.6 0.32 8 0.2 0.21 3.7 0.59 0.29 .9 0.4 0.57 4.6 3-5 1.6 . . 0.41 10 1.0 2.1 5.0 2.5 6.3 0.63 Due to a long i n i t i a l t r a n s i e n t the d i f f e r e n t i a l f i e l d c a l c u l a t i o n was not meaningful . Table 2 - Current and F i e l d . D a t a f o r sample 2 29 shown i n f i g . 10. A f i r s t crude approximation to the p o t e n t i a l d i f f e r e n c e w i t h i n the oxide i s V = V - V„ . This neglects d i f f e r e n c e s i n ox s fp to plasma p o t e n t i a l over the sample to probe d i s t a n c e , sample -probe work f u n c t i o n d i f f e r e n c e s , and changes i n the p o t e n t i a l drop across the space charge sheath i n the plasma adjacent to the oxide when the l a t t e r draws a net current (Appendix I I I ) . This approximation was used to c a l c u l a t e oxide f i e l d s f o r sample 1 and r e s u l t e d i n a la r g e degree of s c a t t e r when these f i e l d s were p l o t t e d w i t h the l o g a r i t h m of the i o n i c current d e n s i t y l o g J , i n a 'T a f e l ' p l o t . The e r r o r s should be smallest f o r very low currents through a t h i c k oxide, when the changes i n sheath p o t e n t i a l drop should be l e s s s i g n i f i c a n t compared with the oxide p o t e n t i a l drop. A second approximation i s to deduct any p o t e n t i a l d i f f e r e n c e between the sample and the nearby probe when both of these are f l o a t i n g , i . e . , V = (V - V„ ) ... - (V - V„ ) ox s fp anodizxng s fp open c i r c u i t s fp I s fp 0 This should c o r r e c t f o r plasma p o t e n t i a l v a r i a t i o n s and work f u n c t i o n d i f f e r e n c e s . For sample 2, l o g i s p l o t t e d against i n t e g r a l oxide f i e l d E at the end of each formation 0 0 ox on t h i s approximation as the points © i n f i g . 11. There i s s t i l l some s c a t t e r , p a r t i c u l a r l y f o r the e a r l y formations i n v o l v -i n g r e l a t i v e l y small values of V . The same approximation app l i e d to p o t e n t i a l measurements u 12 10 8 fv) 0 ANODIZING CURRENT OFF ANODIZING CURRENT ON 10 20 30 40 t (min) F i g . 10 T y p i c a l v a r i a t i o n of sample p o t e n t i a l with respect to a f l o a t i n g probe duri n g a formation F i f e . 11 ' T a f e l ' p l o t f o r sample 2 32 on sample 3 y i e l d e d the points © i n f i g . 1 2 . These measurements u t i l i z e d a f i n e tantalum wire probe w i t h i n 2mm of the oxide surface. Apart from the s t r a y i n g of formations 4 to 6 from the o r i g i n a l l i n e , which i s a t t r i b u t e d to the presence of water i n the vacuum system (see s e c t i o n 3 . 3 - 4 ) , there i s remarkably close agreement between i n t e g r a l and d i f f e r e n t i a l f i e l d s (the points x) f o r the l a t e r formations. Although the d i f f e r e n t i a l f i e l d c a l c u l a t i o n should always el i m i n a t e the "unknown e r r o r H, i . e . , the p o r t i o n of (V - V„ ) T which i s not across the oxide, such r e s u l t s f o r s f p I ' samples 1 and 2 showed even more s c a t t e r than the i n t e g r a l f i e l d r e s u l t s , due p o s s i b l y to changes i n the value of (V^ - V-^) d u r i n a formation, where i s the p o t e n t i a l j u s t i n s i d e the outer oxid surface, and e r r o r s i n e x t r a p o l a t i n g through the i n i t i a l voltage t r a n s i e n t . The good agreement obtained w i t h sample 3 may have r e s u l t e d from more s t r i n g e n t pressure c o n t r o l and a l s o from the improved probe measurements: when the constant current generator i s connected to the sample, a small f l o a t i n g probe l o c a t e d .close to the oxide surface may undergo a p o t e n t i a l change almost equal to the change at the oxide-plasma i n t e r f a c e . I f the i n t e g r a l f i e l d data f o r low c u r r e n t - t h i c k oxide formations on samples 1 and 2 are combined with the i n t e g r a l f i e l d data f o r formations 1 to 3 on sample 3 (making t h i s s e l e c t i o n on the basis of the arguments above), the ' T a f e l ' p l o t of f i g . 1 3 i s obtained. Also shown i s the l o g 1 - E l i n e f o r wet anodization of niobium at 25°C from r e f . ( 1 9 ) . A procedure f o r e s t i m a t i n g the unknown p o t e n t i a l Eox (106Vcm~1) F i g . 12 ' T a f e l ' p l o t fo r sample 3 34 F i g . 1 3 Composite ' T - f e . l ' p l o t w i t h d a t a from samples 1, 2 and 3 d i f f e r e n c e H would be to carry out a s e r i e s of formations at the same constant current, p l o t oxide thickness versus (V g - Vj> ) T from measurements at the end of each formation, and extrapolate back to zero thickness to obtain Hj f o r t h i s one p a r t i c u l a r current I as the voltage i n t e r c e p t , assuming the oxide f i e l d and H-j- are the same at the ends of a l l these formations. This approach was not followed d e l i b e r a t e l y , but (V s - ) / t h i c k -ness data from groups of same t o t a l current formations ( s e l e c t e d f o r s i m i l a r growth rates so that the above assumption should apply) are p l o t t e d f o r samples 1 and 3 i n f i g s . 1 4 and 1 5 . The good l i n e a r i t y j u s t i f i e s the e x t r a p o l a t i o n , and- some corrected i n t e g r a l f i e l d s are included i n f i g s . 1 1 and 1 2 , showing that the s c a t t e r i s g e n e r a l l y reduced. An a l t e r n a t i v e and l e s s l a b o r i o u s approach would be i n i t i a l l y to obtain the 'Langmuir probe' current - p o t e n t i a l c h a r a c t e r i s t i c of the unanodized sample over the range of anodizing currents to be used, measuring the sample p o t e n t i a l w i t h respect to the same i n v a r i a n t probe. I f the i n i t i a l oxide present on the sample i s t h i n enough tha.t the p.d. i n the oxide may be neglected or corrected f o r with s u f f i c i e n t accuracy, then the value of Hj f o r any formation current I can be obtained from the sample c h a r a c t e r i s t i c and deducted from the measured (V g - Vfp)j> p r o v i d i n g c o n d i t i o n s such as gas pressure, discharge current can be a c c u r a t e l y reproduced. The assumption i s that the only change during the formation i s the e x t r a oxide, so that the change i n (V g - from H^ . must be the p.d. i n t h i s grown oxide. A s i m i l a r argument has been used r e c e n t l y to point out the r e l a t i v e l y small e r r o r i n assuming that the outer surface of germanium samples plasma anodized at constant voltage (with respect to the anode) down to a current density of 0.12 mAcm 25 had reached f l o a t i n g or w a l l p o t e n t i a l . To t e s t the f e a s i b i l i t y of t h i s method f o r future constant current plasma an o d i z a t i o n experiments, the c i r c u i t shown i n f i g . 16 was used to determine the c h a r a c t e r i s t i c s of a 0.015 i n . tantalum wire probe and an ex t r a e l e c t r o p o l i s h e d niobium sample. The r e s u l t s are shown i n f i g s . 17 and 18. No s p e c i a l precautions were taken to minimize the oxide i n i t i a l l y present, and comparison w i t h the f i r s t formations on samples 1 and 2 suggests that a s i g n i f i c a n t p o r t i o n of the measured sample p o t e n t i a l changes (with respect to the sample f l o a t i n g p o t e n t i a l V^) occur i n the i n i t i a l oxide. The a p p l i c a t i o n of Langmuir probe theory to these c h a r a c t e r i s t i c s n e g l e c t i n g the e f f e c t of negative ions (Appendix IV) leads to a mean e l e c t r o n energy of 8.5 eV. This appears to be erroneously high and the e r r o r i s presumed due to the i n i t i a l r e s i s t i v e oxide f i l m . 3.3.3 P e r m i t t i v i t y and Loss Factor Transformer bridge measurements on c a p a c i t o r s t r u c t u r e s d i s t r i b u t e d over each sample area gave values f o r the r e l a t i v e p e r m i t t i v i t y of the niobium oxide f i l m s i n the range 31-38 and values of l o s s f a c t o r between 0.01 and 0.07. The higher l o s s f a c t o r values may have been caused by the presence of oxide flaws under c e r t a i n of the ccunterelectrodes. 39 •2kv SAMPLE PROBE s \ / 1 1 1 1 1 / -I ~rn ikv STANDARD VARIABLE SUPPLY EL'R CURRENT METER F i g . 16 C i r c u i t used, t o o b t a i n s a m p l e and. p r o b e c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s wo 40 WO P • O-p=60juHg JDiS. = * 5 m A 80. 60] I PROBE (JJ A) 40\ 20. •160 -NO -O- -o-•o- -o--O' o--120,® -20. G O O O O O / G / G / -tOO -95 VPROBE ( V > F i g . 17 C h a r a c t e r i s t i c of a tantalum v.-ire probe p = 60juHg 7 D / S . = 1 0 m A 10. 8 !SAMPLB, 00 4A) 4^ 2. 41 O O o r o i o o -180 -160 -140 -120 6 0 -o- •o- -o •O' / 0 -2 -100 V (v) SAMPLE 42 3.3-4 The I n t r o d u c t i o n of Water to the Discharge The absence of water from the i o n i z e d medium i n plasma a n o d i z a t i o n i s one of the main f a c t o r s d i s t i n g u i s h i n g the process from wet a n o d i z a t i o n . Moreover, i t i s thought tha t the a c c e l e r -a t i o n of the thermal o x i d a t i o n of s i l i c o n i n the presence .of 26 water i s a c a t a l y t i c e f f e c t . I t i s p o s s i b l e , then, tha t the low growth ra tes of the plasma process may be r e l a t e d to the absence of water . To t e s t t h i s hypo thes i s , and more g e n e r a l l y to i n v e s t i g a t e the e f f ec t of v a r y i n g the c o n s t i t u t i o n of the i o n i z e d gas, sample 3 was plasma-anodized f i r s t i n dry oxygen and then w i t h va r ious concent ra t ions of water vapour added to the oxygen source gas . This was achieved by opening a v e s s e l c o n t a i n i n g d i s t i l l e d water at 20°C to the vacuum t i g h t oxygen feed system as shown i n f i g . 19 and v a r y i n g the system pressure . The r e s u l t s are g iven i n Table 3. The oxide growth ra te decreased by almost 2-3% from the dry oxygen value (formation 2) on adding a 2% p a r t i a l pressure of water to the source gas ( format ion 3)• The growth ra te decreased fo r subsequent form-a t i o n s (4 to 6) a l s o , a l though a f t e r i n c r e a s i n g the water content to — 100% the r a t e f e l l to a l i m i t apparen t ly e s t a b l i s h e d by the contaminat ion of the system through a b s o r p t i o n . Some I n d i c a t i o n of the d i f f e r i n g c o n d i t i o n s of these anod iza t ions i s obtained from the R . G . A . outputs i n f i g s . 20 to 23. I t i s found by a n a l y z i n g f i g . 20 that for the ' d ry oxygen' formations 1 and 2 the major i m p u r i t i e s (apart from i n e r t gases) are CO and p o s s i b l y N . The a d d i t i o n a l water content of form-Formation Order T o t a l Sample Current Percentage P a r t i a l Pressure of Water Vapour Mean Growth Rate Est ima I n t e g r a l ted F i e l d D i f f e r e n t i a l I o n i c Current Dens i ty Current E f f i c -i ency ml 0 -1 Amin , n 6 -1 10 vcm , „ 6 -1 10 vcm 10"6 Acm~ 2 1 0.5 - 0.93 4.0 4 .2 2.7 0.53 2 1.0 - 3-6 4.5 4.3 1.0 J 1.0 2.2 2.7 4.4 4.4 7.7 0.77 4 1.0 ~100 1.7 4.6 4 .6 4 .9 0.49 5 1.0 ~ 70 (1.4) 4.6 . (5 .9) (4 .0) (0.40) 6 1.0 < 70 1.4 4.7 4 .7 4 .0 0.40 The sample temperature was g rea te r than 30 C f or the f i r s t h a l f of fo rmat ion 5. Table 3 - Curren t , F i e l d and Water Content Data f o r sample 3. 44 TO DISCHARGE CELL LEAK VALVE VACUUM VALVES REGULATOR X ) = ( X DISTILLED WATER VACUUM-PRESSURE GAUGE CONSTANT TEMPERATURE WATER BATH COMPRESSED OXYGEN F i g . 19 System used to feed oxygen/water mixture to discharge c e l l RG.A. SIGNAL J U L_A. P i g . 20 j I I i i i i I I J I L R. G. A. SIGNAL JL) L A J Pis-. 21 A J l L 2 4 j i i i i_ 72 16 1718 20 22 J I L 28 30 32 a.m.u. —— 44 H20 02 Fig.. 20 R.G.A. output scan t y p i c a l of dry oxygen formations Pig.•21 R.G.A. output scan during formation 3 on sample 3 VJ1 R. G A. SIGNAL a f t e r discharge on —(2) -4 L A before discharge on (D J L _J I I L 2 4 1718 20 22 28 32 a m u H2 H^O 02 Via-. 99 R . f r . A . m i t n i i t . R r a n s for format inn A on sanrnl e ^  R.G.A. SIGNAL 7L/\_A A J -1 L _1 I—1 L J 1 L 2 4 16 1718 20 H^O 28 30 32 0-> 44 a.m.u. e*-F i g . 23 R.G.A. output scan during formation 6 on sample 3 48 a t i o n 3 can be detected i n f i g . 21. The scan ( l ) i n f i g . 22 taken p r i o r to format ion 4 shows the major cons t i t uen t to be water , w i t h 0^ n e g l i g i b l e . When the d ischarge i s s t r u c k , however, most of the water d i s -s o c i a t e s i n t o - H and 0 ^ , as i n d i c a t e d by scan ( 2 ) . Accompany-i n g t h i s r e a c t i o n was an increase i n the thermocouple pressure gauge read ing from ~60 mTorr to ~100 mTorr, the r ead ing decay-i n g to i t s o r i g i n a l va lue a f t e r some minutes . (A s i m i l a r pressure inc rease has been noted by other workers"'") . The and 0^ content remained h igh and the H^O low w h i l s t the d ischarge was main ta ined . S i m i l a r but l e s s pronounced e f f ec t s were observed du r ing format ion 5, i n v o l v i n g approximate ly 70% water i n water p lus oxygen. The scan taken du r ing format ion 6 ( f i g . 23) , fo r which the water con-t a i n e r was shut o f f and the gas supply system evacuated p r i o r to r e f i l l i n g w i t h dry oxygen, s t i l l shows a r e s i d u a l water content which may have o r i g i n a t e d from absorbed surface l a y e r s . 4 . DISCUSSION The r e f r a c t i v e index and p e r m i t t i v i t y of anodic f i l m s grown on niobium i n a d . c . glow d i scha rge , as determined by e l l i p s o m e t r y and br idge measurements, are lower than those of so lu t ion -g rown f i l m s , be ing 2.14 (outer l a y e r ) and ~34 as com-19 pared to about 2-37 and 41 - 43 r e s p e c t i v e l y . A l s o s ince the e l l i p s o m e t r i c r e s u l t s are f i t t e d by a two l a y e r model, i t appears tha t the plasma-grown f i l m s are non-uniform through t h e i r t h i c k -ness . This may be an i n d i c a t i o n that oxide growth occurs at both 49 t h e p l a s r n a / o x i d e a n d m e t a l / o x i d e i n t e r f a c e s , a s h a s b e e n d e m o n -s t r a t e d f o r some s o l u t i o n - g r o w n f i l m s , 1 ^ a n d t h a t t h e r e i s some d i f f e r e n c e b e t w e e n t h e o x i d e s p r o d u c e d a t t h e t w o . i n t e r f a c e s . T h i s l a s t p o i n t m i g h t be e x p e c t e d i n v i e w o f t h e c o n t i n u a l - b o m b a r d -ment o f t h e o u t e r o x i d e ' s u r f a c e by p o s i t i v e i o n s f r o m t h e p l a s m a . S u c h b o m b a r d m e n t may m o d i f y t h e s t r u c t u r e o f t h e o u t e r o x i d e l a y e r , p o s s i b l y r e d u c i n g t h e d e n s i t y a n d h e n c e r e f r a c t i v e i n d e x a n d p e r -m i t t i v i t y . A n o t h e r f a c t o r w h i c h c o u l d a f f e c t .the g r o w t h a t t h e . o u t e r o x i d e s u r f a c e i s t h e u l t r a v i o l e t r a d i a t i o n f r o m t h e p l a s m a . 2 3 I t h a s b e e n f o u n d i n w e t a n o d i z a t i o n s t u d i e s t h a t u - v r a d i a t i o n -s t i m u l a t e d g r o w t h p r o d u c e d f i l m s o f l o w e r r e f r a c t i v e i n d e x o n t a n t a l u m . The c u r r e n t e f f i c i e n c i e s f o r t h e p l a s m a a n o d i z a t i o n p r o c e s s a r e v e r y l o w c o m p a r e d w i t h t h o s e f o r w e t a n o d i z a t i o n , w h i c h a p p r o a c h 1 0 0 % . The m u c h l a r g e r p r o p o r t i o n o f e l e c t r o n i c c u r r e n t i n t h e p l a s m a c a s e i s n o d o u b t r e l a t e d t o t h e c o p i o u s s u p p l y o f e l e c t r o n s i n t h e p l a s m a , some o f w h i c h w i l l r e a c h t h e o x i d e s u r -f a c e w i t h c o n s i d e r a b l e k i n e t i c e n e r g y ( t h e v e l o c i t y d i s t r i b u t i o n o f e l e c t r o n s r e a c h i n g t h e o x i d e w i l l be a p p r o x i m a t e l y t h e same a s i n t h e u n p e r t u r b e d p l a s m a , e . g . , M a x w e l l i a n ) . The d a t a i n f i g s . 1 1 t o 1 3 i n d i c a t e t h a t t h e i o n i c current and' o x i d e f i e l d , r a n g e s f o r p l a s m a a n o d i z a t i o n a x e s i m i l a r t o t h o s e o f t h e w e t p r o c e s s . I n b o t h p r o c e s s e s , t h e o x i d e f i e l d 6 f o r a. g i v e n c u r r e n t d e n s i t y i s l o w e r f o r n iobium t h a n f o r t a n t a l u m . I t a p p e a r s t h a t t h e r e i s a m o n o t o n i c r e l a t i o n b e t w e e n l o g ( i o n i c c u r r e n t d e n s i t y ) a n d f i e l d , a l t h o u g h t h e r e l a t i o n c a n n o t be s t a t e d t o be l i n e a r r a t h e r t h a n , s a y , q u a d r a t i c . I f l i n e s a r e 50 a t t r i b u t e d to the plasma, data these l i n e s always have a lower slope and i f extrapolated to zero f i e l d would have a l a r g e r l o g i n t e r c e p t than the s o l u t i o n anodization l i n e . Before i n t e r p r e t -i n g these T a f e l - l i k e p l o t s i t should be emphasized that we have p l o t t e d values of estimated e l e c t r o s t a t i c f i e l d i n the oxide (not the s t r i c t equivalent of o v e r f i e l d used i n wet a n o d i z a t i o n ) and are r e s t r i c t i n g ourselves to the s i m p l i f i e d high f i e l d i o n i c conduction model of oxide growth. Rigorous thermodynamic t r e a t -ment of anodic o x i d a t i o n would include the e f f e c t s of concentra-t i o n gradients of reactant species i n the oxide i n 'addition to e l e c t r o s t a t i c f i e l d s i n accounting f o r the free energy of the r e a c t i o n 4Nb + 50g = 2Fb20^, but t h i s leads to a complicated and as yet unsolved f o r m u l a t i o n of the problem. On the c l a s s i c a l model of high f i e l d i o n i c conduction (Appendix I) then, a lower T a f e l slope i m p l i e s a smaller value of the a c t i v a t i o n distance a. This q u a n t i t y a could include f a c t o r s a l l o w i n g f o r the e f f e c t i v e f i e l d being d i f f e r e n t from the a p p l i e d f i e l d E and f o r the e f f e c t i v e charge being d i f f e r e n t from the valence charge g_. Thus the smaller plasma value of a ( i n qaE) could mean a smaller e f f e c t i v e f i e l d and/or lower e f f e c t i v e charge than i n the wet a n o d i z a t i o n case. The estimated f i e l d s i n f i g s . 11 to 13 may be too l a r g e f o r the experimental reasons mentioned i n s e c t i o n 3-3.2, or i t may be that the e f f e c t i v e e l e c t r o s t a t i c f i e l d i n the oxide producing i o n i c conduction i s i n f a c t lower than the e x t e r n a l l y a p p l i e d f i e l d . For an oxide f i l m c o n s i s t i n g of two l a y e r s of d i f f e r e n t r e f r a c t i v e index, i t could be expected that the l a y e r s would d i f f e r i n p e r m i t t i v i t y c and a l s o other 51 p r o p e r t i e s a f f e c t i n g i o n i c conduction. Thus i n the case of plasma-grown oxides, the outer l a y e r i s expected to have a lower pe r m i t t -i v i t y than that of the inner l a y e r , which i s assumed to be close to the value of ~ 4 3 e f o r s o l u t i o n grown f i l m s i n view of the o to close agreement i n r e f r a c t i v e index. Furthermore, i f the i o n i c current was a f u n c t i o n of some kind of e f f e c t i v e f i e l d which was p r o p o r t i o n a l to displacement D = . eE r a t h e r than j u s t E, then a lower p e r m i t t i v i t y would r e s u l t i n a lower e f f e c t i v e f i e l d and the 'Ta f e l ' slope would be smaller than f o r growth i n s o l u t i o n . The accumulation of a p o s i t i v e space charge i n the oxide near the oxide/plasma i n t e r f a c e , such as has been observed i n the e l e c t r o n 28 bombardment of s i l i c o n d i o x i d e , could also produce such i n t e r n a l f i e l d lowering. I f the lower slope i n the plasma case i s not the r e s u l t of experimental e r r o r s , then comparison of the extrapolated zero f i e l d i n t e r c e p t s might f u r t h e r suggest a l a r g e r concentration of Frenkel defects i n the plasma grown oxides, or p o s s i b l y a smaller value of the f i e l d - f r e e p o t e n t i a l b a r r i e r ¥ . However, such a ^ o comparison i s not s t r i c t l y v a l i d since a value of oxide de n s i t y measured on s o l u t i o n grown f i l m s was assumed i n computing i o n i c current density.Use of a lower oxide de n s i t y ( c o n s i s t e n t w i t h the lower r e f r a c t i v e ind.ex and p e r m i t t i v i t y ) would reduce a l l the l o g Rvalues by a constant amount. Further extension of the arguments above would re q u i r e more c r i t i c a l experiments, i n c l u d i n g the c a r e f u l a p p l i c a t i o n of probes,, to obtain more accurate data at s e v e r a l temperatures. I t may be p e r t i n e n t to mention here a theory proposed r e c e n t l y concerning the wet anodic o x i d a t i o n of s i l i c o n , f o r which the i o n i c current i s al s o only a small percentage ( of the e l e c t r o n i c current. I t was proposed that the-mobile ions are produced by c o l l i s i o n i o n i z a t i o n i n v o l v i n g e l e c t r o n s : when an elec t r o n - h o l e p a i r i s produced a valence bond may be considered to have been broken, and t h i s process was postulated to be a necessary p r e l i m i n a r y to i o n motion. The theory can account f o r an increased current e f f i c i e n c y at higher c u r r e n t s , as observed i n t h i s work. The r e s u l t s of the experiments i n v o l v i n g i n t r o d u c t i o n of water vapour i n t o the discharge were unexpected i n the sense that decreased growth rates were obtained, but they do i n d i c a t e that a measure of c o n t r o l over the anodization process i s po s s i b l e through discharge gas m o d i f i c a t i o n s . The redu c t i o n i n current e f f i c i e n c i e s may be due to the f a c t that the process of d i s s o c i a -t i v e e l e c t r o n attachment i n H^O, for'which the e l e c t r o n capture cross s e c t i o n i s r e l a t i v e l y l a r g e (5 x 10 ~^cm2 c.f. 1.3 x 10 "^cm2 f o r attachment i n 0^)^, produces H ions r a t h e r than OH i o n s : e~ + H 20 — ( H 2 0 ~ ) — H " + OH However, that c e r t a i n gas mixtures might increase growth r a t e s i s s t i l l an open p o s s i b i l i t y . 5. CONCLUSION" Thin d i e l e c t r i c f i l m s have been formed by plasma anodiz-a t i o n of p o l y c r y s t a l l i n e niobium i n an oxygen d.c. glow discharge. 53 o The growth rates were about 2 A per minute, and the current e f f i c i e n c i e s of the growth process were t y p i c a l l y 0 - 5 % . The technique of i n s i t u e l l i p s o m e t r y has i n d i c a t e d these f i l m s to have a two l a y e r s t r u c t u r e , c o n s i s t i n g of an inner l a y e r of r e f r a c t i v e index s i m i l a r to solution-grown oxides, and an outer l a y e r of lower r e f r a c t i v e index. This c o r r e l a t e s with a lower value of p e r m i t t i v i t y f o r plasma-grown f i l m s , as determined by capacitance measurements, than f o r wet anodized f i l m s . Compar-i s o n of oxide f i e l d strengths deduced from probe measurements, wit h i o n i c currents, c a l c u l a t e d using Faraday's law i n d i c a t e d the growth data to be consistent w i t h the c l a s s i c a l high f i e l d i o n i c conduction model, w i t h some devi a t i o n s from the wet anod i z a t i o n r e l a t i o n s h i p . However, experiments using water vapour demon-s t r a t e d that the rat e of growth could a l s o be in f l u e n c e d by con d i t i o n s i n the i o n i z e d reactant gas. 54 APPENDIX I C l a s s i c a l Theory of Ionic Conduction i n S o l i d s at High. F i e l d Strengths In the c l a s s i c a l approach the p o t e n t i a l energy of an io n i n the l a t t i c e i s considered to he a time-independent p e r i o d i c f u n c t i o n of the coordinates of the i o n . The a p p l i c a t i o n of a f i e l d E (the macroscopic f i e l d i n the d i e l e c t r i c ) i s supposed to add a term (-qxE) to the p o t e n t i a l energy, where x i s the coordinate of the i o n resolved i n the d i r e c t i o n of E and a. i s the charge on the i o n ( f i g . 2 4 ) . Thus to a f i r s t approximation the energy b a r r i e r opposing a jump from one s i t e to the next i s reduced from W to W aqE, where a i s the distance between o o ^ ' — the p o s i t i o n s of p o t e n t i a l energy minima and maxima. T r e a t i n g the i o n as a nea r l y independent harmonic o s c i l l a t o r l o o s e l y coupled to the l a t t i c e at temperature T, the chance of the i o n having the a c t i v a t i o n energy W - qaE i s exp-(W Q - qaE)/kT. I f the frequency of v i b r a t i o n of the i o n about i t s mean p o s i t i o n i s and the concentration of vacant i o n s i t e s (Frenkel defects) i s n, then at f i e l d s high enough to make jumps against the f i e l d u n l i k e l y , the i o n i c current d e n s i t y w i l l be • J ±= q(2an)vexp-(¥o- qaE)/kT or J = J Q exp-W(E)/kT. Thus l o g J.should be l i n e a r i n E, p r o v i d i n g W i s l i n e a r i n E. Distance F i g . 24 Supposed p o t e n t i a l energy of ion versus distance w i t h and without an a p p l i e d f i e l d 56 APPENDIX I I E l l i p s o m e t r i c Method of Measuring Thickness and R e f r a c t i v e  Index of Thin Films Grown on R e f l e c t i n g Surfaces In t h i s method the d e s i r e d information i s obtained by measuring the e f f e c t of r e f l e c t i o n from the f i l m covered surface on the s t a t e of p o l a r i z a t i o n of monochromatic p o l a r i z e d l i g h t . The s t a t e of p o l a r i z a t i o n i s c h a r a c t e r i z e d by the phase and amplitude r e l a t i o n s h i p s between the two components, p and s, i n t o which the t o t a l e l e c t r i c vector may be r e s o l v e d , i n and normal to the plane of incidence (and both normal to the d i r e c t i o n of pro-pagation) . The e l l i p s o m e t e r enables A , the change i n phase, andV'', the arc tangent of the f a c t o r by which the amplitude changes, to be determined. These angles are r e l a t e d by the fund-amental equation of e l l i p s o m e t r y : tanVe 3^ = R /R p' s where R and R denote the complex r e f l e c t i v i t i e s of the f i l m -p s ^ coated surface. I f the f i l m i s a uniform s i n g l e l a y e r of r e f r a c -t i v e index N=n - i k and thickness D , and the l i g h t of wavelength X i s i n c i d e n t at an angle 0Q, then each R i s of the form D r n + r e~ 2^ S • , c 2JCNDCOS0-, . , R = 1 2 where 5 = _1 i s the phase -2iS X 1 + ^ 1 r 2 e r e t a r d a t i o n f o r a s i n g l e passage through the f i l m , 0^  being the angle of r e f r a c t i o n , and'r-^ and are the F r e s n e l r e f l e c t i o n c o e f f i c i e n t s f o r the outer and inner i n t e r f a c e s i n the appropriate 31 s or p l i g h t . Archer^ and others have shown t h a t , as a non-5 7 absorbing d i e l e c t r i c l a y e r forms on a su b s t r a t e , the various p a i r s of values f o r H> and A cyc l e around loops i n the (/J- A plane. A t h e o r e t i c a l curve f o r a s i n g l e f i l m of r e f r a c t i v e index 2.25 growing on a substrate of index 5.60 - j 5«6(e.g. Nb^O^ on Nb) i s shown i n f i g . 25. I f the f i l m c o n s i s t s of two uniform l a y e r s of oxide as shown i n f i g . 26, each R has the form R = r± + r 2 e " 2 j 5 ' + r ^ e " 2 ^ 8 ' + S* } + r ^ i y T 2 ^ * 1 + r n r 0 e ~ 2 j 8 , + r, r%e~2J ( % ' + S* } +r 0r„e" 2 ; 5 S* 1 2 1 5 2 5 where r-, , r„, r ^ r e f e r to the i n t e r f a c e s s t a r t i n g at the outer surface, and S, and £ x r e f e r to the phase change f o r a s i n g l e passage through the i n d i v i d u a l oxide l a y e r s . The r's have s i m i l a r forms f o r a l l three i n t e r f a c e s , f o r instance = N cos01 - N: cos0 = N ocos0 o - N 1ccs0 1 l p l s ^0030-^ - N cos0o N Qcos0 o + N_Lcos01 In t h i s case 'the ^ A values do not i n general r e t r a c e t h e i r f i r s t l o o p , but t h e i r locus remains i n the v i c i n i t y of a s i n g l e f i l m loop. The q u a n t i t i e s <p and A are derived, from e l l i p s o m e t e r readings corresponding to c e r t a i n s e t t i n g s of the p o l a r i z e r and quarter wave pla.te which r e s u l t i n the l i g h t r e f l e c t e d from the film-covered surface being plane p o l a r i z e d , and the s e t t i n g of the analyzer which extinguishes t h i s r e f l e c t e d l i g h t . These sets of readings may be obtained i n four d i f f e r e n t 'zones' f o r 52 increased accuracy . The complex quotient' R /R^ can be w r i t t e n P i g . 25 Computed e l l i p s o m e t r y curve f o r s i n g l e f i l m (N^ = 2.25) on niobium (N = 3.6-35.6) at 0 = 65° and \ = 5461 1 59 INCIDENT LIGHT REFLECTED LIGHT NjZDj-jkj INDEX OF REFRACTION OF i MEDIUM <ft ={2tN-bfOS 0,y\ PHASE RETARDATION OF ith FILM F i g . 26 Two l a y e r model 60 R P -'A p— = A + jB = tan^e J ' s g i v i n g </> = arc tan | A + jB | A = a rc tan(B/A) The computer so lves these l a s t two equat ions for g iven values of X, 0 Q , N Q , 11 ±, K" 2 , N , , , D 1 and f>2. For \ , 0 Q, N Q , known, N •, N ^ , and can he found us ing a program for curve f i t t i n g computed va lues of A and to exper imenta l data obtained a t va r i ous stages dur ing the growth of the f i l m , i f a constant r a t i o of l a y e r . thicknesses D^/D i s assumed throughout the growth. 61 APPENDIX I I I Measurements using Plasma Probes The f o l l o w i n g p o i n t s should be considered i n the use of probes: (1) Any surface' exposed to a plasma of s w i f t l y moving el e c t r o n s and slower p o s i t i v e ions w i l l , i f i t cannot draw a net current from the plasma, acquire a negative charge such that the p o t e n t i a l gra.dient through the adjacent p o s i t i v e space charge sheath allows a s u f f i c i e n t e l e c t r o n f l u x to reach the surface to cancel the random i o n f l u x j . . i r (2) For a surface to draw a negative current from the plasma i t s negative charge must be decreased from the above con-d i t i o n by e x t e r n a l b i a s i n g so that the p o t e n t i a l drop across the space charge sheath i s reduced. I f biased p o s i t i v e l y u n t i l the p o s i t i v e sheath j u s t disappears, the surface receives both random f l u x e s of e l e c t r o n s and ions i + j . which would be i n c i d e n t on er i r one side of the plane of the surface i n the absence of the l a t t e r . For t h i s c o n d i t i o n the r e s t energy of an e l e c t r o n i n the plasma i s constant at i t s plasma p o t e n t i a l l e v e l up to the surface. This plasma p o t e n t i a l could be defined as the s o l u t i o n to Poisson's equation V 0 = - P where p i s an imaginary space and time-averaged s charge de n s i t y r e p r e s e n t a t i v e of the e l e c t r o n and i o n populations i n the plasma. ( 3 ) Any e x t e r n a l l y measured d i f f e r e n c e i n p o t e n t i a l between two metal probes (or a sample and probe) i s the d i f f e r e n c e 6 2 i n Fermi l e v e l between the probes, since p r a c t i c a l instruments respond to the tendency f o r e l e c t r o n flow. ( 4 ) The p o t e n t i a l s of two probes of d i f f e r e n t metals but i n i d e n t i c a l plasma environments, measured with respect to the same reference e l e c t r o d e , w i l l d i f f e r by the d i f f e r e n c e of t h e i r work f u n c t i o n s , whether they are both f l o a t i n g or both at plasma p o t e n t i a l . .. . (5) Any d i f f e r e n c e i n the p o t e n t i a l s of i d e n t i c a l probes i n d i f f e r e n t plasma l o c a t i o n s should rema.in constant whether the probes draw zero net current or equal currents up to the random f l u x 2QT + J-j_r> unless the i o n or e l e c t r o n energy d i s -t r i b u t i o n s vary, and t h i s d i f f e r e n c e gives the p o t e n t i a l gradient i n the plasma. A' one-dimensional e l e c t r o n energy band diagram f o r an oxide-covered metal surface 'drawing an a r b i t r a r y current d e n s i t y l e s s than ( j e r + J i r ) from the plasma, with a f l o a t i n g probe l o c a t e d nearby, i s shown below: SAMPLE OXIDE PLASMA FLOATING PROBE Where q = Magnitude of e l e c t r o n charge. 0 = Work f u n c t i o n of sample metal i n v o l t s , ^s 0 = Work f u n c t i o n of probe metal i n v o l t s . X - E l e c t r o n a f f i n i t y of sample metal oxide i n v o l t s . (JJ^ = P o t e n t i a l d i f f e r e n c e across a sheath between plasma and f l o a t i n g surface. / ty/ - P o t e n t i a l d i f f e r e n c e across a sheath between plasma and a surface drawing an anodizing current. AV = Diffe r e n c e i n plasma p o t e n t i a l between the sample sp and probe l o c a t i o n s . The measured p o t e n t i a l d i f f e r e n c e i s = V + « B - V ' AV + (V/f " "a' Thus work f u n c t i o n d i f f e r e n c e s , changes i n plasma p o t e n t i a l and sheath p o t e n t i a l drops should be considered i n the i n t e r -p r e t a t i o n of probe measurements. 64 • APPENDIX IV Langmuir Probe Theory f o r Plane Probe i n the Absence of Negative Ions (1) The f l o a t i n g probe (zero net current) Since ele c t r o n s i n a plasma d i f f u s e much more r a p i d l y than i o n s , any i s o l a t e d probe i n s e r t e d i n a plasma w i l l assume a p o t e n t i a l (with respect to some a r b i t r a r y reference point) such that the p o t e n t i a l j u s t outside of i t s surface i s negative to the surrounding plasma (at space p o t e n t i a l V )so that f u r t h e r e l e c t r o n s are r e p e l l e d , except a f l u x equal to the f l u x of p o s i t i v e i o n s . The probe i s covered by a space charge of p o s i t i v e i o n s , across which the p o t e n t i a l d i f f e r e n c e ty^ i s developed. (2) Strongly negative probe I f a probe i s bia.sed n e g a t i v e l y from i t s f l o a t i n g p o t e n t i a l by means of an e x t e r n a l c i r c u i t as shown i n f i g . 1 6 , then more and more e l e c t r o n s are r e p e l l e d by the i n c r e a s i n g f i e l d across the space charge u n t i l the current drawn by the probe i s e s s e n t i a l l y a l l due to p o s i t i v e i o n s . This s a t u r a t i o n current i . i s the random i o n current c r o s s i n g the outer surface i s to of the space charge sheath. (3) Unsaturated negative probe As the p o t e n t i a l d i f f e r e n c e across the sheath V between the probe and plasma i s decreased, more el e c t r o n s are able to overcome t h i s r e t a r d i n g p o t e n t i a l , namely those which have a 65 v e l o c i t y component y p e r p e n d i c u l a r l y towards the probe such that Y mv ^ eV (assuming no c o l l i s i o n s i n the sheath, i . e . , m.f.p. > sheath thickness) and t h i s number of el e c t r o n s increases u n t i l V = 0, i . e . , the probe reaches plasma p o t e n t i a l V . Throughout t h i s region the probe draws the constant p o s i t i v e i o n current i . , and the v e l o c i t y d i s t r i b u t i o n of the elect r o n s w i l l i s J determine the v a r i a t i o n of the probe current w i t h p o t e n t i a l . A t y p i c a l c h a r a c t e r i s t i c i s sketched i n f i g . 27. Assuming a Maxwellian d i s t r i b u t i o n at temperature T , the random f l u x of el e c t r o n s c r o s s i n g u n i t area i n one d i r e c t i o n i s Y.-g-nv where mean random v e l o c i t y v 8k T e ran n = e l e c t r o n density and the two f a c t o r s of \ a r i s e from the f a c t that only h a l f the .population d e n s i t y are heading toward the area, and that the average of the d i r e c t i o n cosine over a hemisphere i s \. Therefore random e l e c t r o n current i = ne / kT /'2irm. J e r v e' Now the number of electrons which have v e l o c i t y greater than v i s p equal to n exp (-mv /2kT ). Hence the e l e c t r o n current to the probe against the r e t a r d i n g p o t e n t i a l V i s j e ( V ) = ne /JkTe/2.itm exp(-eV/kT ) assuming a l l e l e c t r o n s e n t e r i n g the sheath w i t h s u f f i c i e n t energy are c o l l e c t e d , i . e . , probe dimensions>m.f.p., Thus I n i = constant - eV/kT Hence i n t h i s region a graph of In i against probe voltage w i l l be a s t r a i g h t l i n e of slope e/kT i f the e l e c t r o n d i s t r i b u -t i o n i s Maxwellian, from which the mean energy eV = 3kTe/2. can be POSITIVE SPACE CHARGE SATURATED? ION CURRENT NEGATIVE SPACE CHARGE SATURATED ELECTRON CURRENT PROBE AT PLASMA POTENTIAL I f-PROBE CURRENT 0 In i. .PROBE VOLTAGl is PROBE VOLTAGE RELATIVE TO ANODE F i g . 27 Ideal current-voltage c h a r a c t e r i s t i c s of a Langmuir probe cn cn 67 obtained. The value of i i s found by adding to the net probe current the random i o n current i . . 1 s In the case of two Maxwellian. groups at d i f f e r e n t temperatures, the l n i - V p l o t would comprise two s t r a i g h t l i n e segments, the d i f f e r e n t slopes of which would give the tempera-tures of the two groups. 68 REFERENCES 1. J.L. Miles and P.H. Smith, J . Electrochem. S o c , 110, 1240 (1963)• 2. G . J . T i b o l and R.W. H u l l , J. Electrochem. S o c , 111, 1368 (1964) . 3. K. Asano, M.Sc Thesis, Univ. of Minnesota (1964). 4. M. Scharfe, Tech.' Rep. USAF, AFAL TR-67-72 (1967). 5. L.D. Locker and L.P. Skolnick, Appl. Phys. L e t t . , 12, 396 (1968) . 6. W.L. Lee, D.L. P u l f r e y and L. Young, Ext. Abstr., New York Electrochem. Soc. Meeting (1969). 7. P.L. Worlege and D. White, B r i t . J . Appl. Phys., 18, 1337 (1967). 8. J.R. Ligenza, J . Appl. Phys"., £6, 2703 (1965). 9. J . Kraitchman, J . Appl. Phys., 18, 4323 (1967) 10. K.H. Zaininger and A.S. Waxman, I.E.E.E. Trans. E.D. 16, 333 (1969). 11. A.S. Waxman and G. Mark, S o l i d State E l e c t r o n i c s , 12, 751, (1969) . 12. C . J . Dell'Oca, D.L. P u l f r e y and L. Young,review a r t i c l e i n "Physics of Thin F i l m s " , i n press. 13- D. Rapp and D.D. B r i g l i a , J . Chem. Phys. 4J>, 1480 (1965). 14. See f o r instance J.D. Cobine, "Gaseous Conductors" , Dover: New York (1958). 15- G-. Francis , " I o n i z a t i o n Phenomena i n Gases " ,Butterworth: London (i960) . 69 16. A.G. Revesz and. K.H. Zaininger, R.C.A. Review, March, 22 (1968), or A.G. Revesz and. R.J. Evans, I.E.E.E. Trans. E.D., 14, 789 (1967). 17. J . J . R a n d a l l , J r . , W.J. Bernard and R.R. Wilkinson, E l e c t r o -chim. Acta 10, 183 (1965). 18. S. Kumagai and L. Young, J . Electrochem. S o c , 111 1411 (1964)• 19. L. Young and E.G.R. Zobel, J . Electrochem. Soc. I l l , 277 (1966) . 20. C.J. Dell'Oca and L. Young, Surf. S c i . , 16, 331' (1969) 21. H. Musal, J . Appl. Phys., J7, 1935 (1966). 22. J . P e l l e g , J . Less-Common Metals, 12, 421 (1967). 23. C J . Dell'Oca, Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia, i n p r e paration. 24. A.J. S c h r i j n e r and A. Middlehoek, J . Electrochem. S o c , 111. 1167 (1964). 25. J.P. O'Hanlon, Appl. Phys. L e t t e r s l i , 127 (1969). 26. E. Kooi "The Surface P r o p e r t i e s of Oxidized S i l i c o n " , p. 35, Springer-Verlag: New York (1966). 27. L. Young, "Anodic Oxide F i l m s " , Academic Press, London and New York ( 1 9 6 1 ) 28. M. Simons, L.K. Monteith, J.R. Hauser, NASA Report (NASA-CR-1088), (1968). 29- C.R. F r i t z s c h e , S o l i d State Comm., 6, 341 (1968). 3 0 . R.I. Reed, "Ion Production by E l e c t r o n Impact", p. 87, Academic Press, London and New York (1962). 3 1 . R.J. Archer, J . Opt. Soc. Am. 5_2, 970 (1962). F. L. McCrackin, E. P a s s a g l i a , R.R. Stromberg, and H.A. Steinberg, J . Res. Nat. Bur. Stand. A, 6 7 , 303 ' ( 1 9 6 3 ) . 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0101999/manifest

Comment

Related Items