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Ellipsometric studies of electro-optic and ionic conductivity effects in thin oxide films Cornish, William Duncan 1972

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ELLIPSOMETRIC STUDIES OF ELECTRO-OPTIC AND IONIC CONDUCTIVITY EFFECTS IN THIN OXIDE FILMS by WILLIAM D. CORNISH B.Sc. (Hon), Queen's University at Kingston, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of E l e c t r i c a l Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER, 1972 In present ing th i s thes is in pa r t i a l f u l f i lmen t o f the- requ i remen t s fo r an advanced degree at the Un ivers i t y of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extensive copying of th i s thes i s fo r s cho la r l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i c a t i on of th i s thes is fo r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of BU^hric^l ^ J>^cty /h The Un ivers i t y o f B r i t i s h Columbia Vancouver 8, Canada Date S£.f~l 1*,!^ ABSTRACT An automated ellipsometer was used to study three topics associated with the anodic oxide f i l m s of tantalum and niobium. The e l e c t r o - o p t i c e f f e c t was measured on tantalum and niobium oxides and was found to be quadratic. The change i n r e f r a c t i v e index upon a p p l i c a t i o n of a f i e l d occurred i n two phases: an instantaneous change followed by a slower change. The e f f e c t s on N t ^ s w e r e greater than on Ta^O^. The e f f e c t of u l t r a v i o l e t l i g h t on the two oxides was found to cause a change i n the r e f r a c t i v e index before appreciable photo-induced growth occurred. The r e s u l t s indicated that i t was u n l i k e l y that the u.v.-induced change i n r e f r a c t i v e index occurred uniformly through-out the f i l m . The -effects..of annealing .and .temperature „are discussed .in r e l a t i o n to the constant f i e l d current t r a n s i e n t . The change i n the r e f r a c t i v e index during the t r a n s i e n t was monitored with the ellipsometer. TABLE OF CONTENTS Page A b s t r a c t . . . . . . . . . . . i T a b l e o f C o n t e n t s i i L i s t o f I l l u s t r a t i o n s i v Acknowledgement . . . . . . . . . . . v i i I . INTRODUCTION . 1 I I . THE GENERAL EXPERIMENTAL ARRANGEMENT. . . . . . 3 1 The E l l i p s o m e t e r / C o m p u t e r I n t e r f a c e . 3 1.1 The E l l i p s o m e t r y E q u a t i o n s 3 1.2 System Hardware. . . . . . . 5 1.3 System Software 8 1.4 E l l i p s o m e t e r A l i g n m e n t . 10 2.1 Sample P r e p a r a t i o n 13 2.2 O p t i c a l C o n s t a n t s o f Ta 15 2.3 The S t r u c t u r e o f T a 2 0 5 18 I I I . THE ELECTRO-OPTIC EFFECT. 20 1 I n t r o d u c t i o n 20 2 Theory . . . . . . . 21 3 E x p e r i m e n t a l Procedure 23 4.1 R e s u l t s f o r T a 2 0 5 25 4.2 R e s u l t s f o r Nb 20 5 31 5 D i s c u s s i o n 36 IV. U. V. IRRADIATION OF ANODIC OXIDES 39 1 I n t r o d u c t i o n . . . . . . 39 2 E x p e r i m e n t a l P r o c e d u r e . . 39 3 R e s u l t s . . . 40 3.1 Changes i n T h i c k n e s s and R e f r a c t i v e Index Due t o Short Exposure t o R a d i a t i o n 40 3.2 P h o t o - S t i m u l a t e d Growth. . " . . 41 4 D i s c u s s i o n 51 V. CONSTANT FIELD TRANSIENTS . 54 1 I n t r o d u c t i o n 54 2 O u t l i n e o f Theory • 54 3*1 A p p a r a t u s . . . . . . . . . . . 57 3.2 E x p e r i m e n t a l Procedure 59 4.1 E f f e c t o f Temperature on the T r a n s i e n t . . 60 4.2 E f f e c t o f A n n e a l i n g on t h e T r a n s i e n t 63 4.3 T h i c k n e s s and R e f r a c t i v e Index Changes i n t h e Oxide F i l m D u r i n g the T r a n s i e n t 65 i i Page 5 Discussion • • ^9 VI. CONCLUSIONS •. . . 71 REFERENCES . 7 3 APPENDIX. 7 5 i i i LIST OF ILLUSTRATIONS Figure Page II-1' Computer-ellipsometer i n t e r f a c e . Dashed l i n e s i n d i c a t e connection to the computer i n t e r -face 6 II-2 Amplifier i n computer i n t e r f a c e . . . . 7 II-3 C a l i b r a t i o n curves f o r p o l a r i z e r and analyzer. (0-0-0) Balancing the p o l a r i z e r with the analyzer constant. (x-x-x) Balancing the analyzer with the p o l a r i z e r constant 11 II-4 Ellipsometry curve for T a ^ O r on Ta i n a i r . S o l i d l i n e for a f i l m with n = 2.185 and substrate con-stants n = 2 . 4 6 - j2.56. oThe numbers beside the curve are thicknesses i n A 17 I I - 5 A (001) p r o j e c t i o n of the structure of L-Ta205« There are three d i s t o r t i o n planes i n t h i s unit c e l l located at d-^ , <$2 and d3. The fourth p o s i -t i o n at d^ i s r e l a t e d by symmetry but i s not used i n t h i s unit c e l l . Black dots represent metal atoms and shaded areas oxygen coordination poly-hedra . . 19 I I I - l The form of the current observed when the f i e l d across the oxide i s suddenly changed 24 III-2 The change i n thickness and r e f r a c t i v e index with f i e l d f o r T a 2 0 5 . n Q = 2.1947; d Q = 2368.0 A. . . 26 2 III-3 Results of Figure 2 p l o t t e d against E 27 I I I - 4 The change i n thickness and r e f r a c t i v e index with time for Ta205 when the applied voltage i s sudden-l y changed from 0 V to the value i n d i c a t e d . d Q = 2 3 6 4 . 6 , n Q = 2.1969. . 29 III-5 Diagram for defining symbols i n equation 9. . . . 30 III-6 The change i n r e f r a c t i v e index and thickness with f i e l d f o r N b ^ . d Q = 649.6 A; n Q = 2.3263 . . . 3 2 III-7 Results of Figure 6 vs. E 2 33 III-8 Change i n thickness and r e f r a c t i v e index with time when the f i e l d i s suddenly changed. (0-0-0) for a decrease i n f i e l d . (x-x-x) for an increase i n f i e l d . d Q = 650.3 A; n Q = 2.3260. 34 III-9 Diagram for second d e f i n i t i o n of symbols i n equation 9. . . . 35 i v Figure Page IV-1 C i r c u i t diagram f o r experimental procedure of s e c t i o n IV, 2 40 IV-2 E l l i p s o m e t e r p o i n t s of Ta20,- on Ta f o r short exposure to u.v. l i g h t 42 IV-3 The change i n r e f r a c t i v e index and t h i c k n e s s during short exposure to u.v. l i g h t . d Q = 2466.8; n Q = 2.206 43 IV-4 The t o t a l and dark current d e n s i t i e s f o r u a v . l i g h t - i n d u c e d growth of Ta2Q5-. dQ - 2510 A. Small l e t t e r s correspond to those on F i g u r e 5. .. . 45 IV-5 E l l i p s o m e t r y curve f o r T a 2 0 5 . (0-0-0) For u.v. s t i m u l a t e d growth. ( ) computed curve f o r f i l m w i t h n = 2.195. Small l e t t e r s correspond* to those on Figure 4 46 IV-6 T o t a l and dark current d e n s i t i e s f o r u.v.—induced o growth of Nb 20^. dQ = 650 A. Small l e t t e r s correspond to those i n Figure 7 47 IV-7 E l l i p s o m e t r y curve f o r Nb205< (0-0-0) For u.v.-s t i m u l a t e d growth. ( ) computed curve f o r a f i l m .with n = .2.319.. ...Small . l e t t e r s correspond to those on F i g u r e 6 48 IV-8 The change i n the r e f r a c t i v e index of a Ta205 f i l m during the i n c u b a t i o n p e r i o d of i l l u m i n a t i o n . o f u.v. l i g h t , assuming a s i n g l e uniform f i l m . n Q = 2.202 49 IV-9 R e s u l t s of Figure 8 v s . the square of the time . . 49 IV-10 The change i n r e f r a c t i v e index of a Nb205 f i l m d uring the i n c u b a t i o n p e r i o d of i l l u m i n a t i o n of u.v. l i g h t ( f i r s t 20 minutes of F i g u r e 6 ) , assuming a s i n g l e uniform f i l m 50 IV- 11 R e s u l t s of Figure 10 v s . the square of time. . . . 50 V- l C i r c u i t diagram f o r t r a n s i e n t s t u d i e s 58 V-2 The e f f e c t of temperature on the constant f i e l d c u rrent t r a n s i e n t 61 V-3 The parameter B of equation 5 as a f u n c t i o n of time . 62 V-4 The e f f e c t of annealing at 100°C f o r 5 minutes on the t r a n s i e n t . (x-x-x) curve f o r annealed sample. (0-0-0) curve f o r a sample that was not annealed 64 v Figure Page V-5 Constant f i e l d transient for Ta205. The letters correspond to those in Figure 6 66 V-6 Ellipsometer points taken during the constant f i e l d transient for  rYa2^>cj- The letters corres-pond to those in Figure 5. Solid lines are computed constant index of refraction curves . . . 67 V-7 The change.in refractive index during the tran-sient of Figure 5. nQ = 2.195 68 V-8 The change in thickness vs. f i e l d during the tran-sient of Figure 5 . 68 v i ACKNOWLEDGEMENT I wish to thank Dr. D. L. P u l f r e y and Dr. L. Young f o r t h e i r assistance and guidance during t h i s i n v e s t i g a t i o n . The Sprague E l e c t r i c Company, who supported t h i s work i s g r a t e f u l l y acknowledged. I am indebted to Miss B. Harasymchuk for her patience i n typing t h i s t h e s i s . I wish to thank Mr. G. O l i v e for many h e l p f u l discussions and t e c h n i c a l assistance with the ellipsometer. F i n a l l y I would l i k e to thank my wife Diane for moral support, f i n a n c i a l assistance and endless patience while I completed t h i s p r o ject. v i i 1 I. INTRODUCTION Because of t h e i r a p p l i c a t i o n i n many s o l i d state devices, t h i n d i e l e c t r i c f i l m s have been studied i n great d e t a i l . In s p i t e of t h i s there are s t i l l many points that have yet to be c l a r i f i e d . In t h i s thesis some of these points are studied. It i s known that a l l substances exhibit the e l e c t r o - o p t i c effect'" and with the advent of holographic memory storage, and o p t i c a l communication, materials are being sought which w i l l d e f l e c t , transmit and modulate l i g h t e f f i c i e n t l y . With t h i s i n mind, studies of the e l e c t r o -o p t i c e f f e c t on T a 2 0 5 and Nb 20 5 were undertaken as described i n Chapter I I I . In Chapter IV, the e f f e c t of u.v. r a d i a t i o n on Ta20^ i s inves-t i g a t e d . Previous work has f a i l e d to reveal an adequate model to describe the processes involved i n photo-stimulated growth. The changes i n thickness and r e f r a c t i v e index of the f i l m during u.v. i r r a d i a t i o n are studied. The f i n a l topic studied i n t h i s t h e s i s invoIves the i o n i c current transient r e s u l t i n g when a constant f i e l d i s applied. An adequate theory of i o n i c conduction i n amorphous s o l i d s must be able to account for t h i s phenomena. Studies of temperature dependence, the e f f e c t of annealing the f i l m and the changes i n thickness and r e f r a c t i v e index during the transient were conducted. Many of the measurements made involved the use of an e l l i p -someter to determine thickness and r e f r a c t i v e index of the t h i n f i l m s involved. Much of the work would have been very t e d i o u s , i f not impossible, without the use of an automated ellipsometer such as the one described i n Chapter I I . The instrument allowed i n .situ measurements to be taken at i n t e r v a l s as small as 2.5 seconds. Transient changes i n thickness and r e f r a c t i v e index that were complete i n 10 or 15 seconds could e a s i l y be detected. The conclusions that can be drawn from the above studies are remarked upon i n Chapter VI. 3 I I . THE GENERAL EXPERIMENTAL ARRANGEMENT 1. The Elli'psometer/Computer I n t e r f a c e 1.1 The E l l i p s o m e t r y E q u a t i o n s The e l l i p s o m e t e r i s an o p t i c a l i n s t r u m e n t which can be used t o study s u r f a c e s and t h i n f i l m s upon s u r f a c e s by t h e r e f l e c t i o n of l i g h t from the s u r f a c e . Because i t can determ i n e t h e t h i c k n e s s and r e f r a c t i v e index of a f i l m s i m u l t a n e o u s l y i t s u s e f u l n e s s i n t h i s a p p l i -c a t i o n i s i n c r e a s e d over o t h e r methods which may determ i n e one o f t h e s e q u a n t i t i e s w i t h perhaps more a c c u r a c y . E l l i p s o m e t r y measures two q u a n t i t i e s ty and A, known as the e l l i p s o m e t r y a n g l e s . These two a n g l e s c h a r a c t e r i z e the change i n the s t a t e of p o l a r i z a t i o n which o c c u r s when 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 s r e f l e c t e d from .a s u r f a c e . The t h e o r y o f e l l i p s o m e t r y w i l l not be d e v e l o p e d i n d e t a i l 2 3 4 h e r e s i n c e i t has been c o v e r e d a d e q u a t e l y e l s e w h e r e ' ' . ty and A a r e r e l a t e d to the p r o p e r t i e s o f the s u r f a c e t h r o u g h t h e fundamental equa-t i o n o f e l l i p s o m e t r y : [tan * ] e i A = - ^ CD s where R and R a r e t h e 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 l i g h t p o l a r i z e d P s p a r a l l e l t o the p l a n e o f i n c i d e n c e ( i . e . t h e e l e c t r i c v e c t o r o f t h e l i g h t i s i n t h e p l a n e o f i n c i d e n c e ) and l i g h t p o l a r i z e d p e r p e n d i c u l a r t o t h e p l a n e of i n c i d e n c e r e s p e c t i v e l y . F o r a s i n g l e l a y e r f i l m on a s u b s t r a t e Rp and R g a r e of the form R „ — J = I ( 2 ) (1 + r ^ e - ^ ) 4 where r ^ and r ^ are the F r e s n e l c o e f f i c i e n t s f o r the outer and inner faces of the oxide f o r s or p l i g h t . The F r e s n e l c o e f f i c i e n t s are of the form n. cos (|>_ - n 0 cos <j> • , rP = _i ? 2 1 ( 3 ) 1 n^ cos <j>2 + ^2  cos ^] n, cos <j)n - n„ cos 4>~ s _ _1 I 2 __2 1 n^ cos <j)^  + cos <j>2 (4) The phase change f o r one pass through the f i l m i s <5 and i s given by . 2v d ,2 . 2.. 1/2 . <$ = — — ( n 1 - s i n <}>) (5) where n^ = index of r e f r a c t i o n of f i l m d = thi c k n e s s of the oxide <f> = angle of incidence ^ = vacuum wavelength of l i g h t . S u b s t i t u t i n g eqn. 2,3, 4 and 5 i n t o 1 gives <|J and A' as f u n c t i o n s of the angle of i n c i d e n c e , the wavelength of l i g h t , the th i c k n e s s of the f i l m , and the o p t i c a l constants of the f i l m s and s u b s t r a t e . For one e l l i p s o m e t r y measurement which w i l l give values f o r $ and A, two equations can be solved f o r the two o p t i c a l unknowns of the f i l m and the s u b s t r a t e . I f more than two unknowns are to be determined, i t i s necessary to curve f i t a number of d i f f e r e n t e l l i p s o m e t r y measure-4 5 ments. Measurements may be taken by v a r y i n g the t h i c k n e s s of a f i l m ' , i by v a r y i n g the angle of incidence , or as a f u n c t i o n of the immersion medium^. For t h i s t h e s i s , measurements were taken by v a r y i n g the thic k n e s s of the f i l m . 5 1.2 System Hardware The Ruldolph Thin F i l m Ellipsometer (type 43603-200B), used in t h i s project, was interfaced to a DEC PDP-8/E computer (Figure 1). The interface consisted mainly of standard components and was almost complete before the star t of t h i s research p r o j e c t . IMC Magnetics Corporation stepping motors (#PIN 008-008) were fix e d to the analyzer and p o l a r i z e r prisms but not to the compensator. Decitrak shaft encoders (TR-511C-CW/D) which were mounted on the analyzer and p o l a r i z e r allowed angles to be read to 0.01 degrees. The Decitrak converted the angles to BCD for input to the computer. The stepping motors and shaft encoders were multiplexed to one device code. The l i g h t source employed was a Spectra Physics helium-neon o laser (model 133) which emitted l i g h t at a wavelength of 6328 A. The detector was an RCA photomultiplier whose analog output voltage was monitored on one of the four analog channels multiplexed to one A/D converter (DEC A 811) with 0.1% F.S. accuracy. The error s i g n a l of the photomultiplier was fed through a v a r i a b l e gain a m p l i f i e r with an adjustable zero c o n t r o l before being directed to the analog channel. A meter connected to the input of the A/D converter was very useful i n n u l l i n g the ellipsometer by hand and i n debugging any program which used the A/D converter. On two of the other analog channels noninverting operational amplifiers were used for impedance matching purposes between the A/D and Fluke 602 Electrometers. The 602 electrometer has a one v o l t f u l l scale output which was amplified by ten to u t i l i z e the ten v o l t f u l l scale l i m i t of the A/D. The c i r c u i t for the l a t t e r a m p l i f i e r i s shown in Figure 2. The electrometers were used for current and voltage MOTOR SHAFT ENCODER LASER SAMPLE .MOTOR -SHAFT ENCODER PHOTO MULTIPLIER VARIABLE GAIN AMPLIFIER F i g u r e 1: Computer-Ellipsometer i n t e r f a c e . Dashed l i n e s ' i n d i c a t e connection to the computer i n t e r f a c e . ON 7 measurements. Figure 2 The small capacitors and C 2 were used to l i m i t noise. Response was not a problem as a l l s i g n a l s monitored were slowly changing d-c l e v e l s . A clock was incorporated into the i n t e r f a c e by using a s i x b i t counter that was t r i g g e r e d with the 60 Hz frequency. This gave a basic unit of 0 . 1 seconds which was adequate for the purposes of t h i s p r o j e c t . A Tyco d i g i t a l voltmeter (model 404) with d i g i t a l output was connected to the i n t e r f a c e . However i t s response time of 0.5 sec. l i m i t e d i t s use to monitoring constant p o t e n t i a l s . A t r a n s i s t o r switch was multiplexed with the motors and was used to drive a large reed r e l a y that opened and closed the main c i r c u i t to the anodization c e l l . 8 1.3 System Software The development of the software was dictated mainly by the nature of the ellipsometer and to a lesser extent by the data to be acquired. The ellipsometer must be nu l l e d i n an acceptable manner and then the p o l a r i z e r and analyzer angles read. The speed of the system i s l i m i t e d by the time i t takes to step the p o l a r i z e r and analyzer motors through the n u l l i n g procedure. Data a c q u i s i t i o n takes only a f r a c t i o n of t h i s time. Data storage i s a problem with a*4K memory machine when a large number of observations are required and no high speed storage devices are a v a i l a b l e . One balancing cycle including data a c q u i s i t i o n required approximately 2 sec., but typing t h i s out onto the teletype required 5 or 6 sec. To a l l e v i a t e t h i s problem 2500 locations of the computer memory were used as a buffer area where data was stored i n i t i a l l y . The interrupt f a c i l i t y was employed to keep the teletype busy outputting the stored data while leaving the computer free to balance the ellipsometer and c o l l e c t more data. The buffer area was set up i n a c i r c u l a r manner so that when the end of the buffer was reached, new data was written on top of the old data that had already been typed out on the teletype. F i n a l l y when the input to the buffer had caught up to the output from the b u f f e r , the e n t i r e balancing routine would be slowed to the speed at which the teletype could empty the b u f f e r . This scheme of reusing the beginning of the buffer area increased i t s effectiveness by about 70%. PDP-8 Program A flow chart of the program i s given i n the appendix. The program began by i n i t i a l i z i n g various pointers, typing out the headings of columns and then s t a r t i n g the clock. The clock has a 5 min. maximum time l i m i t a f t e r which i t i s zeroed. The open c o l l e c t o r switch that c o n t r o l l e d the heavy reed r e l a y i s then opened or closed. Control of t h i s switch i s operator-activated by one of the switch r e g i s t e r b i t s . Following t h i s the ellipsometer i s balanced. The p o l a r i z e r i s balanced f i r s t . The program determines which way i t must step the motor to minimize the error s i g n a l of the photo-m u l t i p l i e r . I t steps the motor i n that d i r e c t i o n u n t i l a set of 16 photomultiplier readings are taken (one a f t e r each step) and summed. The motor continues stepping u n t i l the error s i g n a l goes through a minimum' and begins to increase again. A second sum of readings are taken as the motor steps and i s continuously updated to contain only the 16 most recent readings. VThen t h i s second sum equals the f i r s t sum found on the other side of the minimum, the balance point,which i s midway between the two equal sums, has been located. This method of l o c a t i n g the n u l l point i s v a l i d because the error s i g n a l i s symme-8 t r i c a l about the minimum for small excursions from the minimum . The analyzer i s then balanced i n the same manner. Pro v i s i o n i s made for balancing when beginning from a previous balance by d r i v i n g the motors o f f i n an a r b i t r a r y d i r e c t i o n away from the balance point and then proceeding as above. The clock i s read a f t e r each balance. A f t e r both the analyzer and p o l a r i z e r have been balanced, a comparison i s made between the number of steps each motor takes and the change i n the p o s i t i o n of the shaft encoder. This w i l l i n d i c a t e any error due to backlash or the motors missing steps. The next phase of the program involves data a c q u i s i t i o n and 10 p r i n t out. The peripheral devices are read i n the order, p o l a r i z e r , analyzer, clock analog channels and then the d i g i t a l voltmeter. A f t e r a l l the information i s gathered i t i s converted to BCD and then stored i n the buffer area to await output on the teletype. The A/D converter read 10 v o l t s f u l l s c a l e , however being a 10 b i t converter i t divided i t s scale into 1024 d i v i s i o n s . Data input through the A/D i s divided by 1.024 so that.the output i s the voltage applied to the A/D„ The photomultiplier s i g n a l was not adjusted since only i t s r e l a t i v e magnitude was of i n t e r e s t . Off Line Data Handling The A and P readings obtained from the ellipsometer were processed on the IBM 360/67. Correct values of i p , the f i l m thickness and i t s o p t i c a l constants can be obtained provided s u i t a b l e corrections are made for the errors of the compensator and the angle of t i l t of the sample. McCrackin's program for analysis of ellipsometer measurements^ was mainly used to do these computations. 1.4 Ellipsometer Alignment Perhaps, the most d i f f i c u l t task i n the use of the ellipsometer i s correct alignment. Since the instrument i s extremely s e n s i t i v e , i t i s imperative to a l i g n i t properly i f r e s u l t s are to be meaningful. A method has been d e v i s e d ^ i n which the alignment procedure i s purely geometrical and only requires components normally used with the e l l i p -someter. This eliminates errors from c a l i b r a t i n g instruments that would perhaps be not as s e n s i t i v e as the ellipsometer i t s e l f . A b r i e f out-l i n e of t h i s procedure follows. 11 P (DEG) F i g u r e 3: C a l i b r a t i o n curves f o r p o l a r i z e r and a n a l y z e r . (o-o-o) Balancing the p o l a r i z e r w i t h a n a l y z e r s t a t i o n a r y . (x-x-x) Ba l a n c i n g the a n a l y z e r w i t h , p o l a r i z e r s t a t i o n a r y . 12 The telescope arms were set i n the straight-through p o s i t i o n and the analyzer telescope was rotated about 0.0° u n t i l maximum i n t e n -s i t y of the l a s e r beam was achieved. With the telescope i n t h i s p o s i t i o n the,error i n the angle of the scale was read. In our case the e r r o r was -0.05°. Adjustment of the analyzer and p o l a r i z e r prisms was now c a r r i e d out with the compensator removed. A transparent quartz d i e l e c t r i c r e f l e c -tor was used as a sample because such a surface eliminates the e f f e c t of f i r s t order e l l i p t i c i t i e s i n the p o l a r i z e r and analyzer prisms"*"^ at any angle of incidence, since s i n A=0 for a transparent surface. To e s t a b l i s h the plane of incidence, the analyzer telescope was set at the desired angle and with A = P = 90°, the quartz surface was aligned to give maximum i n t e n s i t y of the beam. This establishes the plane of incidence. Now A i s nu l l e d near 0° for d i f f e r e n t set values of P about 90° to obtain a s t r a i g h t l i n e p l o t of A vs. P. Then P i s n u l l e d near 0° f o r d i f f e r e n t set values of A about 90°. The r e s u l t s are p l o t t e d i n Figure 3. The point where the two s t r a i g h t l i n e s i n t e r s e c t gives the correction to be made to the A and P sca l e s . With the A and P scales set to these values the shaft encoders were adjusted u n t i l the output of the Decitrak read 0.00° f or the one scale and 90.00° f o r the other s c a l e . The alignment of the quarter wave plate (QWP) was checked using an Inconel s l i d e with a m i r r o r - l i k e surface. The s l i d e was aligned by maximizing the s i g n a l with the QWP removed. The QWP was replaced and two zone readings were taken from which Tc and 5c were 13 computed using McCrackin's program. Tc i s the transmission r a t i o of the fast and slow axes and i s i d e a l l y equal to 1. <$c i s the phase ret a r d a t i o n and i d e a l l y equals 90°. For t h i s alignment Tc•= .99449 and 6c = 90.819 °. In subsequent alignments of experimental samples the same method was used as i n the i n i t i a l alignment of the ellipsometer. The o i n t e n s i t y of r e f l e c t e d l i g h t was maximized with P = A = 90 and with the QWP removed. The angle of t i l t of the sample was then measured.from 2 zone readings. The actual value of the angle was obtained from compu-t a t i o n s ^ on the IBM 360/67 and was used to correct a l l future readings taken i n 1 zone. T y p i c a l values of the angle of t i l t using t h i s O 0 procedure were i n the range of 0.08 to 0.02 . 2.2.1 Sample Preparation Tantalum: Two methods were used i n sample preparation. Samples to be used i n o p t i c a l studies required a f l a t r e f l e c t i n g surface and were elect r o p o l i s h e d to achieve t h i s . A l l other samples were chemi-c a l l y polished because the process was simpler yet gives a surface conducive to growth of the anodic oxide. Chemical p o l i s h i n g leaves a wavy surface. A l l samples were prepared at room temperature. In the chemical p o l i s h i n g procedure specimens were dipped i n a f r e s h s o l u t i o n of 98% H 2S0 4, 70% HN03 and 48% HF i n the r a t i o 5:2:1 by volume. This was followed by a 10 sec. HF dip and a d i s t i l l e d water r i n s e . The specimen was then degreased i n b o i l i n g t r i c h l o r e t h y l e n e and r i n s e d . In the e l e c t r o p o l i s h i n g procedure, one side of the specimen was mechanically polished on 0/0, 2/0, 3/0, 4/0 emery p o l i s h i n g papers i n 14 tha t o r d e r . The specimen was then e l e c t r o p o l i s h e d i n a t e f l o n c e l l w i t h a l a r g e p l a t i n i z e d p l a t i n u m e l e c t r o d e . The b a t h c o n s i s t e d of 10% by 11 -2 volume 487o HF i n 98% H SO. and a c u r r e n t of 100 ma cm was passed . 2 4 r O p t i c a l l y acceptable sur faces took about 30 m i n . i n the bath to p r e p a r e . R e s u l t s were found to be b e t t e r i f the cathode was l a r g e . E l e c t r o p o l i s h i n g removes the work-hardened s u r f a c e l a y e r and leaves a s u r f a c e w i t h p r o p e r t i e s as c l o s e as p o s s i b l e t o the b u l k m a t e r i a l . R i n s i n g and degreas ing werd the same as above. Tantalum specimens to be used i n t r a n s i e n t s t u d i e s ( chemica l p o l i s h ) were F a n s t e e l p o l y c r y s t a l l i n e t a n t a l u m and measured 2" x 1 x 0 . 1 3 cm w i t h a mounting t a b . A copper w i r e was spot welded to the t a b . The tabs were masked about ha l fway down w i t h A p i e z o n N grease and j u s t b e f o r e "j a n o d i z a t i o n the samples were dipped i n chromic a c i d and then r i n s e d , A n o d i z a t i o n of batches of samples was c a r r i e d out i n 0 . 2 N H^SO^ at I . . 2 .6 ma cm up t o 100 v o l t s a f t e r which the batch was l e f t at cons tant v o l t a g e f o r 12 h o u r s . The f i n a l leakage c u r r e n t was a p p r o x i m a t e l y 1 uA cm . 1 ' A l l samples except those noted were annealed i n 12 b o i l i n g water f o r 5 m i n . , to m i n i m i z e any d e f e c t s i n the o x i d e P r i o r t o an experiment the tabs were c o m p l e t e l y masked w i t h A p i e z o n N grease so that the edge of the annealed ox ide was w e l l p r o t e c t e d . The samples were then dipped i n chromic a c i d f o r 10 sec . and r i n s e d be fore i n s e r t i o n i n t o the c e l l . The g l a s s c e l l c o n t a i n e d a s t i r r i n g p r o p e l l o r to m i n i m i z e temperature g r a d i e n t s and a l a r g e p l a t i n i z e d p l a t i n u m e l e c t r o d e . The c e l l was submerged i n a thermostated water b a t h . The e l e c t r o l y t e was 0 . 2 N H SO, . Tantalum specimens used i n o p t i c a l s t u d i e s were F a n s t e e l s i n g l e 15 c r y s t a l tantalum with the o p t i c a l surface oriented i n the (111) d i r e c t i o n . They were 1 cm i n diameter and 0„2 cm t h i c k . Connection was made to the sample with a heavy aluminum wire. A blob of s i l v e r conducting paint ensured good contact while epoxy offered strength tp the j o i n t . The e n t i r e d i s c was masked with Apiezon N. ALUMINUM Ta OR Nb DISC Niobium: Niobium samples used i n o p t i c a l studies were prepared by a 13 chemical p o l i s h . The s o l u t i o n consisted of 1 part phosphoric acid (85%), 1 part HF (48%) and 1 part HN03 (70%). The r e s u l t i n g surface was very good. Continuous, gentle a g i t a t i o n was provided by moving the sample about and upon removal the sample was rin s e d immediately i n d i s t i l l e d water. 2.2 Optical Constants of Tantalum" Before any work could be c a r r i e d out with our present system, the o p t i c a l constants of tantalum had to be c a l c u l a t e d . The l i g h t source for the ellipsometer was a helium-neon laser which emitted l i g h t at Carried out i n conjunction with Graham Olive. SILVER CONDUCTING PAINT 16 o 6328 A. The sample was a p o l y c r y s t a l l i n e piece of Fansteel tantalum cut i n the same shape as the samples used i n the transient studies. Surface preparation followed the e l e c t r o p o l i s h i n g procedure of I I , 2.1, (p. 13). Anodization was c a r r i e d out i n a 0.2N I^SO^ s o l u t i o n . For each measurement the sample was removed from the bath, r i n s e d i n d i s t i l l e d water and blown dry with nitrogen gas. To ensure that sample alignment did not change between readings, the sample was mounted i n a f i x t u r e which f i t t e d into a j i g mounted on the ellipsometer. The angle of incidence used was 70°. A t o t a l of 32 (i>,h) points were measured encompassing three cycles on the ellipsometry curve. The f i n a l f i l m thickness was o 3307 A. Four zone measurements were taken for each point and the r e s u l t s arranged to give ^ and A, From F i g . 4 i t can be seen that the cycles overlap i n d i c a t i n g that the oxide i s a si n g l e layer f i l m . The numbers beside the curve are thickness i n angstroms. The word 'bare' r e f e r s to the f i r s t measurement taken for which there was an i n i t i a l t h i n f i l m on the substrate. The s o l i d l i n e i s a curve for n-^  = 2.185 + 0.005 and n 2 =2.46 - j2.56 where n-^  and n 2 are the index of r e f r a c t i o n of the f i l m and the tantalum substrate r e s p e c t i v e l y . The accuracy to which n^ was computed was +.01 for both the r e a l and imaginary p a r t s . 14 The points were f i t t e d to the l i n e with a computer program using the U.B.C. IBM 360/67 computer. The Hartman equation reported by Young''"' for fi l m s formed at ° - o 25 C and 10 ma cm was n i = 2.14 + ° - 2 9 2 „ (6) (r~) - 2.305 L10 1.2 This gives a r e f r a c t i v e index of 2.195 at 6328 A which i s i n good agre-ement with our r e s u l t . Ord et a l . have published data for t a n t a l u m ^ and found that 20 Figure 4: 40 50 IfJ (DEG) 70 E l l i p s o m e t r y curve f o r H&^O on Ta i n a i r . S o l i d l i n e i s f o r a f i l m w i t h n« 2.185 and su b s t r a t e constants n= 2.46 - .12.56. The o numbers, beside the curve are t h i c k n e s s i n A n^ = 2.2 and n 2 =3.02 - J2.57. Their values were determined by i n s i t u ellipsometry and should be i n good agreement with the r e s u l t s presented here. The values of the oxide index (n^) are. c l o s e , however the r e a l parts of the indices f o r the substrates do not agree. It has been pointed o u t ^ that measurements made on niobium indicated that the amount of oxygen absorbed i n the metal can cause a v a r i a t i o n i n the o p t i c a l constants. This may also be the case f o r tantalum. 2.3 The Structure of Ta^Og 18 The low temperature form of T^O^ has rec e n t l y been published o The orthogonal unit c e l l has dimensions a = 6.198, b = 40.29, c = 3.88 A and contains 11 formula units (22 metal atoms and 55 oxygen atoms). The metal atoms are arranged i n sheets and are surrounded by oxygen atoms which form either d i s t o r t e d octahedral or pentagonal bipyramidal coordina-t i o n polyhedra. The ide a l structure can be generated from a chain of 8 edge-sharing pentagons which i s r e g u l a r l y folded. The i d e a l unit c e l l contains 22 metal ions and 58 oxygen ions. The r e a l unit c e l l d i f f e r s from the i d e a l unit c e l l i n the way i n which i t accommodates the d i s t o r t i o n planes imposed upon i t by the f o l d i n g process. There are an average of 3 d i s t o r t i o n planes per unit c e l l with four p o s s i b l e locations w i t h i n the c e l l . Figure 5 shows a unit c e l l with d i s t o r t i o n planes located at d^, d-> and d^. The fourth p o s i t i o n , d^ i s not used i n t h i s c e l l but may be in others. 19 Structural changes can occur and can be thought of as changes in the p o s i t i o n s and i n the concentration of the d i s t o r t i o n planes. As an example, heating the system can cause some of the d i s t o r t i o n s to be annealed out. "Figure "5. A(00l) projection of L-Ta20 . 'There are three distortion planes i n this unit c e l l located at d^d^ and d_. The fourth position at d i s related by symmetry but is not used i n this unit c e l l . Black dots represent metal atoms and shaded areas oxygen coordination polyhedra. (after Ref. 18) 20 I I I . ELECTRO-OPTIC EFFECT 1. Introduction The electro-optic effect exhibited by "^a.^^^ films has recently 1 9 been investigated by several authors. Ullman et a l . have suggested that the field-induced modulation i s accompanied by an e l e c t r o s t r i c t i v e 20 compression of the oxide. Frova and Migliorato , using multiple interference theory, have concluded that the o p t i c a l path change i s mainly due to a change i n the' r e f r a c t i v e index rather than a change 1 6 i n thickness caused by e l e c t r o s t r i c t i o n . However Ord, Hopper and Wang using i n s i t u ellipsometry have found that a change i n r e f r a c t i v e index i s associated with a proportional change i n the thickness when the f i e l d i s altered. They changed the f i e l d by suddenly changing the ionic current .passing through the f i l m and found ..that the thickness increased l i n e a r l y with f i e l d and that the index of r e f r a c t i o n decreased l i n e a r l y with f i e l d . However, Ord's experiment did not cover a wide range of f i e l d , making i t d i f f i c u l t to establish whether the relationship i s purely line a r or merely apparently so, e.g..a small portion of a parabolic curve could be assumed l i n e a r . The following experiment was designed s p e c i f i c a l l y to measure the electro-optic effect over a s u f f i c i e n t l y wide range of f i e l d to determine whether the dependence of the r e f r a c t i v e index i s predominantly linear or quadratic. The range from zero f i e l d to just below the forming f i e l d was chosen so that there would be no appreciable change i n thickness due to passage of ionic current. 2. Theory 1 The electro-optic effect is defined as the change in the refractive index of a substance produced by an electric f i e l d . There are 2 possible components which cause this change. One is known as the primary electro-optic effect and is s t r i c t l y a change of index due to an electric f i e l d . The second is the secondary electro-optic effect: If an electric f i e l d is applied to a crystal and the crystal is not constrained then a change in dimensions w i l l result by the con-verse piezoelectric effect (linear dependence of strain on field) or by electrostriction (quadratic dependence of strain on f i e l d ) . This in turn w i l l cause a change in refractive index by the photoelastic effect. If the crystal is clamped the primary effect only is observed. If the crystal is free to move then the observed effect is the sum of the primary and secondary effects. In an isotropic medium, the dielectric properties at optical frequencies are given by where £Q is the permittivity of a vacuum, £^ is the dielectric constant, D the displacement and E the electric f i e l d . The refractive index n i s defined as n = /T • . • (2) In an anisotropic medium equation 1 must be written in tensor form. Dealing just with the case where D and E are pa r a l l e l , i t can be shown"'" that the relation between n and E may be written as a power series, 22 n ? n „ + a E + b F ? + (3) where a and b are constants and i s the r e f r a c t i v e index for E = 0. If a f i e l d i s applied to a centrosymmetric c r y s t a l (one that i s unchanged by inversion) then reversing the d i r e c t i o n . o f the f i e l d leaves the r e f r a c t i v e index unchanged. However equation 3 w i l l become n = n Q - a E + b E 2 - (4) Equations 3 and 4 are equal only i f a = 0. Therefore i f a centre of symmetry i s present no f i r s t order e f f e c t s can e x i s t . The e l e c t r o -o p t i c e f f e c t i n amorphous fil m s would be expected to show quadratic dependence on the f i e l d because they can be considered to have a centre of symmetry because of t h e i r random structure. The s t r a i n produced by a f i e l d i s i n general given by e., = d. E. + y. „ E. E + . . . (5) j k l j k I 'i£jk l £ where e i s the s t r a i n , and d and y are the p i e z o e l e c t r i c and e l e c t r o -s t r i c t i v e c o e f f i c i e n t s . The s t r a i n i s r e l a t e d to the r e f r a c t i v e index through the r e l a t i o n = p. . e (6) 2 . . l j r s rs n i j where the p's are the photo-elastic c o e f f i c i e n t s . The subscripts i n equations 5 and 6 represent the various components of the tensors that are associated with the reference axes. (For a complete explanation see Chapt. 1, Ref. 1 .) The same argument applied to equation 4 can be applied to equation 6 so that for i s o t r o p i c materials, the change i n the r e f r a c t i v e index caused by e l e c t r o s t r i c t i o n must be quadratic i n nature. Therefore the t o t a l e l e c t r o - o p t i c e f f e c t i n an amorphous f i l m such as Ta20^ or J^^C-j. would be expected to exhibit quadratic dependence on the f i e l d . 3. Experimental Procedure Investigation of the e l e c t r o - o p t i c e f f e c t on tantalum and niobium was c a r r i e d out with i n s i t u ellipsometry. The ellipsometer o was aligned with an angle of incidence of 63.46 to accommodate one corner of the tr i a n g u l a r o p t i c a l c e l l . The angle of incidence required for normal transmission of l i g h t through the windows was measured with the ellipsometer. The specimen was aligned i n a i r and then the c e l l was positioned. Alignment of the c e l l was achieved by adjusting i t s p o s i t i o n u n t i l both r e f l e c t i o n s from the two windows of the c e l l returned to the aperture that was emitting the l i g h t . Since b i r e f r i n g e n c e i n the windows mainly 21 a f f e c t s the P o l a r i z e r reading , the alignment was not accepted unless the change i n A was small. -2 Specimens were anodized at a constant current of 1 ma cm to a predetermined constant voltage. In the case of tantalum the voltage was 124 v o l t s and for niobium i t was 20 v o l t s . The constant voltage -2 was l e f t on overnight and the f i n a l current was less than 1 uA cm i n a l l cases. The s o l u t i o n used for anodization was 0.2N H^SO^. I t was o s t i r r e d and thermostated at 25 + ,05 C. During the experiments the voltage was monitored with the d i g i t a l voltmeter and was recorded on the teletype v i a the computer. The current was monitored with an electrometer across a small sampling r e s i s t o r and was recorded on a chart recorder. I f a sudden change i n the f i e l d was applied to the f i l m a charging current was recorded as i n Figure 1. Beginning at zero voltage, the voltage across the sample was stepped up to just below the forming f i e l d . Ellipsometer measurements were taken at each step when the current as depicted i n F i g . 1 was i n the range C-D. This seemed to give more reproducible r e s u l t s than i f readings were taken i n the range B-C. Relaxation e f f e c t s were inves-ti g a t e d i n the region B-C. The thickness to which the f i l m s were grown was chosen because o o these gave readings of tp between 70 and 90 . In t h i s region the ellipsometer i s very s e n s i t i v e to o p t i c a l thickness. For tantalum, the f i l m was i n the second c y c l e of the ellipsometer curve and for niobium the f i l m was i n the f i r s t c y c l e . The r e s u l t s of the ellipsometer measurements were analyzed on 9 the IBM 360/67 using a program developed by McCrackin . The program was modified s l i g h t l y to extend the computations past the f i r s t c y c l e of the ellipsometry curve i n the tp-A: plane. Appropriate c o r r e c t i o n s were made for c e l l window er r o r s , angle of t i l t of the sample and for errors i n the compensator. To give an idea of the s e n s i t i v i t y of the ellipsometer under the present conditions, Table 1 compares the p o l a r i z e r and analyzer 6 readings for zero f i e l d with those at 5.07 x 10 V/cm. F i e l d V/cm P Deg. A Deg. Ad A An 0 49.11 81.20 0 - 0 6 5.07 x 10 46.06 81.45 4.6 -4.6 x 10" 3 For Ta 0 d = 2368 A n = 2.1947 .2 5 0 0 Table 1 The s e n s i t i v i t y i n the P and A readings i s 0.01°. 4.1 Results for T a ? 0 g When f i e l d s of d i f f e r e n t strengths were applied across the Ta 20^ f i l m both the r e f r a c t i v e index and the thickness changed. The r e f r a c t i v e index became smaller and the thickness became l a r g e r . Resul are p l o t t e d i n Figure 2 for Ad and An vs. E. These r e s u l t s are for a o f i l m i n which the o r i g i n a l thickness, dQ,was 2368 A and the o r i g i n a l r e f r a c t i v e index, no,was 2.19471. Computations of the r e f r a c t i v e index gave values within a 957« confidence l i m i t . For an error of 0.015 i n the p o l a r i z e r and analyzer readings the l i m i t s were about 0.00050 apart. A l l values of n used i n t h i s work were the mid point within the ca l c u l a t e d l i m i t s . Figure 2 shows that neither the thickness nor the r e f r a c t i v e index change i s a l i n e a r e f f e c t . Figure 3 however, ind i c a t e s that both e f f e c t s are d e f i n i t e l y quadratic i n nature as would be expected of an 26 o \ o I I I 1 ; L_ 0 1 2 3 4 5 E (l06V/cm) Figure 2: The change i n thickness and refractive index with f i e l d for Ta„O c. n = 2.1947; d= 2368.0 A. 27 amorphous f i l m or any i s o t r o p i c medium''. To a f i r s t approximation, an equation of the form n = n (1-bE2) (7) can be used to f i t the data. In t h i s case b would have the value © 2 0.759 (A/V) . The r e s u l t , that the e l e c t r o o p t i c e f f e c t i s a quadratic 16 effect,opposes Ord's statement that the e f f e c t i s l i n e a r . However Ord et a l . only considered a small range of f i e l d s . Ord et a l . concluded that the changes seen upon switching were due to the e n t i r e f i l m and not just an e f f e c t of one of the in t e r f a c e s because the e f f e c t was larger for thicker films even though the o p t i c a l s i t u a t i o n had not changed ( i . e . at the same point on the if>,A curve but i n d i f f e r e n t c y c l e s ) . The same r e s u l t s were found to hold true i n t h i s experiment. If the f r a c t i o n a l change i n thickness and i n r e f r a c t i v e index ..are ..computed., both r e s u l t s are about equal i n ..magnitude but opposite i n sign. In an expression of the form M = - c ^ (8) d n c has an average value of 0.912. The standard d e v i a t i o n from t h i s value i s .0572 or 6.43%. The change of n with f i e l d seemed to involve 2 processes. When the f i e l d was applied, the r e f r a c t i v e index jumped suddenly to a lower value and then began changing at a slower rate as shown i n Figure 4. The balancing time to the f i r s t balance does not allow the sudden change to be followed. However when the points on the curve of Figure 4 l a b e l l e d 120 v o l t s were f i t t e d to an equation of the form 29 20 30 TIME (sec) c 10 20 30 TIME (sec) 40 SO Figure 4: The change i n t h i c k n e s s and r e f r a c t i v e index w i t h time f o r Ta^O^-when the a p p l i e d v o l t a g e i s suddenly changed from O.V to the value i n d i c a t e d , d = 2 3 6 4 . 6 A ;n = 2 . 1 9 6 9 -30 n(t) = n + ( n 0 - n f ) e - t / T (9) 0 F i g u r e 5• • where the various symbols are as defined i n • Figure 5, i t was found that n^ was not equal to zero, and so i t i s assumed that' a sudden step did occur. The f i t t e d values of the parameters, using a least squares f i t t i n g routine were: n = - 4.02 + .021 x 10 n - n f = 0.682 + .034 x 10 -3 -3 1/x = 0.119 + .030 x sec" This curve i s for a 2364 A f i l m that was o r i g i n a l l y at zero v o l t s and had 6 120 v o l t s (5.07 x 10 V/cm) applied. The same e f f e c t was evident upon removing the f i e l d . The thickness and r e f r a c t i v e index changed suddenly towards the o r i g i n a l values and then decayed more slowly. Applying and then removing a f i e l d seems to have l i t t l e e f f e c t on the f i l m . Table 2 shows the deviations from n^ and d^ when the f i l m has been returned to zero f i e l d a f t e r stepping to 120, 130 and 135 v o l t s . VOLTAGE STEP £>d A &n x 10"3 120V to 0 V .2 -.13 v ~v 130 to 0 -.3 -.15 135V to 0 V -.1 -.01 2367.7 A n = 2.19525 0 Table 2 31 The question of what effects would be seen i f the applied f i e l d was greater than the forming f i e l d was investigated. The film in question was originally formed at 125 V overnight. A 130 V step was applied for about six seconds which allowed two or three ellipsometer balances to be taken. This was not long enough to allow the ionic current to begin building up though. The same procedure was carried out at 135 V. The transient effects at 130 and 135 volts are plotted in Figure 4. It is d i f f i c u l t to f i t so few points to a curve. If more points were taken, complications from the ionic current causing growth would occur. The values of n and d measured at 130 and 135 volts do not f a l l on the curves of Figure 3, however, given time they probably would. 4.2 Results for Nb^0^ The same procedures were carried out on N°2^5 a s w e r e u s e d on ^a2^5* ^ e b e h a v i ° u r °f fc^e o n e * s similar to the other and only the magnitudes of the effects d i f f e r . The niobium sample was anodized to a film thickness, dp,of 650 A with a refractive index, ng,of 2.326. The optical constants used 22 for the nibioum substrate were n g =3.5 - J3.75. Figures 6 and 7 2 show the change in n and d plotted against E and E . F i t t i n g the curve in.Figure 7 to equation 7, n ^ n Q(l-b F 2) , ( 7) o 2 requires b to be 3.55 (A /V) . The value of c in equation 3 has an. average value .9795.with a standard deviation of .0719. This.is a deviation of 7.347». 32 1.6 1.4 1.2 1.0 0.8 0 0.6 0.4 0.2] 0 i o c 0 1 . . • _ 2 E (I0b V/cm) Figure 6 : The change in refractive index and thickness with f i e l d for Nt^Cy d = 6 4 9 . 6 A ; n = 2 .3263-33 Figure 7: R e s u l t s of Figure 6 Vs. E . 20 30 TIME (sec) 10 20 30 TIME (sec) Figure 8: The change in thickness and refractive index with time when the f i e l d i s suddenly changed., (o-o-o) for a decrease in f i e l d . (x-x-x) for an increase in f i e l d , d = 650.3 A ; n = 2.3260. 35 The oxide of niobium also exhibited two processes of thickness and r e f r a c t i v e index change when a f i e l d was suddenly a p p l i e d . Figure 8 shows t h i s change with time. The curves through the c i r c l e d points of Figure 8 are for a sudden change from 2.89 x 10^ V/cm to 1.67 x 10^ V/cm, and the curves through the x's are for a sudden change from zero f i e l d to 1.67 x 10 6 V/cm. The r e s u l t s for a p o s i t i v e step i n the f i e l d can be f i t t e d to equation 9 where the symbols are defined as i n Figure 5. For t h i s curve the value of the constants were : n f = -3.02 + .015 x 10" 3 (n Q-n f) = 1.35 + .019 x 10" 3 I/T = .004 s e c " 1 The r e s u l t s shown i n Figure 8 for the negative step i n the f i e l d can-be described by equation 9 i f the symbols are as -shown in Figure 9 . Figure 9. 36 The values of the constants for t h i s case were n f = -2.94 ± 0.042 x I O - 3 (n f-ng) = 1.30 + 0.14 x I O - 3 1/T = 0.112 + 0.014 s e c " 1 5. Discussion Anodic oxide f i l m s of tantalum and niobium have generally been thought of as being completely amorphous and should therefore exhibit quadratic dependence on the f i e l d due to symmetry arguments. However, i t i s quite conceivable that since the boundary on one side of the f i l m i s not the same as the other, the f i l m may have graded proper-t i e s or i n any case properties that are not completely amorphous. It was found that for both Ta 20^ and IM^O^ the r e f r a c t i v e index, n, varied with the square of the f i e l d . It was also found that a change i n the f i e l d caused n to change i n two d i s t i n c t phases. There was a sudden change followed by a much slower change as n approached a l i m i t i n g value. The e l e c t r o - o p t i c e f f e c t can have a number of sources: there w i l l be a d i r e c t e l e c t r o n - f i e l d c o n t r i b u t i o n inwhich the applied f i e l d w i l l modify the e l e c t r o n i c p o l a r i z a b i l i t y (or r e f r a c t i v e index); the applied f i e l d w i l l cause a l a t t i c e displacement which w i l l modify the el e c t r o n i c p o l a r i z a b i l i t y ; any defect ions w i l l rearrange themselves under the influence of the f i e l d which w i l l i n turn e f f e c t the elec-t r o n i c p o l a r i z a b i l i t y ; and i n a d d i t i o n , the e n t i r e structure w i l l slowly change when the f i e l d i s applied and e f f e c t the e l e c t r o n i c polar-i z a b i l i t y . 37 The second slower change i n n seen when the f i e l d i s applied i s between 17% of the t o t a l change f o r Ta2°5 a n c * a b o u t ^5% of the change for ^ 2 0 ^ . The instantaneous change i n the r e f r a c t i v e index can be accounted for by the e l e c t r o n - f i e l d c o n t r i b u t i o n and by the f i e l d -induced l a t t i c e displacement. The slower change i n n may be caused by the d r i f t of defect ions caused by the applied f i e l d and by the e f f e c t that the f i e l d has upon the en t i r e structure of the f i l m (the apparent thickness of the f i l m increases as the f i e l d i s a p p l i e d ) . Another explanation of t h i s slow change i n n could be that proposed by Chen for LiNbO-^ and s i m i l a r c r y s t a l s . When the f i e l d i s applied, electrons i n traps close to the conduction band w i l l be excited and begin to d r i f t towards the p o s i t i v e side of the f i l m . This process w i l l continue u n t i l s aturation occurs and the space charge so created has reached a steady state when the generation and recombination processes are equal. The build-up of the space charge f i e l d w i l l cause the r e f r a c t i v e index to change and f i n a l l y approach a l i m i t i n g value. I f t h i s model i s cor r e c t , then upon removal of the applied f i e l d , the e f f e c t should be reversed. There should be a comparatively slow change of n as the electrons r e d i s t r i b u t e and are f i n a l l y a l l trapped. It should be noted that the time constant for the decay of the current when the f i e l d i s suddenly changed i s smaller than the time constant associated with the slow change i n the r e f r a c t i v e index. I f the current seen when applying the f i e l d i s a charging current associated with the build-up of space charge, then t h i s would suggest that space charge i s not the primary cause of the slow change i n n. Many authors c a l c u l a t e the magnitude of the quadratic e l e c t r o - o p t i c e f f e c t i n terms of the l a t t i c e p o l a r i z a t i o n rather than 38 the e l e c t r i c f i e l d , E. For the case of Ta205 and s i m i l a r structures the r e l a t i o n An = - \ g 1 2 P 2 n 3 (10) holds , where An i s the change i n the r e f r a c t i v e index, g^ 2 i s the transverse e l e c t r o - o p t i c c o e f f i c i e n t and P i s the l a t t i c e p o l a r i z a t i o n . The p o l a r i z a t i o n Is r e l a t e d to the f i e l d by P = eo(e - 1) E (11) C a l c u l a t i o n of g^ 2 from the data on Ta20,^ given i n t h i s chapter shows that the r e s u l t i s of the same order of magnitude as that given by 29 30 Frova et a l . for Ta 20^ and that given by Chen et a l . for KTN These t h i n films do not e x h i b i t the e f f i c i e n c y of KTN and other such c r y s t a l s as e l e c t r o - o p t i c l i g h t modulators because the o p t i c a l path length i s considerably smaller. IV. U.V. IRRADIATION OF ANODIC OXIDES 1. Introduction It i s known that i n some i n s u l a t o r s such as I^O,., e*posure to u l t r a v i o l e t l i g h t causes a large e l e c t r o n i c current to flow. If the specimen i s l e f t illuminated for some time, the oxide f i l m grows th i c k e r . I f the u.v. l i g h t i s turned o f f o c c a s i o n a l l y , the secondary or dark current can be monitored. The dark current increases a f t e r 10 or 20 minutes from i t s i n i t i a l l y low value and f i n a l l y decays again a f t e r having reached a peak. A l l t h i s occurs at f i e l d s too low to support ordinary anodic oxide growth. To date, no theory has been put forward to adequately explain t h i s phenomena. Previous experiments interrupted the i r r a d i a t i o n for up to 30 minutes i n order to carry out ellipsometer r e a d i n g s ^ . In t h i s experiment, i n s i t u measurements of thickness and r e f r a c t i v e index were made on tantalum and niobium to further investigate these phenomena. Measurements during the incubation period (before the dark current b u i l d s up) should i n d i c a t e whether the i n i t i a l process can be regarded as a space charge build-up or not. 2. Experimental Procedure The arrangement of the c e l l and the alignment of the sample i n the ellipsometer were exactly the same as i n 111, 3 (p. 23). The u.v. l i g h t source (G.E. - G4T4) was a mercury arc lamp with about 95% o of i t s r a d i a t i o n at 2537 A. Sample preparation was as indicated i n I I , 2.1 (p. 13). The e n t i r e unmasked surface of the sample was i r r a d i a t e d . Specimens were formed to various thicknesses and held at constant voltage overnight u n t i l the i o n i c current was less than 1 yA cm so that the growth rate was n e g l i g i b l e . In experiments to test the r e v e r s i b i l i t y of e f f e c t s due to short periods of i r r a d i a t i o n , the ellipsometer monitored the f i l m while the u.v. l i g h t was turned on for about 15 seconds and then turned o f f . During t h i s time, a f i e l d close to the forming f i e l d was applied. In experiments i n which the f i l m was grown under u.v. l i g h t , the u.v. would be turned o f f for periods of about 10 seconds i n order to see the b u i l d -up of the secondary current. Figure 1 shows the c i r c u i t arrangement. When current measure-ments were taken, s 2 was opened Figure 1. 3. Results 3.1 Changes i n Thickness and Refractive Index due to Short Response  to Radiation o Ta205 fi l m s were i n i t i a l l y formed at 25 v o l t s to 668 A. This o gave ellipsometer readings i n the f i r s t c ycle with ty > 75 . Before turning on the u.v. l i g h t , 20 v o l t s was applied across the f i l m and s u f f i c i e n t time was allowed for the f i l m to s t a b i l i z e . The u.v. l i g h t was then turned on for about 15 seconds and then turned o f f . The ellipsometer tracked the change i n n and" d while the l i g h t was on and after the l i g h t was turned o f f . Figure 2 shows the type of s A p l o t that was obtained. Continued a p p l i c a t i o n s of u.v. l i g h t for short periods gave the same type of r e s u l t , but the i n i t i a l change i n 4> and A became smaller. During photo-stimulated growth, when the u.v. l i g h t was turned off frequently, i t was found that the change i n ifj and A upon switching of f the l i g h t decreased as the experiment progressed u n t i l there was no change. Figure 3 shows the change i n n and d vs. time f o r a short a p p l i c a t i o n of u.v. l i g h t . The u.v. l i g h t had a small e f f e c t on the f i l m which a f t e r the l i g h t was extinguished appeared to be erased. The magnitude of these e f f e c t s were very much smaller than those found after extensive i r r a d i a t i o n with u.v. l i g h t . 3.2 Photo-Stimulated Growth o The Ta2C>5 f i l m was grown to a thickness of 2477 A and a f i n a l -2 current density of less than 1 uA cm . The u.v. l i g h t was then applied for about two and a h a l f hours. Occasionally i t was turned o f f for 10 or 15 seconds i n order to monitor the dark current. Figure 4 shows the r e s u l t i n g t o t a l and dark currents. Figure 5 shows the ellipsometry r e s u l t s which correspond to Figure 4. Figures 6 and 7 are the corresponding curves for niobium. D e l l ' O c a 1 1 found that a model co n s i s t i n g of a two layer f i l m growing on the substrate gave a reasonable f i t for h i s data. Neither f i l m had the index of the o r i g i n a l f i l m . The outer index was lower and the inner index was higher. In the r e s u l t s of the present experiment i t was found that i f ellipsometry 42 215.0.\ FIELD ON 214.8 Uj 2U.6\ U.V ON * U.V OFF J _ 1 1_ L J !_ J _ I I L 76.60 76.70 (DEG) 76.80 Figure 2: Ellipsometer points f o r Ta^Cv on Ta f o r short exposure to u.v. light'. 8 10 12 14 16 18 20 22 24 26 TIME (sec) Figure 3: The change i n r e f r a c t i v e index and t h i c k n e s s during short exposure to u.v. l i g h t . . . d = 2466.8 A ; n = 2.206. 44 points for the entire u.v. r a d i a t i o n period were f i t t e d to a two layer model, the f i t was very poor. If however the points taken during the incubation period (points up to "a", Figure 5) were omitted, the f i t t i n g parameter was minimized to a value 100 times smaller than before,giving a good f i t . As i n Dell'Oca's case, the index of the outer layer was smaller and the index of the inner layer was larger than that of the o r i g i n a l f i l m . It i s apparent that before the onset of the increase i n the dark current, the u.v. r a d i a t i o n modifies the properties of the oxide. In Figure 8, the change i n r e f r a c t i v e index during the incuba-9 t i o n period i s plotted against time. These values were c a l c u l a t e d assuming a s i n g l e uniform f i l m on the tantalum substrate. The thickness o of the o r i g i n a l f i l m was 2477 A and i n a period of 60 minutes of u.v. r a d i a t i o n , the thickness was c a l c u l a t e d to increase by 1.9%. Figure 9 indicates that t h i s process i s mainly quadratic i n nature. Experiments on Nb,^ (Figures 10 and 11) gave s i m i l a r r e s u l t s however a s l i g h t n o n l i n e a r i t y of n vs. t 2 was observed. If the data i s f i t t e d to a power series 2 (n n-n) = a n + a 0 t + a„t + .... U 1 I 3 ( 1 ) where &l = 0, i t i s found that a 2 = 2.47 x 10" 0 and = 2.09 x 10 . A f t e r the i n i t i a l peak i n the t o t a l current had dropped o f f , (Figures 4 and 6) the u.v. l i g h t was turned o f f for about two hours. At the end of t h i s period ellipsometer measurements showed that the o p t i c a l constants of the f i l m s had not changed appreciably. It must be con-cluded then that the change i n the f i l m Is permanent or that any relaxa-t i o n e f f e c t s have a very long time constant. Relaxation cannot be r u l e d 230 P 220\ < 210\ 200 1D0 THEORETICAL fn= 2.195} 20 2700A 2800A 290OA EXPERIMENTAL 50 V (DEG) Figure 5: Ellipsometry curve for Ta_0 . (o-o-o1) for u.v.-stimulated growth. 2 o • (_j ) computed curve for a film with n= 2.195- Small letters correspond to those on Figure 4. 47 WITH U.V 40 60 80 TIME (min) 140 Figure 6: Total and dark current densities for u.v.-induced growth o of TUb^O . d = 650. A .. Small letters correspond to those on Figure 7. ; ! 1 I I | 30 40 50 60 70 80 V .(DEG) Figure 7: Ellipsometry curve for NbgO^. (o-o-o) for u n -stimulated growth. ( 1 ) computed curve for. a film with n= 2.319. Small letters correspond ' to those on Figure 6. , -20 ' ' I I L 0 10 20 30 40 50 60 TIME (sec) F i g u r e 8: The change i n the r e f r a c t i v e index of a Ta o0,_ f i l m d u r i n g the i n c u b a t i o n p e r i o d of i l l u m i n a t i o n of u.v. l i g h t , assuming a s i n g l e uniform f i l m , n = 2.202 0 -2--4 ' . -6--8--70-T> 8 -12->< -78-• -20 • 0 I 2 TIME2 (103 min2) Figure 9: R e s u l t s of Figure 8 Vs. the square of the time. 50 f=-12-< Figure 10: The change in refractive index of a Fbo0._ film during the i n -cubation period of illum-ination of u.v. light • assuming a single uniform film. 0 2 4 6 8 10 12 14 TIME (min) 1, c 80 IPO 240 320 TIME2 (min2) Figure 11: Results of Figure 10 Vs. the square of the time. 5 1 o u t . C r y s t a l s o f LiNbO^ and o t h e r s i m i l a r i n s u l a t o r s e x h i b i t o p t i c a l i n d e x damage when exposed t o a l a s e r beam. The o p t i c a l change w i l l s l o w l y r e l a x back towards i t s o r i g i n a l s t a t e o v e r a p e r i o d o f da y s . Reasonably, one would e x p e c t t h e v a l u e o f n t o a p p r o a c h some f i n a l v a l u e s i n c e t h e p r o p e r t i e s o f t h e f i l m c l e a r l y c a n n o t c o n t i n u e t o change a t such a r a t e i n d e f i n i t e l y . F o r t h e s i n g l e u n i f o r m f i l m assumed i n t he c a l c u l a t i o n s the change i n n d i d not s a t u r a t e . Perhaps a more r e a s o n a b l e model wou l d be one i n w h i c h t h e change i n r e f r a c t i v e i n d e x c a u s e d by u.v. r a d i a t i o n was a d i s t r i b u t e d e f f e c t where t h e o x i d e c l o s e s t t o t h e l i g h t changed i n i t i a l l y a t a f a s t e r r a t e t h a n t h e o x i d e t h a t was f u r t h e r away. / 4. D i s c u s s i o n I t i s n e t y e t c l e a r what p r o c e s s e s w i t h i n t h e o x i d e a r e r e s p o n s i b l e f o r t h e o p t i c a l damage t o t h e f i l m . C h e n ^ , i n h i s a t t e m p t t o e x p l a i n o p t i c a l damage i n LiNbO^ has s u g g e s t e d t h a t t h e e f f e c t i s due t o a space c h a r g e b u i l d - u p w h i c h c a u s e s a change i n n v i a t h e e l e c t r o -o p t i c e f f e c t . I n h i s e x p e r i m e n t s he assumes t h a t e l e c t r o n s , w h i c h a r e p h o t o - e x c i t e d by a l a s e r beam d r i f t out of t h e beam under t h e i n f l u e n c e o f an i n t e r n a l e l e c t r i c f i e l d . T h i s c a u s e s t h e space c h a r g e b u i l d - u p and subsequent change i n n. I n our c a s e t h e r e i s no i n t e r n a l f i e l d , e x c e p t when an e x t e r n a l f i e l d i s a p p l i e d . That photo e x c i t e d e l e c t r o n s a r e moving under t h e i n f l u e n c e of t h e f i e l d i s e v i d e n t f r o m t h e l a r g e i n c r e a s e i n c u r r e n t upon a p p l i c a t i o n o f t h e u.v. l i g h t - When t h e e x t e r n a l f i e l d i s a p p l i e d n d e c r e a s e s i n p r o p o r t i o n t o t h e s q u a r e o f the f i e l d . T h i s change must be a s s o c i a t e d w i t h the p o l a r i z a t i o n o f t h e f i l m such t h a t t h e p o l a r i z a -t i o n i s i n the opposite d i r e c t i o n to the f i e l d causing i t . Now i f u.v. r a d i a t i o n causes the r e l e a s e of e l e c t r o n s from t r a p s , which cause a build-up of space charge, then the r e s u l t i n g p o l a r i z a t i o n would be i n the same d i r e c t i o n as that caused, only by the a p p l i e d f i e l d . The r e f r a c t i v e index would be expected to change i n the same d i r e c t i o n as b e f o r e , but more so. This i s what i s observed. However i t would a l s o be expected that the p o l a r i z a t i o n would s a t u r a t e as the c u r r e n t dropped o f f , causing the r e f r a c t i v e index to reach a steady s t a t e v a l u e . This does not appear to be the case. Another p o s s i b l e e x p l a n a t i o n could be that the u.v. r a d i a t i o n causes a change i n the s t r u c t u r e of the f i l m such that the d e n s i t y of the f i l m decreases. From the c a l c u l a t i o n s (assuming a s i n g l e uniform f i l m ) the change i n n i s accompanied by an i n c r e a s e i n the t h i c k n e s s . Assuming that t h i s i s the only dimension that changes then, Ap Ad . . IT = - T ' ( 2 ) where P i s the d e n s i t y . The Lorentz-Lorenz r e l a t i o n between d e n s i t y and r e f r a c t i v e index can be w r i t t e n as (n +2) where A i s a c o n s t a n t . D i f f e r e n t i a t i o n of equation 3 and s u b s t i t u t i o n of equation 2 g i v e s , Ad = 6 An d 2 , • 2 . n (4) (n + 1 2") n . or Ad _n_ = 6  d An . 2 • 2. (n + 1 2") n (5) Substituting n = 2.195 for Ta,-^ i n the r i g h t hand side of equation 5 gives a value of 1.13. For the l e f t hand side of equation 5: _'M'JL = _ 4 7 2.195 = 2 08 " d A n = " 2 4 7 7 X _ 2 - 3 x l 0 - 2 - ' Computations for Nb^ O^ . (n = 2.32), give for the r i g h t hand side of equation 5 a value of 0.998 and for the l e f t hand side, Ad n 8 2.32 •d An 676 ' -.0206 = 1.33 The c a l c u l a t i o n s indicate i t i s not l i k e l y that the change i n n i s s o l e l y due to a change i n density. Coupled with t h i s , i t must be kept i n mind that some of t h i s thickness change could be photo-stimulated growth. 12, P. 1 3 9 It has been suggested that photo-grown oxide contains water or s u l f a t e ions because the weight/charge r a t i o of the new f i l m , where the charge i s c a l c u l a t e d from the dark current, i s larger that i t should be. If incorporation of these f o r e i g n ions began i n the incubation period, t h i s could account for the change i n n. 54 V. CONSTANT FIELD CURRENT TRANSIENTS 1. Introduction 25 The constant f i e l d current transient i s a p e c u l i a r phenomenon that upon a p p l i c a t i o n of a f i e l d e x h i b i t s i n i t i a l l y a peak i n the current and then a decay followed by a slow current build-up that becomes in c r e a s i n g l y f a s t e r u n t i l a saturation value i s reached. The maximum current reached i s the steady-state value for the applied f i e l d . To describe t h i s process, a p a r t i a l l y c u r r e n t - c o n t r o l l e d 25 ' model i s needed. Young proposed a model consistent with the Frenkel defect theory i n which ions moved i n channels that were i n i t i a l l y blocked. The unblocking of channels by a momentum transfer process caused the increasing build-up of current through generation of Frenkel defects. Later, Dignam proposed an e f f e c t i v e f i e l d , slow p o l a r i z a t i o n theory , i n which the time development of p o l a r i z a t i o n depends on the io n i c current. This section investigates various e f f e c t s occurring during the transient including temperature e f f e c t s , the e f f e c t of annealing the f i l m , change i n thickness and change i n r e f r a c t i v e index. 2. Outline of Theory The e f f e c t i v e f i e l d slow p o l a r i z a t i o n theory was proposed by 26 Dignam to describe the constant f i e l d t ransients not explained by other theories. Only a b r i e f o u t l i n e of the theory w i l l be given here. The e l e c t r i c f i e l d a s s i s t i n g the migration of ions i s taken to be an e f f e c t i v e f i e l d so that J = J . exp F(E ) (1) 0 e where E g i s defined as 6 P E e B E + ^ (2) E i s the macroscopic f i e l d i n the d i e l e c t r i c , P i s the p o l a r i z a t i o n and <5 i s a numerical f a c t o r . The p o l a r i z a t i o n i s made up of the ordinary p o l a r i z a t i o n PQ, due to e l a s t i c displacement of charge, and of a slow p o l a r i z a t i o n PG which i s associated with mass ion transport. The tran-sient conduction phenomena a r i s e as a r e s u l t of the time dependence of the slow p o l a r i z a t i o n process which i s postulated to be proportional to the current density. dP = BJ(eo< E-P ) dt K .0' s a (3) where B i s a constant and X g i s the s u s c e p t i b i l i t y . Equation 3 i s the 1 same as the normal Debye equation with BJ r e p l a c i n g ~. From equations 1, 2 and 3 i t can be shown that dF " 3 <4> which i s of the required form for the i n i t i a l part of the t r a n s i e n t . The saturation of J i n the l a t t e r stages of the transient a r i s e s from the saturation of P . Dignam and Ryan have shown2'' that for a constant s applied f i e l d , the slow p o l a r i z a t i o n model gives f ^ B l o g f (5) where J g i s the f i n a l steady state current density for the applied f i e l d . B i s assumed independent of f i e l d and temperature. Equation 5 gives the best f i t to the experimental r e s u l t s of any theory developed to date. To indicate that other explanations of the transient are possibl e , a b r i e f summary of the channel model w i l l be given. Reference 28 compares various features of the models. Although the channel model was not derived s p e c i f i c a l l y with the constant f i e l d transient i n mind, an extension of i t produces the main features of the tra n s i e n t . The model was o r i g i n a l l y proposed to 4 explain the n o n - l i n e a r i t y i n log J-E p l o t s and gave for* the steady state current density J 0 6 X p ( - kT (6) To explain the build-up of current i n the constant f i e l d t r a n s i e n t , i t was l a t e r suggested t h i s occurred by the unblocking of the channels. The unblocking process might occur from momentum transfe r of ions 28 moving i n adjacent channels. Young has shown that the model gives - i - l J t ( J ) = 7 i (-f - ¥ +^2 1o§ [ir—] (7) 0 AB | - 1 which reproduces the main features of the transient although not as well as Equation 5. Here A and B are constants and J( t=0) = J . For a better f i t a re-blocking term would have to be incor-porated to better account for the saturation of J . E f f e c t s of temperature: The steady state equation for i o n i c conduction has the form^ J = J Q e x P e - g % (8) ' 57 It i s apparent that as the temperature T r i s e s the current density for a given f i e l d w i l l r i s e exponentially. During the constant f i e l d transient the current w i l l increase to the steady state value for the given temperature and f i e l d c o n d i t i o n s . It i s the nature of the increase that i s of i n t e r e s t i n t h i s s e c t i o n . In equation 5, the factor B i s proposed to be constant with temperature. Three factors a f f e c t the rate of current build-up i n the t h e o r e t i c a l equation. The f i r s t i s the i n i t i a l value given to J . The i n i t i a l peak i n the transient i s not accounted for i n equation 5 and so the i n i t i a l value of J must be estimated. The lower the value the longer the t r a n s i e n t . The second f a c t o r a f f e c t i n g build-up i s the value of B. B w i l l change the slope of ascent of the t r a n s i e n t . A higher value of B causes a steeper slope i n the curve, and causes the build-up of current to begin sooner (Figure 1). The t h i r d f a c t o r i s the value assumed for the f i n a l current density. 3.1 Apparatus The computer was used as an experimental c o n t r o l device to record current transients at constant f i e l d s . These t r a n s i e n t s increase from an i n i t i a l current to a f i n a l current that i s about 100 times larger than the i n i t i a l current. More than one range of a current recording device must be used i f adequate r e s o l u t i o n i s to be achieved. The duration of the t r a n s i e n t s can vary from 2 to 3 min. at O O 0 C to a few seconds at 30 C and so a method of c o n t r o l l e d data acqui-s i t i o n i n t e r v a l s i s needed i f an excessive number of readings are to be avoided. Four reed-relays were operated by standard DEC lamp d r i v e r s . 58 The drivers were wired to a device selector i n a manner that allowed any one re l a y to be closed while the others were open. A f i f t h and heavier r e l a y was used to make the main c i r c u i t . Figure 1 shows how the four reed-relay sequence was employed i n the c i r c u i t . I n i t i a l l y Relay 1 would be closed. As the current increased the voltage l e v e l presented to the A/D would be compared to a l e v e l near f u l l scale. When t h i s l e v e l was reached Relay 1 would open and Relay 2 would close there-by decreasing the sampling r e s i s t a n c e . Only 3 of the r e l a y s were usually required i n an experiment while the fourth guarded against unexpected overshoot. The response of the relays was much fas t e r than the fa s t e s t sampling i n t e r v a l (0.1 s e c ) . Figure 1. 59 PDP-8 Program The program begins by opening the main c i r c u i t r e l a y and then h a l t s . The operator can select the sampling rate by pl a c i n g various numbers i n the switch r e g i s t e r before r e s t a r t i n g the program. When the program i s r e s t a r t e d , the main r e l a y i s closed and the clock i s i n i t i a l i z e d . The current through the r e s i s t o r s i s then continuously sampled. When the top of the scale i s reached,the computer "up-ranges" the A/D by changing the status of the re l a y sequence. The time and voltage, including an indicato r for the approp-r i a t e range, i s stored i n a buffer area to await p r i n t out v i a the int e r r u p t . About 190 readings can be stored. The program used output and data a c q u i s i t i o n subroutines of the ellipsometer program. Off Line Data Handling The time and voltage readings gathered with the PDP-8/E were processed on the IBM 360/67. The voltages were converted to current readings and then c u r v e - f i t t e d using the U.B.C. Computing Centre fourth order Runge-Kutta program to c a l c u l a t e the t h e o r e t i c a l points and least squares regression analysis to f i n d the best f i t . 3.2 Experimental Procedure Samples were prepared as noted i n I I , 2.1 (p. 13) and put i n the c e l l . A l l samples were about 2100 A thick and exhibited the same interference colour. The e l e c t r i c portion of the c e l l was connected as shown i n F i g . 1 with shielded cable used throughout to avoid excessive noise. The system was quite s e n s i t i v e to noise when not shielded. The 60 voltage across the sampling r e s i s t o r s was measured with a Keithley 602 Electrometer. The one-volt f u l l - s c a l e output of the electrometer, which reverses the p o l a r i t y of the reading, was directed through another Keithley 602 Electrometer to regain the o r i g i n a l p o l a r i t y . The s i g n a l was then amplified by a factor of 10 and fed to the a n a l o g - t o - d i g i t a l converter of the computer i n t e r f a c e . The computer c o n t r o l l e d and gathered data during the experiment. The voltage drop across the sampling r e s i s -tors was about 300 mV or , 2 5 7 o , the actual value depending on the r e s i s t o r used for various temperatures. This s l i g h t change i n the f i e l d should show n o a f f e c t on B since B i s reputed to be independent of the f i e l d . The value of B was found by solving equation 5 using fourth order Runge-Kutta methods on the U.B.C. I.B.M. 360 computer and f i t t i n g the experimental r e s u l t s to the computed curve while varying the i n i t i a l value of the current density and B. 4.1 E f f e c t of Temperature on the Transient A l l transients exhibited the same form with an i n i t i a l peak, followed by a rapid drop i n current which slowly went through a minimum and f i n a l l y rose i n an a c c e l e r a t i n g manner to the steady state value for the applied f i e l d . Figure 2 shows the e f f e c t of temperature on the tr a n s i e n t . The constant B i n Dignam's theory should remain constant with temperature and only be a function of the preparation of the f i l m . Figure 3 shows t h i s to be so within experimental l i m i t s , over the tem-perature range considered. 4 OX TIME (sec) Figure 2: The e f f e c t of temperature on the constant f i e l d current t r a n s i e n t . 62 5 10 15 20 25 30 35 40 ' T (°C) F i g u r e 3. ' The parameter B o f e q u a t i o n 5 as a f u n c t i o n o f t emperature. Measurements on different batches gave values of B that were a l l in the same region even though the applied f i e l d was not exactly . o the same. Runs were only done up to 40 C because beyond that, the tran-sients were complete in a few seconds.. The time involved would have dictated using another method for gathering data such as a storage oscilloscope. The accuracy of the measurements would be greatly decreased making any comparison of data.at lower temperatures inaccurate. 63 4.2 E f f e c t of Annealing on the Transient Specimens that have been formed at constant voltage u n t i l the current density has dropped to within the microampere range contain many fewer defects than those formed at higher current d e n s i t i e s . I f these well-formed films are now annealed in some manner such as b o i l i n g i n water for f i v e minutes then the concentration of defects should be lower s t i l l . 18 Stephenson and Roth have shown that Ta20^ i s made up of a sequence of herring-boned chains of fused pentagonal bipyramids or d i s t o r t e d octahedral bipyramids with d i s t o r t i o n planes which occur i n pairs running through the structure. When energy (heat) i s added to the system, the length of some of these chains w i l l decrease and the number of d i s t o r t i o n planes w i l l decrease. If these d i s t o r t i o n planes are associated with the i o n i c conductivity then i t would be -expected that as the number of planes i s decreased, the i o n i c conductivity would also decrease. Heating the f i l m should therefore, decrease the c o n d u c t i v i t y of the f i l m and slow down the t r a n s i e n t . The f i l m s were prepared as noted i n I I , 2.1 (p.13) except that some films were not annealed i n b o i l i n g water. The f i l m s were o about 2100 A thick. The annealing process has been reported to have no e f f e c t on the thickness of the f i l m ^ ' P * 127 # The c e l l and e l e c t r i c a l c i r c u i t r y was the same as that described i n V, 3.1 (p. 57). Figure 4 shows t y p i c a l t r a n s i e n t s for each case. The annealed 3 2 sample f i t t e d a curve with B = 5.8 x 10 cm /C while the other sample 3 2 f i t t e d a curve with B = 6.4 x 10 cm /C. The i n i t i a l peak caused by the charging current was 25% lower f o r the unannealed sample than for the annealed sample, however the minumum current reached by the annealed sample dropped to a lower value than for the unannealed sample. The 64 0 5 10 15 20 25 30 TIME (sec) o Figure 4: The e f f e c t of annealing at 100 C f o r 5 minutes on the t r a n s i e n t . (x-x-x) curve f o r annealed sample (o-o-o) curve f o r a sample that was not annealed. f i n a l current reached was the same i n both cases because the f i e l d and temperature were the same, however i t took the transient i n the annealed sample nearly twice as long to be completed. The r e s u l t s indicate that annealing has a d e f i n i t e e f f e c t on the physical structure of the f i l m s and that the phy s i c a l change controls the rate of build-up of i o n i c current through the f i l m . The i n i t i a l p o l a r i z a t i o n current which drops o f f approximately as 1/t i s nearly the same for both cases and i t i s the build-up of the i o n i c current transient which stops the current i n the unannealed sample from dropping off to the value the current does i n the annealed sample. The i o n i c motion through the unannealed f i l m i s easier i n i t i a l l y than through the annealed f i l m . 4.3 Thickness and Refractive Index Changes i n the Oxide F i l m  During the Transient As was previously pointed out, a high f i e l d applied to a t h i n ^ a2^5 causes a change In the thickness and r e f r a c t i v e index. In t h i s section t h i s e f f e c t i s investigated during the constant f i e l d t r a n s i e n t . The experimental setup was l e f t unchanged except that a O t r i a n g u l a r o p t i c a l c e l l (angle of incidence =63.46 ) was used and the o p t i c a l constants were monitored with the ellipsometer. The i n i t i a l o thickness of the f i l m was 2090.5 A. The current transient i s shown i n Figure 5 and the corresponding ip, A points are given i n Figure 6. When the f i e l d was applied the r e f r a c t i v e index and thickness changed abruptly, which was to be expected. The r e f r a c t i v e index then decreased and leveled out (Figure 7) i n approximately 10 seconds. This corresponds to what happened when a f i e l d below the forming f i e l d was applied ( I I I , 4.1, p. 28). As the 6 7 CO U J < 82.0 -81.6 39.0 .2 .4 .6 ty (DEG) .8 40.0 .2 Figure 6: Ellipsometry points taken during the constant f i e l d transient for Ta^O^. The letters correspond to those in figure. 5. Solid lines are computed constant index of refraction curves. 5.89 5.90 5.91 5.92 5.93 5.94 5.95 E (106 V/cm) Figure 8: The change in thickness Vs. f i e l d during the transient of figure 5. 69 current began to b u i l d up the r e f r a c t i v e index again began to decrease and f i n a l l y leveled out at the end of the t r a n s i e n t . The only p r e d i c t -able change i n n would be associated with the change due to the e l e c t r o -o p t i c e f f e c t . One might expect that the curve of Figure 7 should not change af t e r the plateau at 10 seconds. A possible explanation of the further decrease associated with current build-up i s that the f i l m i s being heated by the passage of current. Although the bath was thermostated and s t i r r e d the very large current increase could cause the temperature of the f i l m to f l u c t u a t e momentarily. Figure 8 shows that the change i n thickness during the tr a n s i e n t O (neglecting that caused by applying the f i e l d ) i s about 19 A or 1.39%. The change i n the f i e l d would also be 1.39% since i t i s c a l c u l a t e d from the thickness. The fact that d vs. E i s l i n e a r i s not meaningful 2 because the E scale has been expanded to such a de.gree that- d vs. E would appear just as l i n e a r . 5. Discussion It i s known that films formed at higher current d e n s i t i e s have more defects than those that are not. If these defects are considered 18 to be the d i s t o r t i o n planes noted by Stephenson and Roth then i t could be concluded that the higher currents through the f i l m produce more d i s t o r t i o n planes i n the f i l m . The number of d i s t o r t i o n planes can be decreased by forming at I Q low currents or by annealing. Stephenson and Roth also noted that as the oxygen/metal r a t i o i s decreased, the concentration of d i s t o r t i o n planes increases. If the concentration of d i s t o r t i o n planes i s r e l a t e d to the io n i c conductivity then less oxygen i n the f i l m should Increase 70 the c o n d u c t i v i t y . This r e s u l t seems reasonable s i n c e a f i l m t h a t i s s t r u c t u r a l l y complete w i l l not have any d e f e c t s that a l l o w i o n movement. However a f i l m that has some of the oxygen ions m i s s i n g w i l l c r eate a l a r g e r c o n c e n t r a t i o n of d i s t o r t i o n planes that a l l o w f o r i o n i c move-ment w i t h i n the s t r u c t u r e . I t would appear then, that a f i l m t h a t has been annealed i s more f u l l y oxygenated and th a t the c o n c e n t r a t i o n of d i s t o r t i o n planes i s low. I f t h i s i s considered i n r e l a t i o n to the constant f i e l d t r a n s i e n t , then what might be considered t o occur when a constant f i e l d i s a p p l i e d i s - the fl o w of i o n i c current through the f i l m causes more d i s t o r t i o n planes to be created which i n t u r n a l l o w s more current to f l o w . This process increases u n t i l the maximum current that the f i e l d w i l l m aintain i s reached. At t h i s p o i n t the t r a n s i e n t i s complete. This view of the i o n i c conduction process i s s i m i l a r to the 2'8 Channel Model i n which channels become unblocked as the ions f l o w through them. The c r e a t i o n of d i s t o r t i o n planes could be viewed as the unblocking of channels of l e a s t r e s i s t a n c e or i t could be viewed as the c r e a t i o n of more channels. 71 VI. CONCLUSIONS The topics discussed in this thesis were the electro-optic effect on Ta2C>5 and M^ O,., the effects of u.v. radiation on and Nb 0^  and the constant f i e l d transient on Ta 0 . 2 5 2 5 The studies on the electro-optic effect showed that for both ^^2^5 and Nb^ O^  the refractive index decreased linearly with the square of the f i e l d . During this change the thickness increased linearly with the square of the f i e l d . Both effects were reversed when the f i e l d x<ras removed. It was found that when the electric f i e l d was applied, the thickness and refractive index change occurred in two steps. There was an instantaneous change followed by a slow change that approached a limiting value in a few tens of seconds. This double process occurred either when the f i e l d was increased or decreased. The studies of the effect of u.v. radiation on the growthof Ta20^ and ft^O^ concerned mainly the period of incubation before the dark current began to increase. It was found that the index of refrac-tion decreased considerably during this time while l i t t l e growth occurred. This indicated that some kind of structural rearrangement of the film occurred prior to the induced growth of the oxide. The oxide layer after u.v.-Stimulated growth was not a single uniform layer. Studies of the constant f i e l d current transient showed that increasing the temperature decreases the time length of the transient, however the parameter B in equation 5 of Chpt. V (p. 55 ) which is associated with the speed of current build-up relative to the total time of the transient, remains constant. It was also found that annealing the film slows down the transient and decreases the value of B. The change i n r e f r a c t i v e index during the transient was s i m i l a r to the change found when f i e l d s less than the forming f i e l d were applied. However, i n addi t i o n there was a further change when the transient was w e l l under way. More work i s necessary before the above topics are f u l l y under-stood. Notably a conclusive theory for i o n i c conduction has yet to be developed. The u.v.-stimulated growth of Ta^O^ and Nb^O^ seems to be a fundamental process common to these oxides. Other metal oxides apparently react i n a s i m i l a r manner to various wavelengths of r a d i a t i o n . This clue to the mechanism of i o n i c conductivity has yet to be explained. The constant f i e l d current transient i s another process that o f f e r s i n s i g h t into i o n i c c onductivity. Although Dignam has proposed a theory that represents the transient f a i r l y w e l l mathematically, there i s s t i l l controversy over the p h y s i c a l basis of h i s theory. His theory has not been applied to the evidence pf u.v.-stimulated growth. This should be done to see i f the theory can give a p l a u s i b l e explanation or whether the experimental evidence can expose any i n c o n s i s t e n c i e s . 18 Stephenson and Roth have brought to l i g h t some i n t e r e s t i n g points along with t h e i r c a l c u l a t i o n of the structure of Ta20^ _. The presence of d i s t o r t i o n planes i n the oxide, the e f f e c t s of annealing on these d i s t o r t i o n planes, and the a s s o c i a t i o n of the amount of oxygen i n the oxide with the concentration of d i s t o r t i o n planes a l l can o f f e r i n s i g h t into the mechanism of i o n i c conduction. It is' c l e a r that a conclusive theory must consider and be compatible with these s t r u c t u r a l phenomena. 73 REFERENCES ].. J . F . Nye, " P h y s i c a l P r o p e r t i e s of C r y s t a l s " , Oxford Press (1957). 2. R. J . A r c h e r , " E l l i p s o m e t r y M a n u a l " , Gaer tncr S c i e n t i f i c Corp . (1968) . 3. A . B. Winterbot tom, " O p t i c a l s t u d i e s of metal s u r f a c e s " , The Royal Norwegian S c i e n t i f i c S o c i e t y Report No. 1, 1955. P u b l i s h e d by F . Bruns . 4. F . L . M c C r a c k i n , E. P a s s a g l i a , R. R. Stromberg and H . S t e i n b e r g , J . Res. Nat . Bur . S t d s . , 67A, 363 (1963). 5„ L . Young and F . R. Z o b e l , J . E l e c t r o c h e m . S o c , 113, 277 (1966) . 6. D. G. S c h u l e r , p . 104, "Proceedings of the symposium on Recent Developments i n E l l i p s o m e t r y " , Nebraska (1968) , Surface S c i e n c e , 16, (1969) . 7. E . P a s s a g l i a , R. R. Stromberg and I . K r u g e r , E d i t o r s , " E l l i p s o m e t r y i n the measurement of t h i n f i l m s " , N . B . S. M i s c . P u b l i c a t i o n 256, (1963). 8 . R. J . A r c h e r , J . Opt. Soc. A m . , 52 , 970 (1962) . 9. F . L . M c C r a c k i n , ""A F o r t r a n Program f o r ' A n a l y s i s of E l l i p s o m e t r y Measurements", N . B . S. T e c h n i c a l Note 479, (1969). 10. D. E . Aspnes and A . A . Studna, A p p l . O p t i c s , 10, 1024, (1971) . 11. W. J . T e g a r t , "The E l e c t r o l y t i c and Chemical P o l i s h i n g of M e t a l s " , •PergamQn-, London, (1956) . 12. L . Young, "Anodic Oxide F i l m s " , Academic P r e s s , London (1961) . 13. M. L . K i n t e r , I . Weissman and W. W. S t e i n , J . A p p l . P h y s . , 41 , 828 (1970). 14. C. J . D e l l ' O c a , P h . D . T h e s i s , U . B . C . , Dept . of E l e c . E n g . , (1969) . 15. L . Young, P r o c . Roy. S o c , A244, 41 (1958) . 16. J . L . O r d , M . A . Hopper and P . W. Wang, J . E l e c t r o c h e m . S o c , 119, 439, (1972). 17. J . J . B e l l i n a J r . , R. J . L e d e r i c h and J . E . O ' N e a l , J . A p p l . P h y s . , 43 , 287, (1972). 18. N . C. Stephenson and R. S. R o t h , A c t a , c r y s t . B27, 1037 (1971) . 74 19. B. J . Holder* and F. G. Ullman, J. Electrochem. S o c , 116, 280 (1969). 20. A. Frova and P. M i g l i o r a t o , Appl. Phys. L e t t e r s , 15, 406 (1969). 21. F. L. McCrackin, J. Opt. Soc. Am., 60, 57 (1970). 22. G. Olive, Personal communication. 23. C. K i t t e l , "Introduction to Soli d State Physics", 3rd Ed., John Wiley & Sons (1966). 24. F. S. Chen, J . Appl. Phys., 40, 3389 (1969). 25. L. Young, Proc. Roy. S o c , A263, 359 (1961). 26. M. J . Dignam, J. Electrochem. S o c , 112, 722 (1965). 27. M. J . Dignam and P. J . Ryan, Canad. J . Chem. 46, 549 (1968). 28. L. Young, Canad. J . Chem., 50, 574 (1972). 29. A. Frova and P. M i g l i o r a t o , Appl. Phys. L e t t e r s , J L 3 , 328 (1968). 30. F. S. Chen, J . E. Geusic, S. K. Kurtz and S. H. Wemple, J . Appl. Phys.._37, 388 (1966). 75 APPENDIX Ellipsometer Program: ( START J) Type date and' ask f o r d e l a y time between r e a d i n g s ' I n i t i a l i z e c o u n t e r s . Take i n i t i a l r e a d i n g s of s h a f t encoders Set up output B u f f e r and l o a d headings i n t o B u f f e r Turn on I n t e r r u p t Zero the Clock ] Check s t a t u s o f SB b i t #1 to see i f a n a l o g s w i t c h i s to be opened o r c l o s e d © c POLARIZER BALANCE ROUTINE I n i t i a l i z e c o u n t e r and notor a c c e l e r a t i o n constant Begin s t e p p i n g motor and r e a d i n g P h o t o m u l t i p l i e r a t each s t e p 76 fieverse direction of motor Sum up to 16 Error Signal readings (Old Sum) Keep stepping u n t i l Error Signal begins to increase a#ain NO Drive motor away from minimun 48 steps Step and take read-ings u n t i l 16 entries in New Sure Drop 1st entry of New Sum and add another u n t i l Old Sum=« New Sum Drive motors to bal-ance point (halfway between 2 equal Sums) 77 C BALANCE ANALYZE 5 (BALANCE PROCEDURE COMPLETE) Same as f o r P o l a r i z e r but s u b s t i t u t e A f o r B ^INTERRUPT) Output da t a on Tel e t y p e D i g i t a l v o l t m e t e r P o l a r i z e r s h a f t encoder An a l o g ch a n n e l 1 Time A n a l o g ch a n n e l 2 A n a l y z e r s h a f t encoder F i n d out i f motors have missed any s t e p s and. s t o r e r e s u l t C onvert above d a t a to de c i m a l and tout onto o u t r u t 'Buffer scsuenl;l;;Tly Check s t a t u s o f B i t / / l f o r o p e r a t i o n o f a n a l o g s w i t c h Wait f o r p e r i o d a l r e a d y s p e c i f i e d by o p e r a t o r © Program for Transient studies: 78 (START i 3 I n i t i a l i z e c o u n t e r s a n d o p e n m a i n s w i t c h (INTERRUPT) O u t p u t d a t a o n T e l e t y p e ( RETURN ]) U p - r a n g e t h e s e q u e n c e r e l a y ( START 2^) C l o s e m a i n c i r c u i t s w i t c h a n d s t a r t t h e c l o c k b e t r e l a y s e q u e n c e f o r b o t t o m r a n g e W a i t f o r a t i m e s p e c i f i e d by number i n SW - C a n * R e a d A n a l o g c h a n n e l a n d t h e c l o c k YES d o w n - r a n g e t h ? r e l a y s e q u e n c e YES C o n v e r t t i m e a n d a n a l o ; c h a n n e l r e a d i n g s t o d e c i m a l S t o r e i n o u t p u t B u f f e r 

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