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Galvomagnetic properties of evaporated bismuth films Peria, William Thomas 1951-12-31

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GALVOMAGNSTIC PROPERTIES o f EVAPORATED BISMUTH FILMS by WILLIAM THOMAS PERIA A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f Physics s We a c c e p t t h i s t h e s i s as conforming t o the s t a n d a r d r e q u i r e d f r o m c a n d i d a t e s f o r the degree o f MASTER OF APPLIED SCIENCE Members o f t h e Department o f P h y s i c s THE UNIVERSITY OF BRITISH COLUMBIA September 19,51 ABSTRACT A s t u d y has been made o f t h e H a l l c o e f f i c i e n t and r e s i s t i v i t y o f e v a p o r a t e d b i s m u t h f i l m s . S p e c i a l a t t e n t i o n has been g i v e n to the d e t e r m i n a t i o n o f t h e e f f e c t s o f the c o n d i t i o n s o f p r e p a r a t i o n on the r e s u l t a n t p r o p e r t i e s . A s u g g e s t i o n has been o f f e r e d t o e x p l a i n t h e s t r o n g dependence o f th e s e p r o p e r t i e s on t h e t e m p e r a t u r e of t h e s u b s t r a t e d u r i n g d e p o s i t i o n . C r i t i c a l p o i n t s have been found i n the c u r v e s of the r e s i s t i v i t y and i t s magnetic f i e l d dependence v e r s u s t h i c k n e s s . T h i s c r i t i c a l t h i c k n e s s i s thought to be t h a t a t w h i c h a p r e v i o u s l y r e p o r t e d a b r u p t change i n c r y s t a l l i t e s i z e o c c u r s . ACKNOWLEDGEMENTS The r e s e a r c h d e s c r i b e d i n t h i s t h e s i s was s u p p o r t e d by the Defence R e s e a r c h Board o f Canada. The problem.was d i r e c t e d by D o c t o r A. J . Dekker whose a s s i s t a n c e and a d v i c e a r e s i n c e r e l y a p p r e c i a t e d . W. F e r i a September 1951. TABLE OF CONTENTS Page I INTRODUCTION 1 I I EXPERIMENTAL 2 - I l l RESULTS A . R e p r o d u c i b i l i t y 9 B V a r i a t i o n o f t n e P r o p e r t i e s w i t h T h i c k n e s s 10 C C o o l i n g the T a r g e t 11 D N e g a t i v e H a l l C o e f f i c i e n t s 12 E V a r i a t i o n o f the P r o p e r t i e s w i t h Temperature 13 G The E f f e c t o f A n n e a l i n g 14 H C a l c u l a t i o n s 15 I V DISCUSSION A R e p r o d u c i b i l i t y 19 B V a r i a t i o n o f the P r o p e r t i e s w i t h T h i c k n e s s : 2 0 C C o o l i n g the Ta r g e t 21 D V a r i a t i o n o f the P r o p e r t i e s w i t h Temperature 22 E The E f f e c t o f A n n e a l i n g 23 F C a l c u l a t i o n s 24 V CONCLUSION 25 ILLUSTRATIONS F i g u r e F a c i n g Page 1 E v a p o r a t i n g V e s s e l J> 2 P r o b e p o s i t i o n s 5 2 (a) Probe assembly 6 (b) P r obe mounting J? Low t e m p e r a t u r e a p p a r a t u s 7 6 S i l v e r p a i n t p r o b e s 7 7 C h a r t i l l u s t r a t i n g r e p r o d u c i b i l i t y o f r e s u l t s 9 8 P l o t of e l e c t r i c a l p r o p e r t i e s v e r s u s t h i c k n e s s 10 (1) I. INTRODUCTION During a study of the e lectr ica l properties of evaporated bismuth fi lms, ( l) i n this department, i t became apparent that the trapping of ourrent carriers i n local ized energy levels plays an important role i n determining these properties. The research described i n this thesis was carried out to investigate the effects of the conditions of preparation of the films, on the amount and type of trapping which occurs. The influence of the f i lm thickness, the rate of evaporation and the temperature of the substrate during evaporation, were studied. The properties measured to this end were the Hall constant, the conductivity and the variation of these quantities with magnetic f i e l d . By a trapped ourrent carrier we signify one situated in an energy level which i s provided by some deformation of the l a t t i ce potential (crysta l l i te boundaries, surface states) (2,3) such that the carrier does not take part in the conduction process. The Hal l coefficient, R, i s defined by the relat ion R » By IxHz (2) where Sy i s the transverse e l e c t r i c f i e l d developed i n a conductor which c a r r i e s l o n g i t u d i n a l l y a current density I x , perpendicular to a magnetic f i e l d . E y i s perpendicular to both I z and H z . I I . EXPERIMENTAL Preparation of the Samples. Bismuth was deposited by vacuum evaporation onto glass targets about 7 , 5 x 2 . 5 x 6 . 1 cm. The metal used was Johnson, Matthey 4 Co., speotroscopioally standardized. Table I i s the l i s t of impurities as supplied by the company. Table 1 - L i s t of Impurities. Chemical Spectroscopic Fe .0011% Barely v i s i b l e Cu ,0024> Very f a i n t l y v i s i b l e Ag Trace Very f a i n t l y v i s i b l e Ca Not detected F a i n t l y v i s i b l e Mg Not detected F a i n t l y v i s i b l e The vacuum ves s e l A ( f i g . 1) i s that employed i n the previous work ( l ) except that the geometry has been somewhat altered to secure more uniform samples. I t consists e n t i r e l y of Vyeor, a h i g h - s i l i c a glass usable up to 1100°C. The construction i s such that e f f e c t i v e l y the target B receives metal from two sources. P> O CD CD (3) I n use a f u r n a c e a l r e a d y a t t h e d e s i r e d t e m p e r a t u r e i s l o w e r e d t o the l e v e l x-x . When t e m p e r a t u r e e q u i l i b r i u m has been e s t a b l i s h e d i n t h e c r u c i b l e C , ( f i g . 1 ) the e x t e r n a l l y m a n i p u l a t e d g l a s s b a f f l e D i s w i t h d r a w n a l o n g t h e r a i l s E and c o n d e n s a t i o n on t h e t a r g e t b e g i n s . The t h i c k n e s s o f the f i l m was d e t e r m i n e d by w e i g h i n g the t a r g e t b e f o r e and a f t e r d e p o s i t i o n and assuming t h e d e n s i t y o f b u l k b i s m u t h . A l l samples were weighed Immediately a f t e r removal f r o m the vacuum system i n o r d e r to m i n i m i z e e r r o r s due t o a b s o r p t i o n f r o m th e atmosphere. T h i s e f f e c t was measured f o r one sample; an i n c r e a s e i n w e i g h t o f 0 . 2 mg. i n 20 min. was o b s e r v e d f o r t h i s 6 mg. sample. The u n i f o r m i t y o f the f i l m s was i n v e s t i g a t e d by w e i g h i n g t h e q u a n t i t y o f m e t a l d e p o s i t e d on s e v e r a l b i t s o f g l a s s , o f known a r e a , o c c u p y i n g t h e space o r d i n a r i l y o c c u p i e d by t h e t a r g e t p r o p e r . The samples were found t o have a c r o s s - s e c t i o n w h i c h was u n i f o r m t o 1% but\.i/vhich was not r e c t a n g u l a r i . e . t h e f i l m s a r e t h i c k e r i n t h e c e n t r e t h a n on t h e s i d e s by about 10f. . T h i s f a c t does not a l t e r the v a l u e o f any o f t h e c a l c u l a t e d c o n s t a n t s s i n c e t h e y i n v o l v e o n l y t h e c u r r e n t d e n s i t y . However, the v a l u e o f t h i c k n e s s t o which they a p p l y must be t a k e n as t h e average t h i c k n e s s o f the f i l n u (4) The t a r g e t may be c o o l e d t o some e x t e n t by p l a c i n g r e f r i g e r a n t i n t h e d o u b l e - w a l l e d b r a s s c o n t a i n e r F. The j o i n t between t h i s c o n t a i n e r and t h e V y c o r v e s s e l i s made l e a k - p r o o f w i t h paper g a s k e t s p r e v i o u s l y soaked i n w a t e r . The c o o l i n g p r o c e s s was made s l i g h t l y more e f f i c i e n t by c l a m p i n g t h e t a r g e t t o a b r a s s p l a t e G ( f i g . 1) whose under s u r f a c e conformed t o t h e i n n e r s u r f a c e o f the vacuum v e s s e l . The t e m p e r a t u r e o f t h e t a r g e t as a f u n c t i o n o f time a f t e r . t h e f u r n a c e was p l a c e d on was measured by s i m u l a t i n g t h e c o n d i t i o n s o f an e v a p o r a t i o n , e x c e p t t h a t ( i ) t h e c r u c i b l e was empty ( i i ) the " t a r g e t " was a bismuth f i l m o f known r e s i s t a n c e - t e m p e r a t u r e r e l a t i o n . A r o u g h measure o f the s u r f a c e t e m p e r a t u r e o f t h e t a r g e t was t h e n o b t a i n e d by m e a s u r i n g th e f i l m r e s i s t a n c e . M e a s u r i n g A p p a r a t u s . The magnetic f i e l d was produced by a w a t e r - c o o l e d e l e c t r o m a g n e t w i t h 4 - i n c h d i a m e t e r p o l e f a c e s and an a d j u s t a b l e gap w i d t h . A maximum f i e l d o f 10 k i l o g a u s s c o u l d be o b t a i n e d w i t h a 1 - i n c h gap and was u n i f o r m w i t h i n 0.5 p e r c e n t over the volume between the p o l e f a c e s . The f i e l d was measured by means o f a s e a r c h c o i l FIG 2 To f a c e page .5. (5) and f l u x m e t e r , c a l i b r a t e d i n t h e a c c u r a t e l y known f i e l d s o f the n u c l e a r magnetic resonance s p e c t r o m e t e r i n t h i s department. The s e a r c h c o i l was mounted on a s p r i n g - l o a d e d s p i n d l e so t h a t i t s p l a n e was p a r a l l e l t o t h e p o l e f a c e s when i n i t s e q u i l i b r i u m p o s i t i o n . To measure the f i e l d , t h e s p i n d l e was r o t a t e d t h r o u g h 180°, t h e f l u x m e t e r a d j u s t e d t o z e r o and t h e s p i n d l e r e l e a s e d . F o r t h e one sample measured a t d r y i c e t e m p e r a t u r e s , a s e a r c h c o i l N ( f i g . j>) was f i x e d w i t h i n t h e vacuum chamber and t h e f i e l d measured by s w i t c h i n g the magnet c u r r e n t o f f o r on. The s m a l l f i e l d r e m a i n i n g f o r z e r o magnet o u r r e n t was c a n c e l l e d by a d j u s t i n g a s m a l l c u r r e n t i n t h e r e v e r s e d i r e c t i o n u n t i l a compass needle between the p o l e f a c e s j u s t changes o r i e n t a t i o n . F o r t h e measurements a t room t e m p e r a t u r e t h e sample was clamped t o an i n s u l a t i n g b o a r d , as i n t h e p r e v i o u s work, between s t r i p s o f t i n f o i l w h i c h a l s o s e r v e d as c u r r e n t e l e c t r o d e s . The i n s u l a t i n g s h e e t was s u p p o r t e d v e r t i c a l l y so t h a t a l l measurements were made w i t h the m agnetic f i e l d normal t o the p l a n e o f t h e sample. Three probes were used, p l a c e d on the sample as shown i n f i g . 2. Probes 1 and 2 s e r v e d t o measure the H a l l v o l t a g e , p robes 2 and 3 t h e r e s i s t a n c e . f a c e page 6 (6) The probes consisted of 1/8 inch bronze bear ings mounted i n a brass assembly ( f i g . 3a). These were threaded into a bakelite sheet A, (f i g . 3b) pivoting about point X on an aluminium sheet B which was firmly bolted to the same insulating sheet C as was the sample D. Between probes 1 and 2, there appears, as well as the Hall voltage, the IR drop between them i f they are not situated on the same equipotential. This could be made small relative to the Hall voltage by rotating the whole contact assembly about point X. Before making this adjustment the probes were withdrawn so that the sample was not scratched. To replace the probes, a direct current was passed through the sample and each probe i n turn was screwed down until contact was indicated by the deflection of a galvanometer. In an average case the IR drop could be made 10% or less of the Hall voltage without d i f f i c u l t y . The damage sustained by the sample during this adjustment consisted of two or three small holes (about 0.1 mm.) i n the region of probes 1 and 2 and one at probe 3. The fundamental difference between this type of probe and those previously employed, i s that the two operations of fastening down the probe assembly and making contact between probe and film, are distinct. To f a c e page 7 (7) The sample whioh was measured at low temperatures ( A , f i g . 5) was clamped to a luc i te s tr ip B by luc i te blocks C and strips of t i n f o i l D which served as current electrodes. The previously described probes are too bulky for use i n this s i tuation and were replaced by s i lver paint (Dupont #4817) electrodes which terminated, on the under side of the sample, in a wide patch ( f ig . 6). When the sample,was i n position these three patches each made contact with a drop of mercury E, contained i n a 1/8 inch hole d r i l l e d In a corresponding position i n the luc i te s t r ip B ( f ig . 5). These holes were closed on the other side by strips of copper f o i l 3F cemented to the luc i te s t r ip and running longitudinally past the end of i t , where connections were made to copper wires. Current leads were brought out from the t i n f o i l electrodes i n a similar fashion. Temperatures were measured by means of two copper- constantan thermocouples cemented i n grooves between the specimen and s t r ip B. A third thermocouple between B and the copper wall G was for control purposes. Chamber G was wound with a copper heating c o i l to enable readings to be taken above the temperature of the brass wall H. Heat exchange between containers (8) G- and H was made small by using luci te spacers J and by evacuating the outer container through pipe K. The demountable vacuum joint was sealed with a lead gasket L between flanges M. The whole apparatus was set i n a COg-alcohol mixtuiB in a Styrofoam container. Styrofoam (Dow) is an insulating material made by "foaming" l iqu id polystyrene and was easily formed to the shape needed to f i t between the pole faces of the magnet. Measuring Apparatus. The AC method and equipment previously employed (l) were used for the measurement of Hal l voltages. In a l l cases the voltage between probes 1 and 2 for zero f i e l d was corrected to allow for i t s increase i n the magnetic f i e l d , before being added algebraically to the voltage with f i e l d . The sign of the Hall coefficient was determined for each sample by using DC i n the sample and measuring the voltage between probes 1 and 2 with a potentiometer. The re s i s t iv i ty was determined using a DC method. Current was obtained from a regulated 300 volt supply through a high resistance, so that the sample current i s constant irrespective of applied magnetic f i e l d . The voltage between probes 2 and 3 was measured with a Rubicon. •|-3 O H > P o CD •O P> CR3 CO 0 8 - 0-6- E i t OA-1 e 3L R Group I • • n e Others o o ® -CL •«r O v e o e o Group I (D « n ® Others e - _ Q - 0 - (D e e Full lines - Mean of group. Broken lines- + one standard deviation. 58 62 + + + 66 70 Sample Number FIG- 7 + + 74 4- + 78 2 + 3 0 X e - -2 0 (?) portable potentiometer. III . RESULTS A . Reproducibility. In order to test the reproducibil ity of the results , a series of samples (nos. 5>8-80) were made from a single melt under as nearly similar conditions as possible. That is to say the target was never cooled, the furnace was always preheated to the same temperature and the baffle always withdrawn for the same length of time. F ig . 7 is a chart of the results obtained. Note that with certain exceptions the samples up to #72 may be divided roughly into two groups with respect to the Hall coefficient and the r e s i s t i v i t y . In every case the values of R and p f a l l i n g outside these two groups belong either to (i) the f i r s t sample of the melt or ( i i ) the f i r s t sample evaporated after leaving the melt in vacuum for one or more days. In addition each of these exceptions i s thinner than groups I and II although the conditions of preparation were the same. The high values of p indicated for these films ( f ig . 7) must be ascribed to this latter cause, but i n view of the results of the following section their high Hal l coefficients cannot be so explained. For nos. 73-8:0 the results are scattered and a l l are thinner than would be expected on comparison with groups I and II . (10) I n subsequent e x p e r i m e n t s a q u a n t i t y o f b i s m u t h c o r r e s p o n d i n g t o O.Jy*»on the t a r g e t was a l w a y s e v a p o r a t e d w i t h t h e b a f f l e c o v e r i n g the t a r g e t , b e f o r e any samples were p r e p a r e d . I n a d d i t i o n , e v a p o r a t i o n was ne v e r c a r r i e d beyond a p o i n t c o r r e s p o n d i n g to t h e end o f group I. ( I . e . l e s s t h a n one h a l f o f each melt was u s e d ) . B. V a r i a t i o n o f t h e P r o p e r t i e s w i t h T h i c k n e s s . A s e r i e s of samples was p r e p a r e d a l l under i d e n t i c a l c o n d i t i o n s e x c e p t t h a t t h e bismuth was h e a t e d t o a d i f f e r e n t t e m p e r a t u r e f o r each o f them. F i l m s f r o m 0.2 t o 1.4^u t h i c k were o b t a i n e d by v a r y i n g t h i s t e m p e r a t u r e from 800°C t o 880°C. The r a t e s o f e v a p o r a t i o n r a n g e d f r o m 1.7 t o 9.5 ug/cm 2-sec. The r e s u l t s o f t h i s experiment a r e shown i n f i g . 8 and Table I I . The f r a c t i o n a l change o f r e s i s t i v i t y appears to depend on the magnetic f i e l d a c c o r d i n g to an e x p r e s s i o n o f the form where A i s a c o n s t a n t . The v a l u e s o f A quoted a r e the best ones i n t h e sense o f l e a s t s q u a r e s . (11) Table II Variation of the Properties with Thickness (at 20OC). No. 2 x 10? 113 111 110 112 108 109 106 107 115 114 104 105 0.200 +0.519 '2.69 2.06 18.0 0.288 0.602 2.55 2.76 20.2 0.354 0.637 2.40 .3.24 21.7 0.396 0.522 2.25 4.56 11.8 0.541 0.680 1.90 6.43 19.9 0.584 0.621 1.86 6.58 17.0 0.771 0.684 1.78 6.36 23.1 0.908 0.540 1.65 8.30 12.9 0.966 0.534 1.71 7.20 14.0 0.985 0.399 1.57 9.80 6.6 1.260 0.403 1.54 9.48 7.2 1.431 0.483 1.51 10.30 9.9 t = thickness of sample i n microns R£ = Hall coefficient (e.m.u.) in a fie l d of 6 kilogauss p = r e s i s t i v i t y i n electromagnetic units. A series of samples of varying thickness was also prepared by heating the melt to the same temperature in each case but withdrawing the baffle for various lengths of time. Quite a different variation of the properties was obtained for this series but the results are not considered significant i n view of the fact that the temperature of the target would be higher for thicker films. The temperature of the target during deposition i s a v i t a l factor i n determining the properties, as i s shown in part C. C. Cooling the Target. Two samples were prepared under the same conditions as those of part A except that the targets were cooled by placing a C02-alcohol mixture in the (12) c o o l i n g box F of f i g . 1. The p r o p e r t i e s o f t h e s e samples a r e l i s t e d i n t a b l e I I I a l o n g w i t h some p r e p a r e d a t the same time w i t h o u t c o o l i n g t h e t a r g e t . Table I I I - E f f e c t o f C o o l i n g t h e Target (Measurements a t 20OC). -5 No; t{jjj T ( o Q R£ p x 10 A x 1 0 1 U R 2/Ap 2xlO 84 0.6^8 30 ' +0.62 6 1.86 5.89 19.3 85 0.777 -18 +0.054 2.19 6.02 0.10 119# 0.657 37 +1.06 2.00 4 .66 13.1 120? 0.525 -6 +0.255 3 . 4 4 1.97 2.9 T = e s t i m a t e d s u r f a c e t e m p e r a t u r e o f t h e t a r g e t a t t h e i n s t a n t d e p o s i t i o n b e g i n s . § i n d i c a t e s t h a t the s u b s t r a t e i s m i c a . N o t i c e t h a t i n b o t h c a s e s c o o l i n g t h e t a r g e t d e c r e a s e d R£ and A and i n c r e a s e d p compared t o a sample o f the same t h i c k n e s s whose t a r g e t was not c o o l e d . The magnitudes o f t h e changes a r e such t h a t the q u a n t i t y R2/A^> 2 d e c r e a s e s . D. N e g a t i v e H a l l C o e f f i c i e n t s . S e v e r a l specimens were p r e p a r e d on c o o l e d t a r g e t s by p r e h e a t i n g t h e f u r n a c e t o 950°C or more and o m i t t i n g the b a f f l e a l t o g e t h e r . I n t h i s way the b i s m u t h c o u l d be v e r y q u i c k l y r a i s e d t o a t e m p e r a t u r e a t w h i c h a p p r e c i a b l e e v a p o r a t i o n o c c u r r e d and t h e f u r n a c e c o u l d be removed a f t e r a s h o r t t i m e i n t e r v a l . Thus the t a r g e t t e m p e r a t u r e s f b r t h e s e samples were l e s s t h a n f o r those o f p a r t C. The r e s u l t s f o r 2 such samples a r e shown , i n Table I V . " (15) T a b l e I V - N e g a t i v e H a l l C o e f f i c i e n t s ( a t 20°C). No. t(^/) T(QC) R 6 1 p x 10^ A x 1 0 1 0 & x 10? 29 0.923 -30 - 3 . 5 9 4 .47 121 1.23 0 -3 .11 3 .57 6.1 2 .4 T = e s t i m a t e d surface,-temperature o f t h e t a r g e t when the d e p o s i t i o n ended. These samples a r e f o u n d not to obey t h e q u a d r a t i c l a w mentioned i n p a r t B, but t o approximate a l a w 4-£ = AH2 I n a d d i t i o n the H a l l c o n s t a n t fer t h e s e f i l m s i n c r e a s e s as t h e f i e l d i n c r e a s e s and seems to r e a c h a r a t h e r i l l - d e f i n e d maximum o r a c o n s t a n t v a l u e a t about 6 k i l o g a u s s . E. V a r i a t i o n of the P r o p e r t i e s w i t h Temperature. One sample f r o m the group d e s c r i b e d i n p a r t B ( t h i c k n e s s 0.908pu) was measured down to d r y i c e t e m p e r a t u r e s , (see Table V ) . Table V - V a r i a t i o n o f t h e P r o p e r t i e s w i t h Temperature (#107). Temp . (°0) RQ p x l O " ^ A x l O 1 0 B x l O 1 0 R 2 / A P 2 x l Q ? 20 .540(6 K g a u s s . ) l . 6 5 8.32 12.9 0 .597- 1.66 11.8 6.7 10 .9 -20 • .619 1.68 15.2 3.3 8.9 -40 .654 1.70 18.6 7.9 - 6 0 .480 1.78 24 . 2 1.1 3 . 0 -70 .028 1.85 26.8 0 .1 Here RQ i s t h e H a l l c o e f f i c i e n t f o r z e r o magnetic f i e l d e xcept where o t h e r w i s e i n d i c a t e d . B i s d e f i n e d by t h e (14) e x p r e s s i o n R(H) = R Q - B H 2 w h i c h i s known to h o l d (1) f o r t h i s t y p e o f l a y e r at room t e m p e r a t u r e . RQ and B were c a l c u l a t e d f rom v a l u e s o f R measured at 3 k i l o g a u s s and 5 k i l o g a u s s . G. The E f f e c t of A n n e a l i n g . S e v e r a l samples were a n n e a l e d i n vacuum o r i n 20 cm. Hg. p r e s s u r e o f 002. No l o s s i n w e i g h t c o u l d be d e t e c t e d f o r f i l m s a n n e a l e d i n e i t h e r manner. S i n c e no d i f f e r e n c e c o u l d be d e t e c t e d between the e f f e c t s a c h i e v e d by the two methods o f a n n e a l i n g , t h e y a r e not d i s t i n g u i s h e d i n what f o l l o w s . Table V I E f f e c t of A n n e a l i n g . No. Ta) 26 p x l O 5 A x 1 0 1 0 R2/Ap 2 a 59 0.533 +0.637 1.94 6.29 17 .2 59* +0.764 1.74 8 .82 21.8 61 0.546 +0.645 2.01 6.08 16 .9 6l38 *0.696 1 .79 9 .05 16 .7 62 0.576 +O.616 1.86 8.05 13.6 6 2 H ' +0.610 1.68 10.0 13.2 83 0.731 +0.633 1.87 6.87 16 .7 83s +0.724 1 .61 9.65 20.9 86 0 .560 +0.547 2.20 5.39 11.5 86x +0.743 1.84 8.12 20.0 (b) 0 .776 6.01 85 +0.054 2.19 0.10 85x +0.285 1.92 8.55 2.6 ( c ) ( S e e Table I I I ) \ C 1 29 0.924 -3.59 4.47 29s T a b l e -3.98 3 .08 (See I V ) (15) SE s i g n i f i e s t h a t t h e sample was a n n e a l e d a p p r o x i m a t e l y 4 0 min. a t 260OC.• • , Because the change i n R on a n n e a l i n g v a r i e d f r o m sample t o sample and because t h e s i g n o f t h e change i s i n c o n t r a d i c t i o n t o t h e r e s u l t s o f L e v e r t o n and Dekker ( l ) , one sample was a n n e a l e d i n s e v e r a l s t a g e s , and measured a t 20°C a f t e r each a n n e a l i n g . The r e s u l t s appear i n Table V T I. Table V I I - S t e p - b y - s t e p A n n e a l i n g . 10 -5 No. tfjjj) Tlme(min.) TemP.(°C) Rr>(e.m.u.) BxlO p x l Q A*! 0 64 0.544 +0.618 7.2 2 .06 5.95 641 10 150 O.616 7.0 2.04 6.39 642 3 <240 0.645 7.0 1.97 7.40 643 13 247 0.659 6.6 1.92 6.90 64 4 20 258 0.616 5.1 1.87 7.16 64| 30 258 0.679 5.5 1.86 7.62 64 6 ~ 40 268 0.701 1.86 7.48 Colums 3 and 4 i n d i c a t e the a n n e a l i n g w h i c h produced the changes between any g i v e n row and t h e row p r e o e d i n g i t . N o t i c e t h e d d e c r e a s e i n A o c c u r r i n g a f t e r t he t h i r d a n n e a l and the de c r e a s e i n RQ a f t e r t h e f o u r t h . H. C a l c u l a t i o n s . Jones (4) has p r e s e n t e d a model by means o f w h i c h most o f t h e galvanomagnetic e f f e c t s o b s e r v e d i n b u l k b i s m u t h can be e x p l a i n e d . The two assumptions on which h i s c a l c u l a t i o n s a r e based a r e ( i ) t h e s u r f a c e s o f c o n s t a n t energy i n k-space t a k e t h e form o f e l l i p s o i d s and ( i i ) the r e l a x a t i o n t i m e o f the c u r r e n t c a r r i e r s i s independent o f 10 ' (16) t h e i r energy. Two e q u a t i o n s a r e p r e s e n t e d which t a k e t h e form . = A H 2 . f 1 1 + 6 H 2 (1) R » . Rp-BH 2 1-+6HZ (2) I f o u r f i l m s a r e assumed t o c o n s i s t of c r y s t a l l i t e s whose p r i n c i p a l a x i s i s p e r p e n d i c u l a r t o t h e s u b s t r a t e a s found by Lane ( j ? ) , then a l l t h e measurements p r e v i o u s l y l i s t e d a r e f o r c u r r e n t f l o w p e r p e n d i c u l a r t o and magnetic f i e l d p a r a l l e l t o t h i s a x i s . Under t h e s e c i r c u m s t a n c e s , Jones g i v e s f o r p , A, R 0, B and 8 ) Here G* i s t h e t o t a l c o n d u c t i v i t y p e r p e n d i c u l a r to the p r i n c i p a l axis,©*, t h a t due t o e l e c t r o n s a l o n e and 9\ to h o l e s a l o n e . rti,h» a r e the d e n s i t y o f e l e c t r o n s and h o l e s r e s p e c t i v e l y . T h e r e f o r e (TJ * £. n«V, , <Ta* ^ V» (17) where v-j_ and V£ a r e the c a r r i e r m o b i l i t i e s . Note t h a t t h e use o f a s i n g l e symbol f o r the c o n d u c t i v i t y p e r p e n d i c u l a r to t h e p r i n c i p a l a x i s i m p l i e s c i r c u l a r symmetry about t h i s a x i s . A c t u a l l y t h e r e i s o n l y t r i g o n a l symmetry. S i n c e those o f our samples which were d e p o s i t e d on u n c o o l e d t a r g e t s f o l l o w , f o r the f i e l d s used,laws o f the t y p e s ( l ) and (2) w i t h S H 2 ^ 1, e q u a t i o n s 3, 4 , jj> and 6 were s o l v e d f o r n^, n2, and v p f o r a few of t h e s e samples. The q u a n t i t y ARQ was formed f r o m e q u a t i o n s 4 , 5 and 6 and t h e q u a n t i t y R § from e q u a t i o n s 2, 4 , and j>. B o t h a r e p i d i m e n s i o n l e s s q u a n t i t i e s and may be e x p r e s s e d i n terms of y = tf= E-2 and ^= V£ as f o l l o w s ; AHo B ^ t e ( 8 ) 5° . ( 9 ) E q u a t i o n s 8 and 9 were s o l v e d f o r i v {3 by t r i a l and e r r o r . These were s u b s t i t u t e d i n t o 5 w r i t t e n I n the form, l i o ) and i n (3) i n t h e form ° ( I I ) e (18) and hence ng and Vg o b t a i n e d . As mentioned p r e v i o u s l y t h e change o f r e s i s t a n c e w i t h magnetic f i e l d was n o t q u a d r a t i c f o r those f i l m s w i t h n e g a t i v e H a l l c o e f f i c i e n t s . An e q u a t i o n o f t h e f o r m ( l ) f i t t e d t h e e x p e r i m e n t a l r e s u l t s much b e t t e r and a rough v a l u e o f S c o u l d be e v a l u a t e d . I n t h i s c a s e t h e q u a n t i t i e s R§ and k/A were e x p r e s s e d i n terms o f # and p. Ap n^, n 2 , v-j_ and Vg were t h e n e v a l u a t e d a s b e f o r e . I t s h o u l d be emphasized t h a t & i s not a c c u r a t e l y known. However, even;:if 6 were 5°% l o w e r than t h e v a l u e used i n t h i s c a l c u l a t i o n one i s s t i l l l e d t o t h e c o n c l u s i o n t h a t t h e d e n s i t y o f h o l e s i s much l e s s t h a n t h a t o f t h e e l e c t r o n s . (Table V I I I ( d ) ) . Ta b l e V I I I - C a l c u l a t e d C a r r i e r D e n s i t i e s and M o b i l i t i e s . No Ta) 62s (b) 64? 64? 644 645 -18 -3 n i x l 0 ( c m ) -18 -3 n g x l O j c m ) 5 / V]_xl0 (e.m.u.j 5 v g x l O 7.5 11.5 2.2 2.2 4 . 6 7.1 2.8 2 .5 5.5 9.0 2.2 2.0 4 . 5 6.2 3 . 0 2.9 5.2 7.5 2.6 2.5 5.4 7.1 2.7 2.7 5.1 6.8 2.8 2.8 (o) 107 3.8 3 .8 0OC 4.5 5.4 -20°C 4.7 5.0 3 .7 3 .9 -60°C 3.1 3 .1 5.5 5.8 (d) 121 8 . 4 0 . 4 1.9 5.7 (1?) F o r s e c t i o n s ( a ) and (b) o f t h i s t a b l e r e f e r t o p a r t G, f o r s e c t i o n ( c ) to p a r t E and f o r s e c t i o n (d) to p a r t D. I V DISCUSSION OF RESULTS A. R e p r o d u c i b i l i t y . The o b s e r v a t i o n t h a t t h e f i r s t sample o f a m e l t p o s s e s s e d d i f f e r e n t p r o p e r t i e s t h a n s u c c e e d i n g ones i s v e r y l i k e l y due t o a c o n c e n t r a t i o n o f t h e low b o i l i n g p o i n t i m p u r i t i e s i n t h i s sample. Lever t o n and Dekker ( l ) o b s e r v e d t h i s c o n c e n t r a t i o n o f i m p u r i t i e s t o o c c u r i n the case o f antimony f i l m s p r e p a r e d by a s i m i l a r t e c h n i q u e . I t i s more d i f f i c u l t t o e x p l a i n t h e o b s e r v a t i o n s on the f i r s t sample p r e p a r e d a f t e r l e a v i n g t h e me l t i n vacuum f o r a day o r more. However, i t seems f e a s i b l e t h a t , i f a s u r f a c e f i l m o f o x i d e forms on t h e m e l t , the vapour p r e s s u r e over t h e m e l t w i l l be l o w e r t h a n , over an u n o x i d i z e d m e l t and t h a t the vapour w i l l c o n t a i n o x i d e m o l e c u l e s . I f t h i s i s the case we may e x p e c t a specimen made fr o m such a me l t t o be t h i n n e r t h a n o t h e r w i s e and t o p o s s e s s a h i g h e r r e s i s t i v i t y and a d i f f e r e n t H a l l c o n s t a n t . The d i f f e r e n c e between groups I and I I ( f i g . 7) w i t h r e s p e c t to R^ and p may be a t t r i b u t e d t o t h e c o n c e n t r a t i o n o f the h i g h e r b o i l i n g p o i n t i m p u r i t i e s ( Fe-j &u ) i n t h e samples o f group I I . The e r r a t i c (20) r e s u l t s o b t a i n e d f rom samples 73 - 80 a r e p r o b a b l y due t o r e l a t i v e l y l a r g e amounts o f i m p u r i t i e s e v a p o r a t e d , as the end o f the m e l t i s approached. I t i s b e l i e v e d t h a t subsequent samples p r e p a r e d as d e s c r i b e d i n s e c t i o n I I I - A , a r e as pure a s can be o b t a i n e d by t h i s t e c h n i q u e and t h e r e f o r e t h a t any p o s t u l a t e d i n e q u a l i t y i n the numbers o f p o s i t i v e and n e g a t i v e c a r r i e r s must be e x p l a i n e d by t h e remo v a l o f one o r the o t h e r type o f c a r r i e r (or both) by t r a p p i n g (see S e c t i o n I . ) B.. V a r i a t i o n o f the P r o p e r t i e s w i t h T h i c k n e s s . The maximum i n the. c u r v e o f R | v e r s u s • "^""2 t h i c k n e s s ( f i g . 8b) o c c u r s a t a -^ P t h i c k n e s s of about 0.4yju. Lane (5) , w o r k i n g a l s o w i t h e v a p o r a t e d bismuth f i l m s , has p l o t t e d the tem p e r a t u r e dependence o f the i n c r e a s e o f r e s i s t i v i t y i n a magnetic f i e l d v e r s u s f i l m t h i c k n e s s and found an abrupt change i n s l o p e t o o c c u r a t about 0.4y-*>. He i d e n t i f i e s t h i s c r i t i c a l t h i c k n e s s as t h a t a t w h i c h Goetz (6) r e p o r t e d t h e c r y s t a l l i t e s i n e v a p o r a t e d bismuth f i l m s t o undergo a sudden i n c r e a s e i n s i z e . The work o f Gro s s (7) and L e v i n s t e i n (8) shows t h a t below t h e c r i t i c a l t h i c k n e s s the average c r y s t a l l i t e s i z e i n c r e a s e s a s the t h i c k n e s s i s i n c r e a s e d . The shape o f our R | c u r v e i s not i n c o n s i s t e n t w i t h t h i s e v i d e n c e . \ R 2 , i s a f u n c t i o n o f & and ^ o n l y (21) (see eq. 9 ) . I f we p o s t u l a t e with. L e v e r t o n and Dekker ( l ) t h a t a c e r t a i n number o f t h e c u r r e n t c a r r i e r s may be t r a p p e d i n l o c a l i z e d l e v e l s a t c r y s t a l l i t e b o u n d a r i e s t h e n c l e a r l y the number o f t r a p p e d c a r r i e r s w i l l d e c r e a s e as the c r y s t a l l i t e s i z e i n c r e a s e s . A l s o the c a r r i e r m o b i l i t i e s w i l l i n c r e a s e w i t h i n c r e a s i n g t h i c k n e s s s i n c e t h e y depend t o some e x t e n t on s c a t t e r i n g a t c r y s t a l l i t e b o u n d a r i e s . We may e x p e c t t h e n t h a t at l e a s t s m a l l changes w i l l o c c u r i n jr and |3 as the t h i c k n e s s i s v a r i e d . I n s p e c t i o n o f e q u a t i o n 9 shows t h a t o n l y s m a l l changes i n & and |3 a r e r e q u i r e d t o produce th e o b s e r v e d 2 v a r i a t i o n i n R£ . £p2 C. - C o o l i n g the T a r g e t . The e x p e r i m e n t a l r e s u l t s p r e s e n t e d i n s e c t i o n s I I - C and D i n d i c a t e t h a t the main e f f e c t a c h i e v e d by c o o l i n g the s u b s t r a t e d u r i n g d e p o s i t i o n i s t h e t r a p p i n g of a l a r g e f r a c t i o n (see t a b l e V I I I ( d ) ) o f the a v a i l a b l e p o s i t i v e c u r r e n t c a r r i e r s o r " h o l e s " . I t i s i m p o s s i b l e , on t h e p o s t u l a t e o f s e c t i o n XV-B, to e x p l a i n why the t r a p p i n g o f h o l e s s h o u l d predominate i n t h e s e specimens. The e f f e o t cannot be due m e r e l y to a r e d u c e d c r y s t a l l i t e s i z e f o r , as we have seen ( s e c t i o n IV-B) the r a t i o o f the c a r r i e r d e n s i t i e s does not appear t o depend v e r y s t r o n g l y on t h i s v a r i a b l e . However, i f we p o s t u l a t e t h a t t h e (22) c o o l i n g o f t h e t a r g e t r e s u l t s i n a l e s s p e r f e c t l a t t i c e , ( i . e . more l a t t i c e d e f e c t s ) t h e n t h e o b s e r v a t i o n s may be e x p l a i n e d by assuming t h a t h o l e s become t r a p p e d i n vacant l a t t i c e p o i n t s . That i s t o say we assume t h a t t h e p o t e n t i a l f o r an e l e c t r o n i n the immediate neighbourhood o f a l a t t i c e p o i n t v a c a t e d by a p o s i t i v e i o n c o r e i s such t h a t t h e r e i s a tendency to r e p e l a s many e l e c t r o n s ( i . e . a t t r a c t as many h o l e s ) as c o r r e s p o n d t o t h e v a l e n c y o f the c o r e . T h i s p o s t u l a t e i s analogous to t h a t advanced (9) i n c o n n e c t i o n w i t h F - c e n t r e s i n i o n i c c r y s t a l s . These a r e thought to be e l e c t r o n s t r a p p e d i n n e g a t i v e i o n v a c a n c i e s . D. - V a r i a t i o n o f the P r o p e r t i e s w i t h Temperature. The o n l y f a c t worthy o f comment i n t h i s s e c t i o n i s the n e g a t i v e t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t a n c e . Lane (5) and L e v e r t o n and Dekker ( l ) f i n d t h i s same r e s u l t but n e g a t i v e t e m p e r a t u r e c o e f f i c i e n t s a r e never found f o r o t h e r m e t a l f i l m s o f comparable t h i c k n e s s . (10) T a b l e v T I I ( c ) shows t h a t f o r t h i s sample a t l e a s t the e f f e c t i s due t o a r e d u c t i o n i n the number o f c a r r i e r s , s i n c e the m o b i l i t i e s i n c r e a s e w i t h d e c r e a s i n g t e m p e r a t u r e as i n b u l k b i s m u t h . Mott a r d Jones ( l l ) suggest t h a t t h e (23) n e g a t i v e t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t a n c e o b s e r v e d - : i n d i l u t e s o l u t i o n s o f t i n and l e a d i n bismuth, i s due t o a r e d u c t i o n i n the number o f o v e r l a p p i n g e l e c t r o n s . This, w o u l d r e s u l t i n a l o w e r i n g o f t h e F e r m i l e v e l so t h a t f o r a c e r t a i n range o f t e m p e r a t u r e s i t would be p o s s i b l e f o r the number o f c a r r i e r s to i n c r e a s e w i t h i n c r e a s i n g t e m p e r a t u r e as i n s e m i c o n d u c t o r s . T h i s i d e a may a p p l y t o t h i n f i l m s o f b i s m u t h where the e l e c t r o n d e n s i t y i s presumably l o w e r t h a n i n b u l k bismuth due t o t r a p p i n g . I t i s t o be-not ed however t h a t i n our case t h e h o l e d e n s i t y a l s o appears t o i n c r e a s e w i t h i n c r e a s i n g t e m p e r a t u r e (Table v T I I ( c ) ) . I t i s not p o s s i b l e t o d i s c u s s t h i s e f f e c t f u r t h e r on the b a s i s o f the few measurements made. E. - E f f e c t o f A n n e a l i n g . I t i s d i f f i c u l t t o be c e r t a i n , on the b a s i s o f t h e few c a l c u l a t i o n s made, but t h e r e s u l t o f a n n e a l i n g a t 260°G appears ( t a b l e V T I l ( b ) } t o be an i n c r e a s e i n the d e n s i t y o f n e g a t i v e c a r r i e r s and a d e c r e a s e i n t h e d e n s i t y o f p o s i t i v e c a r r i e r s . I f t h i s i s the c a s e , a c o m b i n a t i o n o f t h e e x p l a n a t i o n s advanced by t e v e r t o n and Dekker ( l ) f o r antimony and b ismuth f i l m s would be c o n s i s t e n t w i t h t h e o b s e r v a t i o n s . These a u t h o r s p o s t u l a t e d t h a t ( i ) a n n e a l i n g antimony f i l m s i n c r e a s e d t h e c r y s t a l l i t e s i z e , ( 2 4 ) t h e r e b y d e c r e a s i n g the e x t e n t o f o v e r l a p p i n g o f t h e two c o n d u c t i o n bands and e f f e c t i v e l y " r e c o m b i n i n g " some o f the e l e c t r o n s and h o l e s ; ( i i ) t h a t a n n e a l i n g bismuth f i l m s r e l e a s e d some o f t h e t r a p p e d c a r r i e r s . I f both t h e s e p r o c e s s e s a r e o p e r a t i v e t h e change i n R on a n n e a l i n g would be e x p e c t e d to depend even more s t r o n g l y on t h e c o n d i t i o n s o f p r e p a r a t i o n than t h e H a l l c o n s t a n t i t s e l f . A comparison of t h e r e s u l t s f o r d i f f e r e n t samples, b o t h i n t h i s and t h e p r e v i o u s work shows t h a t i n d e e d R may i n c r e a s e o r d e c r e a s e on a n n e a l i n g . A n n e a l i n g those samples w i t h n e g a t i v e H a l l c o e f f i c i e n t s causes the c o e f f i c i e n t t o become more n e g a t i v e ( t a b l e 7 1 ( c ) ) . On t h e o t h e r hand those specimens d e p o s i t e d on c o o l e d p l a t e s and h a v i n g s m a l l p o s i t i v e H a l l c o e f f i c i e n t s were found t o s u f f e r an i n c r e a s e i n t h e c o e f f i c i e n t on a n n e a l i n g . L a c k i n g enough d a t a t o c a l c u l a t e the a c t u a l c a r r i e r d e n s i t i e s i n these samples we cannot say whether o r not t h e s e changes a r e c o n s i s t e n t w i t h the f o r e g o i n g p o s t u l a t e s . I t s h o u l d be n o t e d however t h a t a change i n n]_ o r n 2 may produce a change o f e i t h e r s i g n i n R, (eq.. 5 ) , depending on t h e i n i t i a l v a l u e o f t h e s e d e n s i t i e s . F. - C a l c u l a t i o n s . T a b l e v T I I shows t h a t t h e number o f f r e e e l e c t r o n s i n a "normal" ( i . e . d e p o s i t e d on an u n c o o l e d t a r g e t ) a n n e a l e d f i l m i s about 7 x l O 1 ^ p e r crn^. and t h a t (25) t h e c a r r i e r m o b i l i t y i s about 3000 cm2-voltT1-sec"1*. a t room tempe r a t u r e . Mott and Jones (l(L) e s t i m a t e t h e e l e c t r o n (and hence a l s o t h e h o l e ) d e n s i t y t o be 3 x 10"^ per cm^. on the b a s i s o f some measurements on t h e s p e c i f i c magnetic moment of b i s m u t h s i n g l e c r y s t a l s . We c o n s i d e r our v a l u e to be i n e x c e l l e n t agreement w i t h t h i s one. So f a r as we know no o t h e r e x p e r i m e n t a l v a l u e has been quoted f o r the c a r r i e r m o b i l i t y i n b i s m u t h . V. CONCLUSION. The e l e c t r i c a l p r o p e r t i e s o f e v a p o r a t e d bismuth f i l m s depend s t r o n g l y on t h e temp e r a t u r e o f the s u b s t r a t e d u r i n g d e p o s i t i o n and on t h e t h i c k n e s s o f t h e f i l m . V a l u e s o f t h e c o n s t a n t s d e f i n i n g t h e s e p r o p e r t i e s depend t h e r e f o r e on the sample measured and a r e not a p p l i c a b l e t o b i s m u t h i n b u l k . ; The o b s e r v e d r e s u l t s can be q u a l i t a t i v e l y e x p l a i n e d by assuming t h a t c a r r i e r s ( p o s i t i v e o r n e g a t i v e ) may be t r a p p e d i n l o c a l i z e d l e v e l s a t c r y s t a l l i t e b o u n d a r i e s and t h a t p o s i t i v e c a r r i e r s may be t r a p p e d i n va c a n t l a t t i c e p o i n t s . One o t h e r a s s u m p t i o n may or may not be n e c e s s a r y , v i z . , t h a t t h e e x t e n t o f t h e average o v e r l a p o f t h e two h i g h e s t energy bands depends on t h e average c r y s t a l l i t e s i z e . REFERENCES l l ) W.E. L e v e r t o n and A . J . Dekker - Phys. Rev., . . 80, 732 (1950) and 8 l , 156 (1951). (2) S l a t e r - Phys. Rev., 2i» 1592, (1949). (3) B i l l i g and L a n d s b e r g - P r o c . Phys. S o c , 63A, 101, (1950). (4) Jones - P r o c . Roy. S o c , 155A, 653 (1936). (5) l a n e - Phy s . Rev., 48, 193 (1935). (6) Goetz - N a t u r e , 132, 206 (1933). (7) Gross - Z e i t s . f . P h y s i k , 64, 520, 537 (1930). (8) L e v i n s t e i n - J . App. Phys., 20, 306 (1949). (9) S e i t z - Modern Theory o f S o l i d s , p. 406 (McGraw - H. 1 1 , 1940). (10) Suhrmann and B a r t h - Z e i t . f . P h y s i k 103. 133 (1936). (11) M o t t and Jones - Theory of the P r o p e r t i e s of M e t a l s and A l l o y s p^ 304 ( O x f o r d , 1936) . 

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