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Some properites of thin film aluminum superconductors for use as a megahertz second sound detector Lenz, John William 1971

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i SOME PROPERTIES OF THIN FILM ALUMINUM SUPERCONDUCTORS FOR USE AS A MEGAHERTZ SECOND SOUND DETECTOR by JOHN WILLIAM LENZ B.A., The University of Iowa, U.S.A., 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Physics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Br it ish Columbia, I agree that the Library shall make it freely available for reference and 'study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. n . c Physics Department of • ~ The University of Brit ish Columbia Vancouver 8, Canada Date 28 September 1971 i i ABSTRACT Some p r o p e r t i e s o f t h i n f i l m aluminum s u p e r c o n d u c t o r s (80 - 1 3 0 A) were i n v e s t i g a t e d f o r use as a h i g h f r e q u e n c y second sound d e t e c t o r . The f i l m s ' t r a n s i t i o n t e m p e r a t u r e s , Tc, /were r a i s e d t o near the lambda p o i n t o f He by a s u r f a c e enhancement o f the BCS c o u p l i n g c o n s t a n t . The f i l m s were u s e f u l as s e n s i t i v e thermometers o v e r t h e tem p e r a t u r e range o f t h e i r t r a n s i t i o n , & Tc = 0.06 K, w i t h a s e n s i t i v i t y g i v e n by th e t r a n s i t i o n s l o p e , 2 - 3 x 10 ^ ohms/K. The f i l m s m e c h a n i c a l l y and e l e c t r i c a l l y w i t h s t o o d the t h e r m a l shock o f f i v e t h e r m a l c y c l e s from room t e m p e r a t u r e to 2 K. The i n s t a b i l i t y o f Tc a f t e r c y c l i n g was a t most 0 . 0 5 K. By i n c r e a s i n g t he b i a s c u r r e n t , Tc ( t h e He b a t h t e m p e r a t u r e a t t h e t r a n s i t i o n ) c o u l d be decreased by a t most 0 . 0 2 5 K. The s l o p e o f t h e t r a n s i t i o n c u r v e , dR, i n c r e a s e d by a t dT most 30$ upon t h e r m a l c y c l i n g and w i t h i n e x p e r i m e n t a l a c c u r -acy t h e b i a s c u r r e n t had no e f f e c t on dR, f o r the range 2-60^A. dT From measurements o f one f i l m ' s time response t o t h e r m a l e x c i t a t i o n , t h e time c o n s t a n t was found t o be l e s s t h a n 4 5 . 5 n s e c , whic h means t h a t the f i l m i s c a p a b l e o f f u l l y r e s p o n d i n g t o second sound o f f r e q u e n c i e s o f a t l e a s t 3 . 5 MHz. i l l TABLE OF CONTENTS Chapter s Page I I n t r o d u c t i o n 1 II Theory 2 A. Enhancement of T c 2 B. Thermal Time Constant Estimate 6 I I I Experimental Apparatus and Procedure 10 A. F i l m P r e p a r a t i o n 10 B. T r a n s i t i o n Curve Measurements 12 C. Time Constant Measurement 13 IV R e s u l t s and A n a l y s i s 17 A. T r a n s i t i o n Temperature Behaviour 17 B. Thermal Time Constant 2A V Conclusions 28 References and Footnotes 30 Iv LIST OF FIGURES Figure Page 1 Film Evaporation Pattern and Dimensions 11 2 Typical Detector Signal 14 3 Film Thickness versus T c 18 4 Typical E f f e c t of Thermal Cycling on T c and Ft^ 21 5 Typical Transition Curves Showing T c Dependence 22 o n Idc 6 Top - Compensated and Normalized Detector Response Bottom - Amplifier and Cable Response 25 V ACKNOWLEDGEMENTS I wish to f i r s t thank Dr. M.J. Crooks f o r h i s timely-suggestions at the c r i t i c a l p o i n t s of t h i s i n v e s t i g a t i o n , d e t a i l e d c r i t i c i s m of t h i s t h e s i s , and our many thought-provoking d i s c u s s i o n s . I am indebted to Dr. P.W. Matthews f o r h i s c r i t i c i s m of t h i s t h e s i s and s u p e r v i s i o n of i t s completion. I a l s o wish to thank Mr. R. Weisbach and Mr. G. Erooks f o r t h e i r t e c h n i c a l a s s i s t a n c e . -1-CHAPTER I INTRODUCTION To detect second sound In He II w i t h i n the microscopic c r i t i c a l r e g i o n , where the wavelength of the second sound i s l e s s than the s u p e r f l u i d coherence l e n g t h , the experimental apparatus must be capable of measuring high frequency second sound very c l o s e to the lambda p o i n t , T^. Second sound —6 1 measurements have been made as c l o s e as 5 x 10 K below T^  . For t h i s temperature, a second sound frequency of 0.4 MHz i s required to produce a thermal wavelength equal to the super-f l u i d coherence l e n g t h ; higher frequency generation and d e t e c t i o n i s required f o r temperatures f u r t h e r below T^. Because of the high a t t e n u a t i o n of second sound near the lambda poi n t and the dc heat flow a s s o c i a t e d w i t h operating the thermometer, t h i s d e t e c t o r must have high thermal s e n s i -t i v i t y , low operating r e s i s t a n c e «500 ohms), as w e l l as the required low thermal time constant. Superconducting t h i n f i l m s operated at t h e i r t r a n s i t i o n temperatures f u l f i l the s t r i n g e n t requirements of the needed thermometer. This t h e s i s describes an i n v e s t i g a t i o n of t h i n f i l m aluminum superconductors f o r p o s s i b l e use as a high frequency second sound d e t e c t o r . The f i l m p r o p e r t i e s which w i l l be discussed a r e : a) the method of s e t t i n g the t r a n s i t i o n temperature, T c, near the lambda p o i n t of He b) the e f f e c t of the operating dc bias c u r r e n t , Ia c, on T and the slope of the t r a n s i t i o n , dR c d f c) the s t a b i l i t y of T c and dR w i t h thermal c y c l i n g dT d) the thermal time response to heat impulses. -2-CHAPTER I I • THEORY A. Enhancement of T c A superconductor i s u s e f u l as a second sound d e t e c t o r only over a narrow temperature range about i t s t r a n s i t i o n temperature, where the r e s i s t a n c e drops from i t s normal val u e , R n, to at most a few ohms. The t r a n s i t i o n temperature i s u s u a l l y defined as the temperature of the superconductor at which the m a t e r i a l ' s r e s i s t a n c e i s one-half of i t s normal s t a t e r e s i s t a n c e . In t h i s i n v e s t i g a t i o n , we are Int e r e s t e d i n the fl;lms as detectors of thermal waves propagating i n the He bath, not i n the f i l m ' s p r o p e r t i e s as a f u n c t i o n of the f i l m temperature. Therefore, f o r t h i s i n v e s t i g a t i o n the more meaningful d e f i n i t i o n of the t r a n s i t i o n temperature, T c, which w i l l be used i s the temperature of the He bath at which the f i l m ' s r e s i s t a n c e i s one-half of i t s normal s t a t e r e s i s t a n c e . Since superconductors are u s e f u l as s e n s i t i v e thermometers only over a narrow temperature range, the f i r s t problem i s to prepare a f i l m such t h a t i t s s e n s i t i v e temperature region i s at the r e q u i r e d temperature. Because more t h e o r e t i c a l and experimental work has been done on s h i f t i n g the t r a n s i t i o n temperatures of the elements and the s i m p l i c i t y of f a b r i c a t i o n , aluminum was chosen as the thermometer m a t e r i a l . The tr a n s -i t i o n temperature of bulk aluminum i s 1.175 K; a s i z e e f f e c t enhancement phenomenon was used to r a i s e T c near T^=2.172 K. An expression f o r T c i n bulk superconductors derived from the Bardeen-Cooper-Schrieffer (BCS) theory i s the s t a r t i n g p o i n t of most t h e o r i e s p r e d i c t i n g the enhancement of T c. This expression i s ^ : kT c = 1 . 1 4 tiw exp(-l/p) , f o r p « l ( 1 ) where -u/=the c h a r a c t e r i s t i c c u t o f f frequency corresponding to the Debye temperature p=the BCS c o u p l i n g constant, which i s the product of the e l e c t r o n d e n s i t y of s t a t e s , N, of one s p i n at the Fermi s u r f a c e , and the average net a t t r a c t i v e phonon mediated e l e c t r o n - e l e c t r o n i n t e r a c t i o n , V. From Eq. ( 1 ) , i t i s c l e a r that T c can be increased by i n c r e a s -i n g e i t h e r ftv or p. Ginzberg-^ has suggested that a surface enhancement of T c may a r i s e from i n c r e a s i n g the specimen's BCS c o u p l i n g constant, p. The e f f e c t i v e p would be a super-p o s i t i o n of the bulk metal e l e c t r o n - e l e c t r o n i n t e r a c t i o n i n the centre volume of the specimen and the enhanced i n t e r a c t i o n at the geometrical boundaries. He a l s o suggested that the enhanced surface i n t e r a c t i o n may be due to surface phonons and the v a r i a t i o n of electron-nucleus screening at the s u r f a c e . Aluminum f i l m s deposited on a room temperature substrate are p o l y c r y s t a l l i n e . Therefore, the surface enhancement of T c can a r i s e from e i t h e r the f i l m t h i c k n e s s , d, or the c r y s t a l l i t e g r a i n s i z e , g, i f e i t h e r dimension i s small enough to produce a lar g e enough surface to volume r a t i o . I f g«,d, as w i t h aluminum f i l m s deposited i n a l a r g e p a r t i a l pressure of oxygen^, the g r a i n s i z e w i l l p r i m a r i l y determine T c. I f <K<8» a s w i t h u l t r a t h i n f i l m s deposited at pressures below 1 0 " 6 T o r r 5 , the f i l m thickness w i l l determine T c . An expression f o r T c has been derived by Abeles et a l . f o r aluminum f i l m s where g«d. They assumed an ordered array of oxide bounded aluminum c r y s t a l l i t e s and developed a three-dimensional g e n e r a l i z a t i o n of de Gennes' expression^ f o r the - 4 -enhancement of T "I The de Gennes derivation assumed a slab c geometry of superconducting-normal-superconducting metals, whereas Abeles et a l . were dealing with a three-dimensional superconductor-oxide-superconductor geometry. In the d e r i -vation, de Gennes was able to simplify a boundary condition by assuming the normal layer was not an i n s u l a t i n g b a r r i e r . Abeles et a l . were able to make the same s i m p l i f i c a t i o n a f t e r comparing t h e i r films' normal resistances to those predicted 7 by a model where each c r y s t a l l i t e was an isolated supercon-ductor. Since the experimental was more than three orders of magnitude larger than those predicted, they assumed that each c r y s t a l l i t e was strongly coupled to i t s neighbour, and that they too could simplify the boundary condition. De Gennes also assumed that the coherence length,£, of his d i r t y superconductor model was larger than the width of the normal slab. Correspondingly, Abeles et a l . found at l e a s t 100 grains contained within t h e i r calculated volume £. . Both de Gennes and Abeles et a l . assumed that fn^and N of the sample were those of the bulk superconductor'. The r e s u l t i n g exoression for T„ by Abeles et a l . was: T c = 1.14 ftwexp (-l/p) (2) (3) hw-BCS c u t o f f frequency for bulk aluminum pQ=.BCS coupling constant for bulk A l _pe =:BCS coupling constant within the surface region thickness of the surface region g=average c r y s t a l l i t e size. -5-As can be seen from Eq. ( 3 ) , p i s a c t u a l l y the volume weighted a d d i t i o n of the b u l k and s u r f a c e BCS c o u p l i n g cons-B t a n t s . From the work of P i n e s " , they a s s i g n e d v a l u e s to fi-ui and p . The s u r f a c e r e g i o n t h i c k n e s s , d , was taken as 5 A, the approximate t h i c k n e s s of an oxide monolayer, and the-v a l u e of p was obtained from the b e s t f i t of Eq. (2) to s t h e i r e xperimental d a t a . With these v a l u e s s u b s t i t u t e d f o r the above parameters, Eqs. (2) and (3) reduce t o : T c = 216.6 exp(-l/p) (A) where p =0.19 + 0.08 [I-(1-10/g) ^] , f o r g « d and g has u n i t s of Angstroms. For the case d « g , S t r o n g i n et a l . have d e r i v e d an e x p r e s s i o n f o r T c . They assume a s l a b geometry of an aluminum f i l m w i t h a s u r f a c e oxide l a y e r . The Ginzberg s u r f a c e l a y e r , which enhances T , l i e s Just below the oxide l a y e r and i s a r b i t r a r i l y assumed to be the same t h i c k n e s s as the oxide l a y e r , about 20 A. F o l l o w i n g the above theory of de Gennes^, the r e s u l t i n g e x p r e s s i o n f o r T c i s : T_ = 1.14 fi-ui exp(-l/p) where p = ( p 0 d n + p 8 d g ) / d , f o r d « g . A l l the parameters have the same d e f i n i t i o n as i n the theory by Abeles e t a l . except f o r d, which i s the t o t a l f i l m t h i c k -n ess. Both t h e o r i e s a s s i g n e d the same v a l u e s to the param-e t e r s fi-w and p Q . S t r o n g i n e t a l . assigned d i f f e r e n t v a l u e s t o d g and p g ( d s = 2 0 A and p gr:0.35) than d i d Abeles e t a l . The r e s u l t i n g e x p r e s s i o n f o r T c by S t r o n g i n et a l . , i s : -6-T c - 2 1 6 . 6 exp(-l/p) (6) where p = 0.19/d fd-20) + 36.84) , f o r d « g and d has u n i t s o f A n g s t r o m s . The two t h e o r e t i c a l curves are shown i n F i g . 3. B. Thermal Time Constant Estimate An estimate can be made of the f i l m ' s frequency response to thermal e x c i t a t i o n from the f i l m ' s p h y s i c a l dimensions and steady s t a t e dc measurements. In the s i m p l e s t model, one assumes t h a t the time response of the d e t e c t o r to thermal e x c i t a t i o n i s analogous to the response of a low-pass RC f i l t e r to e l e c t r i c a l e x c i t a t i o n . N e g l e c t i n g the thermal c a p a c i t a n c e of the s u b s t r a t e and t h i n f i l m l e a d s , the d e t e c t o r ' s capac-i t a n c e i s t h a t of the superconducting f i l m . The thermal conductance, G, from the f i l m to the heat s i n k i s i d e n t i f i e d w i t h the r e c i p r o c a l of R. Pure superconductors e x h i b i t a sharp r i s e i n t h e i r s p e c i f i c heat ( & C ) i n going from the normal s t a t e (C^) to the superconducting s t a t e ( C s ) . The magnitude of the s p e c i f i c heat r i s e , f o r pure superconductors, i s g i v e n by Rutgers' o formula . In the absence of a magnetic f i e l d , the s p e c i f i c heat r i s e i n MKS u n i t s i s : A C = Cl - Cl = Tc ItjBA n |dT/T=T c where AC' has u n i t s of J-Kg^-K"* 1 £ = f i l r a d e n s i t y (Kg/m^), assuming the d e n s i t y i s t h a t of bulk aluminum B c = JJKC i n f r e e space and assuming a demagnetizing f a c t o r of zero, w i t h u n i t s of T e s l a s . d_Bc\ = s l o p e of the c r i t i c a l magnetic f i e l d dT / TrT„ strength-tempera t o r e curve at T=T_ . The value of ( d B c / d T ) T _ T c was taken as -183 G/K from Abeles et al.*° f o r a granular aluminum f i l m whose T c was near those of this work. One calculates that A C = 0.19 J-Kg _ 1-K 1 . Now C N = 0.11 J - K g " 1 - ^ 1 f o r bulk aluminum at T Q 1 1 . Assuming that Rutgers' formula c o r r e c t l y gives A C f o r granular alum-inum thi n f i l m s , the upper l i m i t of the film's s p e c i f i c heat i s C N + A C = 0.30 J - K g ' 1 - ^ 1 . With th i s upper l i m i t on C , knowing the film's thickness, and the area of the f i l m acting as the detector, one can estimate the upper l i m i t of the film's thermal capacitance. To determine the detector's thermal conductance, G, we 12 followed the analysis of Martin and Bloor . The steady state heat flow equation for the f i l m i s : G (T-T s) = i 2 R (8) where i 2 R = e l e c t r i c a l power dissipated, i n the fi l m from the dc operating current G = e f f e c t i v e thermal conductance from the f i l m to the heat sink (substrate and surrounding He bath T-T s =temperature difference between the f i l m (T) and the heat sink ( T 8 ) . The resistance i n Eq. (8) i s a function of T. For low operating currents, joule heating raises the film's r e s i s -tance by r a i s i n g i t s temperature. However, with high enough currents, the film's resistance r i s e i s due to a combination of the above Joule heating temperature r i s e and. a downward s h i f t of T c, caused by the magnetic f i e l d produced by the high current. Since, i n writing Eq. (8) - 8 -one assumes that the film's temperature r i s e (and therefore resistance r i s e ) i s due only to Joule heating, the equation i s v a l i d only for currents smaller than those causing a magnetic f i e l d s h i f t i n T c. D i f f e r e n t i a t i n g Eq. (8) with respect to T, with T s held constant, we have: & = fo(l2R)) (9) The change i n temperature of the f i l m , AT, can be related to i t s change i n resistance by using the t r a n s i t i o n slope IR: dT AT r dT AR J<m') • ' (10) dR Substituting Eq. (10) into (9) results i n : & = f ? a ( i 2 R ) ) a£l j{dR / T 8 dTj dT/ T| =.TC. The slope of the t r a n s i t i o n curve i s actually dR , not dT s dR, since the temperatures measured are those of the He bath, dT, However, i f the temperature difference ( A T f ) between the f i l m and the He bath i s constant over the t r a n s i t i o n region, 2 then dR - dR. Now AT/. = T-T_ = i R/G-. In constant current dT s dT. T measurements of the t r a n s i t i o n curves, one would expect A fcosdecrease as the film's resistance decreased, with this decrease i n AT^ becoming larger for higher constant opera-t i n g currents (See F i g . 5). This would r e s u l t i n a current dependent value of [dR ) . For the range of currents used T 8 i i n t h i s investigation,[dR ] was found to be indeoendent of UTJI the operating current within experimental accuracy. We therefore conclude that AT^ was constant over the t r a n s i t i o n region and that dR _ dR, f o r the range of currents used. dT a dT By measuring the film's resistance as a function of current, with the He bath temperature set on the l i n e a r portion of the dR alone, /d(i^R) ) can be found from the dT s \ dR /T s slope, of the r e s u l t i n g power versus resistance curve. Again we must be c a r e f u l to take the slope of this curve at current values below those which cause a magnetic f i e l d s h i f t i n T c. I f the film's temperature (resistance) r i s e i s due only to Joule heating, the slope of the power yersus resistance curve w i l l be of one value over most of the range of power values. Since the physical dimensions of the f i l m and the calcu-lated s p e c i f i c heat places an upper l i m i t on C, one can calculate the upper l i m i t of the detector's thermal time constant TTCCr, T^-C/G, where f C f t. - 1 and -u^le the RC corner frequency of the detector. - 1 0 -CHAPTER I I I EXPERIMENTAL APPARATUS AND PROCEDURE A. F i l m P r e p a r a t i o n Aluminum, 99.999$ pure, was evaporated from an aluminum oxide c r u c i b l e 1 - 5 , at pressures of 3-6 x 1 0 " ^ Torr, onto poly-c r y s t a l l i n e quartz or microscope s l i d e s u b s t r a t e s . The substrates were degreased, u l t r a s o n i c a l l y cleaned i n a de-t e r g e n t - d i s t i l l e d water s o l u t i o n , r i n s e d u l t r a s o n i c a l l y i n d i s t i l l e d water, and d r i e d j u s t before evaporation i n a stream of i n e r t gas. The aluminum was degreased and etched i n a KOH s o l u t i o n p r i o r to evaporation. The aluminum vapour was masked to the shape of a b a r - b e l l and deposited omto the ambient temperature s u b s t r a t e . The evaporator was then opened to a i r , to change sources, and approximately 2,000 A of gold was evaporated on top of the aluminum to serve as e l e c t r i c a l l e a d s . Then # AO AWG copper wires were indium soldered to the Al-Au-In overlap r e g i o n (see F i g . 1 ) . With the b a r - b e l l shape, one can reasonably assume th a t the sensing area of the d e t e c t o r i s the bar of the b a r - b e l l . Since the s m a l l e s t c r o s s - s e c t i o n a l area of the A l f i l m Is i n the bar, that region c a r r i e s the highest and most uniform current d e n s i t y . Also the Al-Au-In a l l o y e d regions are kept w e l l away from the sensing area. The gold d i f f u s e d through the aluminum oxide l a y e r to provide e l e c t r i c a l contact which withstood f i v e thermal c y c l e s from room temperature to 2 K. A quartz c r y s t a l thickness monitor connected to a recorder was used to measure the f i l m t h i c k n e s s , s i n c e the -11-V Gold 2 , 0 0 0 A 6 mm "Bar" S L Aluminum V f — 1.5mra Gold 2 , 0 0 0 A Indium Solder FIGURE 1. Film Evaporation Pattern and Dimensions. films were too t h i n to be d i r e c t l y measured by an i n t e r f e r -ometer. The monitor was calibrated with thicker films by p l o t t i n g the frequency change of the quartz c r y s t a l against the interferometer measured f i l m thickness. From th i s c a l i b r a t i o n and the frequency change measured by the recorder, the thickness of the 80-130 A films were accurate to ±10 A. B. Transition Curve Measurements Steady state resistance-temperature measurements over the t r a n s i t i o n region were made for measuring currents ranging from 2-60//A. The temperature of the He bath was 14 set by a pressure regulator which kept the bath tempera-ture constant to 1 mK during the resistance measurements; for temperatures above the lambda point, a time lapse of 5 minutes was allowed for the system to come to thermal equi-librium before the resistance measurements were made. The He vapour pressure above the bath was measured by a butyl phthalate o i l manometer and the corresponding bath tempera-tures were found from the "1958 He^ Scale of Temperatures" 1^. The r e s u l t i n g He Bath temperature values were accurate to ± 3 mK. The films' resistance was determined using a 4-point measurement technique. V/ith a constant current flowing i n one d i r e c t i o n through the f i l m , two voltage measurements were made; a po s i t i v e voltage i n the d i r e c t i o n of the current and a negative voltage i n the d i r e c t i o n opposite to the current. The average of these voltages was then used to calculate the resistance. This procedure n u l l i f i e d the -13-e r r o r s due to voltmeter d r i f t s . The r e s u l t i n g e r r o r f o r a l l r e s i s t a n c e measurements was at most ± 0.7 ohms. C. Time Constant Measurement The f i l m s were thermally excited, by sweeping a l a s e r beam across them. A 50 mW beam (4416 A wavelength) from a helium-cadmium l a s e r was r e f l e c t e d from a r o t a t i n g m i r r o r 11 meters from the f i l m . At the dewar, the 3 cm diameter beam swept across a v a r i a b l e i r i s and through a 10 cm f o c a l l e n g t h convergent lens onto the f i l m . The r e s u l t i n g voltage pulse was tr a n s m i t t e d out of the dewar through an u l t r a m l n -i a t u r e c o a x i a l cable"^ and a m p l i f i e d by a wide band a m p l i f i e r . The s i g n a l was dis p l a y e d on an o s c i l l o s c o p e ; the sweep being t r i g g e r e d by a l i g h t s e n s i t i v e r e s i s t o r placed l n the beam's sweep path. The method used to determine the f i l m ' s time response to the l i g h t pulses was to measure the s i g n a l amplitude as the r i s e time of the beam I n t e n s i t y was v a r i e d . I f the beami-s i n t e n s i t y versus time p r o f i l e could be equated to a sine wave of some "equivalent frequency", then a p l o t of the s i g n a l amplitude as a f u n c t i o n of the "equivalent frequency" would give the RC corner frequency of the d e t e c t o r , and there-for e i t s time constant. A t y p i c a l s i g n a l i s shown i n F i g . 2 . In t h i s f i g u r e , the camera s h u t t e r was open f o r about 100 o s c i l l o s c o p e sweeps, so the r e s u l t i n g photograph shows the s i g n a l superimposed on the wide band, of a m p l i f i e r n o i s e . The s i g n a l to noise r a t i o observed, during the amplitude FIGURE 2. T y p i c a l Detector S i g n a l V e r t i c a l Axis - 5 rav per d i v i s i o n H o r i z o n t a l Axis - 100 na*per d i v i s i o n . -15-measurements., varied from about 5:1 to becoming l o s t i n the amplifier noise. The si g n a l appeared to remain approximately symmetric during the measurements. The following procedure was used to determine the beam's intensity-time p r o f i l e . With a l i g h t sensitive re-s i s t o r placed i n the film's position, an oscilloscope trace of i t s voltage was photographed as the beam swept by; the beam repefcion rate was also measured by the oscilloscope. Since the minimum r i s e time of the l i g h t s e n s i t i v e r e s i s t o r was approximately 5 m sec, the beam's r e p e t i t i o n rate was adjusted so that the r e s i s t o r would accurately follow the in t e n s i t y r i s e . An intensity-voltage c a l i b r a t i o n was then used to transform the voltage-time p r o f i l e to an i n t e n s i t y -time p r o f i l e . Since the laser beam was l i n e a r l y polarized, i t s i n t e n s i t y could be quantitatively varied r e l a t i v e to i t s minimum by rotating a p o l a r i z e r . The r e s u l t i n g i n t e n s i t y -voltage curve was normalized to the highest i n t e n s i t y transmitted by the p o l a r i z e r . Renormalized i n t e n s i t y - v o l -tage curves were drawn f o r each photograph of the r e s i s t o r ^ s voltage-time p r o f i l e , with the renormalized i n t e n s i t y corres-ponding to the minimum voltage across the r e s i s t o r during a sweep (the voltage decreased as the Intensity increased). From the voltage-time p r o f i l e of the photograph and the in t e n s i t y c a l i b r a t i o n , an i n t e n s i t y - ^ m e i p r o f i l e was plotted for the corresponding r e p e t i t i o n rate. To obtain the intensity-time p r o f i l e for a fas t e r r e p e t i t i o n rate, one merely reduced the time scale of the p r o f i l e by a factor -16-equal to the r a t i o of the two r e p e t i t i o n rates. To determine the e f f e c t of the amplifier and coaxial cable on the detector si g n a l amplitude, the frequency res-ponse of the .two components was measured f o r d i r e c t e l e c t r i c a l e x c i t a t i o n ; the results are shown i n F i g . 6. -17-CHAPTER IV RESULTS AND ANALYSIS A. Transition Temperature Behaviour As previously defined, T c i s the temperature of the He bath at which the f i l m resistance i s one-half of i t s normal state resistance. From the f i t of the experimental t r a n s i -tion temperatures to the t h e o r e t i c a l curve of Eq. (6), which assumes that the f i l m thickness determines T c, one notices a lack of T c dependence on f i l m thickness (see F i g . 3). This lack of thickness dependence indicates that the parameter enhancing T c i s probably the grain s i z e , not the thickness, and that a l l the films have approximately the same grain s i z e . T&ais explanation of F i g . 3 i s supported by work done 17 by Cohen and Abeles . They produced granular aluminum films (g^C^) with an alumina c r u c i b l e source, where the pressureifrefore evaporation was lO'^Tor*?, increasing to 3 x 10~5 _ 1G~^ Torr during evaporation. Normally aluminum films evaporated at these pressures are not granular since the p a r t i a l pressure of oxygen i s too low. Cohen and Abeles assumed that the c r u c i b l e outgassed enough oxygen when heated to produce a f i l m composed of pure aluminum c r y s t a l l i t e s , each surrounded by an oxide layer. From Eqs. (2) and (3), we can conclude that the 80-130 A film*'prepared i n this i n -vesti g a t i o n a l l have an average grain size of 83-88 A. If one wishea to increase the t r a n s i t i o n temperature closer to the lambda point, i t could be done by two methods. - I B -FIGURE 3 . F i l m Thickness versus T c O r d i n a t e f o r Eq. ( 4 ) Is g r a i n s i z e , g O r d i n a t e f o r data p o i n t s and Eq. ( 6 ) i s f i l m t h i c k n e s s , d Dots - Thermal C y c l e 1 Crosses - Thermal C y c l e 4 Quartz s u b s t r a t e , Id c =1 0 < / / A . - 19-Th e f i r s t way would be to increase the oxygen p a r t i a l 4 pressure during evaporation, as was done by Abeles et a l . This has been done by the author by bleeding oxygen into the evaporator at a rate about equal to the pump speed. With a low flow rate valve, the pressure can be s t a b i l i z e d totlO"''' Torr. The pressure would then be the reproduceable parameter predominantly determining T c. The other method of achieving a higher T c would be to evaporate thinner films using the procedure of this work. With thinner films ( <C 60 A), one should "be able to enter the region where d ^ < g and the thickness would determine T c. The l i m i t a t i o n to this method, however, i s that the lower l i m i t to e l e c t r i -c a l l y continuous aluminum films i s about 30 A . Six films were thermally cycled f i v e times from room temperature to 2 K, with no spe c i a l precautions taken to avoid thermal shock. The f i r s t reason for thermally c y c l i n g the films was to determine whether they were securely adhered to the substrate and to ensure that they would remain e l e c t r i c a l l y continuous upon c y c l i n g . One f i l m , out of the six thermally cycled, became e l e c t r i c a l l y discontinuous on the fourth cycle. Since the other f i v e , f i l m s remained e l e c t r i c a l l y continuous, one concludes that they mechanically withstood the thermal shock of the f i v e thermal cycles. The e f f e c t of thermal c y c l i n g on Rn, dR, and T c was dT determined f o r three f i l m s . The normal resistance, R n (resistance at (temperatures Just above the t r a n s i t i o n ) , was t y p i c a l l y 180 ohms for the f i r s t thermal cycle. Upon thermal -20-c y c l i n g , rose monotonlcally f o r a l l f i l m s ; by the f i f t h thermal c y c l e , was as much as 80% l a r g e r than f o r the f i r s t c y c l e (see F i g . A). The slope of the t r a n s i t i o n curve, dR, was t y p i c a l l y 2,000 ohm/K f o r the f i r s t thermal c y c l e . dT For the f i l m s of thickness l e s s than 100 A, thermal c y c l i n g increased dR by at most 30$. dT This increase i n dR and the decrease i n T c upon thermal dT c y c l i n g (to be discussed) may have been caused by the reanneal-i n g of the f i l m s as they were c y c l e d . Since the cycled values of these two q u a n t i t i e s are c l o s e r to the expected values of a bulk aluminum superconductor, the trends i n d i c a t e an Increase of the f i l m s ' average c r y s t a l l i t e s i z e upon thermal c y c l i n g . W i t hin experimental accuracy, there was l i t t l e , i f any, e f f e c t of the measuring current on dR f o r the ranece 2-60 »k. dT Another reason f o r thermally c y c l i n g the f i l m s was to determine the s t a b i l i t y of T and to check i f the " f i n e tuning" of T c by v a r y i n g the b i a s current could compensate f o r the thermal c y c l i n g i n s t a b i l i t y of T c. T y p i c a l r e s u l t s of the e f f e c t of thermal c y c l i n g on T c are shown i n F i g . A. For the tree f i l m s t e s t e d , T c v a r i e d over a range of 0.05 K durin g the f i v e thermal c y c l e s . The v a r i a t i o n of T c w i t h I d c , f o r currents of the range 6-60 j/k, was at most 0.025 K, and only i n the d i r e c t i o n of lower temperatures (see F i g . 5 ) . Since the slope of the power versus r e s i s t a n c e curve of eleven f i l m s was constant over most of the b i a s current range (see d i s c u s s i o n of Chapter I I , p. 8 ) , we assume th a t the dependence of T c on I^c i s due only to j o u l e heating. -21-1.95 2 . 0 0 2 . 0 5 2.10 2.15 2 . 2 0 Ttath (K) . FIGURE 4 . T y p i c a l E f f e c t of Thermal C y c l i n g on T c and R n I d c = 1 0 // / A« -22-1195 2.00 2.05 2.10 2.15 2.20 Tbath (K) FIGURE 5. T y p i c a l T r a n s i t i o n Curves Snowing T c Dependence on Ir]C Thermal C y c l e 3, F i l m Thickness -96 A, R e s i s t a n c e E r r o r -^ + 0.7 ohms. -23-For, as I d c i s increa s e d , £>Tfr T-Ts =12R/G (the d i f f e r e n c e between the f i l m temperature and the s i n k temperature) i n c r e a s e s . So even though the f i l m ' s t r a n s i t i o n to the superconducting s t a t e occurs at the same temperature T, the t r a n s i t i o n temperature T c, as defined by the He bath temp-e r a t u r e , decreases w i t h i n c r e a s i n g c u r r e n t . The l i m i t to the " f i n e tuning" range In these f i l m s was the maximum current at which the f i l m s could be operated without d e s t r o y i n g t h e i r e l e c t r i c a l c o n t i n u i t y . One 130 A f i l m became e l e c t r i c a l l y discontinuous w i t h an operating c u r r e n t of SO^A. A l a r g e r " f i n e tuning" range can be r e a l -i z e d i n very narrow f i l m s , i f the width i s l e s s than a c r i t i c a l width (about one micron) and i f the thickness i s 10 l e s s than the pe n e t r a t i o n depth. T.K. Hunt • has reported c u r r e n t induced s h i f t s of T c of 2.6 K i n 500 A t i n f i l m s of width 1.9 microns. - 2 4 -B. Thermal Time Constant F o l l o w i n g the a n a l y s i s of Chapter I I , the i n t e n s i t y -time p r o f i l e of the l a s e r beam was found to be approximately Gaussian i n shape. I t i s assumed th a t the detector's response to t h i s Gaussian shaped e x c i t a t i o n i s equivalent to i t s response to a s i n u s o i d a l e x c i t a t i o n of some "equivalent frequency". The "equivalent frequency" i s defined as t h a t frequency of a sin e wave whose r i s e time ;(the time between 10% and 90% of maximum amplitude) i s the same as the r i s e time of the Gaussian shaped pulse - w i t h i t s " t a i l " replaced by the e x t e n t i o n of i t s steepest s l o p e . Since the "equivalent frequency" of the f a s t e r l i g h t pulses were past the corner frequency of the a m p l i f i e r , the corresponding d e t e c t o r s i g n a l amplitudes were compensated f o r the lower a m p l i f i c a t i o n . The bottom curve of F i g . 6 shows the frequency response of the c o a x i a l cable and a m p l i f i e r , normalized to low f r e -quency s i g n a l s . The top curve shows the compensated frequency response of the d e t e c t o r alone. From the graph, one can s a f e l y assume th a t the detector's RC corner frequency, f c , i s g r e a t e r than 3.5 MHz, which means that the f i l m ' s RC time constant, T^ C» i s l e s s than 45.5 n sec. One can check the v a l i d i t y of the above measurement, and the u n d e r l y i n g assumptions, by c a l c u l a t i n g t C S r , f o r the f i l m of F i g . 6, as discussed i n Chapter I I . R e c a l l i n g that " £ - C F R ; C / G , one needs only to c a l c u l a t e C and G. From the f i l m ' s power versus r e s i s t a n c e curve, we f i n d dPj v _ 8 / dR I T S = T C > 2.25 x 10 0 W/ohm, and from the t r a n s i t i o n curve of t h i s f i l m , - 2 5 -Detector l . o Response 0.9 Ampli f i e r and Cable Response 0.2 1.0 2.0 3.0 "Equivalent Frequency" (MHz) 4.0 FIGURE 6. Top - Compensated and Normalized Detector Response Bottom - Amplifier and Cable Response, Normalized to Low Frequency Response. -26-dRl = 3,040 ohm/K. So t h a t : d T l T s = T c G = IdP dR] ^ 6 . 8 5 x 10" 5 W . [dR cLTJT 8 = Tc K From d i r e c t measurements o f boundary thermal r e s i s t i v -i t i e s by H o l t , one c a l c u l a t e s t h a t , w i t h i n an order o f magnitude, H o l t ' s v a l u e of G f o r t h i s f i l m should be G r 5 x 10~ 2 W/K, with 10% of the t o t a l heat flow p a s s i n g a c r o s s the film-He bath boundary. The reason f o r the l a r g e d i s c r e p a n c y between the above valu e s of G i s probably a r e s u l t of the d i f f e r e n t f i l m s t r u c t u r e s . The aluminum f i l m s o used, by Hol t were at l e a s t 2,000 A t h i c k and were evaporeted a t a pressure of 10~^ T o r r . Therefore, H o l t ' s f i l m s prob-a b l y contained a lower c o n c e n t r a t i o n of l a t t i c e d e f e c t s than the g r a n u l a r f i l m s used i n t h i s i n v e s t i g a t i o n . Since the mechanism of thermal conduction i s mainly phonon t r a n s m i s s i o n a c r o s s i n t e r f a c e boundaries, the h i g h e r c o n c e n t r a t i o n of l a t t i c e d e f e c t s i n the g r a n u l a r f i l m s would i n c r e a s e the s c a t t e r i n g o f l o n g i t u d i n a l phonons w i t h i n the f i l m and a t the boundary and i n t e r f e r e with the c o u p l i n g of the t r a n s -v e r s e phonons across the boundary. The val u e of G used i n c a l c u l a t i n g 7 ^ w i l l t h e r e f o r e be the e x p e r i m e n t a l l y d e t e r -mined v a l u e f o r the f i l m of F i g . 6, G=.6.85 x 10" 5 W/K. To c a l c u l a t e C, we use the equation C = C'(*LWd, where: C ' x O.30 J - K g " 1 - ^ 1 , as determined i n Chapter II £ =2.7 gm/cm^, assuming the f i l m ' s d e n s i t y i s th a t of bulk aluminum d = 80 1 10 A, the f i l m t h i c k n e s s W 4= 1.5 mnf> the area of the f i l m covered by the L =• 5amm J* l a s e r p u l s e (from v i s u a l i n s p e c t i o n ) . - 2 7 -From these v a l u e s , one f i n d s that C= 5.4 x 10 J/K. Since we have now found, the upper l i m i t of C and the lower l i m i t of G, the r e s u l t i n g 1 ^ f rshall be an outside upper l i m i t . For the f i l m of F i g . 6, we f i n d T j^^800 n sec, which i s i n agree-ment w i t h the experimental time constant, 7"!c-^ 5.5 n sec. - 2 8 -CHAPTER V CONCLUSIONS Some of the properties of superconducting t h i n aluminum f i l m s , with T c near the lambda point of He, have been tested. The f i lms are useful as s e n s i t i v e thermometers over the temp-erature range of t h e i r superconducting t r a n s i t i o n , A T C = 0 . 0 6 K . An i n d i c a t i o n of the thermometer's s e n s i t i v i t y i s given by the slope of the t r a n s i t i o n curve, t y p i c a l l y dR = 2-3 x lO^ohm. dT K Because of the high adhesion of aluminum to p o l y c r y s t a l -l i n e quartz substrates and the technique used to attach the leads, these f i lms mechanically and e l e c t r i c a l l y withstood the thermal shock of f i v e thermal cycles from room temperature to 2 K. The i n s t a b i l i t y of T c during the thermal c y c l i n g was at most 0 .05 K. By increasing the bias current , T c could be decreased by at most 0 .025 K. Therefore, the thermal c y c l i n g i n s t a b i l i t y of T c could not be.<QWh6;lely compensated by the bias current " f ine tuning" of T . However, wi th f i lms of a smaller c r o s s - s e c t i o n a l area, with a corresponding higher degree of current " t u n i n g " , the thermal c y c l i n g i n -s t a b i l i t y may be compensatable. The normal res is tance , F^, rose monotonically for a l l the f i lms tested upon thermal c y c l i n g . By the f i f t h thermal c y c l e , Rn was as much as 80$ l a rger than for the f i r s t thermal c y c l e . The t r a n s i t i o n slope increased by at most 30$ upon thermal c y c l i n g , but was not effected by bias current v a r i a -t i o n , for the range 2 -60j/A . This increase i n the t r a n s i t i o n -29-slope by thermal c y c l i n g would not subt r a c t from these f i l m s ' usefulness as a second sound d e t e c t o r. I f , however, the f i l m s were to be used to measure the absolute amplitude of second sound, the t r a n s i t i o n slope would have to be determined each time the f i l m ' s temperature was lowered from room temp-erat u r e to T c. From measurements of one f i l m ' s time response to thermal e x c i t a t i o n , the RC time constant was found to be l e s s than 4 5 . 5 n sec, which means t h a t the f i l m i s capable of f u l l y responding to second sound frequencies of at l e a s t 3 . 5 MHz. -30-REFERENCES AND FOOTNOTES 1. D.L. Johnson and M.J. C r o o k i , Phys. Rev. 185, 253 (1969). 2. K.L. Chopra, Th i n F i l m Phenomena (McGraw-Hill, New York, 1969), p. 544. 3. V.L. Ginzberg, Phys. L e t t e r s 13, 101 (1964). 4. See, f o r example, B. Abeles, Roger W. Cohen, and G.W. C u l l e n , Phys. Rev. L e t t e r s 17, 632 (1966). 5. See, f o r example, Myron S t r o n g i n , O.F. Kammerer, and A r t h u r P a s k i n , Proceedings of the I n t e r n a t i o n a l Symposium, Ba s i s Problems i n Thin F i l m P h y s i c s (Vandenhoeck and Ruprecht, Gottingen, West Germany, 1966), p. 505. 6. P.G. de Gennes, Rev. Mod. Phys. 36, 225 (1964). 7. C.J. Thomson and J.M. B l a t t , Phys. L e t t e r s f , 6 (1963). 8. D. P i n e s , Phys. Rev. 109, 280 (1953). 9. A.C. Rose-Inhes and E.H. Rhoderick, I n t r o d u c t i o n to  S u p e r c o n d u c t i v i t y (Pergamon P r e s s , London, 1969), p. 60. 100. B. Abeles, Roger Cohen, and W.R. S t o w e l l , Phys. Rev. L e t t e r s 18, 902 (1967). 11. V . J . Johnson, ed., A Compendium of the P r o p e r t i e s of  M a t e r i a l s at Low Temperature, Phase I, WADD T e c h n i c a l Report 60-56, P a r t II (Wright-Patterson A i r Force Base, Ohio, U.S.A., I 9 6 0 ) , p. 4.132. 12. D.H. Martin.and D. B l o o r , Cryogenics 1, 159 (1961). 13. I n t e g r a l Tungsten Ceramic C r u c i b l e (A10), S y l v a n i a Type"CS-1002-A, S y l v a n i a Emissive Products, E x e t e r , New Hampshire, U.S.A. 14. Edward J . Walker, Rev. S c i . I n s t r . 30, 834 (1959). 15. The "1958 He^ S c a l e of Temperatures", U.S. Department of Commerce, N a t i o n a l Bureau of Standards, NBS Monograph 10 (U.S. Government P r i n t i n g O f f i c e , Washington, D.C, U.S.A., I960). 16. U l t r a m i n i a t u r e Cable, BTX-42-1950, Berk-Tek Inc., Reading, Pa., U.S.A. 17. Roger Cohen and B. Abeles, Phys. Rev. 168, 444 (1968). -31-18. R. Meservey and P.M. Tedrow, J . A p p l . P h y s . 42, 51 (1971). ~ 19. T.K. Hunt, P h y s . Rev. 151, 325 (1966). 20. V. E. H o l t , J . A p p l . P h y s . 37, 798 (1966). 

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