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SURFACE ACOUSTIC WAVE INVESTIGATION OF
SUPERCONDUCTING FILMS
M. Levy
To cite this version:
SURFACE ACOUSTIC WAVE INVESTIGATION OF SUPERCONDUCTING FILMS+
M. LEVY
Department of Physics, University
of
Wisconsin-Milwaukee. Milwaukee, W I 53201, U. S.A.A b s t r a c t
-
The a t t e n u a t i o n c o e f f i c i e n t o f surface acoustic waves SAW prop- a g a t i n g through t h i n superconducting f i l m s o f Nb3Sn, NbsGe, g r a n u l a r Al, g r a n u l a r Pb and NbN has been measured a t frequencies up t o 2 GHz. I n Nb3Sn, NbgGe and g r a n u l a r A 1 t h e a t t e n u a t i o n i s produced by e l e c t r o n phonon i n t e r - a c t i o n . I n t h e g r a n u l a r Pb f i l m and NbN f i l m t h e SAW a t t e n u a t i o n i s pro- duced by p i e z o e l e c t r i c c o u p l i n g t o t h e sheet r e s i s t i v i t y o f t h e f i l m . T h e o r e t i c a l models f o r i n t e r p r e t i n g t h e data a r e presented and some o f t h e r e s u l t s obtained from t h e a n a l y s i s are discussed.I. INTRODUCTION
We would l i k e t o r e p o r t on t h e use o f surface a c o u s t i c waves (SAW) t o measure t h e p r o p e r t i e s o f t h i n superconducting f i l m s . The SAW'S a r e attenuated by t h e superconducting f i l m s e i t h e r v i a /1/ e l e c t r o n phonon i n t e r a c t i o n o r v i a /2/ t h e a c o u s t o e l e c t r i c e f f e c t .
A t t e n u a t i o n data produced by t h e f i r s t mechanism may y i e l d t h e temperature dependence o f t h e superconducting energy gap, t h e superconducting f r a c t i o n as a f u n c t i o n o f temperature o f an inhomogeneous f i l m , i n f o r m a t i o n about f l u c t u a t i o n c o n t r i b u t i o n s t o t h e i n t e r a c t i o n near t h e superconducting phase t r a n s i t i o n o f a two dimensional f i l m , and t h e value o f t h e e l e c t r o n mean f r e e path i n t h e m e t a l l i c granules o f such a f i l m . I n a d d i t i o n , magnetic f i e l d measurements may y i e l d i n f o r m a t i o n about t h e temperature dependence o f b o t h t h e upper c r i t i c a l f i e l d Hc2 and t h e second Gingsburg Landau parameter K2.
A t t e n u a t i o n data produced by t h e second mechanism may y i e l d i n f o r m a t i o n about t h e d i s t r i b u t i o n o f Josephson t u n n e l i n g j u c t i o n s i n a g r a n u l a r superconductor and about t h e existence o f Kosterlitz-Thouless vortex a n t i v o r t e x p a i r s i n a h i g h sheet r e s i s t i v i t y two dimensional superconducting f i l m . I n a d d i t i o n measurements w i t h magnetic f i e l d s perpendicular t o t h e f i l m plane may y i e l d data which can be analyzed t o deduce magnetization curves f o r t h e g r a n u l a r f i l m s .
"Research supported by A i r Force O f f i c e o f S c i e n t i f i c Research under AFOSR Grant No. 84-0350.
JOURNAL
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PHYSIQUE11. SAW DEVICES
The b a s i c device used f o r performing these measurements i s shown i n F i g u r e 1. The p i e z o e l e c t r i c s u b s t r a t e i s o p t i c a l l y p o l i s h e d and i s u s u a l l y made o f yz- c u t LiNbO3. The i n t e r d i g i t a l e l e c t r o d e s a r e deposited by means o f a p o s i t i v e m i c r o p h o t o l i t h o g r a p h i c technique. The s e p a r a t i o n between i n d i v i d u a l i n t e r d i g i t a l e l e c t r o d e s as w e l l as t h e w i d t h o f t h e e l e c t r o d e s i s 1.25pm y i e l d i n g a wavelength o f 5vm and a fundamental frequency ranging from 660 MHz up t o 1200 MHz depend- i n g upon t h e speed o f sound i n t h e p i e z o e l e c t r i c s u b s t r a t e . The f o u r w i r e r e s i s t a n c e t e r m i n a l s were deposited under t h e g r a n u l a r Pb F i l m and over t h e NbN f i l m . These devices were used f o r SAW measurements i n g r a n u l a r A1 /I/, NbN /2,3/ Nb3Ge /4/, Nb3Sn /5/ and g r a n u l a r Pb /6/.
Fig. 1. Schematic o f device used f o r SAW a t t e n u a t i o n measurements 111. ELECTRON PHONON INTERACTION
The f i r s t measurements o f e l e c t r o n phonon i n t e r a c t i o n were performed by Bomnel i n a s i n g l e c r y s t a l o f Pb /7/. S h o r t l y t h e r e a f t e r Pippard /8/ developed an elegant t h e o r e t i c a l model t o d e s c r i b e t h e i n t e r a c t i o n . He found t h a t t h e r e l e v a n t parameter f o r p r e d i c t i n g t h e a t t e n u a t i o n i n t h e normal s t a t e was q l where q i s t h e phonon wave v e c t o r and 1 i s t h e e l e c t r o n mean f r e e path. Bardeen Cooper and S h r i e f f e r /9/ (BCS) t h e n d e r i v e d a famous expression f o r t h e r a t i o o f t h e u l t r a - sonic a t t e n u a t i o n c o e f f i c i e n t i n t h e superconducting s t a t e t o t h a t i n t h e normal s t a t e which was v a l i d i n t h e q l > 1 l i m i t f o r l o n g i t u d i n a l waves
3.5kTc0 where Tco i s t h e superconducting t r a n s i t i o n temperature and k i s
Boltzmann's constant. The observed good f i t implies t h a t t h e d a t a would y i e l d a temperature dependent energy gap curve t h a t agrees well with t h e BCS r e s u l t f o r t h i s curve. Such good BCS f i t s have a l s o been obtained f o r g r a n u l a r Al(1) and f o r Zn /13/. The d a t a f o r In and Pb /11/ f i l m s l i e below t h e BCS curve.
Although t h e BCS curve was derived f o r bulk samples, t h e f a c t t h a t t h e same r e s u l t i s obtained f o r longitudinal and t r a n s v e r s e waves i n t h e q l << 1 l i m i t j u s t i f i e s i t s use f o r s u r f a c e waves. The SAW a t t e n u a t i o n due t o e l e c t r o n phonon i n t e r a c t i o n i n a t h i n metal f i l m may be expressed a s t h e sum of t h e mean r a t e s of energy l o s s f o r shear and compressional waves divided by t h e t o t a l energy i n t h e wave i n t e g r a t e d over t h e half space containing t h e f i l m and t h e s u b s t r a t e /16, 17, l a / . These computations have been extended t o s p e c i f i c a l l y t a k e i n t o account t h e f a c t t h a t t h e longitudinal and t r a n s v e r s e components of a SAW a l s o contain shear and compressional s t r a i n s r e s p e c t i v e l y /19/. I t i s found t h a t t h e a t t e n u a t i o n i s proportional t o t h e shear v i s c o s i t y of t h e e l e c t r o n g a s , which i s r e l a t e d t o t h e a t t e n u a t i o n of shear waves i n t h e ql << 1 l i m i t . Since i t has been shown t h a t t h e a t t e n u a t i o n of shear waves follows t h e BCS r e l a t i o n i n t h e small ql l i m i t / l o / , i t i s reasonable t o expect t h a t t h e a t t e n u a t i o n of s u r f a c e a c o u s t i c waves should a l s o follow t h e BCS r e l a t i o n i n t h e superconducting s t a t e i n t h e l i m i t of q l << 1 ; and, t h e r e f o r e , comparing SAW d a t a t o t h e BCS r e l a t i o n appears j u s t i f i a b l e .
REDUCED TEMPERATURE
Fig. 2 SAW a t t e n u a t i o n i n Nb3Sn f i l m a s a function of reduced temperature. Triangles a r e d a t a , s o l i d l i n e i s BCS curve with ZA(0) = 3.5 kTCo. The SAW a t t e n u a t i o n dependence of t h e same Nb3 Sn f i l m a t t h e same frequency i n a magnetic f i e l d applied perpendicular t o t h e f i l m plane /5/ i s shown i n Figure
3.
As
may be seen t h e a t t e n u a t i o n c o e f f i c i e n t i s l i n e a r l y dependent on t h e appli- ed f i e l d c l o s e t o t h e upper c r i t i c a l f i e l d Hc2 of t h e f i l m , which may be d e t e r - mined from t h e i n t e r s e c t i o n of t h e l i n e a r portion of t h e curve with t h e normalized h o r i z o n t a l l i n e representing t h e normal s t a t e a t t e n u a t i o n . This l i n e a r dependenceJOURNAL
DE
PHYSIQUE0 10 20 30 40 5 0 6 0 7 0
MAGNETIC FIELD (KG)
Fig. 3 Normalized a t t e n u a t i o n o f SAW i n Nb3Sn as a f u n c t i o n o f magnetic f i e l d f o r various temperatures.
b.
*&
The a t t e n u a t i o n o f SAW1s a t 1200 MHz passing through a 0.5vrn Nb3Ge f i l m /14, 22/ i s shown i n F i g u r e 4. The s u b s t r a t e consisted o f a p i e z o e l e c t r i c a l l y a c t i v e 3.5pm A1N l a y e r which was chemically vapor deposited over a sapphire substrate. The d a t a shown have been e x t r a c t e d from several raw data curves which were analyz- ed t o e l i m i n a t e i n t e r f e r e n c e e f f e c t s due t o s p l i t t i n g o f t h e SAW wave i n t o two components. One o f these i s a t t h e s u r f a c e o f t h e f i l m and t h e o t h e r may be a "surface skimning b u l k mode" which i s a t t h e f i l m s u b s t r a t e i n t e r f a c e . The curve shown i n F i g u r e 4 does n o t f o l l o w a BCS r e l a t i o n . However, Salvo, e t a1 /14/, p o s t u l a t e t h a t t h e shape o f t h e curve r e f l e c t s t h e f a c t t h a t t h e NbgGe
f i l m may have a d i s t r i b u t i o n of regions w i t h d i f f e r i n g superconducting t r a n s i t i o n temperatures. Each o f these regions would f o l l o w a BCS curve a f t e r proper ad- justment i s made f o r i t s d i f f e r e n t Tc. By i n v e r t i n g t h e d a t a t h e y f i n d t h e d i s t r i b u t i o n f u n c t i o n f o r t h e i r Nb3Ge f i l m shown i n Figure 4. Nb3Ge i s an A15 compound which e x h i b i t s t h e h i g h e s t known Tc
-
23OK when a p p r o p r i a t e l y prepared i n f i l m form. T h e i r f i l m had a Tc-
21K. F i g u r e 4 i n d i c a t e s t h a t a l a r g e f r a c t i o n o f t h e f i l m becomes superconducting a t -18K where b u l k Nb3Ge becomes superconducting. There i s another bulge i n t h e data a t -10K. Thus i t appears t h a t SAW data may be used f o r probing t h e s p a t i a l c h a r a c t e r i s t i c s o f super- conducting f i l m s .c. Granular A1
Granular A1 f i l m s d i s p l a y rounding o f t h e i r r e s i s t a n c e versus temperature curves above t h e superconducting t r a n s i t i o n temperature. According t o Aslamazov and L a r k i n /23/ t h i s rounding i s produced by superconducting f l u c t u a t i o n s i n these two dimensional f i l m s . They a l s o p r e d i c t e d t h a t u l t r a s o n i c a t t e n u a t i o n should experience a peak a t Tco, w h i l e Robinson, e t a1 / I / , expected rounding o f t h e BCS a t t e n u a t i o n curve near Tco. The l a t t e r r e s u l t i s produced by an anomalous d i a - gram due t o Maki /I/. The t h i r d harmonic o f a SAW device, was used t o i n v e s t i g a t e a 300A g r a n u l a r A1 f i l m w i t h a sheet r e s i s t i v i t y o f 100Q/sq, i n o r d e r t o d e t e r - mine t h e e f f e c t o f superconducting f l u c t u a t i o n s on e l e c t r o n phonon i n t e r a c t i o n . The r a t i o o f as/an f o r t h i s f i l m i s shown i n F i g u r e 6. The data are f i t very w e l 1 , w i t h a BCS curve w i t h a zero temperature energy gap o f ZA(0) = 3.6kTco. There i s no evidence f o r e i t h e r a peak o r rounding near Tco. However, t h e r e appeared t o be s l i g h t rounding near Tco on t h e f r e s h l y prepared f i l m /17/ and t h e sheet r e s i s t i v i t y o f t h e f i l m d i d e x h i b i t rounding. Robinson, e t a l , d e r i v e ex- pressions f o r t h e a t t e n u a t i o n which i n d i c a t e t h a t t h e Aslamov-Larkin c o n t r i b u t i o n should be several orders o f magnitude s m a l l e r than t h e Maki c o n t r i b u t i o n f o r a d i r t y A1 f i l m ; and, t h a t even t h e Maki c o n t r i b u t i o n becomes n e g l i g i b l e i n a very d i r t y f i l m , such as t h i s g r a n u l a r A1 f i l m .
Fig. 6. Normalized a t t e n u a t i o n as a f u n c t i o n o f reduced temperature f o r g r a n u l a r A1 f i l m .
i n g between t h e granules. By t h e a n a l y s i s o f T a c h i k i , e t a1 /16/, f o r continuous amplitude across t h e f i l m s u b s t r a t e i n t e r f a c e , t h e value o f on = 0.33 dB/cm y i e l d s I,= 1lA. S i m i l a r g r a n u l a r A1 f i l m s have average g r a n u l a r diameters d o f about 50A /24/, and t h e average mean f r e e p a t h produced by boundary s c a t t e r i n g would be 1 = 2d/3 2 331. An 1 o f 111 i s c o n s i s t e n t w i t h t h i s value. The l a r g e
d i f f e r e n c e between t h e two measurements may be a t t r i b u t e d t o t h e f a c t t h a t elec- t r o n phonon i n t e r a c t i o n i s p r o p o r t i o n a l t o 1 and t h e r e f o r e t h e granules which have t h e l a r g e s t 1 ' s i n t h e system c o n t r i b u t e t h e most t o t h e a t t e n u a t i o n , w h i l e t h e t u n n e l i n g j u n c t i o n s c o n t r i b u t e t h e most t o t h e sheet r e s i s t i v i t y . It appears t h a t t h e SAW'S sample t h e granules and j u n c t i o n s i n p a r a l l e l w h i l e t h e e l e c t r i c a l c u r r e n t s go through them i n s e r i e s . Thus, t h e two measurements y i e l d complemen- t a r y i n f o r m a t i o n .
I V . ACOUSTO-ELECTRIC EFFECT
The f i r s t measurement o f t h e e f f e c t o f s u p e r c o n d u c t i v i t y on t h e acousto- e l e c t r i c e f f e c t was r e p o r t e d /3/ i n 1981. According t o a model due t o Adler /25/, t h e a c o u s t o - e l e c t r i c e f f e c t may be understood as f o l l o w s . The p i e z o e l e c t r i c f i e l d s i n t h e s u b s t r a t e produce image charges i n a conducting f i l m which then move w i t h t h e SAW v e l o c i t y . These image charges w i l l be o u t o f phase w i t h t h e wave i f t h e f i l m has a f i n i t e resistance; and, thus, t h e r e s u l t i n g r e s i s t i v e losses w i l l a t t e n u a t e t h e wave. For very t h i n f i l m s t h i s a t t e n u a t i o n i s p r o p o r t i o n a l t o t h e sheet r e s i s t i v i t y when t h e SAW p e r i o d i s small compared t o t h e a c o u s t o - e l e c t r i c r e l a x a t i o n time. The experimental data show t h a t t h i s i s n o t t h e case i n t h e superconducting s t a t e s o f e i t h e r t h e g r a n u l a r Pb /6/ f i l m o r t h e NbN f i l m /3/.
a. Granular Pb Films
t h a t a SAW measures t h e r e s i s t i v i t y o f squares w i t h dimensions comparable t o i t s wavelength. T h e i r r e s u l t s f o r the a t t e n u a t i o n on t h e superconducting s t a t e a r e shown i n F i g u r e 7. Magnetic f i e l d experiments are discussed by Schmidt, e t a1 i n r e f . 27.
REDUCED TEMPERATURE
Fig. 7. Normalized r e s i s t a n c e ( s o l i d l i n e ) , SAW a t t e n u a t i o n ( d o t s ) , and
t h e o r e t i c a l values (crosses) f o r a t t e n u a t i o n according t o reference 26.
t h e d i s s o c i a t e d f l u x l i n e c o n t r i b u t i o n i n o r d e r t o d e t e r m i n e b o t h t h e supercondut- i n g t r a n s i t i o n t e m p e r a t u r e Tco and Tc. U s i n g t h i s v a l u e o f Tc/Tco, t h e y c a l c u l a t e t h e t e m p e r a t u r e dependence o f t h e d e n s i t y o f f l u x l i n e p a i r s . As may be seen i n F i g u r e 3, r e f e r e n c e 28 r e a s o n a b l e agreement w i t h t h e e x p e r i m e n t a l d a t a , p a r t i c u - l a r l y a t l o w t e m p e r a t u r e s , i s o b t a i n e d .
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