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A SIMPLE QUALITATIVE DETERMINATION OF
JOSEPHSON TUNNEL JUNCTION PARAMETERS
NEAR THE TRANSITION TEMPERATURE
N. Pedersen, J. Mygind, O. Soerensen, B. Dueholm
To cite this version:
A SIMPLE QUALITATIVE DETERMINATION OF JOSEPHSON TUNNEL JUNCTION PARAMETERS
NEAR THE TRANSITION TEMPERATURE t
N.F. Pedersen, J. Mygind, O.H. Soerensen, and B. Dueholm
Physios Labevatory I, The Technical University of Denmark, DK-2800 Lyngby, Denmark
Abstract.- The junction capacitance may be determined and the cos<f>-amplitude may be
esti-mated from the switching characteristics seen in the IV curve near the critical tempera-ture. The method relies on the empirical observation that a small area tunnel junction returns from finite to zero voltage when the Josephson frequency is about equal to the plasma frequency.
Within the framework of the shunted junc-tion model (SJM) four Josephson juncjunc-tion parameters are of interest : (1) the critical current I ,(2) the normal state resistance R, (3) the capacitance C, and (4) the cos<j>-amplitude E.The parameters Ic
and R are readily determined from the dc IV curve. For the capacitance, C, essentially two methods exist : (i) a measurement of the geometrical reso-nance frequency from the position of the cavity in-duced step l\l in the IV curve, and (ii) a deter-mination of the McCumber parameter HI B(°=C) using measured values of the hysteresis parameter /2/a. Both methods have drawbacks; the former requires knowledge of the temperature and frequency dependent penetration depth, and the latter /3/ depends on the value of e. With respect to the cos4>-amplitude,
e, it is generally argued /A/ that the IV curve itself does not provide such information. Here we describe how additional information may be obtained using empirical methods deduced from experiments on superconducting tunnel junctions where C and e have been independently determined from more sophistica-ted microwave measurements /5/.
For a tunnel junction close to the transi-tion temperature, T , the IV curve may typically appear as shown in the inset of figure 1. Thus at these temperatures the IV curve is very similar to that of the SJM. Accordingly, the detailed shape is determined by the magnitude /2,3/ of the dimension-less parameter @ = 2eR2I G/Ji, which for an ideal
tunnel junction may hs= written as g = (ir A(T)RC/tt) tanh (A(T)/2kT), where 2A(T) is the energy gap.
Assuming R and C to be temperature independent it is observed that 8 will vary from zero at T = Tc
to a larger value at T-0. A typical feature of an IV-curve with hysteresis is the switching back to zero voltage at a finite voltage, V (c.f. figure 1). The dynamics of the switching is not understood in detail although it has been argued /6/ that the process involves an excitation of an internal reso-nance by the Josephson ac voltage, i.e., the plas-ma resonance or a geometrical resonance /6/.
The switching frequency f = 2eV /h versus
u s s
I ^ is shown in figure 1. The data points are c
Fig. 1 : The switching frequency (circles and full line) and the maximum plasma frequency (dashed line) as functions of I ^-. The inset shows an IV curve : Sn-Snoxide-Sn junction, 20A/cm2 at T = 0 , 0.1x0.2 mm , T/Tc = 0.98, Tc = 3.815 K.
t This work was partly supported by Statens Natur-videnskabelige Forskningsrad, Grant No.: 511-8048
JOURNAL DE PHYSIQUE Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-1232
Résumé.- Il est montré qu'on peut estimer soit la capacité soit l'amplitude du "cos<(>" d'une petite jonction Josephson en analysant la caractéristique courant-tension près de la température de transition supraconductrice. La méthode s'appuie sur l'observation empirique que la tension d'une jonction de petite surface saute d'une valeur finie à zéro lorsque la fréquence Josephson devient voisine de la fréquence plasma.
o b t a i n e d by v a r y i n g t h e t e m p e r a t u r e i n a r a n g e where e n e r g y gap s t r u c t u r e d o e s n o t d i s t u r b t h e SJM beha- v i o u r of t h e I V c u r v e (1 > TITc > 0 . 9 7 ) . F i g u r e 1 shows t h a t i t i s p o s s i b l e t o f i t a s t r a i g h t l i n e t h r o u g h t h e o r i g i n t o t h e d a t a p o i n t s . The maximum 1
plasma f r e q u e n c y , f o = (2eIc/HC)T / 2 r , i s a l s o shown i n t h e f i g u r e ( t h e dashed l i n e ) . The plasma f r e q u e n - cy was i n d e p e n d e n t l y determined from plasma resonan- c e e x p e r i m e n t s 151. The c o n c l u s i o n drawn from f i g u r e
1 i s t h a t t h e j u n c t i o n s w i t c h e s back t o z e r o v o l t a g e a t a v o l t a g e V g i v e n by V = k h f o / 2 e , where k i s a c o n s t a n t o f o r d e r u n i t y . For t h e d a t a i n f i g u r e 1 , k = 1.13; i n o t h e r j u n c t i o n s we have found k = 0 . 9 4 and k = 0.85. The p r e s e n t e m p i r i c a l o b s e r v a t i o n i s of s i m i l a r n a t u r e a s t h e o b s e r v a t i o n of F u l t o n and Dy- n e s /6/ who from a n a l o g computations found t h a t when
<V> becomes l e s s t h a n h f / 2 e t h e u n i f o r m mode of t h e phase, + ( x , t )
,
becomes u n s t a b l e t o s p a t i a l f l u c - t u a t i o n s .I n o r d e r t o o b t a i n a n e s t i m a t e of t h e cos$- a m p l i t u d e , E , we u s e t h e known r e l a t i o n 13.1 between t h e McCumber p a r a m e t e r ,
B ,
and t h e h y s t e r e s i s para-2 m e t e r , a . To a good a p p r o x i m a t i o n B = [ 4 ( 1 + ~ / 3 ) / ? r q
.
A p l o t ofB
v s . a i s shown i n f i g u r e 2 f o r d i f f e r e n t v a l u e s o f1
e1
< I . E x p e r i m e n t a l l y , a may b e d e t e r m i d from t h e d c I V curve. With a n I V c u r v e a s shown i n f i g u r e 1 we o b t a i n a n upper l i m i t f o r a u s i n g t h e va- l u e of t h e b i a s c u r r e n t , ISW, c o r r e s p o n d i n g t o t h e s w i t c h i n g from f i n i t e t o z e r o v o l t a g e : aSW = I SW/ I c' F i g . 2 : B v s . u diagram. C r o s s e s a r e d e r i v e d from t h e d c I V c u r v e a s e x p l a i n e d i n t h e t e x t . C i r c l e s a r e measured by plasma r e s o n a n c e e x p e r i m e n t s . F u l l c u r v e s a r e t h e o r e t i c a l c u r v e s f o r E = - 1 , -0.5, 0 , 0.5, and 1. Upper s c a l e : The t e m p e r a t u r e c o r r e s - ponding t o t h e d a t a p o i n t s .( t h e d o t t e d curve i n f i g u r e I ) , a e x t = ' e x t / I C ' The two a-values d e f i n e t h e h o r i z o n t a l b a r s shown i n f i g u r e 2 o b t a i n e d on t h e same j u n c t i o n a t tem- p e r a t u r e s i n t h e i n t e r v a l 0.97 ( TITc
2
1 .O. At each t e m p e r a t u r e t h e v a l u e ofB
may 5 e d e t e r m i n e d u s i n g t h e v a l u e of c a p a c i t a n c e d e r i v e d from t h e s w i t c h i n g v o l t a g e . S i n c e a C t h e u n c e r t a i n t y i n B i s i 3 0 % a s i n d i c a t e d by t h e v e r t i c a l b a r s . The e x p e r i m e n t a l p o i n t s i n d i c a t e s t h a t t h e c o s + ampli- t u d e i s p o s i t i v e a l t h o u g h t h e magnitude, c a n n o t be d e t e r m i n e d . The t e m p e r a t u r e dependence of E h a s , however, been a c c u r a t e l y measured f o r t h i s j u n c t i o n/5/ and t h e r e s u l t i s a l s o shown i n f i g u r e 2 ( c i r - c l e s ) u s i n g t h e upper h o r i z o n t a l t e m p e r a t u r e a x i s . We can s t a t e t h a t t h e s i m p l e e s t i m a t e o f ~ b a s e d o n d c c h a r a c t e r i s t i c s of t h e j u n c t i o n i s c o n s i s t e n t w i t h t h e more e l a b o r a t e methods. R e f e r e n c e
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47
(1976) 5432./ 2 / Hansma, P.K. and R o c h l i n , G . I . , J.Appl.Phys.42 (1972) 4721.
/ 3 / Belykh, V.N., P e d e r s e n , N.F., and Soerensen,
O.H., Phys. Rev. (1977) 4873.
/ 4 / Langenberg, D.N.,Rev. Phys.App1.
9
(1974) 35. / 5 / Soerensen, O . H . , Mygind, J . , and P e d e r s e n ,N.F., Phys. Rev. L e t t .
2
(1977) 1018./ 6 / F u l t o n , T.A. and Dynes, R.C. S o l . S t . C o m u n
