ieee transactions on magnetics, vol. mag-17, no. 1 ... - Semantic Scholar

IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-17, NO. 1 , JANUARY 1981

STATIC AND DYNAMIC PROPERTIES OF

81

SHORT, NARROW, VARIABLE-THICKNESS MICROBRIDGES

M. D. Feuer*and D. E. Prober BectonCenter,Dept.EngineeringandAppliedScience,YaleUniversity,

New Haven, CT 06520

ABSTRACT The e l e c t r i c a l p r o p e r t i e s , i n c l u d i n g t h e Josephson-effectresponseto microwave radiation, have been studied for extremely small, h i g h - r e s i s t a n c e microbridges of Pb-In a l l o y and unalloyed In, with dimensionsranging from3001 t o 200011. The I c R productof I n and Pb-In microbridgesdecreasessmoothly as t h e bridgecrosssection is reduced,approachingthe Ginzburg-Landau limit of0.64 mV/K f o r t h e s m a l l e s t bridges. The voltagerangeof microwave responseand the temperature range of hysteresis-free operation both i n c r e a s e (improve) as t h e b r i d g e i s made narrower, i n agreementwithJouleheatingtheory.Forexample,an 8 ohm Pbo gInObridgewith a l l dimensions 5 5001has a maximum'step'voltage of Vmax = 1.5 mV and a nonhysteretic temperature range of ATn = 1.2 K. Bridges of unalloyed In can show st?l?'E:tter response due t o a longer coherence length, and non-hysteretic operation over the full temperature range below Tc i s possible. I.

INTRODUCTION

Superconducting microbridges are an important class of Josephson weak-link devices' , with significant potential for application in high-frequency detectors and SQUIDS, due i n p a r t t o t h e i r t h i n - f i l m r e l i a b i l i t y and p o t e n t i a lr e p r o d u c i b i l i t y . It hasbeenrecognized in recent years that improvedmicrobridgeperformance, and remedies for some of the s i g n i f i c a n t problemssuch as Joule heating, could be achieved by making microb r i d g e s as small as, andshaped l i k e , h i g h - q u a l i t y p o i n tc o n t a c t s ,2 I n t h i s work, we r e p o r t on t h e properties of ultrasmall Pb-In and In variable-thicknessmicrobridge? (VTBS), f o r which a l l dimensionscan W e havestudied i n d e t a i lt h e be less than 500A. limits o n t h e J o s e p h s o n e f f e c t i n t h e s e d e v i c e s , a n d t h e i r dependence on material parameters and dimensions. The e f f e c t of boundary s c a t t e r i n g i n v e r y narrow (l. of hysFigure 4(a) illustrates the development Solid line is a visual guide only. Theory result from lwattemperateresis in a narrow %-In microbridgeo Aslamazov and Larkin, Eq. 1. Bridge thickness d.

83

Table 11. -

t u r e s . Due t ot h ef o o ts t r u c t u r e ,t h eh y s t e r e s i sf i r s t appears a t a small f i n i t e v o l t a g e r a t h e r t h a n a t LC. The hysteresis-free temperature range ATno h st i s l i s t e d i n T a b l e I1 f o r a l l b r i d g e s s t u d i e d . %he series of % - I n b r i d g e s c l e a r l y shows t h a t ATno hyst i n c r e a s e s as t h e minimum c r o s s - s e c t i o n a l area Wd decreases (e.g., On t h e o t h e r hand,there is no compare S-6 t o S-7). s t r o n g c o r r e l a t i o n between t h i c k b a n k s and l a r g e ATno hy (The s i n g l ee x c e p t i o nt ot h i sr u l e is b r i d g e 8-8 f o r which D % W.) It must b e t h a t t h r e e dimensional heat flow in the region t h e b r i d g e is t h e dominantsource of t h e r m a l r e s i s t a n c e when t h e b r i d g e is b i a s e d j u s t above i t s c r i t i c a l c u r r e n t .

?9In.1 S-6

t.

S-7

=

The shunted bridge S-10 demonstrates that a small I c R product can be of value in reducing Joule heating ( i . e .i,n c r e a s i n g ATno >,a t a g i v e nb i acs u r r e n t . This bridge had values and Rd a p p r o p r i a t e f o r a 21Q b r i d g e i n p a r a l l e l w i t h a 14Q nonsuperconducting shunt,and ATno hyst = 3.9 K. It i s l i k e l yt h a t duri n g s t o r a g e a t room temperature for a few weeks, a stress-induced hillock or whisker of I n formed t h e shunt,which was nonsuperconducting a t 6-7 K. During later t e s t i n g , e x c e s s i v e microwave power apparently burnedoutthebridge,leavingthe14Qnormal resist a n c ei n t a c t . While thereduced IcR product is h e l p f u l i t w i l l a l s o €ead t o a degraded inreducingheating, signal-to-noise ratio and curtailed frequency response.

2400

6.4

s-8

700

%700

>0.7

0.07

400

500

1100

8.4

1.2

1.5

0.12

S-loa

400

400

1100

8.4

23.9

>1.0

0.12

S-11

0.6

0.17

S-14

2000

~ 4 0 0 3500

5.1

>2.0

1.9

0.21

S-15

900

0.15

0.3

20.3

0.6

1800

750 0.6 6.9

3500

EFFECTS OF MICROWAVE IRRADIATION

The V ( I ) curves o f a l l of our microbridges show many constant-voltage steps under microwave irradiat i o n . The p l o t s of s t e pw i d t h A I n vs. microwave amp l i t u d e are q u a l i t a t i v e l y similar t o those obtained vanfrom t h e RSJ model. However, t h es t e p sg r a d u a l l y i s h a s t h e microwave power becomes l a r g e .

The gap v a l u e i n f e r r e d from t h e t h i r d - o r d e r (i.e., m=3) or higher-order peaks, a l l ofwhichoccur at relaent i v e l y low v o l t a g e s , is i n good agreement with the ergygap a t the bath temperature, computed from 2A(O) = 3.63 kTc. The f i r s t - andsecond-orderpeaks, however,occur a t lower voltages than those predicted on t h e b a s i s of thebath-temperaturegap.Thisbeing s o , a ne f f e c t i v et e m p e r a t u r e Teff = T + AT b . s g s may.be i n f e r r e d fromeachpeak of t h e gap s t r u c t u r e . Tb is thesubstratetemperature.Octavio e t a1.12 have shown t h a t t h e gap s t r u c t u r e r e f l e c t s t h e l o c a l t e m p e r a t u r e a d i s t a n c e .

w

:f;: os

Y

4

K Y

P w z L BIAS

CURRENT. I

0.16

S-9

V.