Ž .Physica C 299 1998 31–35

Collective switching and heat diffusion of stacked intrinsicJosephson junctions

Masahiro Sakai ), Akihiro Odagawa, Hideaki Adachi, Kentaro SetsuneCentral Research Laboratories, Matsushita Electric Ind., 3-4 Hikaridai, Seika, Soraku, Kyoto 619-02, Japan

Received 25 August 1997; revised 25 September 1997; accepted 24 December 1997

Abstract

We have investigated a mechanism for the switching of stacked intrinsic Josephson junctions in current–voltagecharacteristics. In a current-biased measurement, collective switching has been observed, while in a voltage-biasedmeasurement, clear branching structure has been observed. In the voltage-biased measurement, the interaction between

Ž .different intrinsic junctions has clearly appeared in decrease of values of Josephson critical current I with increasing thec

number of junctions in the resistive state. The I decrease leading to the collective behavior has been explained by takingc

effectiÕe heat diffusion into account. q 1998 Elsevier Science B.V.

PACS: 74.50.q r; 74.72.Hs; 74.76.Bz

Ž .Keywords: Intrinsic Josephson junction; Bi,Pb Sr Ca Cu O ; Thin film; Heat diffusion; Collective switching2 2 2 3 10qx

1. Introduction

In recent years, it is clarified that the layeredstructure of oxide superconductors inherently shows

ŽJosephson junction characteristics intrinsic Joseph-. w xson effect 1,2 . We believe that the intrinsic

Josephson junction is a key element to realize super-conducting tunneling-junction devices that is indis-pensable for the applications such as high-speedswitching and high frequency signal processing.

In applications of stacked intrinsic JosephsonŽ .junctions SIJJ , controlling their switching behavior

is very important. If the stacked junctions areswitched collectively, those are considered as a sin-

) Corresponding author. Tel: q81-774-98-2514, fax: q81-774-98-2585; e-mail: sakai@crl.mei.co.jp.

gle junction with large I R product, where I is thec n c

Josephson critical current and R is the normaln

resistance. Such junctions are suitable for powerapplications like high-frequency wave sources. Incontrast, if we can obtain one by one switching, eachjunction is able to be used separately, not as a stackof junctions. In this case, the junction is suitable forlow-power applications like high-speed switchingdevices. To achieve the control of the switchingbehavior, at first, we should clarify the mechanismof the interaction between adjacent junctions in SIJJ.Since each superconductive layer has atomic-scale

Ž .thickness 0.3–0.6 nm in SIJJ, the interaction be-tween adjacent intrinsic junctions is expected to bevery strong. At present, three mechanisms are pre-dicted for the interaction between adjacent intrinsicjunctions. First, screening current in magnetic field

0921-4534r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0921-4534 98 00069-0

( )M. Sakai et al.rPhysica C 299 1998 31–3532

or transport current flowing along the superconduc-w xtive layers couples the stacked junctions 3 , because

the thickness of the superconductive layers is muchsmaller than the London penetration depth. Second,heat diffusion caused by phonons and quasi-particlesgenerated by the switching leads to coupling of the

w xadjacent junctions 4 , because the thickness of thesuperconductive layers is again much smaller thanthe phonon diffusion length and the quasi-particle

w xdiffusion length 5 . In this mechanism, non-equi-librium quasi-particles may be generated and con-

w xtribute to the coupling 3,6 . Third, the chargingeffect in the superconductive layers couples the

w xstacked junctions 7 .Recently, we have confirmed intrinsic Josephson

Ž . ŽŽ . .effect on Bi,Pb Sr Ca Cu O Bi,Pb -22232 2 2 3 10qx

thin films and have investigated the current–voltageŽ .I–V characteristics with clear hysteresis and a

w xmultiple branching structure 8,9 . In this paper, wediscuss a collective switching in I–V characteristicsof SIJJ, and investigate a coupling mechanism ofthose junctions.

2. Experimental

Ž .The Bi,Pb -2223 thin films used in this workŽ .were fabricated on MgO 100 substrates by an r.f.-

w xplanar magnetron sputtering method 10 . In order toobtain high crystalline films and to control carrierconditions, subsequent heat treatment was done in anatmosphere O :N s1:15–25 at 8308C. Thickness of2 2

the films was typically 700 nm. The Bi:Pb:Sr:Ca:Cucomposition of the resultant films was found typi-cally 1.6:0.4:2.0:1.7:3.5 in an electron-probe micro-analysis. X-ray diffraction analysis revealed that thethin films are single phased, and are oriented withthe c-axis perpendicular to the substrates.

The film was etched by Ar-ion milling to fabri-cate mesas on the film surface. The mesa height wasset to about 50 nm and its area was reduced to 2

w xmm=2 mm 9 . The I–V characteristics were eval-uated both by a voltage-biased method and by acurrent-biased method with a three-probe electrodeconfiguration. A 100 V resistance was connected inseries in the voltage-biased measurement to preventan excess current flow.

3. Results and discussion

Fig. 1a shows typical I–V characteristics in acurrent-biased case at Ts4.2 K. We have obtainedcollective switching of the large number of junctions,especially in the high-voltage region. To clarify themechanism of the collective switching, we havemeasured I–V characteristics of the same sample bythe voltage-biased method. A branching structurepeculiar to stacked junctions was observed as shownin Fig. 1b, and 23 branches were confirmed. Ic n

represented as I of the nth branch was gettingc

smaller with increasing the value of n except nF5region. Supposing there is no interaction betweendifferent intrinsic junctions, I is to be largerc nq1

than I , because, in stacked junctions, the junctionc n

with a smaller I value should switch earlier to thec

Fig. 1. Current–voltage characteristics of stacked intrinsic junc-Ž .tions in a voltage-biased measurement a and in a current-biased

Ž .measurement b obtained at T s4.2 K. The area size of the mesais 2 mm=2 mm. A 100 V resistance was connected in series inthe voltage-biased measurement.

( )M. Sakai et al.rPhysica C 299 1998 31–35 33

resistive state. Thus, the I–V characteristics obtainedhere suggest that the I values are reduced by thec

interaction between the different intrinsic junctions.The collective behavior obtained in the current-bi-

ased measurement is reasonable when the result ob-tained in the voltage-biased case is taken into ac-count. When I is smaller than I , the nthc nq1 c n

junction switches not to the nq1th junction but tothe last junction, because the switching takes placefrom lower-I junction to higher-I one in the cur-c c

rent-biased measurement. Thus, when there are nobranches with larger I values than I , collectivec c n

switching takes place and switching voltage onlyjump to the last branch, as seen in Fig. 1a.

Ž .The Josephson critical current density J atc

Ts4.2 K of our sample is 2.5=108 Arm2, whichis much larger than the typical value reported for

Ž . ŽBi Sr CaCu O Bi-2212 single crystals about2 2 2 8qx6 2 .1.5=10 Arm . Moreover, its McCumber parame-

ter was deduced b G200 by the ratio I rI F0.1,c r c

where I is the return current at which the quasi-par-rw xticle I–V curve jumps back to the zero-voltage 11 .

So far, phase-lock switching of SIJJ for lowerŽ .hysteretic junctions b F8 formed in oxygen-an-c

Ž . ŽŽ . .nealed Bi,Pb Sr CaCu O Bi,Pb -2212 single2 2 2 8qxw xcrystals was reported by Regi et al. 12 and by´

w xKleiner et al. 3 with J values at Ts4.2 K ofc

5=107 Arm2 and 7=107 Arm2, respectively,which are smaller than that of our sample, but stillcomparatively large. It is considered that this differ-ence of J values relates to an intensity of thec

interaction between each junction. Thus, the interac-tion between stacked junctions consisting of thinsuperconductive electrodes constructed by two CuO2

Ž . Ž .planes 0.3 nm of Bi,Pb -2212 is probably strongerthan that of the junctions consisting of thicker super-

Ž .conductive electrodes of three CuO planes 0.6 nm2Ž .of Bi,Pb -2223. Consequently, we believe that large

J and thin superconductive electrodes are essentialc

for the interaction, leading to the phase-lock behav-ior.

Let us suppose the temperature rise due to theswitching in the stack leading to the collectiveswitching observed here. The sweep frequency to

Žobtain the I–V curve shown in Fig. 1 was slow 55.Hz enough to realize the steady state of the heat

diffusion for the duration between one junction switchand the next, according to the recent result repre-

w xsented by Takeya et al. 4 using a single crystalsample.

We have measured the temperature dependence ofI as shown in Fig. 2. This data was fitted by a leastc1

square program to a power function expressed as:3.0T

I s I 1y , 1Ž .c1 0 ž /Tc

where I s1.0 mA is the I value at Ts0 K, and0 c1

T s105 K is the superconductive transition temper-c

ature.When the I decrease of SIJJ obtained above isc n

explained by a temperature rise due to the switchingŽ Ž ..inside the mesa DT n , the I decrease should bec n

expressed as:3.0

DT n q4.2Ž .I s I s 1y , 2Ž .c n cmax ž /Tc

Ž .according to Eq. 1 where I s1.3 mA is thecmax

maximum value of I . If the I decrease is ex-c n c n

plained by the equilibrium heat diffusion, we canŽ .represent DT n spI V , where p is a constantc n n

describing the temperature rise in a unit of KrW,Ž .and V sV I is the voltage value at I in the nthn c n c n

branch. In contrast, when the I decrease is ex-c n

plained not only by the equilibrium heat diffusionŽ .but also the quasi-particle injection, DT n is rather

Ž .well expressed as DT n sqn, because the injectedquasi-particles contribute to the I decrease as wellc n

as the phonons caused in the equilibrium state, andthe number of quasi-particles generated by each

Fig. 2. Temperature dependence of the first Josephson criticalŽ . Ž .current I dot-rectangles , and a least square fitting by a powerc1

w Ž .3.0 x Ž .function, I s I 1y TrT solid line , where I is the valuec1 0 c 0

of I at T s0 K, and T s105 K is the superconductive transi-c1 c

tion temperature.

( )M. Sakai et al.rPhysica C 299 1998 31–3534

switch is not so deviated between the differentswitches, where q is a constant describing the effec-tiÕe temperature rise in a unit of Krjunction, consid-ering both the equilibrium heat diffusion and thequasi-particle injection effect.

We plotted the I values with I V in Fig. 3ac n c n n

and with n in Fig. 3b. It was impossible to fit thedata shown in Fig. 3a to the temperature dependence

Ž .of I represented by Eq. 2 using one fitting pa-c n

rameter, p, because the I values still decreasec n

even when the I V value becomes almost constantc n nŽ .I V f560 mW . In contrast, the n dependence ofc n n

Ž .the I decrease was fitted to Eq. 2 by a leastc nŽ .square program as shown in Fig. 3b solid line ,

except the deviation in the nF3 region probablycaused by the unevenness of the junctions near theinterface between the stack and the contact electrode.We obtained the best fit at qs3.1 Krjunction andthe effectiÕe temperature rise due to the switching of

Ž .all the stacked junctions as DT 23 s3.1=23s71

Ž . Ž .Fig. 3. a Josephson critical current of each junction I atc nŽ .T s4.2 K with the electric power I V caused by the switch-c n n

Ž .ing. b I at T s4.2 K with n; n is the number of junctionsc nŽ .having switched to the resistive state, and V sV I is then c n

Ž .voltage value at I in the nth branch. The solid line in b is ac nw ŽŽ . .3.0 xleast square fitting by I s I 1y qnq4.2 rT , wherec n cmax c

I is the maximum value of I of stacked junctions, and q iscmax c n

a constant describing the heat diffusion with the quasi-particleinjection effect. The best fit was obtained at qs3.1 Krjunction.

K. This good fit shows the I decrease was ex-c n

plained by taking into account not only the equilib-rium heat diffusion, but also the quasi-particle injec-

w xtion effect. Takeya et al. 4 confirmed by the pulsemeasurement of I–V characteristics that the super-conductive energy gap was seriously reduced by theheat diffusion. However, the result obtained hereshows that the quasi-particle injection effect at leastpartly contributes to the I decrease of SIJJ.c n

4. Summary

We have discussed a mechanism of collectiveswitching of stacked intrinsic Josephson junctions in

Ž .I–V characteristics formed in Bi,Pb -2223 thin films.In a current-biased measurement, collective switch-ing was observed, while in a voltage-biased measure-ment, clear branching structure was observed. In thevoltage-biased measurement, the interaction betweendifferent intrinsic junctions clearly appeared in Ic n

decrease of SIJJ with increasing the number of junc-tions in the resistive state, n, and the I decrease ledc n

to the collective switching. We believe that large Jc

and thin superconductive electrodes are essential forsuperconductive phase-lock switching of SIJJ. More-over, the I decrease was explained by the effectiÕec n

temperature rise due to the heat diffusion caused bythe switching, and this heat diffusion was consideredas both the equilibrium heat diffusion and the quasi-particle injection effect.

Acknowledgements

We would like to thank Drs. T. Nitta and O.Yamasaki for their support of this work. We alsothank Mr. K. Mizuno and Mr. H. Higashino foruseful discussions and Mr. T. Hirao for his help inthin-film fabrication.

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