0038-1098(95)OOOl5-1

e Pergamon Solid State Communications, Vol. 94. No, l. pp. 45---48, 1995Elsevier Science Ltd

Printed in Great Britain0038·1098/95 $9.50+.00

CURRENT -VOLT J\GE CIIARACTl:RISTICS AND JOSEPHSON AC EFFECTS OF

GRAN U LA R UTSC Y IHa 2Cll ~O y II RInG ES

Sangmin Lee. Hyunkook Kim. Doonce Son". Jaejun Yu and Gwangseo ParkDepartment of Physics. Sogang University. C,I ',n, 1142, Seoul Korea

Kiejin Lee

Institute of Material Science, Lniversity of Tzukuba, Tzukuha, Ibaraki :-105. japan

(Received l\ November 1994 hy A. OkUi)

Ex perimen ta! and theoretical studies are rellorh,d of the cu rrcn t e vottag o

characteristics and josephson radiations from granular Y IBa2Cu~n , (YHCO ibridges. We show that the granular structure of hr idge s can be undr-rs tond

as a series connected indcnendcn t and inhomuaencuu s resistively shuntedjunctionlRSj) array. Wht," W(' take ty p ic a l values of junction eriti':a lparameters, the experimental re sul rs arc well understood quan titutive ly ,

L INTROUUCTION

The josephson

J J, sin '"

..i .2...J;. V'f' h '

errect' is well dellcribed by(I)

(2)

the weakest junction in the series array. Tberelatively strong power of radiation, about 3 pW,is attrihuted to tbe result of coberent radiationfrom many similar junctions.

2, EXPl<:RIMENTAL ItESULTSwhere J, is the critical current, ,p tbe phase

difference between the electrodes andV tbe net voltage drop across tbe junction,Wben a nonzero dc voltage is applied, we candetect the ac field, i.e, Josephson radiation fromtbe junction . of which frequency aI . is

determined hy the josepbson voltage --frequencyrelation2.JA

(1,1. = 2_{ V d,

The direct observation of josepbson radiatioo isthe best method to verify the josephson effect.Recently, several groups including us reportedthe observations of microwave self radiations indc biased high T,- superconducting(IITSC)granular bridges,5,6,7 All of these results sbowseveral peaks of self radiation at the largevoltages , wbich is not consistent with eq.(3).Tbe current -voltage characteristicsUVCsl arealsu nearly parabolic and there arc somewohbling parts at voltages where the selfradiations occur. This suggests that the grainboundaries bebave as weak link s , which aresynchronized at some current values,

In this report. as a step towardunderstaoding the self radiation properties of theIITSC granular bridge , we try to model it as adisordered series array of josephson junctions.Using a simple model of an inhomogeneous andindependent series array of overdamped RSjs.we have studied tbe IVCs and Josenh sonradiation properties of granular bridges , As aresult. it is found that tbe josephson radiationpower PlI) from the IITSC granular bridge canbe analyzrd and determined by t h e distributionfunction n(l,) Le., the num her of junctions w itb

critical cu rrcut I,. The critical current of a

granular bridgc structure corr e suo nd s to tbat of

45

The nTSC YBCO films were prepared by thesurface diUusion method on the Y2BaCu(),subs t ra tes ," Tbe hridge s ize was 100 x 100 pm 2

•

The grain size was about I Pm. The {VCs weremeasured by the four point nrohe method, Forthe direct ohservation of microwave selfradiation. we used a w ide hand noise receiver.The center frequencies were 22 . 36. 47 GIIz. thebandwidth A f was \.8 (;lIz and the sensitivitywas 0.1 K. Tbe detailed setup of noise receiversystem was presented elsewhere.7 We used /I- jn e tal for shielding the magnetic field.

Figure 1 (a) shows a typical IVCs and theself radiation power P(I) at 36 GIl1'. There areseveral wobhling parts in the IVCs, Themicrowave self radiations occur near these parts.The measured radiation power of strongestpeaks A in Fig, I (a) is about :i x 10- 12 W. Thevoltage in (VCs corresponding to tbe strongestradiation peak A is ahout 9 m V. This value isfar from tbe Jo senb sun radiation voltagedetermined by eq. (:-1) . Tbe (Ves and selfradiation power PU) at 22, 36 and 47 GHz areshown io Fig. 2 (h). We can easily find twos im nlc rules from this data. The voltage valuesat which the josephson radiations occur slightlyincrease witb the frequency of receiver. And theincrement of the first neak Ipeak A) is smallerthan tbat of tbe second neak Iueak 0), Werepresent the frequency dependent voltage valuescorresponding to the peaks A and B in Fig, 2,These properties are easily expected from thetwo dissimilar RSJs connected in series.

Figure 3 shows the (VCs under 47 GUzmicrowave irradiation for several attenuationlevels . We can find that the large current stepsoccur at the voltages V n( h l2e)tt>. wbere n =

I , 2, :-1, This is equivalent to the Shapiro stepsof tbe single josepbson junction.

46 CHARACTERISTICS OF GRANULAR HTSC YIB~Cu30y BRIDGES Vol. 94, No.1

B

is a characteristic voltage,

3.SERIES ARItA Y MODEL

o'-~I---L---'-_L--~---l_~_-L.--Jo 20 30 40 50

FREQUENCY(GHz)

where

(TJ r • , " (R,),.iO 1, U'.lt' J/OJ ..." and I the total

current. In general, the characteristic voltage

(VJ'.i " is determined hy the materials and types

of junction. Thus (V,),., iI of junctions in the

granular bridge can be regarded to be nearlyequal to each other i.e., (V.)i.ltl ~ V, for all i ,

where V r , , I I is the voltage drop across the

adjacent granule and N is the total number ofgrains in the series direction. From the ItSjmodel, the eq.(4) can be rewritten as 10

N

V,,,, = ,:E) (Vc)'.'+l V U'.'+12-1 , (5)

In fact, a granular system constructs a twodimensional junction array. However, in theabsence of external magnetic fileds, there is noeffect of vortex configurations on theelectrodynamics of a two dimentional junctionarray." So the two dimensional junction arraycan be approximated as a series array of parallelconnected junctions. Since the electrodynamicsof a parallel junction array is equivalent to thatof the single junction, the granular bridgestructure can be roughly approximated to theone dimensional series junction array in ourexperimental situations. Also, since our attentionis focused un the synchronized josephson accurrent, we can neglect the ac coupling effect ofany two disordered junctions. In this point ofview, we can simplify the granular system as anindependent and inhomogeneous overdampcdRSjs connected in series. Following thisassumption, the net voltage drop across thebridge is written as a sum of the voltage dropsfor each junction, i.e.,

N __

v., = i:E\ V'.'+l , (4)

Fig. 2. The frequency dependent voltage valuescorresponding to the josephson radiation peaks Aand B in Fig. 1. The open cireles represent forthe experimental values and the solid circles forthe fitted ones.

o

50

........:!::c:::J 40

..ci sl.- S0

'-'0::: w 30W (9

3 <!

0 r- 200... -J

0

6 >10

6.0

22GHz

36GHz

A +-

'---------1 0 ~(j)

o

-

A

2.0 4.0

CURRENT(mA)(b)

0.0

40,----------.---------,

o

-6 -4 -2 0 2 4

CURRENT(mA)(0)

60'r---------,---,

>:E 30'-'W(920«~o 10

>

........ 40~'-'W 20(9

«~ 0o>-20

47GHz

The Qualitative feature of PU) is similar tothe inhomogeneous RSjs connected in series, butthe voltages corresponding to the Josephsonradia- tion peaks A and B are much larger thanthe voltages calculated from eq.(3). Moreover theShapiro step data is similar to that of the singlejosephson junction. To resolve these difficultiesin understanding the experimental results weassume as follow s; (i ) the measured josephsonradiations from the granular bridge are thecoherent radiation of many junctions, (ii) thereare also many junctions which have differentcritical currents from each other.

From this point of view, the smallfluctuations of background noise level ofjosephson radiation power P(J) in Fig.1correspond to the radiation of each disorderedjunctions. And the relatively strong peaks arecaused by synchronization of many similarjunctions. And the Shapiro steps are originatedby the coupling between the external microwavesignal and the self radiation from the weakestjunction in the series array.

Fig. 1. The IVCs and Josephson radiations of agranular YHCO bridge for (a) f=36 GIh and (h)f=22, 36, 47 (; lIz at l' =4.2 K.

Vol. 94, No.1 CHARACTERISTICS OF GRANULAR HTSC YIB~CuJOy BRIDGES 47

0.8 wbere n. is the number of junctions with

Fig. 3. The IVCs under 47 GIIz microwaveirradiation at T~4.2 K. The numberscorresponding to the labels from A to j indicatethe attenuation levels.

dynamic resistance dYIdI. If we neglect tbeharmonic generations, the frequency ofJosephson ac current is uniquely determined bythe dc bias current L So the e q, (7) can bemapped as

Ol)V i . i t 1

4.CONCLUSION

If we have any comparable radiation peak formore than two different frequencies, we can fit

the values of V, and (I,)'.i" to the data by

solving simultaneously the simple equations asobtained by eq. (II). From the data in Fig. 2, wecan take two relatively strong josephsonradiation peaks A and B for calculations. Sincewe have two peaks at three differentfrequencies, we can ohtain six combinations ofsimultaneous equations. The characteristicvoltages obtained from these equations are litlledifferent from each other. The averaged value ofV, is 125 IN. This is similar to the I, RN values

recently reported for the YBCO grain boundaryjunctions. 12

. I:J Inserting this value into theeq. (I I) we can calculate the critical currents(J,), and (I,), corresponding to the peaks A and

8. The crirical current OJ, is 1.24 mA and

(U, is 2.53 mA.

The total number of junctions in the seriesarray is estimated to be 200 based on the ratioof hridge length and grain size. The Ok values

for the peaks A and B which is used in ourcalculation are 60 and 10 as determined by theaveraged relative ratio of radiation power ofthese peaks. Other 130 junctions have adistribution of critical current values. We takethe spacing of critical currents of dissimilarjunctions as 0.05 rnA for best fitting withexperimental results. The smallest criticalcurrent 0.3 mA is delermined by the criticalcurrent of tntal IVCs in }o'ig. Ha).

Figure 4 represents (a) fitted IVCs and (b)current dependent power spectrum. The currentvalues (II)' and (II), from the results of our

theory and experiments are compared in Table 1.These values agree with each other very well.The wobbling parts of IVCs are caused by thestarting of resistive state of many similarjunctions. From eq.(lI) we can estimate thelinewidth & of power spectrum Sy(I).

Theoritically & is about 5 pA. In this fit,

however, we use &~70 pA for good matchingwith experimental data. This means the criticalcurrents of weak links which sbow coberentJosephson radiations are not completely equalbut distributed about 3 - 7 96 of I,.

(IJ) ... II {IJh.

Since (IJl. is a function of (I,)., Sy (I) is

directly determined by the distribution function

n(l,), i.e., tbe number of junctions witb critical

current I,. Once V, and n(I,) are determined,

tben we can calculate the fitted IVCs and powerspectrum Sv (I) from cqs, (6) and (10).

The voltage drop as well as the frequency ofjosephson ac current of each junction is only a

function of total current I such as

(8)

R d is the

A' 3dBB' 4dElC' 7dBD' IOdBE' 16dBF' 19dBG' 24dB

H - 2'dB1·29dBJ. ClO dB

0.8

f a 47 GHz

T-4.2K

0.6

Josephson radiation

and the linewidth

R" k u T which is due to

0.4

CURRENT (rnA)0.2

the thermal nuctuations wbere

where 0 1.2.3---, the

frequency "'J (2el h}V

,1", (I 12) (R./R")' (2el h)'

where I is the current value corresponding to

the josephson radiation with freuency '" and

& I) ('" I ,1",) IJ (",) for constant "'.

Since we assumed that the junctions areindependent, the net power spectrum of seriesarray is a simple summation of eq. (8). So the

power spectrum Sv (I) for constant '" at finite

temperature is

(I) ~ (S ) . [ (( IJ)i .i +1 - I )2] ( )Sy = t'"'l 0 ••• +1 Exp - ---Al---- . 9

where a, is I/(I,h.

The josepbson radiation is represented in

terms of power spectrum 5 v ( "') . The power

spectrum of a single junction for constant bias

current I at finite temperature is"

[ ( nw) A,"~- -r ,Sy(w) = So Exp - n~

If we rearrange the order of summation in eu ,(5) to collect the similar junctions which havenearly equal critical current values and define

n. as the number of junctions of which criticalcurrent is o.i., then we can rewrite eq, (5) as

yy,ot = :En. Va~-::'-Ic k

'i 0.6E.....-wo« 0.4I-...Jo> 0.2

(lO)

By rearranging the order of summationcollect the similar junctions, en , (9) becomes

'" . . [ ((lJ). -I )~]Sv (I) = "'k' n , (So>' Exp -- --L1i- ,

to The coherent phenomena of granular bridgestructure was Quantitatively analyzed. It isfound that the dynamic behavior of bridge iswell understood by the inhomogeneous RSJs

48 CHARACTERISTICS OF GRANULAR HTSC YIB~Cupy BRIDGES

40,r---,.-rr----r------,

Vol. 94, No.1

..--..-C::l

..ci....0........0::W

0 ~0

0 0..

0

6.02.0 4.0

CURRENT(mA)(b)

0.0

..--..:;:::.E 30 I........-

W<.920 20K«

1~ 100>

0

--- EXP- THEOR Y

..,2..0 40

CURRENT(mA)(0)

0L.......c......_--'-_~_--'--_~__'

00 60

~'--'W(9<[

~o 2.0

>

Fig. 4. (a) Fitted JVCs of inhomogeneous series junction array. The characteristic

voltage is 125 J,tV. Dotted line corresponds to the experimental data. (It) The power

spectrum s, (I) for f =22 , 36, 47 Gllz .

Table I. The current values ( I J) , and (T 1) 2 at

which the Josephson radialion peak A and 8 arcgenerated for f = 22, 36, 47 C;Uz from the

experiment and the theory.

frequency( 11) , (.A) ( 11}z (IIA)

RSJ exp, RSJ exp,

22GHz 1. 32 1. 36 2.69 2.3036GHz 1. 44 1. 45 2.94 3.1047GHz 1. 57 l. 50 3.20 3.50

reported experimental values by other groups forvnco grain boundary junctions. The weak linksin our granular bridge consist of two groups ofsimilar junctions and fully disordered junctions.Fully disordered junctions make the total IVCssmooth. And the Shapiro steps arc related to theweakest junction only. The strong and broadJosephson radiation and the sudden change ofslope of IVCs are consequences of collectivehehavior of similar junctions .

ACKNOWLED(;MENT

connected in series. The averaged characteristicvoltage computed by RSj model is 125 "V. Thisvalue is in good agreement with the recently

This work was supported by the KoreanMinistry of Science and Technology. Theauthors would like to thank Or. flakhumian inArmenian Academy of Science who designed thesensitive noise receiver.

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