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Vacuum 58 (2000) 149 } 157

Electron transport in high-¹ superconducting grain boundary junctions
Gennady A. Ovsyannikov*, Igor V. Borisenko, Karen Y. Constantinian
Institute of Radio Engineering and Electronics RAS, Moscow 103907, Russia

Abstract The current state and the prospects of the application of high-¹ superconducting grain boundary Josephson junctions in microwave electronics devices are given. It is approached by sketching the typical fabrication technique of the junction. Josephson bicrystal junctions on sapphire substrate are considered in detail. The results of dc microwave and magnetic measurements of YBCO bicrystal junctions on r-cut sapphire are presented. The junctions with high resistance 10}20 and I R "1}2 mV and tolerance of , R S around 30% on the chip allow to create microwave circuits with low integration (up to 10 junctions on , chip). The microwave dynamics of the junction with superconducting current-phase relation "ts with sin relation better than 5%, that clearly indicates the tunnel conductivity between two YBCO electrodes. It was found that critical current density depends on the square root of interface transparency in accordance with the prediction of superconducting current transport via Andreev's bound surface states. The speci"c properties of current transport in high-¹ grain boundary junctions with taking into account d-wave type of gap order in high-¹ superconductor are discussed. 2000 Elsevier Science Ltd. All rights reserved.
Keywords: High-¹ superconductivity; Josephson bicrystal junctions; Andreev's states; Current transport

1. Introduction Low-¹ superconducting electronics is based on the three-layers structure, superconductor}insulator}superconductor (SIS) tunnel junction Nb/Al O /Nb with the tolerance of para meters (critical current and normal resistance) 2}5% on chip (see for example Ref. [1]). Speci"c

Paper presented at the 11th International School on Vacuum, Electron and Ion Technologies, 20}25 September 1999, Varna, Bulgaria. * Corresponding author. Tel.: #7095-203-0935; fax: #7095-203-8414. E-mail address: gena@lab235.cplire.ru (G.A. Ovsyannikov). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 00163 -9


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properties of high-¹ material like low coherence length, strong anisotropy and sensitivity to oxygen de"ciency make the three-layers structure fabrication di$cult. Surface quality for threelayer high-¹ superconducting structure should be 1}2 order better than for low-¹ one. So nontraditional for low-¹ superconducting electronics approach, grain-boundary junction technology, is often used in high-¹ superconducting devices. The experimentally established appearance of weak link coupling between two grains, with the crystallographic axis misoriented on angle , is applied for realization of grain boundary junctions. Depending on the fabrication technique, the grain-boundary junctions are distinct into bicrystal, biepitaxial and step-edge junctions [2]. The high values of normal-state resistance R and critical frequency f "(2 /h)I R , as well as , C , the absence of hysteresis on the I}< curve of high-¹ superconducting (HTSC) Josephson junctions even at liquid-helium temperature ¹"4.2 K, make them appreciably superior to low-temperature superconducting junctions. The high critical temperature gives promising opportunities for applications at frequencies higher than those, corresponding to the energy gap of an ordinary (say, Nb) superconductor. However, the aspects involved in the reproducible fabrication of high-quality HTSC Josephson junctions on one hand, and the mechanism, describing current transport, on the other hand are the problems which have not been solved yet. The most reproducible junctions having a critical current spread of $12% per chip are fabricated on SrTiO bicrystal substrates [3], but because of their high dielectric constant '1000, they are unsuitable for high-frequency applications. Sapphire having a relatively low +9}11 and low losses (tan +10\ at 72 GHz), is the traditional material used in microwave electronics [3}5]. Here, we present the results of fabrication and characterization of HTSC Josephson junctions on sapphire bicrystal substrates both at DC and microwaves. The model based on the contact of d-wave superconductors is used for description of the electron transport mechanism in a bicrystal junction.

2. Experimental 2.1. Fabrication technique The Josephson junctions were fabricated on the r-cut sapphire bicrystal substrates (crystallographic plane (1 1 02) Al O ) consisting of two crystals for which the directions 1112 02 Al O for both parts were misoriented at the angles $123 to the plane of the interface. The YBa Cu O (YBCO) "lm was grown at ¹"750}7703C by dc sputtering (in diode con"guration) at high oxygen pressure (4 mbar) after the CeO epitaxial bu!er layer rf magnetron sputtering at ¹"600}7503C and pressure 0.01 mbar in an Ar/O mixture. The CeO bu!er layer prevents Al atoms dif fusing into the YBCO "lm from the substrate. The following epitaxial relation (0 0 1)YBCO//(0 0 1)CeO //(1 1 0 2)Al O , 111 02YBCO//100 12CeO //11 1 2 02Al O , was ful"lled for the deposited "lms (Fig. 1). Thin-"lm YBCO bridges each 5 m wide and 10 m long, crossing the bicrystal boundary, were initially formed by rf plasma etching of the upper amorphous CeO layer which acts as a mask. YBCO was then subjected to liquid chemical etching in 0.5% ethanol solution of Br through the CeO mask [5]. We have made the samples in which the YBCO bridges crossed the boundary at the angle between the normal to the boundary interface and current direction varied from 0 to 543 (see Fig. 1).


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151

Fig. 1. Crystallographic axes orientations of CeO and YBCO "lms in sapphire bicrystal junction with "333, "!333(D ID ). The domain of the "lm with the direction 11 0 02YBCO misoriented on the angle "903! is \ the twin to YBCO.

Fig. 2. The I}< curve at ¹"4.2 K for a typical bicrystal junction. Temperature dependence of the resistance R(¹) and critical current I (¹) are shown in the left inset. Dependence of the critical current density vs. inverse square root of characteristics interface resistance at ¹"4.2 K is shown in the right inset.

2.2. DC measurement results The junctions with obtained. The typical a behavior very close current: quasiparticle current density 10}10 A/cm < "I R "0.5}2mV at ¹"4.2 K were , I}< curve of the junction is shown in Fig. 2. It obviously demonstrates to the resistive shunted junction (RSJ) model which has two channels for

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excess current on the I}< curve at <'10 mV points to the absence of channels with direct (nontunnel) conductivity. However, I (¹) function shown in the inset of Fig. 2, has a linear ! temperature dependence which distinguishes it from the known theoretical one for superconductor}insulator}superconductor junctions [6]. At ¹ !¹(¹ , where the in#uence of thermal #uctuation is strong, I (¹) is close to (¹ !¹) dependence. I (¹) is possibly depressed by either the existence of the layer with depressed gap or by the speci"cs of proximity e!ect in d-wave superconductors [6,7]. The critical temperature of base electrode of the junction is in the range 86}88 K. We observe a signi"cant reduction of junction resistance in this temperature range. R(¹) has a foot-like temperature dependence at lower ¹ with a plateau equal to the normal resistance of the junction R . The plateau of constant resistance takes place, when the YBCO "lm on both , sides of the step is already in the superconducting state. We think that the two processes determine appearance of plateau. The "rst one is Al di!usion and second is the temperature #uctuation. M The following formula has been used for determination of barrier transparency D: D"2 7 !-17 !-/(3R S), M (1) , where 7 !-17 !-+3.2;10\ cm for YBCO. For typical R S"5;10\ cm, we ob, tained D"4;10\. The bottom inset of Fig. 2 shows the current density dependence jc"I /S M from R S. The experimentally obtained dependence is proportional to j R(R S)\R(D is M , , unusual for junctions of s-superconductors. Typically, j RD for SIS junction [6]. M 2.3. Current}phase relation Current}phase relation I ( ) strongly depends on the type of contacts between superconductors. 1 For ¹ !¹;¹ the deviations of I ( ) from I ( )"I sin are small for any type of supercon1 1 ! ducting junction, but at ¹;¹ I ( )"I sin remains for SIS junction [6] regardless of the 1 ! transparencies of the barrier D;1. To estimate deviation from I ( )"I sin we have measured M 1 ! I}< curves under applied monochromatic mm wave radiation Asin(2 f t), f "40}100 GHz [5]. The Shapiro steps on I}< curves, observed at voltages corresponding to the harmonics of the microwave frequency, demonstrate the presence of Josephson coupling in the junctions. Fig. 3 shows the variation of I (A) and subharmonic Shapiro step I (A) for two junctions with "0 (symmetrical biasing) and "543(nonsymmetrical one). The calculated functions using RSJ model for f '2eI R /h in the case of I ( )"I sin and I ( )"(1! )I sin # I sin 2 at , "0.2 are presented in Fig. 3. For (1, the di!erence between these two theoretical dependencies of I (P ) is small and both cases "t well to experiment. At the same time, a small deviation I ( ) 1 from sin-type dependence yields subharmonic (fractional n/m) Shapiro steps. The maximum are proportional to harmonics sin(n ) in I ( ). The precise amplitude of subharmonic steps I 1 measurements of I (A), as well as I (A) at ¹"4.2 K (¹/¹ +0.05) allow us to state the absence of sin(2 ) components in I ( ) function for BJ with symmetrical biasing ( "0%363) with an 1 accuracy of at least 5%. For '403 increases monotonously. So quite high junction resistance (10}20 ), characteristic voltage I R "1}2 mV and tolerance , of R S around 30% on chip allow to realize microwave circuits with small integration of junctions , on chip. The microwave dynamics of the junction with superconducting current}phase relation "ts


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Fig. 3. Normalized RF current dependence of the "rst and half Shapiro steps for two BJ "0 (crosses), and "543("lled circles). Dashed and solid lines show the calculated curves for "0 and 0.2, respectively. The current}phase relations for these two cases are shown in the inset.

with sin relation better than 5%, which prevents any parasitic e!ect in these Josephson device operations.

3. Discussion 3.1. Andreev's states in Josephson junctions It has been shown [8}10] that the transfer of copper pairs (superconducting Josephson current) is a complex process which takes place via an `intermediatea electron}hole state, where superconducting pairs are dissolved. The states are caused by Andreev's re#ection and realize at the border between two superconductors with di!erent superconducting phases. The induced Andreev re#ection energy levels are responsible for superconducting current transferring through the normal layer. Each time an electron is Andreev re#ected into a hole, a Cooper pair is e!ectively generated. Therefore the state, which represents an in"nite loop of Andreev re#ections (electron}hole}electron) serves as a pump that transfers Cooper pairs from one superconductor to the other. The states localized in the interlayer in the junction with direct conductivity (SNS, ScS junction, N-normal metal interlayer, c-constriction) and at the distance l + /(( !E) in the vicinity of the


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Fig. 4. Scheme of Andreev's re#ection in a high-¹ bicrystal junction.

interface in SIS junctions. Finally, in all types of superconducting junctions (SNS, ScS and SIS) Andreev's levels describe the formula E "$ ((1! Dsin /2). M (2)

The levels are placed close to the gap in tunnel junction with small transparency of the barrier (D;1) and the particularities induced by it is weak as observed from the experiments. Most of the M properties of SIS junctions are well described by the tunnel Hamiltonian model [6]. 3.2. Andreev's states in d-wave Josephson junctions The in#uence of Andreev's state is strong in SNS (ScS) junction (D+1) or in superconducting M tunnel junction with nontrivial superconducting pairing, for example d-wave superconductor. For SNS junction Andreev's levels give other than in SIS junction absolute value and temperature dependence of critical current and nonsinusoidal current}phase relation at low ¹ [7,8]. A superconducting order parameter with d-wave symmetry changes sign in a}b plane, when rotated by 903 around the c-axis. Since a quasiparticle changes its momentum when scattered, and there is a slight di!erence of order parameter before and after scattering, a bound state appears. An electron travelling towards the surface of d-wave superconductor, which is not parallel to a crystal axis, is re#ected back into d-wave superconductor and is subsequently Andreev re#ected into the hole by the positive pair potential. In the next step, the hole follows the same path backwards, re#ected at the surface, and is "nally Andreev-re#ected into another electron by negative pair potential. The surface of d-wave superconductor plays the role of point contact with D"1 and the M sign change in the pair potential corresponds to the phase di!erence (Fig. 4). It is the essential physical di!erence between s-wave and d-wave tunnel Josephson junctions, the position of Andreev's level when the phase di!erence across the junction is zero. For the junction of d-wave superconductors the Andreev energy level is very close to the Fermi level and for s-wave, the energy is close to the gap. These localized midgap energy states opened additional channels for the current leading to the peak for conductivity in DIN junction [11] and to anomalous low-temperature variation of the superconducting current when the orientation angle of the d-wave order parameter is such that the midgap states form in the junction (the angle between a(b)-axis and normal to the border is in the range 10}453) [10,12].


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Fig. 5. (a) Andreev's levels in D ID junction for several , D"10\, " /6. E ( ) coincide with Eqs. (1) and (2) for M ?\ "0 and , respectively with proper ( ), (b) Amplitude of Andreev's levels in D ID , D"10\ for several . M \

For the tunnel junction of two d } -wave superconductors with gaps VW " cos (2 #2 ( )) E depends on four angles, quasiparticle incident angle- , phase- and, 0* misorientation angles and . Andreev levels for mirror symmetric junctions (D ID ) at several ? \? are presented in Fig. 5a. One can see that in the range "10}453 E ( ), dependence is very close E for misorientation angle "453 E "$ ( ) cos[( ! )/2)](D( ). M (3)

The behavior of the amplitude of the Andreev levels with increasing at several incidence angles ( ) is shown in Fig. 5b. For "10}453 for a small amount of quasiparticle in the range "0}103 the condition max"E "'0.1 is satis"ed. Therefore, the averaged income of these quasiparticles would be small. We can use as an approximation the Eq. (3) for describing Andreev's level in D ID junction in the wide range of "10}453. \ 3.3. Determination of superconducting current using Andreev's levels The I ( ) can be determined from the energy of bound Andreev levels E in the junction since 1 I ( )RdE /d [10,13]. The di!erence in E ( ) leads to other temperature and transparency dependence of critical current. In accordance with d-wave theory of superconducting junctions (DID) [10,12,13], various non-linear I (¹) dependencies caused by the existence of bound states at ! the interface should be observed. Our measurements, as well as some other published data [14] instead show a monotonous (smooth) rise of I with decreased ¹. However, there are several ! physics phenomena, in#uencing the I (¹), which have not been accounted for in the theory. The "rst one is the twinning of the "lm, meaning that the current through the junction consists of two


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Fig. 6. Current}phase relation calculated for symmetrical (453,453)-dotted line and mirror symmetrical (453,!453)-solid line bicrystal junctions. The dashed line corresponds to the parallel connection of these two junctions.

components: from mirror symmetrical junction (MSJ, D ID ) and additional symmetrical \ junction (ASJ, D ID ), in our experiment D ID and D ID . There is an essential \ \ di!erence between MSJ and ASJ, MSJ possesses the properties of -contact and ASJ is 0-contact. Since E for misorientation angles in the range 10}453 is very close to E for misorientation angles 453, (Eq. (2)) we will compare our experimental data with the results of I ( ) calculation for symmetrical and mirror symmetrical junction with a misorientation of 453 (Fig. 6). As calculated I ( ) for D ID and D ID are nonsinusoidal, the resulting current through \ the parallel connection of these junctions is I ( )+I sin (see Fig. 6) as we observed in experi ment. A comparison of absolute value and temperature dependence of I is di$cult within the simple model because of the roughness of the interface and consequently the contribution of midgap states is reduced. A distinctive feature of d-wave pairing is the sensitivity of the d-wave superconductor to inhomogeneities and interfaces. Quasiparticle scattering at interfaces distorts the order parameter and causes signi"cant depression of the gap. It happens in the case, when the normal of the interface di!ers from crystallographic axes even for specularly re#ecting boundaries. This phenomenon in#uences the critical current of the junction as N-layer. Consequently at ¹+¹ , gap suppression would lead to quadratic dependence of I (¹), which we observed in the experiment (Fig. 2). In SIS junction, superconducting current is proportional to the transparency of barrier ( j RD) M (see Eq. (1)), since R SR1/D, the product I R is independent of D. In MSJ, ASJ and symmetrical M M , , junction of d-wave superconductor at low ¹ in a wide range of E R(D and as a consequence M j R(D as follows from Eq. (2) and Fig. 5. It happens due to the presence of Andreev's level at M E; . The dependence of j R(D was observed for all out investigated junctions for symmetriM cal and asymmetrical biasing [15]. The same dependence follows from the data for a symmetrical bicrystal junction on SrTiO [16].


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4. Conclusions Experimentally observed temperature (J¹ at ¹(¹ ) and transparency (J(D) dependence of critical current as well as sinusoidal current}phase relation indicate that the transport of superconducting current in high-¹ bicrystal junction possibly realizes by the tunneling of superconducting carrier with participation of bound states at the border caused by multiple Andreev re#ection in superconductor with d } pairing. For a detailed comparison with the theory, the VW roughness of interface and "lm twinning should be taken into account.

Acknowledgements The authors thank M. Darula, A. Mashtakov and P.B. Mozhaev for their help with the experiment and fruitful discussions. The work was partially supported by Russia Foundation of Fundamental Research, Russian State Program `Modern Problems of Solid State Physicsa, `Superconductivitya division, INTAS program of EU (projects NN97-1940-97-11459) and NATO Scienti"c program.

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