Electrical characterisation of single grain boundaries in DyBa2Cu3Ox ceramics

PHYSICA

Physica C 196 ( 1992 ) 1-6 North-Holland

Electrical characterisation of single grain boundaries in DyBa2Cu3Ox ceramics G. Schindler a,b, B. Seebacher b, R. Kleiner

a,

p. Miiller

a

and K. Andres

a

a Walther-Meissner-lnstitut, W-8046 Garching, Germany b Siemens A G, Corporate Research and Development, Otto-Hahn-Ring 6, W-8000 Munich 83, Germany Received 14 March 1992 Revised manuscript received 4 April 1992

Single grain boundaries in polycrystalline DyBa2Cu3Ox bulk were isolated. Measurements of their electrical properties show, that they act as Josephson junctions and that their properties can be described by the RSJ model. The current distribution inside the junction is inhomogeneous and there is evidence for small areas with high current density. A model for calculating It(T) taking into account a depression of the order parameter A at the superconductor insulator interface is introduced. Calculations using a distinct depression of,J are fitting the experimental data very well. Finally, it is shown that the grain boundaries also exhibit the AC-Josephson effect.

1. Introduction The greatest handicap for the application of highTc superconductors is the low critical current density. This is mainly attributed to the grain boundaries. The properties of these grain boundaries were a main subject of research in the last years, either in the form of thin film grain boundaries [ 1-5 ] or in the form of a grain boundary network inside a bulk sample [6]. Up to now the behaviour of grain boundaries is not completely understood. Besides the artificial grain boundaries in thin films a characterisation of as grown grain boundaries in polycrystalline bulk is helpful. The technique of microcontacts allows one to make a direct measurement of the properties of single grain boundaries of a ceramic material and thus is a method of their characterisation.

2. Experimental REBa2Cu3Ox samples were obtained using a solid state reaction method. Contacts had to be made to single grains, so large grained ceramics was needed, This was achieved by high sintering temperatures of

1000°C to 1020°C. By the substitution of Y with Dy grain sizes of several hundred ~tm with only a small amount of second phases were obtained [ 7 ]. After sintering, the samples were polished down to a thickness less than the grain size. Typical values were 30-40 ~tm. Gold pads were sputtered onto the surface of the sample through a metal mask. These pads were 30 × 30 ~tm2 wide and arranged in a square pattern with a midpoint to midpoint distance of 100 lam. So several pads could be fitted on the surface of one large grain. The pads were annealed at 450°C in flowing oxygen resulting in lower contact resistance and better adhesion to the surface. Contact to the sample was made with a 17 ~tm gold wire, which was attached to the pads with thermosonic bonding. To ensure that the electrical properties of only one grain boundary were measured, laser patterning was used. So the sample was divided into two parts with only one electrical connection via this grain boundary. A SEM picture of a grain boundary thus prepared is shown in fig. 1, Measurements were carried out inside a cryostat cooled by flowing helium gas. The sample was cooled by exchange gas. Current-voltage characteristics (IVCs) were mea-

0921-4534/92/$05.00© 1992 Elsevier Science Publishers B.V. All rights reserved.

2

G. Schindler et al. / Electrwal characterisat~on ~/'single gram t~oundarze~

Fig. t. SEM micrograph of a grain b o u n d a r y with contact rods and laser cuts.

sured using the four probe technique. The voltage was taken from pads located on the surface of the grains forming the isolated grain boundary. For current injection mostly pads on neighbouring grains were used. The critical current was determined using a 1 pV criterion. 12

~3,=0.

3. Results and discussion

3. I. Current-voltage characteristics l

The IVCs of single grain boundaries at different temperatures are shown in fig. 2. They can be explained using the model of the resistively shunted junction (RSJ) with nonvanishing capacitance [810]. The properties of the Josephson junction are ruled by the following differential equation for the phase difference ~0: 1 =sin~0+ d~0

I~

dZq~

~ +fl~ d'r 2"

(1

!).5;

l

I

1 2,

(I~1\)

Fig. 2. IVCS at various temperatures. The RSJ curves were calculated using the values offl,, as indicated.

with r = ( 2 e / h ) I c R N t . The McCumber parameter tic = ( 2 e / h ) R 21 c C ( RN is the resistance according to the slope of the IVC, I~, is the critical current and C

G. Schindler et al. /Electrical characterisation of single grain boundaries

is the capacitance of the junction) determines the features of the IVC. tic depends on temperature via I¢(T) and RN(T), which are both increasing with decreasing temperature. So the IVCs should change with temperature. The 77 K IVC is consistent with tic-,0, the so called high damping limit and U.~ (12-12 )1/2 is satisfied. The RSJ-curves for the 42 K and the 7 K IVC were calculated using tic = 0.55 and tic= 0.85, respectively. Up to now only one grain boundary exhibited hysteresis. The IoRN products range between 1 ~tV and 200 ~tV at 77 K and 30 ~tV and 3 mV at 4 K. So/_oRN is far below the BCS value o f x d / ( 2 e ) for all measured samples. A possible explanation of this fact is a depression of the order parameter 3 near the grain boundary.

3.2. Dependence of lc on applied magnetic field In an external magnetic field the critical current shows a Fraunhofer-like pattern [ 10 ] as explained by the DC-Josephson effect (see fig. 3). A magnetic field was applied parallel or perpendicular to the sample's surface. In both cases the field vector was perpendicular to the current flow. The periodicity Bp Ofjc is determined by the projection of the area of the Josephson junction in the field direction and the distribution of the current density inside the junc-

3

tion. In the case of a homogeneous current distribution the extension of the Josephson junction lj perpendicular to the field direction is calculated by

6--

~o ap(2~L +di) '

where 2L is the London penetration depth, di is the thickness of the insulating barrier and ~o = h / (2e) is the flux quantum. In the most cases Ij is found to be smaller than the geometrical diameter of the grain boundary. In the case of an inhomogeneous current distribution, the regions of the highest current density determine the Ic versus H pattern. In the particular case shown in fig. 3 lj is determined as lj = 5 ~tm for B parallel to the surface and lj = 13 ~m for B perpendicular to it. Due to demagnetization effects the second value is an upper limit for Ij. The geometrical cross section of the grain boundary was 40 × 70 ~tm2. The Josephson penetration depth

2el~(22L+d,)fi

2j =

determines whether self-field effects have to be taken into account. This must be done for 2j < Ij. For this s a m p l e 2 j / l j = ~ for B parallel to the surface and 2 / lj = l for B perpendicular to it. The shift of the max-

7

6

(a) 6

+

(b)

××

×

xx

x

×

4

x

x

x

,,_;~

H

'~

x

'

#

× - x field increasing 1

o -80

~

×

~

I

I

I

I

I

I

]

-60

-40

-20

0

20

40

60

*

÷

~

o 80

decreasing " ~

0

5

10

15

'

20

~

- ~ r

25

*

30

*

~

-

35

~

-

40

~oH (G) ~oH (G) Fig. 3. I¢(B) characteristicof a grain boundary. Magnetic field was applied parallel to the surface of the sample (a) or perpendicular to it (b). The temperature was 5 K.

4

G. Schindler et al. /Electrical characterisation of single grain boundartes

imum of I~(B) to a value B#O can be explained by the influence of the field generated by the measuring current [ 10 ]. The characteristic with B parallel to the surface shows no hysteresis between field sweep direction up and down, in the case of B perpendicular to the surface a remarkable hysteretic behaviour is observed. In this case the magnetic field at the grain boundary is enhanced by the high demagnetization factor D of a thin plate perpendicular to the applied field. So the flux will penetrate not only the grain boundary but also the grains themselves and is being pinned there. In the case B parallel to the surface, D is close to 0 and no field enhancement and no pinning is to be expected here.

3.3. Dependence of I,. on temperature The I~(T) characteristic of a single grain boundary is shown in fig. 4. The experimental data can be reproduced very well taking into account the depression of the order parameter A at the grain boundary. De Gennes demonstrated, that for superconductors with very short coherence length 3 will be depressed near the superconductor insulator interface even in a perfect superconductor [ 11,12 ]. A value AcB < Ao with 3o being the bulk value of A

E G s - ( ) . l ,t

is assumed at the interface. The ratio Acm/Ao=e(m shall be constant over the whole temperature range. A(x, T) can be written as [13.14]: x o + .\-

3(_v, 1) = d o tanh/7-.~ . \/-¢(T)

inside the superconducting region .v> 0 . =0

inside the insulating region x < 0 .

A sketch of a grain boundary, with depressed 3 is shown in fig. 5. xo is given by 3(x=O)=dcm resulting in x o = 2 ~/e X { ( T ) artanh(%u). The total Josephson current is given by a sum over all tunneling channels with different A [ 15 ]. Using the Ambegaokar - Baratoff relation for evew tunneling channel [ 16 ], the total critical current results as

I c --

2eAo jf d(x, T)(dA(x, T)/dx). R N (x)

X

,

A(x, T)

tann ~

,

dx.

0

A BCS-like temperature dependence with 3 ( T = 0 ) = 1.76/% T~ was used for A. RN is assumed to depend exponentially on the width of the tunneling channel:

A-I

Ax 1

x

~q;ll

iII

0

I0

~0

30

,to

50

60

70

80

,9o

100

T IK)

m [I

Fig. 4. M e a s u r e m e n t ofl,. vs. 7: B o t h lines were c a l c u l a t e d using the m o d e l w i t h a d e p r e s s e d o r d e r p a r a m e t e r 3 n e a r the g r a i n boundary.

X

Fig. 5. M o d e l o f a g r a i n b o u n d a r y , T h e o r d e r p a r a m e t e r A is depressed n e a r the s u p e r c o n d u c t o r (sc) i n s u l a t o r ( i ) i n t e r f a c e

G. Schindler et al. / Electrical characterisation of single grain boundaries

1

1

RN(X)

-- RN o

( exp

2x+di~ ~ -].

Here ~o is a scaling parameter. RNo was assumed to be temperature independent. For the SI-interface d J / d x results as dA(x=0, T) =AGB(T) ~(x) , dx where 6(x) is Dirac's function. So the integral can be divided in two parts: the tunneling current from the SI-interface and the contributions from the inner part of the grains. Changing the integration variable from x to e(x) with (x) =A (x, T)/Ao (T), the following expression for Ic results: Ic -

Two essential features of the experimental data are reproduced very well: Firstly, for T~ Tc the convex increase of Ic, which is sometimes assigned to the proximity effect of a normal conducting layer ("SNIS"-structure) also appears in the calculated Ic (T)-curves. Secondly, for low temperatures this model predicts an increase of Ic down to some Kelvin as observed in the experiment, while in the normal Ambegaokar-Baratoff model I~ saturates at relatively high temperatures. The original work of De Gennes [ 11 ] introduced the "extrapolation length" b defined by

Calculations using a temperature independent b do not fit the data as well as the previous model. In this case ¢oa becomes temperature dependent and decreases for T--, Tc. So Ic will be strongly depressed for T--, To which is not observed.

n e --di/~o 2eRNo 1

×If

5

. , e3o(T) ~Ao(T) tann 2-~-ST e-2W"'/e°d~

~GB

+ 3 o ( T ) ~ B tanh

3.4. The AC-Josephson effect

~GB3o ( T ) ] 2-~--a77 -3,

The AC-Josephson effect can be observed at a grain boundary irradiated with microwaves. Figure 6 shows several IVCs for various microwave frequencies. The Shapiro steps [ 17 ] are observed up to the order 17.

where w(~) = x f 2 ~(T) [artanh (~) - artanh (~GB) ] denotes the thickness of the insulating layer for the tunneling channel ~. A fit using this model is shown by the broken line in fig. 4. A better fit to the experimental data is obtained, when a disturbance parameter A > 1 is introduced and w(~) is changed to: w (~) = Axf2 ( ( T ) [ artanh (e) - artanh (~GB) ]

3

10.7 GHz

< v • J v~7.7 GHz

•

Thus the region with lower A will be extended into the grains. While the depression of A with A = 1 is an intrinsic effect of the superconductor insulator interface, the extension of the interface region via A > 1 is an extrinsic effect and may be caused by stacking faults, dislocations or strain. This fit is shown by the solid line in fig. 4. A variation ofdi, ~ or RNo changes only the absolute value of I~ but does not affect its temperature dependence. So this model contains only two free parameters: ~GB and A.

....

,

0 ~,1~

4.2 GHz

0

j,.,tS r

J~'.

~4

GHz

0--

Fig.

20

40

60

80

6. Shapiro

steps o b s e r v e d at 60 K.

1O0

(i. Schtndler eta/. / Eleclru'al characlerisat~on ql,stng/{, grain boundarz{'s ~1

(a)

(b)

0.8

<

0.6 -

/)/It;

().{I t 0A O.OZ

0.2

u

().;2

o. I

).{i

0.,~

I

{/

I1 ~"

(~ l

{} t;

1,,

l,v,/l,

o.~

1,

Rg. 7. Shapiro step hmght vs. 1~, peratures of 84 K. The dependence of the step height on the AC-current is shown in fig. 7. The theoretical curve was calculated assuming a homogeneous junction w i t h [ / , £ . = O . 0 5 as used in the experiment. The m i n i m a and the first m a x i m u m of the zeroth step were reproduced very, well. For the first step, the ratio l s t e p / I c and the first m i n i m u m of the calculation are consistent with the experiment, too. The differences between experimental and theoretical curve may be due to a more complex structure of the grain boundary. I ~ ( B ) measurements made on this junction clearly show, that at least a double j u n c t i o n structure is present. In conclusion, we have shown that the grain boundaries in DyBaeCu30~ ceramics exhibit DC- and AC-Josephson effects. The current distribution has proven to be inhomogeneous and there exist small areas with high j~. The l c ( T ) data suggest that the order parameter A is reduced at the superconductor insulator interface. This may be the main reason for the low j~. in this type of ceramics.

Acknowledgements We want to thank Mr. Berchtold tbr b o n d i n g the samples. We are also grateful to Mr. Solaro for allowing us to use the laser equipment. This work was supported by the B u n d e s m i n i s t e r i u m flit Forschung und Technologie (file n u m b e r 13N5688). The au-

thors alone arc responsible i0t thc content. References [I ] P. ('haudhari, ,I. Mannhart, D. I)imos, ('.('. fsaci. J t t n . M.M. Oprysko and M. Scheuerman. Phys. Re~. Loll. 60 11988} 1653. 121 D. Dimos, P. Chaudhari, J. Mannhart and F,K. LcGoucs. Phys. Rev. Lett. 61 (1988) 219. [3] J. Mannhart, P. Chaudhari, D. Dimos, ('.C. Tsuel and I R McGuire, Phys. Rev. Lelt. 61 (1988) 2476. [4] S.E. Russek, D.K. Lathrop, B.H. Moeckly, R.A. Buhrman. D.H. Shin a n d J . Silcox, Appl. Phys. Lcn. 57 (1990) 1155. [ 5 ] P, Chaudhari, Proc. M2S-HTSC 111, Kanazawa, Japan, I ,~c)I. PhysicaC185-189(1991)292. [6] R i . Peterson and J,W. Ekin, Physica C 157 ( 1989 ) 325 [ 7 ] G . Schindler and B. Seebacher, VDI-Berichte Nr, 733 (1989) 381. [8] W.C. Steward, Appl. Phys. Lctt. 12 (1968) 277. [9] D.E. McCumber, J. Appl. Ph~rs. 39 11968) 311 ~. [ 10] A. Barone and G. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982 ). { 1 I ] P.G. De Gcnnes: Superconductivity of Metals and Mlo,vs { Benjamin, New York, 1966 ). [12] G. Deutscher, IBM J. Res. Develop. 33 (1989) 293. [ 13 ] G. Deutscher and K.A, Miiller, Phys. Rev. Left. 5'4 ( 19871 1745. [ 1 4 ] G . Deutscher, P h y s i c a ( 153-155 (1988) 15. [ 15 ] J. Mannhart and P. Martinoli, Appl. Phys. Lett. 58 I 1991 j 643. [ 16] V. Ambegaokar and A. Baratoff, Phys. Rex,. Lett. I0 11963 ) 486.: Erratum. ibid. Phys. Re',. Lcn. 11 (1963) 104. [ 1 7 ] S . Shapiro. A. Janus and S. Holly, Rev. Mod. Phys. 36 1964) 223.