PHYSICAL REVIEW B VOLUME 50, NUMBER 13 1 OCTOBER 1994-1I Evidence for parallel junctions within high- Tc grain-boundary junctions E. A. Early, R. L. Steiner, and A. F. Clark NationalInstitute of Standardsand Technology, MET B-258,Gaithersburg, Maryland20899 K. Char Conductus, Inc., 969 West Maude Avenue, Sunnyvale, California 94086 (Received 15 September 1993; revised manuscript received 11 April 1994) Half-integral constant voltage steps were observed in many high- Tc grain-boundary Josephson junc- tions of YBa2Cu307-li when a microwave field was applied. Five distinct observed behaviors of the widths of both integral and half-integral steps as a function of microwave amplitude, /11 de(l ae)' are reproduced by simulations of two or three junctions in parallel. This provides quantitative evidence that a single high- Tc grain-boundary junction is composed of several junctions in parallel. These junctions are formed by the overlap of superconducting filaments on either side of the grain boundary, and the spacing between ones with relatively large critical currents is - 20 pm. I. INTRODUCTION We present experimental results on half-integral con- stant voltage steps in high- Tc grain-boundary junctions. Quantitative comparisons between these results and those obtained by simulations of parallel arrays of junctions en- able us to draw conclusions about the microstructure of high-Tc grain-boundary junctions. One common method for making Josephson junctions in high- Tc materials is to isolate individual grain boun- daries. 1- 3 There is accumulating evidence that these grain-boundary junctions are inhomogeneous on a micro- scopic scale. Early results on the magnetic-field depen- dence of the critical current of such junctions showed a complicated behavior,I,4,s and one particular behavior was well described by assuming a spatially nonuniform junction.6 A residual critical current even at high mag- netic fieldss-9 has been taken as evidence that a grain- boundary junction is composed of a parallel array of junctions. Measurements of 1/ f noise are also well de- scribed by assuming that there are a number of parallel normal and superconducting connections across a grain boundary. 10,11 Finally, recent electromigration experi- ments indicate that superconductivity within the bulk film and across a grain boundary is filamentary. 12 Recently, we observed unusual half-integral constant voltage steps in high-Tc YBa2Cu307-S grain-boundary junctions.13 A typical current-voltage (l- Y) curve for such a junction at 4.2 K irradiated with microwaves at a frequency v~9. 3 GHz is shown in Fig. 1. Note that the curve is symmetric about the origin. To understand this curve, first consider the usual ac Josephson effect.14 Sub- jecting a junction to an ac field causes constant voltage steps, also called Shapiro steps, IS to appear in the 1-V curve. The voltages, V, of these steps are given by V=nv/KJ , where n is the frequency of the ac field, KJ =2e /h =0.4835979 GHz/JLV is the Josephson con- 0163-1829/94/50( 13)/9409( 10)/$06.00 stant, and n is an integer. Thus, these steps are termed integral steps. For the case shown in Fig. 1, at v~9.3 GHz integral steps occur at V ~n .20 JLVand are labeled accordingly for positive current polarity. The n = 0 step is along the current axis. In addition to these steps, there are distinct steps with voltages given by half-integral n, e.g., with n = t,.h t, etc. These are labeled for negative current polarity and are termed half-integral steps. The concept of step width is important for understand- ing the results presented in this paper. The step width dI de is simply the range of dc current over which the voltage of a step is constant. Thus, for example, the step width of the n = 2 step shown in Fig. 1 is approximately 35 JLA. The step width is a function of the applied mi- crowave power, and at the microwave power at which the curve in Fig. 1 was obtained, the n = t step is absent. We have previously proposed that half-integral steps are a result of a single grain-boundary junction actually being composed of many junctions in parallel. 13 We present here more extensive experimental results of the 20 ~v ! - 56.3 J.1.A FIG. 1. Current-voltage curve of a 50-pm-wide junction at 4.2 K in a microwave field of 9.3 GHz. Both integral and half- integral steps are indicated by arrows and indexed by n. 50 @ 1994 The American Physical Society 9409 --- --- - -- --p- --- --