Junction resistance at room temperature after electrical stressing of the junctions in Table I; indicates positive/negative stress polarity. Despite small differences between individual junctions, the stress-induced irreversible resistance changes are very similar as demonstrated in the inset showing the normalized resistance at room temperature as a function of normalized stress current for the same junctions (see Table I).
(a) characteristics of junction at (initial ) after each application of electrical stress shows increasing , decreasing , increasing subgap conductance, and increasing excess current. The gap voltage and the current step at remain almost unaffected by electric stress in the wide range of stress currents from 0 up to . At higher stress currents the gap structure broadens and diminishes, and at the junction loses all remaining signatures of the tunnel junction. Numbers in the legend indicate the applied positive stress current in milliamperes and identify the curves from top to bottom. (b) Blow up of the return branches of curves of KL1004N5N6 after each stress application clearly shows the development of current steps (subgap structure) at subharmonics of the gap voltage.
product (left scale, dotted lines) and at 2 mV (right scale, solid lines) values after each stress application, normalized to their initial values and in the unstressed junctions. Parameters of the junctions are given in Table I.
A comparison of the curve of a stressed junction KL1023N5P8 (top dashed curve) with poststress Josephson critical current density (initial ) and an as-fabricated, unstressed junction KL1013N1P1 (solid curve) with . Although the as-fabricated junction has an even larger (larger average barrier transparency), its curve is very different from the electrically stressed junction: it has no appreciable subgap conductance, no subharmonic current steps, and no excess current; its product and the current step at are close to the values given by the microscopic theory for tunnel junctions with low transparency. Presumably, the as-fabricated junctions have a uniform tunnel barrier whereas the barrier in electrically stressed junctions becomes nonuniform. The curve of the initial, unstressed junction KL1023N5P8 is also shown (dotted curve).
The return branch of the characteristic (dotted curve) of KL1004N5N6 after application of 80 mA stress along with differential conductance (solid curve) showing peaks corresponding to MARs of quasiparticles. The inset shows the voltages corresponding to conductance peaks; the straight line is a fit to dependence expected for MARs, giving .
Normalized characteristics of the additional conduction channels (SQPCs) created by positive electric stressing at currents . The curves were obtained by subtracting the characteristics of the initial, unstressed junction from the curve after each stress application, . The dip at in the curves is an artifact of the subtraction procedure due to some broadening and slight decrease in the gap after electric stressing. Theoretical curves for a single SQPC with varying transparency (bottom to top) from Ref. 40 are also shown. As can be seen, all the obtained experimental dependences fall within the range of theoretical curves corresponding to .
Circuit diagram of the proposed model. In this model, the application of electrical stress results in the formation of few additional conduction channels in the tunnel barrier which remains largely unchanged and is assumed to be the same as the initial, unstressed junction.
The change in critical current and excess current caused by electric stressing as a function of the change in the normal-state conductance (bottom scale) and the number of created channels (top scale) based on . The straight line is the linear fit giving the average per channel of and .
The number of created channels (assuming ) vs the maximum applied stress voltage. The solid curve is the fit to Eq. (5) yielding . This is very close to the calculated value of .
curve of an as-fabricated 20-junction series array. Two junctions with significantly higher than the rest of the array are shown by arrows. Whereas the characteristics of these two junctions are qualitatively similar to those of the electrically stressed junctions in this study, the amount of electric current that is required to damage the stressed junctions  cannot be supplied by the plasma processes employed during the fabrication. Hence, this fabrication-induced variation in in this array is unlikely to be caused by electron current-induced breakdown of the tunnel barriers.
Summary of initial resistances, initial critical current, and breakdown stress current for the samples shown in Fig. 1
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