^{1,2,3,a)}and Denis Amparo

^{2,b)}

### Abstract

The effect of dc electrical stress and breakdown on Josephson and quasiparticle tunneling in junctions with ultrathin barriers typical for applications in superconductor digital electronics has been investigated. The junctions’ conductance at room temperature and current-voltage characteristics at 4.2 K have been measured after the consecutive stressing of the tunnel barrier at room temperature. Electrical stress was applied using current ramps with increasing amplitude ranging from 0 to corresponding to voltages across the barrier up to , where is the Josephsoncritical current. A very soft breakdown has been observed with polarity-dependent breakdowncurrent (voltage). As the stressing progresses, a dramatic increase in subgap conductance of the junctions, the appearance of subharmonic current steps, and a gradual increase in both the critical and the excess currents as well as a decrease in the normal-state resistance have been observed. The observed changes in superconductingtunneling suggest a model in which a progressively increasing number of defects and associated additional conduction channels [superconducting quantum point contacts (SQPCs)] are induced by electric field in the tunnel barrier. By comparing the characteristics of these conduction channels with the nonstationary theory of current transport in SQPCs based on multiple Andreev reflections by Averin and Bardas, the typical transparency of the induced SQPCs was estimated as . The number of induced SQPCs was found to grow with voltage across the barrier as with , in good agreement with the proposed model of defect formation by ion electromigration. The observed polarity dependence of the breakdowncurrent (voltage) is also consistent with the model. Based on the observed magnitude of breakdowncurrents,electric breakdown of barrier during plasma processing was considered to be an unlikely cause of fabrication-induced, circuit pattern-dependent nonuniformities of Josephson junctions’ critical currents in superconductor integrated circuits.

We would like to thank Daniel Yohannes, Richard Hunt, and John Vivalda for their part in wafer processing. Many discussions with Alex Kirichenko, Timur Filippov, Vasili Semenov, and Dmitri Averin are highly appreciated. We would also like to thank D. Averin for providing the program for calculating the theoretical curves shown in Fig. 6. We are also grateful to Deborah Van Vechten for her interest and support in this research. This work was supported by the ONR Grant Nos. N000140810224 and N000140710093.

I. INTRODUCTION

II. FABRICATION

III. EXPERIMENT

IV. EXPERIMENTAL RESULTS

V. DISCUSSION

VI. CONCLUSION

### Key Topics

- Josephson junctions
- 86.0
- Niobium
- 44.0
- Electric currents
- 31.0
- Josephson effect
- 22.0
- Electrical breakdown
- 18.0

## Figures

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).

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.

(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.

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).

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 .

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 .

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.

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 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 .

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.

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.

## Tables

Summary of initial resistances, initial critical current, and breakdown stress current for the samples shown in Fig. 1

Summary of initial resistances, initial critical current, and breakdown stress current for the samples shown in Fig. 1

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