^{1,2,a)}, Michio Watanabe

^{3}and Jaw-Shen Tsai

^{2,3,4}

### Abstract

We have studied low-temperature electrical transport properties of nanoscale and Josephson junctions (JJs) fabricated by focused-ion-beam(FIB)milling. This FIBfabrication process yields high-quality JJs whose superconducting gap energy agrees with the bulk value. In this paper, we report the improvement in the precision of the fabrication technology by employing a weaker ion beam current and by introducing a step of -gas-assisted milling, which allowed us to reduce the anodization voltage. For Nb JJs, we measured the current-voltage characteristics of single-electron transistors (SETs) and examined the current observed within the superconducting energy gap. At finite voltages, we observed current peaks due to the Josephson-quasiparticle (JQP) cycle. Based on the JQP-peak positions, we estimated the charging energy of the SETs. For all SETs, is larger than , which is consistent with junctions. We also analyzed the superconductingcritical current at zero voltage. The ratio depended on the junction size, where is the measured critical current and is the theoretical one. The curves of NbN single Josephson junctions also depended on the junction size, and they were qualitatively different, especially around the energy gap. We will discuss the possible origins for the junction-size dependence.

The authors are grateful to Y. Nakamura for across-the-board assistance including constructive comments, to Y. Kitagawa for preparation of the Nb trilayer, to Z. Wang for providing the trilayer and for discussion, to M. Ishida for assistance with the FIB system, to T. Yamamoto for assistance with the cryostat, to H. Akaike for valuable comments on anodization, and to K. Inomata and T. Miyazaki for discussion.

I. INTRODUCTION

II. EXPERIMENT

A. Fabrication process

B. Measurement condition

III. RESULTS AND DISCUSSION

A. Niobiumjunctions

B. Niobium-nitride junctions

IV. CONCLUSION

### Key Topics

- Niobium
- 81.0
- Josephson junctions
- 58.0
- Milling
- 24.0
- Focused ion beam technology
- 20.0
- Superconductivity
- 15.0

## Figures

Fabrication of SETs by FIB milling. (A1) After photolithography. (A2) Side view of (A1). (B) Carbon deposition. (C) Milling from 0°. (D1) Side view of dotted circle in (D2). (D2) Milling from 85°.

Fabrication of SETs by FIB milling. (A1) After photolithography. (A2) Side view of (A1). (B) Carbon deposition. (C) Milling from 0°. (D1) Side view of dotted circle in (D2). (D2) Milling from 85°.

SET fabricated by FIB milling. (A) FIB secondary-electron image taken from the direction perpendicular to the substrate. (B) FIB secondary-electron image taken from the direction indicated by the arrow in (A). (C) Scanning electron microscope image. The substrate was tilted by 30°.

SET fabricated by FIB milling. (A) FIB secondary-electron image taken from the direction perpendicular to the substrate. (B) FIB secondary-electron image taken from the direction indicated by the arrow in (A). (C) Scanning electron microscope image. The substrate was tilted by 30°.

Anodization. (A) Schematic diagram. (B) Scanning electron micrograph of an anodized Nb SET.

Anodization. (A) Schematic diagram. (B) Scanning electron micrograph of an anodized Nb SET.

Current-voltage characteristics of Nb-SJJ1 (see Table I). The curve can be divided into three parts: (A) supercurrent, (B) superconducting gap, and (C) quasiparticle current.

Current-voltage characteristics of Nb-SJJ1 (see Table I). The curve can be divided into three parts: (A) supercurrent, (B) superconducting gap, and (C) quasiparticle current.

(A) Current-voltage characteristics (upper data set) and the differential resistance vs bias voltage (lower data set) of Nb-SET1. (B) Enlarged part of the dotted circle in (A). JQP peaks are in the two encircled fields.

(A) Current-voltage characteristics (upper data set) and the differential resistance vs bias voltage (lower data set) of Nb-SET1. (B) Enlarged part of the dotted circle in (A). JQP peaks are in the two encircled fields.

Diamonds of JQP-peak positions in the superconducting state at . Lower data set: Current vs gate voltage at (dotted line in the upper data set of Fig. 6), where is the bias voltage. Upper data set: JQP peak current positions on the plane.

Diamonds of JQP-peak positions in the superconducting state at . Lower data set: Current vs gate voltage at (dotted line in the upper data set of Fig. 6), where is the bias voltage. Upper data set: JQP peak current positions on the plane.

(A) Electrostatic energy [ in Eqs. (4) and (5), in units of the single-electron charging energy ] of the charge states of a SET for a given number of extra electrons in the island, plotted as a function of the normalized gate charge . The solid curves are parabolas of the lowest even- states, and the dashed curves are parabolas of the lowest odd- states when in Eq. (5). (B) Theoretical gate modulation of the normalized critical current of the SET in the superconducting state. The solid curve is for the case that the period of dependence is 2 ( periodic), and the dashed curve is for the case that the period is 1 ( periodic). For both (A) and (B), was used for the calculations. (C) Measured critical current of Nb-SET1 at as a function of the gate voltage.

(A) Electrostatic energy [ in Eqs. (4) and (5), in units of the single-electron charging energy ] of the charge states of a SET for a given number of extra electrons in the island, plotted as a function of the normalized gate charge . The solid curves are parabolas of the lowest even- states, and the dashed curves are parabolas of the lowest odd- states when in Eq. (5). (B) Theoretical gate modulation of the normalized critical current of the SET in the superconducting state. The solid curve is for the case that the period of dependence is 2 ( periodic), and the dashed curve is for the case that the period is 1 ( periodic). For both (A) and (B), was used for the calculations. (C) Measured critical current of Nb-SET1 at as a function of the gate voltage.

Current-voltage characteristics of single junctions at . (A) NbN-SJJ1, estimated junction area is . (B) NbN-SJJ2, .

Current-voltage characteristics of single junctions at . (A) NbN-SJJ1, estimated junction area is . (B) NbN-SJJ2, .

## Tables

List of samples. SJJ and SET represent SJJ and SET, respectively; is the measurement temperature; is the normal-state resistance; is the measured superconducting gap energy; for SJJ and for SET is the estimated junction area, where is the critical current density and we assumed for Nb junctions and for NbN junctions; is the measured critical current; for SJJ and for SET is the estimated Josephson energy, where is the flux quantum; is the Boltzmann constant; is the single-electron charging energy estimated from the positions of JQP peaks (see Fig. 6); for both SJJ and SET is the theoretical maximum of the critical current; is the ratio of the theoretical maximum to when dependence of has a period of 1 ( periodic), where is the normalized gate charge.

List of samples. SJJ and SET represent SJJ and SET, respectively; is the measurement temperature; is the normal-state resistance; is the measured superconducting gap energy; for SJJ and for SET is the estimated junction area, where is the critical current density and we assumed for Nb junctions and for NbN junctions; is the measured critical current; for SJJ and for SET is the estimated Josephson energy, where is the flux quantum; is the Boltzmann constant; is the single-electron charging energy estimated from the positions of JQP peaks (see Fig. 6); for both SJJ and SET is the theoretical maximum of the critical current; is the ratio of the theoretical maximum to when dependence of has a period of 1 ( periodic), where is the normalized gate charge.

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