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Applied Physics Letters

Geometric dependence of critical-current variation in Al/AlO x /Al Josephson junctions: A model-based analysis

Kosuke Kakuyanagi, N. Teran, Hiraku Toida, Shiro Saito

Published Jun 8, 2026• 0 citations
Publisher

Abstract

Achieving uniform critical current across Josephson junctions is essential for the large-scale integration of superconducting quantum circuits. In this work, we statistically analyzed the variation of the critical current of Al/AlOx/Al junctions using room-temperature tunnel resistance statistics and identified the dominant contribution among the modeled sources of the variation based on their dependence on geometry and deposition conditions of junctions. Our model-based analysis reveals that fluctuations in the Al film thickness play the dominant role among the modeled contributing factors. Based on this analysis, we found that, in Dolan-bridge double-angle deposition, adopting a deposition angle of 30° for bilayer junctions significantly improves uniformity, yielding a relative standard deviation of 1.2% (0.5%) across a 9.75 mm (1.5 mm) square region.

DOI
10.1063/5.0325097

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Achieving uniform critical current across Josephson junctions is essential for the large-scale integration of superconducting quantum circuits. In this work, we statistically analyzed the variation of the critical current of Al/AlOx/Al junctions using room-temperature tunnel resistance statistics and identified the dominant contribution among the modeled sources of the variation based on their dependence on geometry and deposition conditions of junctions. Our model-based analysis reveals that fluctuations in the Al film thickness play the dominant role among the modeled contributing factors. Based on this analysis, we found that, in Dolan-bridge double-angle deposition, adopting a deposition angle of 30° for bilayer junctions significantly improves uniformity, yielding a relative standard deviation of 1.2% (0.5%) across a 9.75 mm (1.5 mm) square region.
Geometric dependence of critical-current variation in Al/AlOx{\rm _x}x​/Al Josephson junctions: a model-based analysis
Achieving uniform critical current across Josephson junctions is essential for the large-scale integration of superconducting quantum circuits. In this work, we statistically analyzed the variation of the critical current of Al/AlOx{\rm _x}x​/Al junctions using room-temperature tunnel resistance statistics, and identified the dominant contribution among the modeled sources of the variation based on their dependence on geometry and deposition conditions of junctions. Our model-based analysis reveals that fluctuations in the Al film thickness play the dominant role among the modeled contributing factors. Based on this analysis, we found that, in Dolan-bridge double-angle deposition, adopting a deposition angle of 30-degree for bilayer junctions significantly improves uniformity, yielding a relative standard deviation of 1.2% (0.5%) across a 9.75 mm (1.5 mm) square region.
Josephson junctions (JJs) are critical components in superconducting quantum circuits, where their electrical properties directly determine qubit transition frequencies. While advances in fabrication have enabled precise control over junction area and oxide thickness, the influence of junction geometry beyond area has remained largely unexplored. Here, we report clear and reproducible evidence that the normal-state resistance (Rn) of JJs depends strongly on geometric parameters, demonstrating that (Rn) exhibits a systematic and reproducible dependence on junction geometry beyond simple area scaling. To account for this behavior, we introduce an edge-resistance model that incorporates perimeter-related contributions to (Rn). Our findings highlight the crucial role of geometric design in JJ electrical characteristics and provide a practical framework for improving frequency precision and uniformity in large-scale superconducting quantum processors.
Abstract The uniformity of Josephson-junction (JJ) characteristics is crucial in wafer-scale superconducting quantum-bit (qubit) integration. To achieve the level of accuracy demanded the circuits, every detail of the fabrication process needs to be optimized. Here we reveal that the junction-resistance (R N) variations of Al/AlO x /Al JJs are affected by the metal deposition on the sidewall of the resist mask during shadow evaporation. The effect is reproduced in numerical simulation using a simple model taking into account the resist structure and the evaporation angle. To overcome the issue, we introduce a two-step shadow evaporation method to reduce the variation of R N. As a result, the coefficient of variations across a 3-inch wafer decreases from 6.7% to 4.5%, achieving 1.1% in a chip with an area of 10 mm × 10 mm. This method is promising for developing large-scale superconducting quantum computers.
Abstract Josephson superconducting qubits and parametric amplifiers are prominent examples of superconducting quantum circuits that have shown rapid progress in recent years. As such devices become more complex, the requirements for reproducibility of their electrical properties across a chip are being tightened. Critical current of the Josephson junction Ic is the essential electrical parameter in a chip. So, its variation is to be minimized. According to the Ambegaokar–Baratoff formula, critical current is related to normal-state resistance, which can be measured at room temperature. In this study, we focused on the dominant source of non-uniformity for the Josephson junction critical current–junction area variation. We optimized Josephson junction fabrication process and demonstrated resistance variation of 9.8–4.4% and 4.8–2.3% across 22 × 22 mm2 and 5 × 10 mm2 chip areas, respectively. For a wide range of junction areas from 0.008 to 0.12 μm2, we ensure a small linewidth standard deviation of 4 nm measured over 4500 junctions with linear dimensions from 80 to 680 nm. We found that the dominate source of junction area variation limiting Ic{\mathrm{I}}_{\mathrm{c}}Ic​ I c reproducibility is the imperfection of the evaporation system. The developed fabrication process was tested on superconducting highly coherent transmon qubits (T1 > 100 μs) and a nonlinear asymmetric inductive element parametric amplifier.
Abstract Tantalum and aluminum on sapphire are widely used platforms for qubits of long coherent time. As quantum chips scale up, the number of Josephson junctions on Sapphire increases. Thus, both the uniformity and stability of the junctions are crucial to quantum devices, such as scalable superconducting quantum computer circuit, and quantum-limited amplifiers. By optimizing the fabrication process, especially, the conductive layer during the electron beam lithography process, Al/AlOx/Al junctions of sizes ranging from 0.0169 to 0.04 µm2 on sapphire substrates were prepared. The relative standard deviation of room temperature resistances (RN) of these junctions is better than 1.7% on 15 mm×15 mm chips, and better than 2.66% on 2 inch wafers, which is the highest uniformity on sapphire substrates has been reported. The junctions are robust and stable in resistances as temperature changes. The resistances increase by the ratio of 9.73% relative to RN as the temperature ramp down to 4K, and restore their initial values in the reverse process as the temperature ramps back to RT. After being stored in a nitrogen cabinet for 100 days, the resistance of the junctions changed by1.16% in average. The demonstration of uniform and stable Josephson junctions in large area paves the way for the fabrication of superconducting chip of hundreds of qubits on sapphire substrates.
Abstract Alumina Josephson junction has demonstrated a tremendous potential to realize superconducting qubits. Further progress towards scalable superconducting qubits urgently needs to be guided by novel analysis mechanisms or methods to reduce the thickness sensitivity of the junction critical current to the tunnel barrier. Here, it is first revealed that the termination mode of AlOx interface plays a crucial role in the uniformity of critical current, and we demonstrate that the O-terminated interface has the lowest resistance sensitivity to thickness. More impressively, we developed atomically structured three-dimensional models and calculated their transport properties using a combination of quantum ballistic transport theory with first-principles DFT and NEGF to examine the effects of the Al2O3 termination mode and thickness variations. This work clarifies that O-terminated interface can effectively improve the resistance uniformity of Josephson junction, offering useful guidance for increasing the yield of fixed-frequency multi-qubit quantum chips which require tight control on qubit frequency.