Device variability of Josephson junctions induced by interface roughness

TL;DR

This paper models how interface roughness in Al/AlO_x/Al Josephson junctions causes variability in Josephson energy, impacting the performance consistency of superconducting qubits in quantum processors.

Contribution

It introduces a quantitative model linking interface roughness parameters to Josephson energy variability, validated through extensive numerical simulations.

Findings

Josephson energy follows a log-normal distribution due to roughness.

Mean Josephson energy increases with roughness amplitude.

Variance of Josephson energy increases with both roughness amplitude and correlation length.

Abstract

As quantum processors scale to large qubit numbers, device-to-device variability emerges as a critical challenge. Superconducting qubits are commonly realized using Al/AlO$_{\text{x}}$/Al Josephson junctions operating in the tunneling regime, where even minor variations in device geometry can lead to substantial performance fluctuations. In this work, we develop a quantitative model for the variability of the Josephson energy $E_{J}$ induced by interface roughness at the Al/AlO$_{\text{x}}$ interfaces. The roughness is modeled as a Gaussian random field characterized by two parameters: the root-mean-square roughness amplitude $\sigma $ and the transverse correlation length $\xi $. These parameters are extracted from the literature and molecular dynamics simulations. Quantum transport is treated using the Ambegaokar--Baratoff relation combined with a local thickness approximation. Numerical simulations over $5,000$ Josephson junctions show that $E_{J}$ follows a log-normal distribution. The mean value of $E_{J}$ increases with $\sigma $ and decreases slightly with $\xi $, while the variance of $E_{J}$ increases with both $\sigma $ and $\xi $. These results paint a quantitative and intuitive picture of Josephson energy variability induced by surface roughness, with direct relevance for junction design.