Device variability of Josephson junctions induced by interface roughness

TL;DR

This work addresses the problem of device-to-device variability in the Josephson energy $E_J$ of Al/AlO$_x$/Al junctions caused by interface roughness. It introduces a quantitative framework that combines a Gaussian random-field model of interface roughness with a local-thickness quantum-transport approach, using the Ambegaokar-Baratoff relation to relate $I_c$ and $R_N$ and validating this against BdG calculations. The study finds that $E_J$ follows a log-normal distribution across junction ensembles, with its mean increasing with roughness amplitude $\sigma$ and its variance growing with both $\sigma$ and the transverse correlation length $\xi$; increasing $\xi$ reduces self-averaging, leading to larger fluctuations. The results provide a quantitative link between microstructural disorder and qubit-relevant energy scales, offering design guidance for junctions and motivating integration with circuit-level microwave engineering for scalable superconducting quantum processors.

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 $σ$ and the transverse correlation length $ξ$. 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 $σ$ and decreases slightly with $ξ$, while the variance of $E_{J}$ increases with both $σ$ and $ξ$. These results paint a quantitative and intuitive picture of Josephson energy variability induced by surface roughness, with direct relevance for junction design.

Figures (3)

• Figure 1: MD simulation of AlO$_{\text{x}}$ growth. (a) At $t=0$, fcc(100) Al surface and O$_{\text{2}}$ molecules. (b) At $t=3$ ps, oxidized Al surface and O$_{\text{2}}$ molecules. (c) AlO$_{\text{x}}$ layer extracted from (b).
• Figure 2: Josephson energy (log scale) as a function tunnel barrier width, calculated by solving the BdG equation and using the AB relation.
• Figure 3: (a) and (b): Colormaps of Al/AlO$_{\text{x}}$ interface roughness. (c): Histogram of $E_{J}$ over $5,000$ Josephson junctions. The orange line is a fit to Eq. \ref{['eq10']}.