The Josephson energy EJ is a key parameter governing the properties of transmon superconducting qubits. In Al/AlOx/Al junctions, EJ is set by electron tunneling through an ultrathinoxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute EJ by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al2O3 barrier against ten junctions with melt–quenched amorphous Al2O3 barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar–Baratoff relation, we obtain a mean EJ/h of 2.78 GHz for the amorphous ensemble, with a standard deviation of 4.67 GHz, compared with 0.73 GHz for the crystalline reference; individual amorphous values span nearly two orders of magnitude. Scattering-state analysis shows that transport is quantum tunneling and that the variability originates from stoichiometric inhomogeneity of the amorphous oxide: Al-rich, low-barrier regions can connect into percolation-like tunneling pathways that strongly enhance the conductance. A realistic 200×200 nm2 junction self-averages over more than 2×104 such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale EJ.
Hydrogen contamination in Josephson junctions is a potential source of device-to-device variability and two-level-system loss in superconducting qubits. In this work, we investigatehydrogen incorporation in oxidized aluminum barriers by combining molecular dynamics simulations with atomistic quantum transport calculations. The oxide growth simulations are performed using CHGNet for Al surfaces exposed to dense O2 and H$_{\text{2}% }$O environments, yielding amorphous AlOx layers with hydrogen content comparable to experimentally relevant levels. From 400 statistically independent samples, we find that the number of H atoms in the oxide is well described by a beta-binomial distribution, reflecting correlations induced by the self-limiting oxidation process. Structural analysis shows that most hydrogen atoms reside near the AlOx surface and predominantly form Al-OH and Al-OH-Al motifs. To assess the impact of hydrogen on transport, we construct Al/Al2O3/Al junction models and perform NEGF-DFT calculations with NanoDCAL, using a GGA+U scheme to calibrate the band gap and band alignment. H atoms are found to increase the transmission coefficient near the Fermi level and shift the electronic structure in a manner consistent with effective p-type doping. By combining the H atom number statistics from molecular dynamics with the transmission coefficients from quantum transport calculations, we obtain a probability distribution for the Josephson energy. For a Josephson junction with an average hydrogen content of 2.56 at.\%, the resulting Josephson energy is predicted to be GHz. These results provide an atomistic picture of hydrogen contamination and an estimate of device variability in Josephson junctions.
As quantum processors scale to large qubit numbers, device-to-device variability emerges as a critical challenge. Superconducting qubits are commonly realized using Al/AlOx/Al Josephsonjunctions 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 EJ induced by interface roughness at the Al/AlOx 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 EJ follows a log-normal distribution. The mean value of EJ increases with σ and decreases slightly with ξ, while the variance of EJ 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.