Hydrogen contamination in Josephson junctions may contribute to device-to-device variability in superconducting qubits, yet its incorporation, location, and bonding in tunnel barriers remain poorly understood. We combine molecular dynamics simulations of aluminum oxidation in dense O2 and H2O environments with atomistic quantum transport calculations. The simulations produce amorphous AlOx barriers with experimentally relevant hydrogen concentrations. Analysis of 400 statistically independent samples shows that the number of incorporated H atoms follows a beta-binomial distribution, reflecting correlations arising from self-limiting oxidation. Most H atoms reside near the AlOx surface, primarily in Al-OH and Al-OH-Al motifs. Quantum transport calculations for Al/Al2O3/Al junctions reveal that hydrogen enhances transmission near the Fermi level by creating an interface dipole that shifts the oxide bands relative to the electrode Fermi level. Combining hydrogen-number statistics with calculated transmission coefficients yields a probability distribution for the Josephson energy. At an average hydrogen content of 2.56 at.%, we predict E_J/h = 10.23 GHz with a standard deviation of 3.6 MHz. Hydrogen shifts the mean Josephson energy by approximately 11%, proportionally to its concentration, but contributes far less to device-to-device variability than observed in state-of-the-art fabricated junctions. These findings provide an atomistic understanding of hydrogen incorporation and its impact on Josephson energy.
Hydrogen contamination in Josephson junctions may contribute to device-to-device variability in superconducting qubits, yet its incorporation, location, and bonding in tunnel barriers remain poorly understood. We combine molecular dynamics simulations of aluminum oxidation in dense O2 and H2O environments with atomistic quantum transport calculations. The simulations produce amorphous AlOx barriers with experimentally relevant hydrogen concentrations. Analysis of 400 statistically independent samples shows that the number of incorporated H atoms follows a beta-binomial distribution, reflecting correlations arising from self-limiting oxidation. Most H atoms reside near the AlOx surface, primarily in Al-OH and Al-OH-Al motifs. Quantum transport calculations for Al/Al2O3/Al junctions reveal that hydrogen enhances transmission near the Fermi level by creating an interface dipole that shifts the oxide bands relative to the electrode Fermi level. Combining hydrogen-number statistics with calculated transmission coefficients yields a probability distribution for the Josephson energy. At an average hydrogen content of 2.56 at.%, we predict E_J/h = 10.23 GHz with a standard deviation of 3.6 MHz. Hydrogen shifts the mean Josephson energy by approximately 11%, proportionally to its concentration, but contributes far less to device-to-device variability than observed in state-of-the-art fabricated junctions. These findings provide an atomistic understanding of hydrogen incorporation and its impact on Josephson energy.
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 ultrathin oxide 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.
Josephson junctions are the key components used in superconducting qubits for quantum computing. The advancement of quantum computing is limited by a lack of stability and reproducibility of qubits, which ultimately originates in the amorphous tunnel barrier of the Josephson junctions and other material imperfections. Pinholes in the junction have been suggested as one of the possible contributors to these instabilities, but evidence of their existence and the effect they might have on transport is unclear. We use molecular dynamics to create three-dimensional atomistic models to describe $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{AlO}}_{x}\text{\ensuremath{-}}\mathrm{Al}$ tunnel junctions, showing that pinholes form when oxidation of the barrier is incomplete. Following this, we use the atomistic model and simulate the electronic transport properties for tunnel junctions with different barrier thicknesses using the nonequilibrium Green's function formalism. We observe that pinholes may contribute to excess quasiparticle current flow in $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{AlO}}_{x}\text{\ensuremath{-}}\mathrm{Al}$ tunnel junctions with thinner barriers, and in thicker barriers we observe weak-points that facilitate leakage currents even when the oxide is continuous. We find that the disordered nature of the amorphous barrier results in significant variations in the transport properties. Additionally, we determine the current-phase relationship for our atomistic structures, confirming that devices with pinholes and weak-points cause a deviation from the ideal sinusoidal Josephson relationship.
The aluminum oxide tunnel junction is a key component of the majority of superconducting quantum devices. For high-quality, reproducible, and scalably manufacturable qubits, the ability to fabricate Josephson junctions (JJs) with a targeted critical current and high uniformity is essential. We use first-principles modeling to assess fundamental aspects of the atomic structure of both amorphous and crystalline aluminum oxide tunnel junctions and relate the structure to predicted performance metrics. We use modified ab initio molecular dynamics to develop realistic models of the tunnel junction, from which interface roughness and local thickness fluctuations are analyzed in an unbiased manner by training a neural network to identify the boundary between metal and oxide. We show that the effective thickness of the insulating part of the junction can be different from the apparent physical thickness. We calculate the rate of Cooper pair tunneling for the atomically resolved electrostatic potential using direct numerical solution in 3D, which shows a channeling effect that impacts the junction critical current. The predicted critical current is a useful JJ design parameter that can be accessed from the ab initio calculations without fitting parameters. To assess the limits of uniformity and fabrication choices (e.g., oxidation vs epitaxy), we compare the amorphous junctions to crystalline models, which show order of magnitude more efficient tunneling compared to the amorphous case, underlining the connection between atomistic structure and Cooper pair tunneling efficiency. Further, this work provides a foundation for ab initio materials design and evaluation to help accelerate future development of improved tunnel 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 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 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.
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 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 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 5000 Josephson junctions show that EJ follows a lognormal 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.
Al/AlOx/Al Josephson junctions are the building blocks of a wide range of superconducting quantum devices that are key elements for quantum computers, extremely sensitive magnetometers and radiation detectors. The properties of the junctions and the superconducting quantum devices are determined by the atomic structure of the tunnel barrier. The nanoscale dimension and disordered nature of the barrier oxide have been challenges for the direct experimental investigation of the atomic structure of the tunnel barrier. Here we show that the miniaturized dimension of the barrier and the interfacial interaction between crystalline Al and amorphous AlOx give rise to oxygen deficiency at the metal/oxide interfaces. In the interior of the barrier, the oxide resembles the atomic structure of bulk aluminium oxide. Atomic defects such as oxygen vacancies at the interfaces can be the origin of the two-level systems and contribute to decoherence and noise in superconducting quantum circuits.