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.
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.
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.
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.
Reproducible Josephson junction (JJ) characteristics are essential for frequency-deterministic and scalable superconducting quantum processors. We show that the normal-state resistance and its reproducibility in Al/AlOx/Al JJs are governed not by oxide thickness, but by fabrication-history–induced disorder in the tunneling barrier. By comparing junctions fabricated on bare wafers, lift-off–processed base layers, and dry-etched base layers under identical oxidation conditions, we observe large differences in resistance and wafer-to-wafer variability. Atomic force microscopy reveals distinct surface disorder imprinted by prior fabrication steps, while cross-sectional transmission electron microscopy show that the average AlOx barrier thickness is comparable across the three fabrication histories within experimental uncertainty. The enhanced resistance on rough, plasma-damaged surfaces therefore originates from nanoscale barrier disorder rather than thickness variations. These results establish fabrication history as a key determinant of JJ barrier quality and highlight the need for holistic process control to achieve deterministic qubit frequency targeting.
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 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.
Nb/Al-AlOx/Nb Josephson junctions are widely used in superconducting quantum interference devices and rapid single flux quantum (RSFQ) circuits. Very large-scale RSFQ integration often has a strict requirement on wafer-scale junction qualities. In particular, Nb film stress in Nb/Al-AlOx/Nb trilayer based Josephson junctions is a critical factor affecting their qualities. In this work, we develop a multi-step sputtering process to prepare Nb films with different combinations of stress and roughness to investigate the correlation between Nb film stress and junction quality. In particular, this method allows us to prepare Nb films with almost the same roughness but different stress, a key factor to study solely the influence of stress on junction qualities. Our measurements indicate that within a very tight range of film roughness (less than 2 nm), tensile film stress is found to decrease the quality of Nb/Al-AlOx/Nb Josephson junctions and larger film roughness has a positive effect on junction quality. By decreasing the total tensile stress and increasing the film roughness properly, we fabricated Nb/Al-AlOx/Nb Josephson junctions with a high quality factor characterized by Rsg/RN(30 on average). The minimum size of junctions was 1 μm.