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Advanced Theory and Simulations

A COMSOL‐Based Study of the Electrical Transport Properties of Al/α$\alpha$‐Al2O3${\rm Al}_{2}{\rm O} _{3}$/Al Josephson Junctions

Jianing Liu, Yingying Li, Junling Qiu, Xuefei Feng, Kaizhe Fan

Published Mar 22, 2025• 0 citations
Publisher

Abstract

Abstract Superconducting Josephson junctions, as integral components of quantum circuits, are vital for the production of high‐quality, reproducible, and scalable quantum chips. The aluminum tunnel junctions is currently regarded as one of the most high‐performing and well‐established Josephson junctions for application in quantum devices. Nonetheless, the critical current of the junctions is highly sensitive to its thickness, which significantly influences both the tunneling effect and the electrical properties of the device. This study develops a numerical model of the 3D Al/‐/Al Josephson junction employing finite element analysis. At the nanometer scale of the junction, the Cooper pairs tunneling probability of the atomically resolved electrostatic potential as well as the WKB‐equivalent barrier height of the device is calculated. The results of the model reveal a channel effect that influences the critical current of the Josephson junctions, and it is found that the probability of particles tunneling varies with the thickness of the alumina film. The probability current density distribution near the junction for various barrier thicknesses is further investigated, simultaneously employing two tunneling probability calculation methods. Moreover, a 1D square potential barrier model is also established to elucidate the quantum tunneling effect, in which the amplitude of the wave function for tunneled particles diminishes as the thickness of the potential barrier increases.

DOI
10.1002/adts.202401315

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A COMSOL‐Based Study of the Electrical Transport Properties of Al/αα\alphaα‐Al2O3Al2O3{\rm Al}_{2}{\rm O} _{3}Al2​O3​/Al Josephson Junctions
Abstract Superconducting Josephson junctions, as integral components of quantum circuits, are vital for the production of high‐quality, reproducible, and scalable quantum chips. The aluminum tunnel junctions is currently regarded as one of the most high‐performing and well‐established Josephson junctions for application in quantum devices. Nonetheless, the critical current of the junctions is highly sensitive to its thickness, which significantly influences both the tunneling effect and the electrical properties of the device. This study develops a numerical model of the 3D Al/‐/Al Josephson junction employing finite element analysis. At the nanometer scale of the junction, the Cooper pairs tunneling probability of the atomically resolved electrostatic potential as well as the WKB‐equivalent barrier height of the device is calculated. The results of the model reveal a channel effect that influences the critical current of the Josephson junctions, and it is found that the probability of particles tunneling varies with the thickness of the alumina film. The probability current density distribution near the junction for various barrier thicknesses is further investigated, simultaneously employing two tunneling probability calculation methods. Moreover, a 1D square potential barrier model is also established to elucidate the quantum tunneling effect, in which the amplitude of the wave function for tunneled particles diminishes as the thickness of the potential barrier increases.
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.
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.
Abstract Alumina Josephson junction has demonstrated a tremendous potential to realize superconducting qubits. Further progress towards scalable superconducting qubits urgently needs to be guided by novel analysis mechanisms or methods to reduce the thickness sensitivity of the junction critical current to the tunnel barrier. Here, it is first revealed that the termination mode of AlOx interface plays a crucial role in the uniformity of critical current, and we demonstrate that the O-terminated interface has the lowest resistance sensitivity to thickness. More impressively, we developed atomically structured three-dimensional models and calculated their transport properties using a combination of quantum ballistic transport theory with first-principles DFT and NEGF to examine the effects of the Al2O3 termination mode and thickness variations. This work clarifies that O-terminated interface can effectively improve the resistance uniformity of Josephson junction, offering useful guidance for increasing the yield of fixed-frequency multi-qubit quantum chips which require tight control on qubit frequency.
Defects at the interfaces in the Josephson junction (JJ) are well known as a primary source of decoherence in superconducting quantum devices, indicating the necessity of elucidating defect reaction mechanisms to improve qubit performance. However, their micromechanism remains elusive. Here, we reveal the micromechanism of defects affecting the transport properties by building interfacial defective JJ device models combined with density functional theory (DFT) and nonequilibrium Green’s function (NEGF) approach. By comparing the conductance values of various interface classification models with oxygen vacancies (OVs), we find that the aluminum-rich (Al-rich) interface exhibits the smallest conductance variation, resulting in less qubit frequency fluctuations, and this can be further explained by changes in the electrostatic potential relative to the average barrier height. More importantly, the Al-rich interface demonstrates the highest stability. This work provides a theoretical basis and optimization direction for superconducting quantum chip fabrication.
An ultra-thin aluminum oxide layer is a key component for Josephson junctions (JJ) in superconducting quantum bits (qubits). This layer serves as a barrier layer for Cooper pairs tunneling between the superconducting electrodes and significantly influences the overall performance of the junction. In this study, we investigate the impact of aluminum deposition rates on the microstructure and chemical variation of the aluminum oxide layer, as well as the device’s yields and qubits’ lifetimes. Surprisingly, although the oxide layer roughness and thickness variation improve noticeably with an increasing Al deposition rate from 0.5 Å/s to 5 Å/s, the qubit’s coherence time is almost unchanged. We attribute this to the fact that Cooper pairs tunnel only through the thinnest region of the barrier. Additionally, we revealed a stress-induced grain boundary sliding short-circuit failure mechanism in the JJ. Our discovery provides a vital understanding of oxide microstructure and JJ functionality, which are critical for improving the coherence time of superconducting qubits.
The Josephson energy EJE_JEJ​ is a key parameter governing the properties of transmon superconducting qubits. In Al/AlOx_xx​/Al junctions, EJE_JEJ​ is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute EJE_JEJ​ by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al2_22​O3_33​ barrier against ten junctions with melt--quenched amorphous Al2_22​O3_33​ barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar--Baratoff relation, we obtain a mean EJ/hE_J/hEJ​/h of 2.782.782.78 GHz for the amorphous ensemble, with a standard deviation of 4.674.674.67 GHz, compared with 0.730.730.73 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 200×200200\times200200×200 nm2^22 junction self-averages over more than 2×1042\times10^42×104 such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale EJE_JEJ​.