Probing Coordination Environments in Buried Oxides of Aluminum Josephson Junctions by Resonant X-ray Reflectivity

Abstract

Decoherence remains a critical obstacle to achieving high-fidelity, scalable superconducting qubits, with the tunnel barrier of Josephson junctions a key source of loss. Here we apply resonant X-ray reflectivity to non-destructively probe the electronic structure of buried layers in Al/AlO$_x$/Al Josephson junctions. At the Al $K$-edge, energy-dependent modulations in the reflectivity maps enable Kramers-Kronig-constrained extraction of the layer-resolved atomic scattering factors. The analysis reveals that the barrier coordination evolves from more tetrahedral toward predominantly octahedral character with increasing oxidation pressure. At the interfaces, the lower metal-oxide boundary is comparatively under-coordinated and disordered relative to the upper interface. Comparison with simulated X-ray absorption spectra identifies the dominant coordination motifs within the oxide and its interfaces, providing depth-resolved structural insight that constrains microscopic models of two-level system formation. These results link growth conditions, local coordination environments, and junction electronic properties, demonstrating resonant X-ray reflectivity as a powerful tool for probing the microscopic materials properties of Josephson junctions and providing a materials-level framework for mitigating decoherence in superconducting qubits.

Figures (5)

• Figure 1: Probing buried oxides in Al/AlO$_x$/Al Josephson junctions with resonant X-ray reflectivity.(a) False-colored SEM image of a typical Josephson junction with the top electrode in purple and base electrode in red. (b) Cross-sectional TEM image of an Al/AlO$_x$/Al junction which clearly resolves the ultrathin AlO$_x$ tunnel barrier between the Al electrodes. (c) Schematic of the resonant X-ray reflectivity (RXR) geometry, where the specular reflectivity is measured under the condition $\theta_{in} = \theta_{out}$. The layer schematic shown in the figure was used for fitting XRR data. See main text for details. (d) Simulated Al/AlO$_x$/Al junction highlighting the amorphous nature of the junction and disorder at the interfaces. (e) Calculated Al $K$-edge X-ray absorption near edge spectra from the Materials Project Zheng2018Mathew2018Horton2025 for metallic Al (mp-134, fcc), monoclinic Al$_2$O$_3$ (mp-7048, C2/m) with mixed tetrahedral and octahedral Al coordination, and $\alpha-$Al$_2$O$_3$ (mp-1143, corundum, R-3c) with purely octahedral Al coordination. The metallic Al spectrum exhibits a broad, featureless near-edge profile, while both oxide phases show sharper absorption features reflecting the localized Al–O bonding environments, with the monoclinic phase displaying additional spectral complexity due to its inequivalent Al sites. (f)$q_z$ line cuts at fixed photon energies demonstrate that the Kiessig fringe periodicity evolves across the Al $K$-edge, with longer-wavelength oscillations at 1568eV (red, purple in (e)) relative to 1560eV (black in (e)), consistent with resonant modulation of the anomalous scattering factors. Rough estimation of the envelope width in $q$ gives a junction thickness $d$ of 1.6nm.
• Figure 2: Extracting the electronic structure in buried Al/AlO$_x$/Al Josephson junctions via variational fitting of RXR maps.(a) Al $K$-edge RXR map for sample B, showing reflectivity attenuation near $\sim$ 1568 and 1574eV that fingerprints the local electronic environment. The colorbar ranges from low (L) to high (H) intensity. (b) An energy-dependent line cut at $q_z = 0.19\AA^{-1}$ reveals a pronounced dip in specular reflectivity near $\sim$ 1570eV arising from absorption driven by the imaginary scattering factor $f_2$. Al $K$-edge TEY XAS spectrum exhibiting lineshape characteristics predominantly consistent with metallic aluminum. The dip lines up with the peak in XAS. (c) Energy-dependent line cuts at fixed $q_z$ reveal a pronounced peak in specular reflectivity near $\sim$ 1570eV shifting in energy with $q_z$, arising from constructive interference driven by modulation of the real scattering factor $f_1$. (d) Atomic scattering factors $f_{1,2}$ for Al$_2$O$_3$ derived from experimental TEY XAS; triangle basis functions used to parameterize $f_2$ are also shown in the inset. The atomic scattering factors are expressed in units of electrons because they quantify the scattering strength of a multi-electron system relative to that of a single free electron. (e) Simulated RXR map following variational refinement, capturing the reflectivity suppression at 1568eV and 1574eV. (f) Refined $f_2$ spectrum, compared to the $f_2$ derived from XAS, for the buried junction layer obtained from variational fitting, revealing distinct spectral features at energies corresponding to the observed reflectivity minima corresponding to an octahedral coordination environment.
• Figure 3: Resolving the buried interface electronic structure in Al/AlO$_x$/Al Josephson junctions.(a) Interface structure of the AlO$_x$ barrier layer from TEM. The lower metal–oxide interface forms by oxidation of the base Al layer and is characteristically oxygen-deficient, while the upper interface is formed during Al deposition onto the completed oxide and results in structurally and chemically distinct interfaces. (b)$f_2(E)$ for the lower interface, the junction, and the upper interface. The upper interface shows a dominant 6-fold coordination environment while the lower interface shows less apparent structure due to structural disorder and higher Al content. (c) Simulated XAS spectra for Al with differing coordination number. As the coordination increases the main peak shifts towards higher energy and splits into two.(d)$f_1(E)$ for the lower interface, the junction, and the upper interface (same color map as b). The upper interface shows a high effective electron density near 1568eV where the lower interface shows low effective electron density near 1560eV as large variations in $f_2$ drive correspondingly large changes in $f_1$ through KK relations. Curves are offset by a constant amount for visual clarity. (e) Coordination environment analysis for bulk and interfacial AlO$_x$ in simulated Josephson junctions. The interface exhibits a broad distribution of local coordination environments spanning 1- to 6-fold, whereas the bulk is confined predominantly to 4- to 6-fold sites. The curves are the probability distribution function from the histograms. (f) First-principles derived snapshots of different regions in the AlO$_x$ junction. Tetrahedral, trigonal bipyramidal, octahedral (4,5,6) environments are highlighted.
• Figure 4: Growth-dependent electronic structure of Al/AlO$_x$/Al Josephson junctions probed by Al $K$-edge RXR.(a) Non-resonant XRR measured below the Al $K$-edge with the corresponding structural fit for sample A, B, and C. (b) Al $K$-edge RXR maps across the junction growth series. With increasing O$_2$ pressure, the reflectivity exhibits enhanced attenuation near $\sim$1568eV and a suppression of the feature around $\sim$1577eV, indicating systematic changes in the local electronic environment. (c) Difference maps between samples B - A as well and B - C highlight pronounced energy-dependent modulations, reflecting variations in the electronic structure and coordination of the buried oxide layer as well as structural parameters. (d) The extracted $f_2(E)$ of the buried junction layer for A, B, and C as well as the initial condition $f_2(E)$ extracted from the XAS. The $f_2(E)$ moves from having three main peaks in A to two main peaks in B/C representing a change in local coordination from a mixture of tetrahedral and octahedral to mostly octahedral.
• Figure 5: Benchmarking RXR with ELNES and IV characterization of Al/AlO$_x$/Al Josephson junctions.(a) Al $L_{2,3}$-edge of B showing clear intensity change across the junction oxide, with either side displaying metallic aluminum line shapes. O $K$-edge of sample B showing clear O intensity in the junction, exactly where the Al $L_{2,3}$-edge shows a decrease in intensity. (b) Specific Al $L_{2,3}$-edge line cuts in the junction and the Al metal. The JJ oxide has peaks at $\sim$77eV and 80eV whose ratio determines the ratio of tetrahedral to octahedral environments. (c) Simmons model fits to the measured current–voltage characteristics for the junction series. Both the extracted barrier thickness, $d$, and barrier height, $\phi$, increase with increasing oxidation pressure, consistent with the growth of a thicker, more fully oxidized tunnel barrier.