Low-loss frequency-tunable Josephson junction array cavities on Ge/SiGe heterostructures with a tapered etching approach

Abstract: Ge/SiGe heterostructures represent a promising platform for hosting various quantum devices such as hole spin qubits and Andreev spin qubits. However, the compatibility of such heterostructures with high-quality-factor microwave superconducting cavities remains a challenge due to defects in the material stack. In this work, we present an approach to enhance the coherence of cavity modes on a reverse-graded Ge/SiGe heterostructure, which consists of etching the full $\sim 1.6~\mathrm{μm}$-thick Ge/SiGe stack down to its starting high-resistivity Si substrate, in order to pattern superconducting cavities directly on it. We engineer the mesa step to be tapered, so that it can be easily climbed by the superconducting cavities to reach the quantum devices potentially hosted in the Ge quantum well. Using this approach, we observe internal quality factors of $Q_\mathrm{i} \approx 10000-20000$ for high-impedance frequency-tunable Josephson junction array resonators, limited by the junctions' fabrication, and $Q_\mathrm{i} \approx 100000$ for $50~\mathrmΩ$ coplanar waveguide Nb lift-off resonators. These $Q_\mathrm{i}$ are preserved despite the overlap with the mesa structure in the climbing region, and are comparable to the ones obtained for identical resonators fabricated on a high-resistivity Si wafer reference. Thereby, this work paves a practical path toward superconductor-semiconductor hybrid devices, immediately applicable to emerging technologies on planar Ge.