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.

Figures (12)

• Figure 1: (a) Schematic of a Ge/SiGe heterostructure with a resonator defined on top of the structure. Defects, each denoted by two white parallel lines in a circle, reside in various layers and interfaces of the heterostructure, and couple to the resonator (in yellow). (b) Schematic of a Ge/SiGe heterostructure etched down to the Si substrate with a tapered mesa step. The resonator is patterned mainly on the Si substrate and its termination climbs over the mesa to be connected to potential structures defined there. (c) Scanning electron microscope (SEM) image of a Ge/SiGe heterostructure after the tapered etching process. The etching leaves an approximately $45°$ angled mesa step. An approximately $100nm$-deep trench is visible in the Si substrate, due to an increased ion scattering rate at the mask sidewall during the etching step (see Appendix \ref{['supp:fab_JJ_arrays']}). As is visible from the overetched region at the Ge virtual substrate, Ge is etched at a slightly faster rate than SiGe. (d) Schematic of five notch-type Josephson junction (JJ) array resonators coupled to a $50Ω$ photon feedline. (e) Optical micrograph of a JJ array resonator coupled to the $50Ω$ feedline. The JJ array resonator is false-colored in yellow. One end of the resonator consists of a large pad shunting it to ground to form a quarter-wave resonator, while the other end is climbing the mesa (purple shaded structure). A hook (colored in green) extends from the feedline and defines the capacitive coupling between the feedline and the resonator. (f) SEM image of the JJ array resonator at the voltage antinode (yellow color). The tapered etching, in combination with the angled evaporation of the junctions, allows to successfully climb the mesa (purple color) without discontinuity of the metal.
• Figure 2: Spectroscopy of JJ array resonators fabricated on different substrates. Schematic of the cross-section of the resonator on (a) a bare Ge/SiGe heterostructure, (b) a Ge/SiGe heterostructure etched down to Si with one resonator's end climbing the tapered mesa, and (c) an intrinsic Si substrate. (d) Normalized feedline transmission amplitude $|S_{21}|$ as a function of the resonator drive frequency $f_\mathrm{d}$ and drive power $P_\mathrm{d}$ for a resonator on the etched heterostructure (panel (b)). (e) Simulated $|S_{21}|$ as a function of $f_\mathrm{d}$ and $P_\mathrm{d}$, with the parameters extracted from the numerical fit of (d) to an input-output model taking into account the Kerr-nonlinearity of the resonator (see Appendix \ref{['supp:fitting_nonlinear']}). Dashed lines in (d) and (e) denote the power $P_\mathrm{d}^\mathrm{SP} \approx -133\dbm$ corresponding to an average resonator photon number $\langle N_\mathrm{ph} \rangle \approx 1$. (f-h)$|S_{21}|$ measured as a function of $f_\mathrm{d}$ for the respective resonator illustrated in panels (a-c). (i-k) Phase of the normalized feedline transmission $\mathrm{Arg}(S_{21})$ measured as a function of $f_\mathrm{d}$ for the respective resonator illustrated in panels (a-c). Solid lines in (f-k) are fits to an input-output model (see Appendix \ref{['supp:fitting_linear']}), yielding the internal resonator loss rates $\kappa_\mathrm{i}$ reported in (f-k). The power of the drive tone at the feedline $P_\mathrm{d}$ is $-140\dbm$ for all the panels (f-k). (l) Internal quality factor $Q_\mathrm{i}$ as a function of $\langle N_\mathrm{ph} \rangle$ for the resonators respectively on the bare Ge/SiGe heterostructure (green data), on the Ge/SiGe heterostructure etched down to Si with one resonator end climbing the tapered mesa (pink data), and on intrinsic Si (blue data). Different shades of each color denote different resonators on the same type of substrate. The value of $Q_\mathrm{i}$ for the different resonators are extracted from power sweeps similar to the one presented in panel (d) (see Appendix \ref{['supp:power_sweeps_all']}).
• Figure 3: Magnetospectroscopy of the resonators on the intrinsic Si substrate. (a) Normalized feedline transmission amplitude $|S_{21}|$ measured as a function of the resonator drive frequency $f_\mathrm{d}$ and the in-plane magnetic field $B_\parallel$ parallel to the JJ arrays. Five JJ array resonators with a different number of JJs are coupled to the same feedline, as depicted in Fig. \ref{['fig:devices']}d. (b) Internal quality factor $Q_\mathrm{i}$ of the resonators, averaged over multiple drive powers in the low-photon-number regime as a function of $B_\parallel$ (blue data). Red data points represent the $Q_\mathrm{i}$ averaged over the five resonators. The black arrow indicates a resonator with a reduced $Q_\mathrm{i}$ due to the coupling with a TLF (see Appendix \ref{['supp:strong_hybridization']}).
• Figure 4: $50Ω$ Nb superconducting resonators on an etched Ge/SiGe heterostructure and on intrinsic Si. (a) Schematic of three notch-type quarter-wave resonators inductively coupled to a $50Ω$ feedline. (b) Scanning electron microscope (SEM) of a $50Ω$ Nb resonator on the etched Ge/SiGe heterostructure. (c) Internal quality factor $Q_\mathrm{i}$ of the $50Ω$ Nb resonators on the etched Ge/SiGe heterostructure (purple) and on intrinsic Si (orange), as a function of the average number of photons in the resonator $\langle N_\mathrm{ph} \rangle$. Different shades of each color denote different resonators on the same type of substrate.
• Figure 5: Sonnet simulation setup. (a) Cross section and top view of a resonator on top of the bare SiGe heterostructure. (b) Cross section, top view and tilted view of a resonator on top of the Si substrate and climbing the SiGe mesa.