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.
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 ∼1.6μm-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 Qi≈10000−20000 for high-impedance frequency-tunable Josephson junction array resonators, limited by the junctions' fabrication, and Qi≈100000 for 50Ω coplanar waveguide Nb lift-off resonators. These Qi 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.
Spin qubits in semiconductor quantum dots constitute one of the leading platforms for quantum information processing, combining long coherence times, high-fidelity gate operations, and compatibility with semiconductor industry technologies. In particular, holes confined in planar Ge/SiGe heterostructures have recently emerged as promising qubit candidates owing to their low effective mass, high mobility, low percolation density, absence of valley states, and strong spin-orbit interaction, which enables fast all-electrical spin control. At the same time, spin-orbit interaction also gives rise to a highly anisotropic and electrically tunable gyromagnetic response. Understanding and controlling this response is therefore essential for high-fidelity single- and multi-qubit operations. The realization of scalable quantum processors also requires efficient qubit readout and long-range connectivity. Circuit quantum electrodynamics (cQED), based on the coupling between artificial atoms and microwave photons confined in superconducting resonators, provides a natural framework to address these challenges. However, the implementation of hybrid semiconductor-superconductor devices in planar Ge has so far been hindered by large microwave losses originating from the heterostructure. In this thesis, we demonstrate, for the first time in planar Ge, strong coupling between a hole charge qubit in a double quantum dot and a high-impedance microwave resonator, reaching a cooperativity of C â 100. In addition, we leverage the frequency tunability of the resonator to perform detailed spectroscopy of a multi-level energy spectrum of low-lying states arising from strong Coulomb-correlation effects. To further improve the quality of the hole-photon interface, we investigate the source of microwave losses in different Ge/SiGe heterostructures, identifying defects at the lattice-mismatched Si/Ge interface as the dominant source of resonator losses in reverse-graded heterostructures. To mitigate this limitation, a deep tapered-etching approach is introduced, enabling the fabrication of superconducting resonators directly on etched heterostructures. This method yields internal quality factors exceeding Qint > 10 000 for high-impedance Josephson junction array resonators and Qint > 100 000 for 50 â Nb resonators. Finally, this thesis explores the spin properties of multi-hole quantum dots beyond the conventional single-orbital picture. By reconstructing and electrically tuning the g tensors of holes confined in different orbital states, we show that confinement can substantially modify both their magnitude and orientation. These results open new opportunities for engineering qubit properties through orbital occupation. Furthermore, highly coherent singlet-triplet oscillations are demonstrated in the seven-hole regime, yielding a quality factor of approximately 330 at in-plane magnetic fields as low as 2.5 mT. Together, these results establish a foundation for high-fidelity hole-spin-qubit operation based on g-tensor engineering and for the integration of planar Ge quantum dots with superconducting quantum circuits.
Abstract Superconducting resonators integrated with germanium (Ge) quantum wells (QWs) offer a promising platform for hybrid quantum devices. Yet, in the most common heterostructure architectures, they have so far been limited by sizable photon losses. Here, we report the fabrication and characterization of microwave resonators patterned in the aluminum (Al) thin film of an in-situ grown superconductor/semiconductor hybrid heterostructure (HS). The semiconductor part of this hybrid HS is grown on a commercial Ge substrate. We consistently achieve internal quality factors Q i > 1000, surpassing previous results on Ge QW heterostructures grown using the concept of a virtual Ge substrate on silicon (Si) substrates. We reach Q i ≈ 49,000 at single-photon occupation and a plateau of Q i ≈ 20,000 at sub-one photon, an order of magnitude larger than any previously reported value of resonators on Ge QW structures at low power. We further characterize the thin Al film forming the resonator, extracting its kinetic inductance and superconducting gap, and studying its magnetic field dependence. Notably, the resonance remains well-defined up to in-plane magnetic fields of 850 mT. A hysteresis emerges in the out-of-plane magnetic field dependence, for both the resonance frequency and the quality factor, indicating an interesting interplay between vortex-and quasiparticle loss mechanisms.
Superconducting qubit based on superconducting circuits consist of a superconducting capacitor and a Josephson junction with the transmon geometry is extensively used in advanced quantum processors, pursuing scalable quantum computing. The tuning of the qubit frequency of the transmon relies on magnetic flux-dependent interference between the supercurrents of two superconductor-insulator-superconductor (S-I-S) Josephson junctions in a superconducting loop. Josephson junction based on superconductor-semiconductor-superconductor (S-Sm-S) materials opens up a possibility to the gate-tunable transmon, referred to as the "gatemon", in which the qubit frequency can be tuned by electrostatic mean. Recent realizations of gatemons on III-V material platforms show impressive development on the alternative to the transmon, yet still leave a big question on the scalability. The silicon-germanium (SiGe) heterostructure is one of the potential platforms to host hybrid devices due to its high hole mobility and the low Schottky barrier at the Ge-metal interface. Additionally, the compatibility with the silicon-based semiconductor industry is a capable advantage for the scaling-up qubit platform.In this thesis, we develop gatemons based on the Al-Ge-Al Josephson junction in the SiGe heterostructure. Firstly, the robust fabrication recipe, found on a top-down approach, for Josephson Field Effect Transistors (JoFETs) is established. We perform measurements exhaustively on the JoFETs to study their properties as a function of the gate voltage, temperature, and magnetic field. The devices show gate-tunability of the critical current and the normal state resistance . The devices are estimated to have a high-transparency superconductor-semiconductor interface, as demonstrated by the high product on the SiGe heterostructure. In the finite-voltage regime, the features corresponded to multiple Andreev reflections (MARs) are observed. Then, we fabricate and characterize niobium nitride (NbN) superconducting resonators on SiGe heterostructure. We measure the resonators in the transmission mode and extract the resonant frequency , internal quality factor, and coupling quality factor from the transmission coefficient. Following that, we develop the fabrication process to integrate Al-Ge-Al junctions shunted with capacitors, or, in other words, gatemon, into the resonator scheme and perform the fabrication according to the design. We demonstrate the anticrossing feature in one of the fabricated gatemons. The resonant frequency of the gatemon is mapped using the two-tone spectroscopy technique and is found to be gate-tunable. The qubit has large spectral linewidth, implying a low coherence time. Additionally, we conduct the current-phase relationship (CPR) measurement on the junctions in the Superconducting QUantum Interference Device (SQUID) geometry. We can demonstrate that the junctions pose non-sinusoidal CPR. Further, the integer and half-integer Shapiro steps are observed in the current-voltage characteristic curves of irradiated junctions. This indicates that our junctions have the element, which can open up another possibility toward protected qubits.
Superconducting qubit based on superconducting circuits consist of a superconducting capacitor and a Josephson junction with the transmon geometry is extensively used in advanced quantum processors, pursuing scalable quantum computing. The tuning of the qubit frequency of the transmon relies on magnetic flux dependent interference between the supercurrents of two superconductor-insulator superconductor(S-I-S) Josephson junctions in a superconducting loop. Josephson junction based on superconductor-semiconductor-superconductor (S-Sm-S) materialsopens up a possibility to the gate-tunable transmon, referred to as the "gatemon", in which the qubit frequency can be tuned by electrostatic mean. Recent realizations of gatemons on III-V material platforms show impressive development on the alternative to the transmon, yet still leave a big question on the scalability. The silicon-germanium (SiGe) heterostructure is one of the potential platforms to host hybrid devices due to its high hole mobility and the low Schottky barrier at the Ge-metal interface. Additionally, the compatibility with the silicon-based semiconductor industry is a capable advantage for the scaling-up qubit platform.In this thesis, we develop gatemons based on the Al-Ge-Al Josephson junction in the SiGe heterostructure. Firstly, the robust fabrication recipe, found on a top down approach, for Josephson Field Effect Transistors (JoFETs) is established. We perform measurements exhaustively on the JoFETs to study their properties as a function of the gate voltage, temperature, and magnetic field. The devices show gate-tunability of the critical current (IC) and the normal state resistance (RN). The devices are estimated to have a high-transparency superconductor/semiconductor interface, as demonstrated by the high ICRN product on the SiGe heterostructure. In the finite-voltage regime, the features corresponded to multiple Andreev reflections (MARs) are observed. Then, we fabricate and characterize niobium nitride (NbN) superconducting resonators on SiGe heterostructure. We measure the resonators in the transmission mode and extract the resonant frequency (fr), internal quality factor (Qi), and coupling quality factor (Qc) from the transmission coefficient (S21). Following that, we develop the fabrication process to integrate Al-Ge-Al junctions shunted with capacitors, or, in other words,gatemon, into the resonator scheme and perform the fabrication according to the design. We demonstrate the anticrossing feature in one of the fabricated gatemons. The resonant frequency of the gatemon is mapped using the two-tone spectroscopy technique and is found to be gate-tunable. The qubit has large spectral linewidth, implying a low coherence time. Additionally, we conduct the current-phase relationship (CPR) measurement on the junctions in the Superconducting QUantum Interference Device (SQUID) geometry. We can demonstrate that the junctions pose non-sinusoidal CPR. Further, the integer and half-integer Shapiro steps are observed in the current-voltage characteristic curves of irradiated junctions. This indicates that our junctions have the cos 2φ element, which can open up another possibility toward protected qubits.
We present a flip-chip-based sensing scheme to measure effective microwave losses associated with target materials for quantum technologies, without requiring any device fabrication on the material under test. Using this approach, we quantify the microwave losses of a strain-engineered Ge/SiGe quantum well heterostructure and investigate losses arising from its Ge substrate and intermediate layers. The quality factors of the fabricated microwave resonators agree with the losses of dielectric materials independently extracted from flip-chip sensing measurements. We further study the superconductor platinum silicon germanide (PtSiGe) prepared by thermal reaction with a deposited Pt film, finding high microwave losses that limit the suitability of the films studied here as the sole superconductor for high-quality resonator applications. By coating Pt with Nb prior to the reaction, we observe a substantial reduction in microwave loss and a nearly three-fold enhancement of the transport critical temperature. The temperature dependence of the microwave loss is consistent with gap inhomogeneity in both superconducting films. These results identify constraints on material choices, provide design guidance for microwave circuits on planar Ge heterostructures, and demonstrate a fast-turnaround testing method for new materials for superconducting quantum circuits.
Voltage-tunable Josephson junctions (VT-JJs) are an emerging element in superconducting quantum electronics with potential to expand the functionality of conventional designs. While VT-JJs are largely compatible with wafer-scale semiconductor processing, their integration into quantum circuits remains a challenge due to unmitigated semiconductor microwave loss. Here, a deep mesa etch process, wherein the epitaxial material is removed except the VT-JJ device, will facilitate the integration of VT-JJs with low-microwave-loss circuit elements by allowing these circuit elements to be placed directly on a low-loss substrate. A Germanium quantum well is grown by Molecular Beam Epitaxy (MBE) on a float zone silicon substrate with in-situ deposited aluminum contacts. This combination allows the formation of an oxide-free superconductor-semiconductor interface. The deep mesa etch process is optimized to produce a sidewall taper sufficient for continuous metal deposition from the substrate to the top of the mesa for electrostatic gate electrodes and interconnects. The fabricated Josephson junctions demonstrate gate-tunable supercurrents with a maximum critical current over 100 nA and critical-current normal-resistance product of 8.63μV. These results demonstrate a pathway toward improved integration of voltage-tunable superconducting circuit elements with quantum electronic building blocks such as couplers and qubits.