$\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ heterostructures on bulk $\mathrm{Si}$ substrates have been shown to host high-fidelity electron spin qubits. Building a scalable quantum processor would, however, benefit from further improvement of critical material properties such as the valley-splitting landscape. Flexible control of the strain field and the out-of-plane electric field ${\mathcal{E}}_z$ may be decisive for valley-splitting enhancement in the presence of alloy disorder. We envision the $\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ membrane as a versatile scientific platform for investigating intervalley scattering mechanisms which have thus far remained elusive in conventional $\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ heterostructures and have the potential to yield favorable valley-splitting distributions. Here, we report the fabrication of locally etched, suspended $\mathrm{Si}\mathrm{Ge}$/$\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ membranes from two different heterostructures and apply the process to realize a spin-qubit shuttling device on a membrane for future valley mapping experiments. The membranes have a thickness in the micrometer range and can be metallized to form a back-gate contact for extended control over the electric field. To probe their elastic properties, the membranes are stressed by loading with a profilometer stylus at room temperature. We distinguish between linear elastic and buckling modes, each offering mechanisms through which strain can be coupled to spin qubits.

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• Electrical properties
• Quantum information with solid state qubits
• Straintronics
• Valley degrees of freedom
• Layered semiconductors
• Nanotechnology
• Quantum dots
• Single-electron devices