Fabrication, characterization and mechanical loading of Si/SiGe membranes for spin qubit devices

TL;DR

The work tackles the challenge of achieving robust valley splitting $E_{ ext{VS}}$ in Si/SiGe spin qubits by introducing Si/SiGe membranes as a tunable platform that leverages both back-gate induced out-of-plane fields $\mathcal{E}_z$ and controlled shear strain $\varepsilon_{xy}$. It presents a comprehensive fabrication flow for two heterogeneous SiGe membranes, develops an ARDE-aware etch model to precisely tailor membrane geometry, and characterizes the membranes’ thickness, roughness, and mechanical response. The authors demonstrate integration with a spin-qubit shuttle device (QuBus) to show practical applicability for valley mapping experiments, validating the platform's potential to study intervalley scattering and disorder effects. Overall, the membrane-based approach provides a versatile, scalable route to engineer and map valley splitting across qubit networks, with implications for robust, high-fidelity Si/SiGe quantum processors.

Abstract

Si/SiGe heterostructures on bulk 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 Si/SiGe membrane as a versatile scientific platform for investigating intervalley scattering mechanisms which have thus far remained elusive in conventional Si/SiGe heterostructures and have the potential to yield favourable valley-splitting distributions. Here, we report the fabrication of locally etched, suspended SiGe/Si/SiGe 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.

Figures (10)

• Figure 1: Device model and design. (a) Schematic (not to scale) of the geometry of the device with exemplary gate-defined quantum dots (QDs, green dots) in a suspended Si/SiGe membrane with metallic back gate and patterned multilayer front gates (bright gray). Strain may be coupled to the QDs via mechanical loading and/or a deposited stressor (e.g., Si$_3$N$_4$ grown by plasma-enhanced chemical vapor deposition) at the surface. The (virtual) substrate, consisting of handle wafer, linearly graded, and constant-composition buffers of thickness $t_{\text{sub}}, t_{\text{lg}}$ and $t_\text{cc}$, respectively, is locally etched at depth $d_x$. A square membrane of thickness $t_m$ is obtained with base width $w_b$ determined by mask width $w_m$. A mechanical load of force $F$, or stressor, with a thickness $t_s$, induces in-plane strain at the surface ($\varepsilon_s$) as well as in the quantum well ($\varepsilon_m$) hosted by the membrane. Note that $\varepsilon_m$ can be either compressive or tensile. “sSi” refers to (epitaxially) strained silicon. (b) Out-of-plane electric field $\mathcal{E}_z$ in the quantum well as a function of voltage $V_\text{bg}$ applied to the back gate. For negative (positive) $V_\text{bg}$, QDs form on the top (bottom) of the Si/SiGe quantum-well barriers. The white region corresponds to 99.9% probability of electron escape from the QD via tunneling in the $z$ direction within one day. (c) Membrane strain $\varepsilon_m$ as function of stressor and membrane thicknesses.
• Figure 2: Aspect-ratio-dependent anisotropic etching. (a) Scanning electron microscope image of the membrane base corner, showing gradual change in the sidewall angle due to the linearly graded buffer. (b) Apparent etch rates $R(a)$ of silicon as a function of the aspect ratio $a=d_x/w_m$ for a fixed etch time. The solid line represents a least-squares fit of the empirical relation $R(a)=R_0(1+\beta a)$ where $R_0$ is the etch rate for $a=0$ and $\beta$ is a dimensionless factor which determines the strength of aspect-ratio-dependent effects. (c) Membrane thickness $t_m$ and (d) base width $w_b$ as a function of time as predicted by the etch-rate model. Faded lines depict a linear-etch-rate assumption $d_x(t) \approx R_0t$. The inset of (c) shows $t_m$ within 25 minutes of the total etch times for wafers A and B (squares), with the start of the linearly graded buffer indicated by dots.
• Figure 3: Observed membrane geometry. (a) Membrane thickness $t_m$ measured by spectroscopic ellipsometry (dots) and target thickness calculated by the etch-rate model (dashed lines). (b) Optical microscope image of a 10$\times$10 mm$^2$ sample from wafer B containing a 3$\times$3 array of partially transparent membranes. (c) Membrane widths $w_b$ along $x$ and $y$ obtained by optical microscopy for wafers A and B. Targeted widths obtained from the etch-rate model are depicted by stars. (d) Optical polarized microscope image of etched substrate from the back side with visible cross-hatch pattern.
• Figure 4: Surface roughness by atomic force microscopy. (a),(b) Surface topography of wafer A for the bulk (a) and membrane (b), region, respectively. Background curvature is subtracted by a sixth-order polynomial and horizontal scars are corrected by the open-source software gwyddionnecas_gwyddion_2012. (c),(d) Same for wafer B with the bulk (c) and membrane (d) region, respectively. (e) Probability density of the measured height profiles from (a)-(d).
• Figure 5: Membrane elasticity. (a),(b) Membrane vertical deformations $\varphi(x)$ measured by profilometry with increasing force $F_\nearrow = \{9.8, 49, 98\}$ µN corresponding to blue, pink and yellow curves respectively for wafers A (a) and B (b). Each set of curves corresponds to a different membrane on the sample, offset horizontally for better readability. Differences in membrane profiles for increasing $F_\nearrow$ and decreasing $F_\searrow$ scans are shown in partially transparent curves with corresponding colors.