Cross-hatch strain effects on SiGe quantum dots for qubit variability estimation

Abstract: SiGe heterostructures integrated with Si via virtual substrate (VS) growth are promising hosts for spin qubits. While VS growth targets plastic relaxation, residual cross-hatch strain inhomogeneity propagates into heterostructure overgrowth. To quantify strain inhomogeneity's influence on interface structure and qubit properties, we measure strained-silicon (s-Si)/Si${0.7}$Ge${0.3}$ heterostructures on 25 wafers processed via standard commercial chemical vapor deposition. Spatially-aligned images of strain (Raman microscopy) and interface structure (atomic force microscopy and cross-sectional scanning transmission electron microscopy) reveal strain-roughness interplay. A strain-driven surface diffusion model predicts the roughness and its temperature dependence. Measured strains suggest spurious double-dot qubit detunings of 0.1 meV over 100 nm distances may result. Modeling shows that interface roughness (atomic steps), when convolved with alloy disorder, only modestly reduces valley splitting (70$\pm$13 vs. 77$\pm$14 $μ$eV on average). Our findings point to thicker VS buffer layers beneath heterostructures and lower-temperature growth (T $\le$ 700 $^{\circ}$C) to limit roughening.