Theory of valley-splitting in Si/SiGe spin-qubits: Interplay of strain, resonances and random alloy disorder

Abstract

Electron spin-qubits in silicon-germanium (SiGe) heterostructures are a major candidate for the realization of scalable quantum computers due to their long spin coherence times and compatibility with existing semiconductor fabrication techniques. A critical challenge in strained Si/SiGe quantum wells (QWs) is the existence of two nearly degenerate conduction band minima that can lead to leakage of quantum information. To address this issue, various strategies have been explored to enhance the valley splitting (i.e., the energy gap between the two low-energy conduction band minima), such as sharp interfaces, oscillating germanium concentrations in the QW (wiggle wells), and shear strain engineering. In this work, we develop a comprehensive envelope-function theory augmented by the empirical pseudopotential method to incorporate the effects of disorder, strain, and resonances arising from the symmetries of silicon’s crystal structure. We apply our model to analyze common epitaxial profiles studied in the literature and compare our results with previous work. This framework provides an efficient tool for quantifying the interplay of these effects on the valley splitting, enabling complex epitaxial optimization in future work.