Optimization of Valley Splitting in Si/SiGe Spin-Qubits

Silicon-germanium (SiGe) heterostructures are a major candidate for realizing fully scalable quantum computers due to their inherently long spin coherence times and compatibility with existing semiconductor fabrication techniques. A critical challenge in strained Si/SiGe quantum wells is the existence of two nearly degenerate conduction band minima that can lead to leakage of quantum information. In the literature, several strategies have been proposed to enhance the energy splitting between the two valleys such as sharp interfaces [1], oscillating Ge-concentrations (wiggle well) [2] and shear strain engineering [3]. In this work, we formulate the design of the epitaxial profile in the quantum well as a constrained optimization problem and seek an optimized alloy composition profile that maximizes the valley splitting while respecting several manufacturing limitations. Our approach is based on coupled envelope equations combined with empirical pseudopotential theory to incorporate effects of disorder and strain in SiGe alloys. We demonstrate that our approach reproduces existing heuristics such as the wiggle well and the Germanium spike as limiting cases but also finds enhanced epitaxial profiles. Our work thus represents a valuable design tool for Si/SiGe heterostructures to further improve the valley splitting beyond the current state of the art.

[1] Losert et al. Phys. Rev. B 108.12 (2023)

[2] McJunkin et al. Nat. Commun 13, 7777 (2022)

[3] Woods et al. Npj Quantum Inf. 10, 54 (2024)