First-Principles Band Alignment in Strained Si/Si_1-xGe_x and Ge/Si_1-xGe_x Heterostructures

Silicon–germanium alloys and their strained-layer heterostructures are crucial to modern spin-qubit and quantum-well devices. However, their reported band offsets can differ by over 100 meV across experimental techniques. Semi-empirical models, typically fitted at a few discrete compositions, suffer from comparable composition-dependent errors and omit nonlinear corrections. We addressed this challenge with a first-principles density functional theory (DFT) workflow that computes valence- and conduction-band offsets (VBOs and CBOs) for strained Si/Si_1-xGe_x and Ge/Si_1-xGe_x across 0 ≤ x ≤ 1. All calculations were performed using the RESCU solver. Composition-dependent lattice constants were obtained from Perdew–Burke–Ernzerhof equation-of-state fits on special quasirandom structures (SQS) optimized to emulate random-alloy disorder. We then imposed the associated biaxial strains on pure Si and Ge epilayers, which were subsequently relaxed along the out-of-plane direction. Band-edge energies were corrected using the Heyd–Scuseria–Ernzerhof hybrid functional to address band-gap underestimation, and interface lineups were captured by averaging the electrostatic potential across 512-atom SQS heterojunction slabs. The workflow yields offsets with uncertainties on the order of 10 meV, in excellent agreement with experiment, and provides a predictive database for SiGe quantum-well and spin-qubit device design.