Band Offsets
At a semiconductor heterojunction, the alignment of the valence- and conduction-band edges across the interface defines the valence-band offset (VBO) and conduction-band offset (CBO). These offsets govern carrier confinement, charge transport across the interface, and ultimately the performance of devices based on heterostructures, such as modulation-doped field-effect transistors, quantum-well lasers, and Si/SiGe quantum-dot qubits [PAUL].
From a first-principles perspective, band offsets cannot be obtained from a single bulk calculation: they combine bulk band-edge positions of each material, an interface lineup term arising from the dipole built up at the heterojunction [DDZ], and—when relevant—strain [VAND] and spin–orbit [YANG] corrections. For lattice-mismatched systems such as Si grown epitaxially on Si1-xGex, the thin Si layer is biaxially strained to the substrate, which splits degenerate band edges and shifts them, so that the offsets depend strongly on composition x and on the relaxed out-of-plane lattice constant.
In this tutorial we use RESCU to compute the VBO and CBO of strained Si on Si1-xGex at fixed concentration x = 0.3125, going through the full workflow: numerical convergence, equation of state of the alloy, epitaxial relaxation of the strained Si, bulk band-edge calculations on Special Quasirandom Structures (SQS) [ZUNG], interface lineup from a slab calculation, and an optional HSE [HSE] correction of the conduction band.