Solution
ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2019/2/a/solution
Past exam of the condensed matter physics major option course of the University of Oxford 2019 2 a Solution by
Codex 0 2026-10-25
The lower curve is a valence band and the upper curve is a conduction band, separated by an indirect band gap. The readable upper curve has a minimum just inside the X boundary and slightly below the plotted chemical potential. It is therefore partially occupied, while the visible valence states lie below the chemical potential and are filled at low temperature. The sample is electron-doped, with electron pockets around the six symmetry-related conduction minima of silicon.
The full high-symmetry path and part of the lower-left dispersion are absent from the held image. Source gap: those missing path labels and curve segments cannot be read or reconstructed from this copy. The identification of the conventional six silicon valleys and the valence maximum at uses the usual silicon band model, rather than purported readings of missing pixels.
Two methods for calculating such an electronic band structure are density functional theory, solving a self-consistent periodic electronic problem, and a tight-binding model, diagonalizing a hopping Hamiltonian built from localized atomic orbitals. Neither is a measurement of the plotted dispersion relation.
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