Bandstructures

The introduction of the various computation techniques for determining bandstructures, their implications and their pitfalls is the scope of this chapter, which ends up with a realistic representation of the bandstructures of semiconductors. Approaches to the calculation of semiconductor bandstructures—tight binding, orthogonalized plane waves, density functional and k · p—are discussed, with an emphasis on the physical implications through toy models. The effective mass theorem and Wannier functions are introduced as tools to explore nonlocalized and localized behaviors. Spin’s consequence in the valence bandstructure through spin-orbit coupling and the Luttinger Hamiltonian is emphasized. Semiconductor bandgap behavior in group IV, group III-V and group II-VI compounds is explored, including those of nitrides and gapless semiconductors, together with insights into the common semiconductors’ electron bandstructures, density of states and van Hove singularities. The chapter concludes with a discussion of phonon bandstructures.