The properties of electrons inside semiconductors are described by the solution of the Schrödinger equation appropriate for the crystal. The solutions provide us the bandstructure or the electronic spectrum for electrons. The problem of finding the electronic spectrum is an enormously complicated one. Solids have a large number of closely spaced atoms providing the electrons a very complex potential energy profile. Additionally electrons interact with each other and in a real solid atoms are vibrating causing time dependent variations in the potential energy. To simplify the problem the potential fluctuations created by atomic vibrations (lattice vibrations) and scattering of electrons from other electrons are removed from the problem and treated later on via perturbation theory. These perturbations cause scattering of electrons from one state to another.
The problem of bandstructure becomes greatly simplified if we are dealing with crystalline materials. An electron in a rigid crystal structure sees a periodic background potential. As a result the wavefunctions for the electron satisfy Bloch's theorem as discussed in the next section.
There are two main categories of realistic bandstructure calculation for semiconductors:
Methods which describe the entire valence and conduction bands.
Methods which describe near bandedge bandstructures.
The techniques in the second category are simpler and considerably more accurate if one is interested only in phenomena near the bandedges. Techniques such as the tight binding method, the pseudopotential method, and the orthogonalized plane wave methods fall in the first category.