The Electronic Energy Band Structure of Silicon and Germanium

This article, which is of a tutorial character, is concerned with three broad subjects: (a) the theory of electronic energy bands in a perfect crystal; (b) the electronic energy band structure of silicon and germanium crystals; and (c) the relationship between some of the electrical and optical properties of these crystals and their energy band schemes. The article is essentially an introduction to the quantum theory of crystals, with silicon and germanium serving as illustrative examples. As such, the article should appeal particularly to electronic engineers and physicists working in the field of solid state electronics. A knowledge of quantum mechanics is probably not essential to the understanding of major portions of this paper. The following topics are treated: crystal symmetry and crystal geometry; electronic quantum states in a perfect crystal; the energy band scheme; occupancy of the electronic quantum states; the hole concept; the effective mass tensor; velocity and acceleration of electrons and holes; the spin-orbit interaction and its consequences; the energy band structures of silicon and germanium; the band structure of germanium-silicon alloys; theory of lattice vibrations; the phonon concept; collisions between electrons or holes and phonons; the electrical conductivity; optical absorption and emission processes.