A note on the selection rules for optical transitions in alloys

Abstract

It is well known (e.g. Mott and Jones 1936, p. 99) that direct optical transitions in solids are 'vertical', i.e. between states of nearly the same reduced k-vector. Indirect transitions in which a phonon is emitted or absorbed with the photon, have also been studied (Bardeen et al. 1955). These depend on the temperature, but allow the initial and final states to differ by any k-vector. The purpose of this note is to point out that one can also have indirect transitions involving the virtual scattering of the electron by impurities, and that in an alloy the transition probability for such processes may be comparable with the rate for direct transitions, SO that an absorption edge may represent the minimum band gap, rather than the minimum energy difference between states lying directly 'above' each other in a reduced zone.