Optical Absorption Band Edge in Anisotropic Crystals

Abstract

The shape of the optical absorption band edge in insulating crystals is discussed for both direct and indirect electronic transitions. Selection rules are invoked to explain the apparent shift in the band edge with polarization observed in anisotropic crystals. The absorption coefficient obeys a law of the form $K\ensuremath{\propto}{(\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}E)}^{n}$, where $E$ is closely related to the minimum band gap and $n$ is \textonehalf{} for allowed direct transitions, $\frac{3}{2}$ for forbidden direct transitions, and 2 for indirect transitions. The experimental observations of the shift in CdS and Te are analyzed in terms of conduction and valence band extrema at k=0 with symmetry types such that the transition is allowed for light polarization perpendicular to the hexagonal axis and forbidden for the polarization parallel to this axis.