Absorption Band Shape and Urbach's Rule of Localized Excitons

An empirical description of the shape of optical absorption bands due to localized excitons in ionic crystals is proposed. The new formula links a nearly Gaussian description of the band near its maximum with an exponential description of the band on the low-energy tail (Urbach's rule). The applicability of the proposed shape formula over a range of 4\textonehalf{} orders of magnitude of absorption constants is demonstrated for localized excitons in KCl. The theoretical background which led to the proposed formula suggests that the existence of an exponential tail (Urbach's rule) is indicative of a predominantly quadratic interaction of certain lattice modes with the exciton formation.