Calculation of the Urbach Tail Absorption in a Second-Order Cumulant Expansion

The exponentially decreasing intrinsic absorption tail in polar semiconductors is calculated by a second-order cumulant expansion for the interaction of excitons and longitudinal optical (LO) phonons. In the wide class of semiconductors in which exciton self-trapping does not occur, the calculated and measured slopes of the absorption tail agree for the first time quantitatively, where all input parameters are obtained from experimental data which are independent of the absorption tail. This agreement holds for all considered coupling constants and all ratios of the exciton binding energy to the LO-phonon energy.