Numerical Experiments on the Absorption Lineshape of the Exciton under Lattice Vibrations. V. Impurities

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Abstract
The lineshape of exciton absorption bands caused by impurities below the intrinsic absorption edge is calculated numerically on the standard model of exciton-phonon interaction. In the peak region the shape of these bands is found to be Gaussian, in the tail it follows the empirical Urbach rule but the steepness coefficients are markedly smaller than for the respective intrinsic band tails. The analysis of the average oscillator strength per state shows that the impurity bands are caused by localized states in the same way as the intrinsic band tails and explains the insensitivity of the lineshape against changes of the impurity concentration. For different impurity levels the results are shown to be in good agreement with experimental observations.