Revisiting the effect of point defects on the decay of the longitudinal optical mode in semiconductors

In a classic 2002 paper published by P.G. Klemens a theoretical analysis of the effect of point defects on the decay of the longitudinal optical mode in semiconductors was derived. The defect-induced phonon decay rate was analysed using convolution methods and second-order perturbation theory. In re-examining the derivation of these results, a critical error in the evaluation of an integral has been found, which is central to the main finding of the model. This letter demonstrates that the miscalculation leads to an incorrect scaling of the defect-induced broadening. In addition, a corrected derivation of the second-order perturbation result is given, yielding an amended expression for the optical phonon decay rate that aligns more closely with the expected physical behaviour. The revised result has significant implications for the quantitative interpretation of Raman line widths in isotopic mixtures and impurity systems, thereby refining the theoretical framework for analysing optical phonon decay in defective crystals.