Effect of point defects on the decay of the longitudinal optical mode

The longitudinal optical mode at the zone center often has the highest frequency in the phonon spectrum, so that its phonons cannot be scattered elastically into other modes. Their decay rate Gamma is enhanced by defects above the intrinsic anharmonic rate Gamma(ah) by the combined action of anharmonic processes and defects such as point defects. This can occur by a second-order process. The phonon is scattered first into a neighboring mode. This intermediate state is followed by anharmonic decay. The intrinsic anharmonic decay rate Gamma(ah) is almost independent of the intermediate state mode, so that Gamma(ah) can be factored out of the second-order decay rate. An expression of the overall decay rate is obtained. A different result can be obtained by convoluting the point defect scattering over the anharmonic line width. This procedure was used numerically for isotopic mixtures of Ge and Si. An algebraic expression for the convolution is given here. These different approaches are compared to each other and compared to the observed line broadening in the isotopic mixtures. The second-order theory is also applied to line broadening due to Si solutes and their associated Al vacancies in aluminum nitride. (C) 2002 Elsevier Science B.V. All rights reserved.