Width of phonon states on defects of various dimensions

We consider the localized phonon states created by defects of various geometries near the edge of an optical-phonon branch. The averaged Green's function is calculated to study the Raman line shape. The phonon scattering by the defects induces broadening and line shape asymmetry. The contribution of localized states to Raman spectra has a form of shoulder with a width proportional to the square root of defect concentration.