Dispersion considerations affecting phonon-mass impurity scattering rates

This work presents a derivation of phonon-mass impurity scattering rates applicable to dispersive phonon systems. This form of mass impurity scattering is compared with the previously accepted form assuming a nondispersive crystal by calculating the thermal conductivity of Si. The mass impurity scattering rate determined from this approach considering dispersion is in excellent agreement with theoretical calculations, where the scattering rates determined from the dispersionless model under predict the role of phonon-mass impurity scattering in thermal transport by over an order of magnitude.