Three-phonon phase space and lattice thermal conductivity in semiconductors

We present calculations of the phase space for three-phonon scattering events in several group IV, III-V and II-VI semiconductors employing an adiabatic bond charge model to accurately represent the phonon dispersions. We demonstrate that this phase space varies inversely with the measured lattice thermal conductivities of these materials over a wide range of temperatures where three-phonon scattering is the dominant mechanism for scattering phonons. We find that this qualitative relationship is robust in spite of variations in material parameters between the semiconductors. Anomalous behavior occurs in three III-V materials that have large mass differences between constituent elements, which we explain in terms of the severely restricted three-phonon phase space arising from the large gap between acoustic and optic phonon branches.