Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge

Using a first-principles approach, we present forms for the intrinsic phonon relaxation times in semiconductors, which properly reflect the physically distinct behaviors of the normal and umklapp scattering processes. We find that accurate representation of the phonon-phonon scattering strength and inclusion of scattering of acoustic phonons by optic phonons are essential ingredients, which are missing from the decades old derivations of commonly used intrinsic relaxation times. We also assess the validity of the relaxation time approximation itself for silicon and germanium.