Influence of isotope scattering on the thermal conductivity of diamond

The thermal conductivity of diamond crystals with different isotope contents is evaluated in the framework of a microscopic model that considers acoustic- and optical-phonon branches. The phonon Boltzmann equation is solved iteratively, with the phonon wave vectors taken in the real Brillouin zone and the three-phonon normal and umklapp collisions, with the isotope scattering, rigorously treated. As a consequence, the evaluation of the thermal conductivity is done avoiding the relaxation-time approximation for the scattering mechanisms. Good agreement with the experimental data is obtained. The calculation reveals a fundamental role of the optical phonons in determining the thermal resistivity of diamond. Comparison of the theoretical results with the recent experimental data for germanium and silicon is also proposed.