Phonon-isotope scattering and thermal conductivity in materials with a large isotope effect: A first-principles study

The interplay between phonon-isotope and phonon-phonon scattering in determining lattice thermal conductivities in semiconductors and insulators is examined using an ab initio Boltzmann transport equation approach. We identify materials with large enhancements to their thermal conductivities with isotopic purification, known as the isotope effect, and we focus in particular on results for beryllium-VI compounds and cubic germanium carbide. We find that germanium carbide and beryllium selenide have very large room temperature isotope effects of 450$%$, far larger than in any other material. Thus, isotopic purification in these materials gives surprisingly high intrinsic room temperature thermal conductivities, over 1500 Wm${}^{\ensuremath{-}1}$ K${}^{\ensuremath{-}1}$ for germanium carbide and over 600 Wm${}^{\ensuremath{-}1}$ K${}^{\ensuremath{-}1}$ for beryllium selenide, well above those of the best metals. In compound semiconductors, a large mass ratio of the constituent atoms and large isotope mixture for the heavier atom gives enhanced isotope scattering. A frequency gap between acoustic and optic phonons (also due to a large mass ratio) and bunching of the acoustic phonon branches give weak anharmonic scattering. Combined, weak anharmonic phonon scattering and strong isotope scattering give a large isotope effect in the materials examined here. The physical insights discussed in this work will help guide the efficient manipulation of thermal transport properties of compound semiconductors through isotopic modification.