Revisiting the thermal conductivity of Si, Ge and diamond from first principles: roles of atomic mass and interatomic potential

The thermal conductivity (kappa) of nonmetals is determined by the constituent atoms, the crystal structure and interatomic potentials. Although the group-IV elemental solids Si, Ge and diamond have been studied extensively, a detailed understanding of the connection between the fundamental features of their energy landscapes and their thermal transport properties is still lacking. Here, starting from first principles, we analyze those factors, including the atomic mass (rn) and the second- (harmonic) and third-order (anharmonic) interatomic force constants (IFCs). Both the second- and third-order IFCs of Si and Ge are very similar, and thus Si and Ge represent ideal systems to understand how the atomic mass alone affects K. Although the group velocity (v) decreases with increasing atomic mass (v(-1) proportional to root m), the phonon lifetime (tau) follows the opposite trend (tau proportional to root m). Since the contribution to kappa from each phonon mode is approximately proportional v(2)tau, kappa is lower for the heavier element, namely Ge. Although the extremely high thermal conductivity of diamond is often attributed to weak anharmonic scattering, the anharmonic component of the interatomic potential is not much weaker than those of Si and Ge, which seems to be overlooked in the literature. In fact, the absolute magnitude of the third-order IFCs is much larger in diamond, and the ratios of the third-order IFCs with respect to the second-order ones are comparable to those of Si and Ge. We also explain the experimentally measured kappa, of high-quality diamonds (Inyushikin et al 2018 Phys. Rev. B 97 144305) by introducing boundary scattering into the picture, and obtain good agreement between calculations and measurements.