Lattice thermal conductivity of crystalline and amorphous silicon with and without isotopic effects from the ballistic to diffusive thermal transport regime

Abstract

Thermal conductivity of a material is an important physical parameter in electronic and thermal devices, and as the device size shrinks down, its length-dependence becomes unable to be neglected. Even in micrometer scale devices, materials having a long mean free path of phonons, such as crystalline silicon (Si), exhibit a strong length dependence of the thermal conductivities that spans from the ballistic to diffusive thermal transport regime. In this work, through non-equilibrium molecular-dynamics (NEMD) simulations up to 17 μm in length, the lattice thermal conductivities are explicitly calculated for crystalline Si and up to 2 μm for amorphous Si. The Boltzmann transport equation (BTE) is solved within a frequency-dependent relaxation time approximation, and the calculated lattice thermal conductivities in the BTE are found to be in good agreement with the values obtained in the NEMD. The isotopic effects on the length-dependent lattice thermal conductivities are also investigated both in the crystalline and amorphous Si.