Modeling of electronic and phonon thermal conductivity of silicon in a wide temperature range

Abstract

In the present article, using the methods of mathematical modeling, the thermal conductivity of silicon was obtained in a wide temperature range (0.3 ≼ T ≼ 3 kK), including the region of semiconductor-metal phase transformations. As it is known, there are two mechanisms of heat transfer in a solid: elastic lattice vibrations and free electrons, therefore, in the study of the thermal conductivity of silicon, the lattice and electronic components were taken into account. The lattice (phonon) thermal conductivity in this work was determined within the framework of the atomistic approach. The Stillinger–Weber and Kumagai–Izumi–Hara–Sakai interaction potentials were used for modeling. The results of the comparison of the phonon thermal conductivity obtained from the simulation results with the used interaction potentials are presented. The modeling of the thermal conductivity of the electronic subsystem of silicon with intrinsic conductivity in this work is based on the use of the quantum statistics of the electron gas using the Fermi–Dirac integrals. The total thermal conductivity of silicon, obtained as the sum of the electronic and phonon components, is compared with the experimental data.