Anharmonic effect on the thermal properties of Si and Ge

Abstract

The temperature dependence of specific heat C Ω and thermal expansion coefficient α for Si and Ge are studied theoretically from first principle by using the lattice dynamical method based on pseudopotentials. The obtained results of C Ω h and α h in the harmonic approximation are self-consistent with the observed data of these crystals at low temperatures. At high temperatures, the anharmonic contributions to the specific heat C Ω ah = C Ω h (1 + AT) are calculated by using the expression by Trivedi et al . The temperature dependence of the bulk modulus B T are quantitatively obtained by considering the lattice vibrational contributions in addition to the static crystal energy. Then, the anharmonic corrections to the thermal expansion coefficient are estimated at high temperatures. The anharmonic coefficient A for the specific heat and the temperature-dependent decrease of B T are quantitatively important at high temperatures for Si and Ge.