DIELECTRIC CONSTANT AND SEEBECK COEFFICIENT FOR SEMICONDUCTORS: THERMODYNAMIC AND DFT STUDIES

Abstract

Dielectric constants and Seebeck coefficients for semiconductor materials are studied by thermodynamic method plus ab initio quantum density functional theory (DFT). A single molecule which is formed in semiconductor material is treated in gas phase with molecular boundary condition and then electronic polarizability is directly calculated through Mulliken and atomic polar tensor (APT) density charges in the presence of the external electric field. This electronic polarizability can be converted to dielectric constant for solid material through the Clausius–Mossotti formula. Seebeck coefficient is first simulated in gas phase by thermodynamic method and then its value divided by its dielectric constant is regarded as Seebeck coefficient for solid materials. Furthermore, unit cell of semiconductor material is calculated with periodic boundary condition and its solid structure properties such as lattice constant and band gap are obtained. In this way, proper DFT function and basis set are selected to simulate electronic polarizability directly and Seebeck coefficient through chemical potential. Three semiconductor materials Mg 2 Si , β- FeSi 2 and SiGe are extensively tested by DFT method with B3LYP, BLYP and M05 functionals, and dielectric constants simulated by the present method are in good agreement with experimental values. Seebeck coefficients simulated by the present method are in reasonable good agreement with experiments and temperature dependence of Seebeck coefficients basically follows experimental results as well. The present method works much better than the conventional energy band structure theory for Seebeck coefficients of three semiconductors mentioned above. Simulation with periodic boundary condition can be generalized directly to treat with doped semiconductor in near future.