A Shortcut Approximation to the Coupled Equations of Heat and Electric Currents

Abstract

A self-consistent approximation to the coupled equations of heat and electric current densities is developed to facilitate the integration of the relaxation time approximation of the Boltzmann transport equation in a realistic design, analysis, and optimization of energy conversion devices. By introducing two auxiliary energies in the empirical Boltzmann transport equations, the coupled equations can be simply expressed in these auxiliary energies. These auxiliary energies are then determined by optimizing both the heat current through charge neutrality equation without the presence of electric current and the carrier concentrations with the presence of electric current. The heat and the electric current densities as well as the transport properties can then be calculated. The calculated transport properties agreed reasonably well with existing experimental and computational data.