Current and voltage characteristics of a thermoelectric couple

Formulations to determine the electric field and the electrostatic potentials in a thermoelectric couple through solving the Poisson’s equation are introduced in this work. Analytical approximations of the auxiliary energies introduced in the author’s earlier work in the relaxation time approximation of the Boltzmann transport equation are developed based on the coupled equations of heat and electric current. These auxiliary energies are used in the Poisson’s equation at each temperature node along the thermoelectric leg to obtain a set of algebraic equations with the electric field and the electrostatic potentials as unknowns. The algebraic equations are then solved using the derived algorithm and the boundary conditions determined by the continuity and the carrier concentration equations.