Influence of the electron and phonon temperature and of the electric-charge density on the optimal efficiency of thermoelectric nanowires

In this paper we study the thermodynamic efficiency of thermoelectric generators in which the heat transport is driven by phonons and electrons. It is assumed that the phonon temperature and the electron temperature are different, and that the electric-charge density is nonuniform. The mean temperature is defined by observing that the internal energy of the system is the same either in the presence of two temperatures, or of one temperature. In steady states, we determine the influence of the gradients of the mean temperature and of the electric-charge density on the theoretical values of the thermoelectric efficiency. The physical conditions under which such efficiency is optimal are determined as well.