Parametric modeling of energy filtering by energy barriers in thermoelectric nanocomposites

We present a parametric modeling of the thermoelectric transport coefficients based on a model previously used to interpret experimental measurements on the conductivity, σ, and Seebeck coefficient, S, in highly Boron-doped polycrystalline Si, where a very significant thermoelectric power factor (TPF) enhancement was observed. We have derived analytical formalism for the transport coefficients in the presence of an energy barrier assuming thermionic emission over the barrier for (i) non-degenerate and (ii) degenerate one-band semiconductor. Simple generic parametric equations are found that are in agreement with the exact Boltzmann transport formalism in a wide range of parameters. Moreover, we explore the effect of energy barriers in 1-d composite semiconductors in the presence of two phases: (a) the bulk-like phase and (b) the barrier phase. It is pointed out that significant TPF enhancement can be achieved in the composite structure of two phases with different thermal conductivities. The TPF enhancement is estimated as a function of temperature, the Fermi energy position, the type of scattering, and the barrier height. The derived modeling provides guidance for experiments and device design