Seebeck coefficient of graded porous composites

A physical model is developed for the enhancement of the Seebeck coefficient (S) in a porous thermoelectric material with inhomogeneous porosity. The pores are assumed to be hole and of spherical shape. We take into account the presence of trap centers situated at pore/medium interfaces and neglect changes in the carrier effective mass due to the band-bend. We show that the porosity always leads to an increase in the absolute value ofS.A simple relation is derived forSin nondegenerate n-type semiconducting materials in the case when the main contribution in the carrier relaxation time at zero porosity is from the scattering on acoustic phonons. We have shown that the value ofSdoes not depend on the orientation of the porosity gradient with respect to the direction of the temperature gradient. The relative growth of the Seebeck coefficient compared to its value in the bulk material of the same volume is examinated for different number of the pore groups with different characteristic sizes at various pore size distributions.