Minimum entropy production in inhomogeneous thermoelectric materials

Abstract

Due to their potential applications in energy production based on waste heat, direct solar radiation or other energy sources, semiconductor materials have for years attracted the attention of theoretical and experimental researchers. The focus has been on improving the performance of thermoelectric devices through several strategies and special interest has been placed on materials with spatially inhomogeneous transport properties. Inhomogeneity can be achieved in various ways, all of them leading, to a greater or lesser extent, to an improvement of the thermoelectric performance. In this paper, general linear heat and electric charge transport processes in inhomogeneous materials are addressed. The guiding idea followed here is that there exists a relationship between inhomogeneity (structuring), minimum entropy production and performance which may be fruitfully exploited for designing more efficient thermoelectric semiconductor devices. We first show that the stationary states of such materials are minimum global entropy production states. This constitutes an extension of the validity of Prigogine’s minimum entropy principle. The heat and charge transport equations obtained within the framework of classical irreversible thermodynamics are solved to find the stationary profiles of temperature and self-consistent electric potential in a one-dimensional model of a silicon–germanium alloy subjected to an external temperature difference. This allows us to assess the effect of the spatial inhomogeneity on the thermoelectric performance. We find that, regardless of the value of the applied temperature difference, the system may efficiently operate in a regime of minimum entropy production and high efficiency.