On the Composition Function of Graded Thermoelectric Materials

Abstract

It is well known that the performance of a thermoelectric generator can be enhanced by choosing temperature-adapted concentration profiles along the TE legs. Several procedures have been published which are able to obtain a particular profile (out of a given set of materials) that maximizes the efficiency or the electrical power output. However, the role of the temperature dependent figure-of-merit, Z, in performance enhancement is still a contentious issue. We will show here that from a theoretical standpoint a local Z-maximization is not correct for efficiency enhancement. Out recently developed numerical tool for the performance description of arbitrarily composed TE-generators will be used to illustrate this. But: The derived results allow the conclusion that in spite of the wrong theory, a local Z-maximization can be applied if this leads to a homogenization of the overall temperature dependence of Z. Regarding the practical case of designing a stacked generator, the already common procedure to place the material junctions at the Z-curve intersections is thus a posteriori justified. For the electrical power output, however, a different situation occurs. Though there seems to be no local criterion for efficiency enhancement of a graded TE-generator, we show that such a measure for output power maximization indeed exists. An example of a stacked Bi-Te / FeSi 2 -generator is given.