Optimizing Power Factor in SixGe1-x Alloys and Some Other Thermoelectric Materials: Insights and Empirical Relationships

Abstract

In this article, the issue of determining the power factor maximums of SixGe1-x alloy with different compositions is investigated. This issue is discussed also for other thermoelectrics based on literature data. It is shown that for the values of the Seebeck coefficient in the interval (1-4)10-4V/K, (PF)max corresponds to the minimum of the specific electrical conductivity. The interdependence of these thermoelectric parameters has a regular character. The dependences lg(σS2)max – lgσmin for various thermoelectrics based on literature and our data in the corresponding interval of changes of variables are described by a single empirical expression lg(σS2)max \(\cong\) 0.583(lgσmin)2-3.332lgσmin. The temperature dependence of the Seebeck coefficient described by the equation S= \(\frac{3}{2}\) \(\frac{K_B}{qe}\)  lnT+C, where C depends on the concentration and effective bmass of charge carriers, as well as on the Debye temperature. This dependence has the same character as dependence σS2 – T and have maximum around 1100K. Additionally, the dependences of power factor on specific electrical conductivity were studied. For different thermoelectrics they are described by empirical expressions such as σS2≅(a/σ)-b or σS2≅cσ-d, where constants a, b, c and d>0. For a number of thermoelectrics, the dependences σS2 on the Seebeck coefficient are rectilinear, while for another series they are power-law. And this is a more general case. The temperature dependences of σS2 and of scaled power factor (BS) are also studied. Both are described by a quadratic equation. It has been established that the maximum power factor corresponds to the minimum BS. Thus, in this case to estimate (σS2)max can be used as σmin, and (BS)min.