The Maximums of Power Factor, Figure of Merit of alloy SixGe1-x and Some Other Thermoelectric (*)(**)

Abstract

In this article, the issue of determining the maximums of power factor (PF) and figure of merit (ZT) of \(\mathrm{Six}_{\mathrm{x}} \mathrm{Ge}_{1-\mathrm{x}}\) alloy of \(\mathrm{n}\) - and p-type conductivity 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 \((1-4) 10^{-4} \mathrm{~V} / \mathrm{K}\), (PF) max \(_{\max }\) corresponds to the minimum of the specific electrical conductivity. The interdependence of these thermoelectric parameters has a regular character. The dependence of maximums of figure of merit on thermoelectric quality factor (B) for thermoelectric \(\mathrm{Si}_{\mathrm{x}} \mathrm{Ge}_{1-\mathrm{x}}\) of \(\mathrm{n}\) - and \(\mathrm{p}\)-type conductivity has been considered. For all samples, \((Z T)_{\max }\) appear at about \(900^{\circ} \mathrm{C}\). The \((Z \mathrm{ZT})_{\max }-\sigma^{\prime}\) (universal electrical conductivity) dependence allows us to assume with sufficient accuracy the mentioned maxima for other values of \(\sigma^{\prime}\) (that is, for \(\mathrm{Si}_{\mathrm{x}} \mathrm{Ge}_{1-\mathrm{x}}\) with other relative compositions as well. Thus, \(\sigma^{\prime}\) can be used to predict of \((Z T)_{\max }\). With this approach, is not required coefficient of thermal conductivity \(\left(\mathrm{k}_{\mathrm{b}}\right) \cdot \sigma^{\prime} \mathrm{S}^2-\mathrm{S}\) independence is also considered (S - Seebeck coefficient). Experimental points and the averaged curve for a large number of samples calculated from the data of literature match well. The middle part of this dependence \(\left(1 \cdot 10^{-4} \leq \mathrm{S} \leq 2.5 \cdot 10^{-4} \mathrm{~V} \cdot \mathrm{K}^{-1}\right)\) is well described by the parabolic empirical expression. And in the range \(0 \leq \mathrm{S} \leq 6 \cdot 10^{-4} \mathrm{~V} \cdot \mathrm{K}^{-1}\) the equation of exponential type should be used. Experimental points in coordinates \(\sigma^{\prime}-\mathrm{B}_S / \mathrm{S}^2\) are well located on a straight line for all \(x\) in \(n\) - and \(p\) - \(\mathrm{Si}_{\mathrm{x}} \mathrm{Ge}_{1-\mathrm{x}} \mathrm{except}\) of some points for \(\mathrm{p}-\mathrm{Si}_{0.7} \mathrm{Ge}_{0.3}\). The dependence \(\sigma^{\prime}-\mathrm{B}_S / \mathrm{S}^2\) have the form of a straight line with a slope of \(1.347 \cdot 10^8 \mathrm{Sim} \cdot \mathrm{W}^{-1} \cdot \mathrm{K}^{-2}\).