Maximization of the Figure of Merit of Alloy Si\(_x\)Ge\(_{1-x}\)

Abstract

The dependence of maximums of figure of merit ((ZT)max) on thermoelectric quality factor (B) for thermoelectric SixGe1-x of n- and p-type conductivity with a charge carrier concentration of 3.21026m-3 has been considered. The values of x are: 0.7, 0.72, 0.76, 0.8 and 0.83. For all samples, (ZT)max appears at about 900°C. The (ZT)max– σ' (universal electrical conductivity) dependence allows us to assume with sufficient accuracy the mentioned maxima for other values of σ' (that is, for SixGe1-x with other relative compositions as well. Thus, σ' can be used to predict of (ZT)max. With this approach, a coefficient of thermal conductivity (kL) is not required. σ'S2 – S  dependence 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 (1.10-4\(\le\)S \(\le\) 2.5.10-4 V.K-1) is well described by the parabolic empirical expression. And in the range 0\(\le\) S\(\le\) 6.10-4V.K-1 the equation of exponential type should be used. Experimental points in coordinates σ'- BS/S2(BS=σS2/BE, σ - specific electrical conductivity, BE – electronic quality factor) are well located on a straight line for all x in n- and p-SixGe1-x ,except for some points for p-Si0.7Ge0.3. The dependence σ'- BS/S2 have the form of a straight line with a slope of 1.347108 SimW-1K-2.