Fitting thermal conductivity and optimizing thermoelectric efficiency in Si_cGe_(1-c) nanowires

We consider a thermoelectric energy generator constituted by a Si/Ge nanowire of length L. The dependence on composition and temperature of its thermal conductivity is analyzed in view of three series of experimental data obtained at the constant temperatures T = 300K, T = 400K, and T = 500K. The best-fit curve is determined by a nonlinear regression method (NLRM). Then, under the hypothesis of nonlinear constitutive equation for the heat flux, we investigate the thermoelectric efficiency of the system as function of the composition of the nanowire and of the difference of temperature applied to its ends. For each temperature we calculate the values of the composition which realize the optimal efficiency of the thermoelectric energy conversion. The corresponding values of the thermal conductivity are determined as well.