Thermoelectric Efficiency of Silicon-Germanium Alloys in Finite-Time Thermodynamics.

Patrizia Rogolino,Vito Antonio Cimmelli

doi:10.3390/e22101116

Abstract

We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon–Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (, , ), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out.

Highlights

Silicon–Germanium (SiGe) alloys have become very important in technology, since some of their properties such as, for example, their efficiency in energy conversion, may be improved by adjusting their stoichiometry
It can be proven that ηel is an increasing function of the material function ZT, where T is the absolute temperature while the figure-of-merit Z is given by Z = e λσe, where e is the Seebeck coefficient, σe the electrical conductivity, and λ is the thermal conductivity of the material [9]
In [23], we have obtained the analytical representation of the thermal conductivity of a nanowire as function of its composition c, as the sum of two exponentials, each depending on 3 parameters, whose value was determined by the experimental data through nonlinear regression method (NLRM)

Summary

Introduction

Silicon–Germanium (SiGe) alloys have become very important in technology, since some of their properties such as, for example, their efficiency in energy conversion, may be improved by adjusting their stoichiometry. We investigate the dependence of its performance as thermoelectric energy generator as function of the composition and of the effective temperature gradient applied to its boundaries, and determine the conditions under which such an efficiency is maximum. We calculate the heat conductivity at T = 300 K, T = 400 K, and T = 500 K, corresponding to the experimental data at our disposal, and prove that for each temperature there is only one value of c in the interval [0, 1] which minimizes the local rate of entropy production, i.e., which corresponds to the optimal efficiency of the thermoelectric energy production.

Constitutive Equation of Thermal Conductivity

Best Efficiency in Thermoelectric Energy Conversion

Results

Relation with Finite-Time Thermodynamics