Electronic Structure and Thermoelectric Properties of Pseudoquaternary $$\hbox{Mg}_{2}\hbox{Si}_{1-x-y}\hbox{Sn}_{x}\hbox{Ge}_{y}$$ Mg 2 Si 1 - x - y Sn x Ge y -Based Materials

Abstract

A theoretical study is presented on complex pseudoternary Bi-doped $$\hbox{Mg}_{2}\hbox{Si}_{1-x-y}\hbox{Sn}_{x}\hbox{Ge}_{y}$$ materials, which have recently been revealed to reach high thermoelectric figures of merit (ZT) of ∼1.4. Morphological characterization by scanning electron microscopy and energy-dispersive x-ray spectroscopy indicated that the investigated samples were multiphase and that the alloy with nominal composition $$\hbox{Mg}_{2}\hbox{Si}_{0.55}\hbox{Sn}_{0.4}\hbox{Ge}_{0.05}$$ contained three phases: $$\hbox{Mg}_{2}\hbox{Si}_{0.35}\hbox{Sn}_{0.6}\hbox{Ge}_{0.05}$$ (Sn-rich phase), $$\hbox{Mg}_{2}\hbox{Si}_{0.65}\hbox{Sn}_{0.3}\hbox{Ge}_{0.05}$$ (Si-rich phase), and $$\hbox{Mg}_{2}\hbox{Si}_{0.15}\hbox{Sn}_{0.5}\hbox{Ge}_{0.35}$$ (Ge-rich phase). The electronic structure of all these phases was calculated in the framework of the fully charge self-consistent Korringa–Kohn–Rostoker method with the coherent potential approximation (KKR-CPA) to treat chemical disorder. Electron transport coefficients such as the electrical conductivity, thermopower, and the electronic part of the thermal conductivity were studied by combining the KKR-CPA technique with Boltzmann transport theory. The two-dimensional (2D) plots (as a function of electron carrier concentration and temperature), computed for the thermopower and power factor, well support the large thermoelectric efficiency detected experimentally. Finally, employing the experimental value of the lattice thermal conductivity as an adjustable parameter, it is shown that ZT ≈ 1.4 can be reached for an optimized Bi content near T ≈ 900 K in case of the nominal composition as well as the Sn-rich phase. The question of the effect of disorder on the convergence of the conduction bands and thus the electron transport properties is addressed through detailed examination of the Fermi surfaces.