Theoretical investigation of structural, electronic and thermoelectric properties of $p{-}n$ type $\hbox {Mg}_{2}\hbox {Si}_{1-x}\hbox {Sn}_{x}$ system

Abstract

Based on the density functional theory and the Boltzmann transport theory, the thermoelectric properties of $\hbox {Mg}_{2}\hbox {Si}_{1-x}\hbox {Sn}_{x}$ solid solution with $x= 0.25, 0.5 \hbox { and } 075$ were investigated. The calculated structural parameters were in good agreement with the previous work and the mechanical and dynamical stabilities were confirmed. The electronic band structure computed using the Tran-Blaha-modified Becke and Johnson (TB-mBJ) exchange potential indicated that the band gap can be tuned by the alloy effect. We combined first-principles calculations and the semiclassical Boltzmann transport theory by considering the electronic transport in the $\hbox {Mg}_{2}\hbox {Si}_{1-x}\hbox {Sn}_{x}$ solid solution to determine the effect of varying the Sn composition on the thermoelectric performance. Our results have shown exceptionally high electrical conductivity for ${\hbox {Mg}}_{2}\hbox {Sn}$ and higher Seebeck coefficient for $\hbox {Mg}_{2}\hbox {Si}$. The highest figure of merit (ZT) was predicted for $\hbox {Mg}_{2}\hbox {Si}_{1-x}\hbox {Sn}_{x}$ solid solution with $x = 0.5$ where ZT has reached 0.55 with carrier concentration charge $n = 10^{20}\hbox { cm}^{-3}$ (p-type doping) at intermediate temperatures. Consequently, the alloying system with p-type doping may improve the thermoelectric properties compared to the $\hbox {Mg}_{2}\hbox {Si}$ and $\hbox {Mg}_{2}\hbox {Sn}$ pristine compounds.