Electron transport modeling and energy filtering for efficient thermoelectricMg2Si1−xSnxsolid solutions

We present a comprehensive electron transport model to analyze thermoelectric properties of both $n$- and $p$-type bulk ${\text{Mg}}_2$ ${\text{Si}}_{1\text{−}x}$ ${\text{Sn}}_x$ ($0\le x\le 1$) solid solutions. A temperature-dependent multiparabolic bands model is used to describe the band structures of the alloys, and the transport properties are calculated using the linearized Boltzmann transport equations under the relaxation time approximation. A variety of experimental data from literature are fitted very well by this model and analyzed for further material optimization. Our analysis shows that the compositions of $x$ = 0.6 to 0.7 exhibit the highest thermoelectric figure of merit zT among $n$-type ${\text{Mg}}_2$ ${\text{Si}}_{1\text{−}x}$ ${\text{Sn}}_x$ in the midtemperature range 600 to 900 K due to both the high power factors achieved by the convergence of the two conduction bands and low electronic thermal conductivities. For the $p$-type materials, we find that the bipolar electronic thermal conductivity is a major factor limiting the figure of merit. Low Sn content ($x$ < 0.4) alloys show a larger figure of merit among the $p$-type materials due mainly to their lower bipolar thermal conductivities with larger band gaps. Finally, we propose that hot carrier energy filtering can be very useful for these alloys as it can simultaneously reduce the electronic thermal conductivity and enhance the power factor. A zT greater than 3 is possible for $n$-type ${\text{Mg}}_2$ ${\text{Si}}_{0.4}$ ${\text{Sn}}_{0.6}$ ($x$ = 0.6) at 700 K, if electrons with energies lower than 0.4 eV are effectively prevented from participating in transport.