Variation of thermoelectric figure-of-merits for Mg₂Si_xSn_1-x solid solutions

Recent advances in figure-of-merit enhancement for thermoelectric materials are mostly based on alloy material systems, which often require specific conditions to obtain the optimal electrical properties by valley convergence simultaneously with the minimized lattice thermal conductivity through maximum phonon-alloy scattering. However these conditions especially stoichiometry are often hard to control because of microstructural heterogeneity or immiscibility during material processing and prolonged use. This could easily foster the valley edge offset, inducing the negligible valley convergence as well as the abating phonon-alloy scattering. Here Mg₂Si_0.3Sn_0.7 pellets with different spatial uniformity were prepared by varying mixing and annealing time. Mg₂Si_xSn_1-x solid solutions of a wide alloy range were studied because the susceptible ranges for valley convergence (0.6 < x < 0.8) and phonon-alloy scattering (0.1 < x < 0.9) are dissimilar. The power factor ranged from 4.4 mWm⁻¹ K⁻² to 3.2 mWm⁻¹ K⁻² at 573 K and effective mass from 1.1 m ₀ to 0.8 m ₀, and thermal conductivity also varied depending on the degree of homogeneity of Mg₂Si_0.3Sn_0.7 due to the alteration of phonon-alloy scattering, resulting in a large swing of ZT between 1.33 and 0.8 at 673 K. Lastly we found the dependency of single valley effective mass (m^*) on valley edge offset (ΔE _c) where conduction band valley X3 and X1 are broadened with valley convergence (i.e. m ^* at ΔE _c = 0 > m ^* at ΔE _c ≠ 0), proposing a modification on material parameter B ∼ N_V(ΔE _c)/m^*(ΔE _c), where both valley degeneracy (N_V) and m ^* are functions of ΔE _c, on which none of any literature has paid attention so far. Our thorough investigation with an example of Mg₂Si_0.3Sn_0.7 can be utilized for other thermoelectric materials most of which are fundamentally relying on high valley degeneracy and alloying at the base. (paper)