First-principles study on thermoelectric transport properties of C a 3 S i 4

Thermoelectric properties of a semiconducting silicide, $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$, were investigated by first-principles calculations. The calculation results revealed that $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ has a relatively low lattice thermal conductivity of around $1.2\phantom{\rule{0.16em}{0ex}}\mathrm{W}{\mathrm{m}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$ at 800 K. The Seebeck coefficients and the electrical conductivities of $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ were evaluated by using the Boltzmann transport equation with an energy-dependent relaxation time under the assumption of electron scattering by acoustic phonons. The Seebeck coefficient of $n$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ along the $x$ axis is larger than that along the $z$ axis, while the Seebeck coefficient of $p$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ along the $x$ axis is smaller than that along the $z$ axis. The electrical conductivity of $p$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ is higher than that of $n$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ owing to the smaller effective mass of holes, which results in the higher power factor of $p$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$. Maximum $ZT$ (a dimensionless figure of merit) of single-crystalline $p$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ is higher than that of $n$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$, reaching 0.9 at 800 K. Grain-size effects on the lattice thermal conductivities and power factors were also investigated. Reducing lattice thermal conductivities overcomes the decrease of electrical conductivities and thereby enhances $ZT$, taking maximum of 1.0 for $n$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ and 1.5 for $p$-type $\mathrm{C}{\mathrm{a}}_{3}\mathrm{S}{\mathrm{i}}_{4}$ when the grain size is 10 nm.