Electronic structure and thermoelectric properties ofn- andp-type SnSe from first-principles calculations

We present results of the electronic band structure, Fermi surface, and electron transport property calculations in the orthorhombic $n$- and $p$-type SnSe, applying the Korringa-Kohn-Rostoker method and the Boltzmann transport approach. The analysis accounted for the temperature effect on crystallographic parameters in $Pnma$ structure as well as the phase transition to $CmCm$ structure at ${T}_{c}\ensuremath{\sim}807$ K. Remarkable modifications of the conduction and valence bands were noticed upon varying crystallographic parameters within the structure before ${T}_{c}$, while the phase transition mostly leads to the jump in the band-gap value. The diagonal components of the kinetic parameter tensors (velocity, effective mass) and resulting transport quantity tensors [electrical conductivity $\ensuremath{\sigma}$, thermopower $S$, and power factor (PF)] were computed for a wide range of temperature (15--900 K) and hole $(p$-type) and electron $(n$-type) concentrations $({10}^{17}\text{--}{10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$. SnSe is shown to have a strong anisotropy of the electron transport properties for both types of charge conductivity, as expected for the layered structure, with the generally heavier $p$-type effective masses compared to $n$-type ones. Interestingly, $p$-type SnSe has strongly nonparabolic dispersion relations, with the ``pudding-mold-like'' shape of the highest valence band. The analysis of $\ensuremath{\sigma},S$, and PF tensors indicates that the interlayer electron transport is beneficial for thermoelectric performance in $n$-type SnSe, while this direction is blocked in $p$-type SnSe, where in-plane transport is preferred. Our results predict that $n$-type SnSe is potentially even better thermoelectric material than $p$-type SnSe. Theoretical results are compared with the single-crystal $p$-SnSe measurements, and good agreement is found below 600 K. The discrepancy between the computational and experimental data, appearing at higher temperatures, can be explained assuming an increase of the hole concentration versus $T$, which is correlated with the experimental Hall data.