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Strain tunable pudding-mold-type band structure and thermoelectric properties of SnP$_3$ monolayer

Recent studies indicated the interesting metal-to-semiconductor transition when layered bulk GeP3 and SnP3 are restricted to the monolayer or bilayer, and SnP3 monolayer has been predicted to possess high carrier mobility and promising thermoelectric performance. Here, we investigate the biaxial strain effect on the electronic and thermoelectric properties of SnP3 monolayer. Our first-principles calculations combined with Boltzmann transport theory indicate that SnP3 monolayer has the pudding-mold-type valence band structure, giving rise to a large p-type Seebeck coefficient and a high p-type power factor. The compressive biaxial strain can decrease the energy gap and result in the metallicity. In contrast, the tensile biaxial strain increases the energy gap, and increases the n-type Seebeck coefficient and decreases the n-type electrical conductivity. Although the lattice thermal conductivity becomes larger at a tensile biaxial strain due to the increased maximum frequency of the acoustic phonon modes and the increased phonon group velocity, it is still low, only e.g. 3.1 W/(mK) at room temperature with the 6% tensile biaxial strain. Therefore, SnP3 monolayer is a good thermoelectric material with low lattice thermal conductivity even at the 6% tensile strain, and the tensile strain is beneficial to the increase of the n-type Seebeck coefficient.