First-principles calculations of Ag-Sb nanodot formation in thermoelectric $\mathrm{Ag}{\mathrm{Pb}}_m\mathrm{Sb}{\mathrm{Te}}_{2+m}$ $(m=6,14,30)$

We have performed first-principles calculations for the $\mathrm{Ag}{\mathrm{Pb}}_m\mathrm{Sb}{\mathrm{Te}}_{2+m}$ ($m=6$, 14, and 30) to clarify the effect of simultaneous doping of Ag and Sb on PbTe. The atomic positions were optimized for the model structures with $m=6$, 14, and 30. We calculated the formation energy and the lattice constant by varying the distance between Ag and Sb atoms in each model structure and revealed that the Ag-Sb pair is stabilized when it forms the nearest neighbor in the PbTe matrix, which is consistent with recently reported experimental data. The temperature dependence of the Seebeck coefficient for $\mathrm{Ag}{\mathrm{Pb}}_{14}\mathrm{Sb}{\mathrm{Te}}_{16}$ was also calculated in the framework of the Bloch-Boltzmann transport theory. The calculated Seebeck coefficient for $\mathrm{Ag}{\mathrm{Pb}}_{14}\mathrm{Sb}{\mathrm{Te}}_{16}$ turned out to be close to that of PbTe below $300\mathrm{K}$. However, the value at high temperatures tends to be saturated and becomes less in magnitude than that of PbTe. The lattice thermal conductivity is found to be significantly lowered with increasing the Ag-Sb doping as a result of a shortening of the mean free path. We conclude that there exists an optimum Ag-Sb concentration, at which the thermal conductivity is substantially reduced but a large Seebeck coefficient of PbTe is essentially preserved, so that the dimensionless figure of merit can be increased beyond that of PbTe at high temperatures around $800\mathrm{K}$.