Resonant States in the Electronic Structure of the High Performance Thermoelectrics ${\mathrm{A}\mathrm{g}\mathrm{P}\mathrm{b}}_m\mathrm{S}\mathrm{b}\mathrm{T}{\mathrm{e}}_{2+m}$: The Role of Ag-Sb Microstructures

Ab initio electronic structure calculations based on gradient corrected density-functional theory were performed on a class of novel quaternary compounds $\mathrm{A}\mathrm{g}{\mathrm{P}\mathrm{b}}_m\mathrm{S}\mathrm{b}{\mathrm{T}\mathrm{e}}_{2+m}$, which were found to be excellent high temperature thermoelctrics with a large figure of merit $ZT\sim 2.2$ at 800 K. We find that resonant states appear near the top of the valence and bottom of the conduction bands of bulk PbTe when Ag and Sb replace Pb. These states can be understood in terms of modified Te-Ag(Sb) bonds. The electronic structure near the gap depends sensitively on the microstructural arrangements of Ag-Sb atoms, suggesting that large $ZT$ values may originate from the nature of these ordering arrangements.

Figure 1

Electron diffraction pattern showing a lowering of the crystal symmetry from cubic to orthorhombic. It corresponds to $[1\overline{1}\overline{2}]$ zone axis in fcc symmetry with cubic unit cell ($a=6.4Å$). Superstructure spots can be indexed in orthorhombic symmetry according to $a_0\sim 9.1Å$, $b_0\sim 15.8Å$, and $c_0\sim 22.3Å$ unit cell. The corresponding zone axis is $[012{]}_0$. Indexation is given for both symmetries.

Figure 2

Unit cell models for (a) single Ag atom in ${\mathrm{A}\mathrm{g}\mathrm{P}\mathrm{b}}_{31}{\mathrm{T}\mathrm{e}}_{32}$, (b) Ag-Sb layer perpendicular to [001] direction in ${\mathrm{A}\mathrm{g}\mathrm{S}\mathrm{b}\mathrm{P}\mathrm{b}}_{18}{\mathrm{T}\mathrm{e}}_{20}$, (c) Ag-Sb layer perpendicular to the fcc [111] direction in ${\mathrm{A}\mathrm{g}\mathrm{S}\mathrm{b}\mathrm{P}\mathrm{b}}_{10}{\mathrm{T}\mathrm{e}}_{12}$, (d) Ag-Sb chain parallel to the [001] direction in ${\mathrm{A}\mathrm{g}\mathrm{S}\mathrm{b}\mathrm{P}\mathrm{b}}_{30}{\mathrm{T}\mathrm{e}}_{32}$, and (e) Ag-Sb cluster in ${\mathrm{A}\mathrm{g}\mathrm{S}\mathrm{b}\mathrm{P}\mathrm{b}}_{16}{\mathrm{T}\mathrm{e}}_{18}$. For the reason of clarity, we show only Pb fcc lattices with Pb in blue, Ag in red, and Sb in green colors.

Figure 3

Total DOS of (a) single Ag atom, (b) single Sb atom, (c) Ag-Sb pair with the Ag-Sb distance of $\sim 11.19Å$, and (d) Ag-Sb pair with Ag-Sb distance of $\sim 4.57Å$ in PbTe. For comparison, the total DOS of PbTe is shown in dashed lines.

Figure 4

Total DOS of (a) Ag-Sb layer model perpendicular to [001] direction, (b) Ag-Sb layer model perpendicular to [111] direction, (c) Ag-Sb chain model, and (d) Ag-Sb cluster model. The total DOS of PbTe is shown in dashed lines.