Prediction of Band Structure of $Bi_2Te_3$-related Binary and Ternary Thermoelectric Materials

Density functional calculations have performed to study the band structures of $Bi_2Te_3$-related binary ($Bi_2Te_3$, $Sb_2Te_3$, $Bi_2Se_3$, and $Sb_2Se_3$) and $Sb$/$Se$ doped ternary compounds [$(Bi_{1-x}Sb_x)_2Te_3$ and $Bi_2(Te_{1-y}Se_y)_3$]. It is found that the band gap can be increased by $Sb$ doping and it is monotonically increased by $Se$ doping. In ternary compounds, the change of the conduction band structure is more significant, as compared to the change of valence band. The band degeneracy of valence band maximum is maintained to be 6 in binaries and ternaries. However, as going from $Bi_2Te_3$ to $Sb_2Te_3$ ($Bi_2Se_3$), the degeneracy of conduction band minimum is reduced from 6 to 2(1). Based on the results of band structures, we suggest the suitable stoichiometries of ternary compounds for high thermoelectric performance.