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Density functional calculations have performed to study the band structuresof $Bi_2Te_3$-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 tothe change of valence band. The band degeneracy of valence band maximum ismaintained 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 isreduced from 6 to 2(1). Based on the results of band structures, we suggest thesuitable stoichiometries of ternary compounds for high thermoelectricperformance.

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