A first-principles study of thickness dependent thermoelectric power in topological insulating thin-films: Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$, and Sb$_{2}$Te$_{3}$

Three-dimensional topological insulator Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$ and Sb$_{2}$Te$_{3}$ are good thermoelectric materials. We study the semi-classical thermoelectric properties of this topological insulating thin films with the 4-10 quintuple-layer thickness using first-principles calculations and the two-channel model combined with the Boltzmann transport equations. We observe the thickness and material dependent Seebeck coefficients of n- and p-type doped films which is associated the bulk and surface gap, surface to bulk ratio and relative position of surface states with respect to bulk states.