First-principles study of native point defects in topological insulator Bi$_2$Se$_3$

The \emph{p}-type Bi$_{2}$Se$_{3}$ is much desirable as a promising thermoelectric material and topological insulator, while the naturally grown Bi$_{2}$Se$_{3}$ is always \emph{n}-type doped by native point defects. Here we use first-principles calculations to identify the origin of the \emph{n}-type tendency in bulk Bi$_{2}$Se$_{3}$: The Se vacancies (V$_\text{Se1}$ and V$_\text{Se2}$) and Se$_{\text{Bi}}$ antisite dominate the donorlike doping with low formation energy, while the predisposed Bi$_{\text{Se1}}$ defect results in the pair of V$_\text{Se1}$ and Bi interstitial, which is also a donor rather than an acceptor. Moreover, for Bi$_{2}$Se$_{3}$(111) surface, we find that the band structures modulated by the defects explicitly account for the existing experimental observations of \emph{n}-type preference.