By means of positron annihilation lifetime spectroscopy, we have investigated the native defects present in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, which belongs to the family of topological insulators. We experimentally demonstrate that selenium vacancy defects $\left({\text{V}}_{\text{Se1}}\right)$ are present in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ as-grown samples, and that their charge is delocalized as temperature increases. At least from 100 K up to room temperature both ${\text{V}}_{\text{Se1}}^0$ and ${\text{V}}_{\text{Se1}}^{+}$ charge states coexist. The observed charge delocalization determines the contribution of ${\text{V}}_{\text{Se1}}$ defects to the $n$-type conductivity of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. These findings are supported by theoretical calculations, which show that vacancies of nonequivalent Se1 and Se2 selenium atoms are clearly differentiated by positron annihilation lifetime spectroscopy, enabling us to directly detect and quantify the most favorable type of selenium vacancy. In addition to open-volume defects, experimental data indicate the presence of defects that act as shallow traps, suggesting that more than one type of native defects coexist in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. As will be discussed, the presence of a dislocation density around ${10}^{10}{\mathrm{cm}}^{-2}$ could be the source of the detected shallow traps. Understanding the one-dimensional defects and the origin of the charge delocalization that leads ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ to be an $n$-type semiconductor will help in the development of high-quality topological insulators based on this material.

• Received 1 June 2016
• Revised 11 July 2016
• Corrected 1 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.014117