Native defects and $p$-type dopability in transparent $\beta$-TeO$_2$: A first-principles study

Although $\beta$-TeO$_2$ is a promising $p$-type transparent conducting oxide (TCO) due to the large optical gap ($\sim$ 3.7 eV) and a light effective hole mass, its hole dopability still remains unexplored. In this work, electronic structure of $\beta$-TeO$_2$ and its point defects are investigated using the HSEsol functional with the band-gap-tuned mixing parameter. Our calculations reveal that $\beta$-TeO$_2$ exhibits a significant difference between the fundamental and optical band gaps because lower energy optical transitions are dipole forbidden. Additionally, it has a low hole effective mass, especially in-plane. The point defect calculations show that $\beta$-TeO$_2$ is intrinsically an insulator. From systematic calculations of the trivalent dopants as well as hydrogen, Bi doping is suggested as the best candidate as an acceptor dopant. This work paves the way for the material design of the $p$-type $\beta$-TeO$_2$.