Exploring Intrinsic and Extrinsic $p$-type Dopability of Atomically Thin $\beta$-TeO$_2$ from First Principles

Two-dimensional (2D) $\beta$-TeO$_2$ has gained attention as a promising material for optoelectronic and power device applications, thanks to its transparency and high hole mobility. However, the underlying mechanism behind its $p$-type conductivity and dopability remains unclear. In this study, we investigate the intrinsic and extrinsic point defects in monolayer and bilayer $\beta$-TeO$_2$, the latter of which has been experimentally synthesized, using the HSE+D3 hybrid functional. Our results reveal that most intrinsic defects are unlikely to contribute to $p$-type doping in 2D $\beta$-TeO$_2$. Moreover, Si contamination could further impair $p$-type conductivity. Since the point defects do not contribute to $p$-type conductivity, we propose two possible mechanisms for hole conduction: hopping conduction via localized impurity states, and substrate effects. We also explored substitutional $p$-type doping in 2D $\beta$-TeO$_2$ with 10 trivalent elements. Among these, the Bi dopant is found to exhibit a relatively shallow acceptor transition level. However, most dopants tend to introduce deep localized states, where hole polarons become trapped at Te's lone pairs. Interestingly, monolayer $\beta$-TeO$_2$ shows potential advantages over bilayers due to reduced self-compensation effects for $p$-type dopants. These findings provide valuable insights into defect engineering strategies for future electronic applications involving 2D $\beta$-TeO$_2$.