Choosing the correct hybrid for defect calculations: A case study on intrinsic carrier trapping in β−Ga2O3

Due to its wide band gap and availability as a single crystal, $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$ has potential for applications in many areas of micro/optoelectronics and photovoltaics. Still, little is as yet known about its intrinsic defects, which may influence carrier concentrations and act as recombination centers. From a theoretical point of view, the problem is that standard (semi)local approximations of density functional theory usually cannot handle wide band-gap oxides, while results of tuned hybrid functional calculations so far have shown little quantitative coincidence with experimental data on $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$. Here, we show a method for selecting the optimal hybrid, which reproduces not only the band gap, but also satisfies the generalized Koopmans' theorem. Unless the screening is strongly orbital/direction dependent in the given material, such an optimal hybrid can reproduce the whole $GW$ band structure quite accurately. With the optimized functional, and introducing a modification into the charge correction process, we are able to give a consistent description of observed carrier trapping by intrinsic defects in $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$. With the exception of gallium interstitials, which can act as shallow donors, all other intrinsic defects are deep. Gallium vacancies are the main compensating acceptors in $n$-type samples, while both oxygen interstitials and vacancies act as hole traps, in addition to small hole polarons. Considering the limitations imposed by a medium-sized (160-atom) supercell in an ionic solid, the calculated adiabatic and vertical transitions are in good agreement with available experimental data.