Ab initio study of carrier mobility in Bi$_2$O$_2$Se

Bi$_2$O$_2$Se is an emerging high-performance layered semiconductor with excellent stability. While experimental studies have explored carrier transport across various doping levels for both $n$-type and $p$-type conduction, a comprehensive theoretical understanding remains incomplete. In this work, we present parameter-free first-principles calculations of the electron and hole mobilities in Bi$_2$O$_2$Se, based on iterative solution of the Boltzmann transport equation that includes electron-phonon scattering and ionized impurity scattering on an equal footing. Intriguingly, we find that Bi$_2$O$_2$Se exhibits high electron mobilities in both the in-plane and out-of-plane directions, whereas the hole mobilities are only significant in the in-plane direction, displaying a unique three-dimensional (3D) electron transport and two-dimensional (2D) hole transport behavior. At 300~K, the calculated intrinsic electron and hole mobilities along the in-plane direction are 447~$\mathrm{cm^2\,V^{-1}\,s^{-1}}$ and 29~$\mathrm{cm^2\,V^{-1}\,s^{-1}}$, respectively, which are primarily affected by Fr\"ohlich electron-phonon interactions. Due to its large static dielectric permittivity, Bi$_2$O$_2$Se exhibits an exceptionally high low-temperature electron mobilities above $1.0\times10^5~\mathrm{cm^2\,V^{-1}\,s^{-1}}$, and its electron mobilities above 50~K is robust against ionized impurity scattering over a wide range of impurity concentrations. By incorporating the Hall effect into our analysis, we predict an in-plane electron Hall mobility of 517~$\mathrm{cm^2\,V^{-1}\,s^{-1}}$ at 300~K, in excellent agreement with experimental data. These results provide valuable insights into the carrier transport mechanisms in Bi$_2$O$_2$Se, and offer predictive benchmarks for future theoretical and experimental investigations.