Three-dimensional anisotropic photoelectric response and carrier transport properties of α − G a 2 O 3 and β − G a 2 O 3

The anisotropic nature of $\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ significantly impacts its device design and performance. However, the understanding of anisotropy is exclusively limited to a few specific crystalline directions. Authors of many studies have been focused on identifying the optimal optoelectronic response direction to enhance device efficiency. In this paper, we thoroughly explore the anisotropic photoelectric properties of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ by systematically analyzing three-dimensional carrier distribution and transport behaviors in energy, momentum, and group velocity spaces. Notably, $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ mainly produce high-energy electrons upon photoexcitation, and the energy range of electrons produced by $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ is 0.7 eV narrower than that of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$, which is beneficial for efficient ballistic transport. Additionally, the electrons in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ are uniformly distributed in initial momentum and group velocity spaces, while the holes exhibit anisotropy. In contrast, both electrons and holes in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$ show significant anisotropy with distinct aggregation directions. These different spatial distributions can result in anisotropic carrier motion in optoelectronic applications. Furthermore, carriers with long relaxation times and mean free paths exhibit distinct optimal transport directions. Notably, for $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$, the optimal transport direction of electrons deviates from their initial group velocity direction, which may lead to low electron utilization during electrical injection. For $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$, the optimal transport directions of carriers are consistent with their initial group velocity directions, indicating the potential of realizing the best optoelectronic and electronic devices along these directions. These results provide insights into the anisotropy of photoelectric properties at the atomic and electronic scales, which guide making the best use of carriers in designing $\mathrm{G}{\mathrm{a}}₂{\mathrm{O}}₃$-based devices.