Understanding the anisotropic response of $\beta$-Ga$_2$O$_3$ to ion implantation
While $\beta$-Ga$_2$O$_3$ is considered a promising wide bandgap semiconductor, the impact of ion-induced defect formation and anisotropic elasticity remains poorly understood. Here, we combine a simulation and experiment X-ray diffraction (XRD) study of the strain-stress dynamics induced by ion implantation into $\beta$-Ga$_2$O$_3$ single-crystals with different surface orientations. The strain accumulation in the out-of-plane direction is observed by XRD to occur in an anisotropic manner, with compressive strain along the [010] direction and tensile strain along the directions perpendicular to (100) and (001). An anisotropic stress/strain accumulation model is proposed and probed via Molecular Dynamics (MD), showing an excellent agreement with the experiments. For higher damage levels, pole figures obtained both experimentally and by MD via a novel reciprocal-space projection method reveal an orientation-independent $\beta$-to-$\gamma$ phase transition, with a fixed crystallographic relationship between the polymorphs. By exploring the strain-stress dynamics in anisotropic systems, this work establishes a method to directly compare macroscale diffraction experiments and atomistic simulations and opens a new path to engineer the properties of such systems utilizing their anisotropic response to ion implantation/irradiation.