Defect analysis of the $\beta$- to $\gamma$-Ga$_{2}$O$_{3}$ phase transition
In this study, we investigate the ion-irradiation-induced phase transition in gallium oxide (Ga2O3) from the $\beta$ to the $\gamma$ phase, the role of defects during the transformation, and the quality of the resulting crystal structure. Using a multi-method analysis approach including X-ray diffraction (XRD), transmission electron microscopy (TEM), Rutherford backscattering spectrometry in channeling mode (RBS/c), Doppler broadening variable energy positron annihilation spectroscopy (DB-VEPAS) and variable energy positron annihilation lifetime spectroscopy (VEPALS) supported by density functional theory (DFT) calculations, we have characterized defects at all the relevant stages before, during, and after the phase transition. Reduction in backscattering yield was observed in RBS/c spectra after the transition to the $\gamma$ phase. This is corroborated by a significant decrease in the positron trapping center density due to generation of embedded vacancies intrinsic for the $\gamma$-Ga2O3 but too shallow in order to trap positrons. A comparison of the observed positron lifetime of $\gamma$-Ga2O3 with different theoretical models shows good agreement with the three-site $\gamma$ phase approach. A characteristic increase in the effective positron diffusion length and the positron lifetime at the transition point from $\beta$-Ga2O3 to $\gamma$-Ga2O3 enables visualization of the phase transition with positrons for the first time. Moreover, a subsequent reduction of these quantities with increasing irradiation fluence was observed, which we attribute to further evolution of the $\gamma$-Ga2O3 and changes in the gallium vacancy density as well as relative occupation in the crystal lattice.