Unraveling the transformation pathway of the β to γ phase transition in Ga2O3 from atomistic simulations

Defect spinel $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ is the least stable polymorph of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, so its frequent appearance as a structural defect within or on the surface of monoclinic $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ remains a mystery. Through first-principles calculations, we explore potential pathways for the phase transition from $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ to $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, and examine two key driving forces: tensile strain and Ga deficiency. When configurational entropy contributions to phase energies are included, the $\ensuremath{\gamma}$ phase becomes energetically competitive with the $\ensuremath{\beta}$ phase, with the free energy difference between these phases diminishing even further under Ga-deficient conditions. Notably, a stability crossover occurs at room temperature at high vacancy concentrations $([{\mathrm{V}}_{\text{Ga}}^{3\ensuremath{-}}]>3%)$. A simple model $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\gamma}$ transformation pathway is identified, comprising two primary reactions, that enables the formation of the $\ensuremath{\gamma}$ phase via simultaneous migration of Ga atoms from tetrahedral lattice sites to octahedral interstitial positions. The transformation barriers are prohibitively large in pristine ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, but can be substantially reduced by: (1) the presence of Ga vacancies, (2) elongational strains along the crystallographic $a$-axis, and (3) when volumetric relaxations are possible during transformation. These results elucidate prior experimental observations, where $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ is seen on damaged surfaces or in highly $n$-type $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ environments, which support Ga deficiency and mechanical strain. The insights into the driving forces and mechanisms of $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ formation enhance understanding of how localized strain and nonequilibrium defect concentrations may facilitate its formation from the $\ensuremath{\beta}$ phase.