Atomic-scale investigation of $γ$-Ga$_2$O$_3$ deposited on MgAl$_2$O$_4$ and its relationship with $β$-Ga$_2$O$_3$
Nominally phase-pure $γ$-$Ga_2O_3$ was deposited on (100) $MgAl_2O_4$ within a narrow temperature window centered at $\sim$470 $^{\circ}$C using metal-organic chemical vapor deposition (MOCVD). The film deposited at 440 $^{\circ}$C exhibited either poor crystallization or an amorphous structure; the film grown at 500 $^{\circ}$C contained both $β$-$Ga_2O_3$ and $γ$-$Ga_2O_3$. A nominally phase-pure $β$-$Ga_2O_3$ film was obtained at 530 $^{\circ}$C. Atomic-resolution scanning transmission electron microscopy (STEM) investigations of the $γ$-$Ga_2O_3$ film grown at 470 $^{\circ}$C revealed a high density of antiphase boundaries. A planar defect model developed for $γ$-$Al_2O_3$ was extended to explain the stacking sequences of the Ga sublattice observed in the STEM images of $γ$-$Ga_2O_3$. The presence of the 180$^{\circ}$ rotational domains and 90$^{\circ}$ rotational domains of $β$-$Ga_2O_3$ inclusions within the $γ$-$Ga_2O_3$ matrix is discussed within the context of a comprehensive investigation of the epitaxial relationship between those two phases in the as-grown film at 470 $^{\circ}$C and the same film annealed at 600 $^{\circ}$C. The results led to the hypotheses that (i) incorporation of certain dopants including Si, Ge, Sn, Mg, Al, and Sc, into $β$-$Ga_2O_3$, locally stabilizes the "$γ$-phase" and (ii) the site preference(s) for these dopants promotes the formation of the "$γ$-phase" and/or $γ$-$Ga_2O_3$ solid solutions. However, in the absence of such dopants, pure $γ$-$Ga_2O_3$ remains the least stable $Ga_2O_3$ polymorph, as indicated by its very narrow growth window, lower growth temperatures relative to other $Ga_2O_3$ polymorphs, and the largest calculated difference in Helmholtz free energy per formula unit between $γ$-$Ga_2O_3$ and $β$-$Ga_2O_3$ than all other polymorphs.