Phase stability of ( AlxGa1−x)2O3 polymorphs: A first-principles study

Abstract

Monoclinic ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and ${({\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x})}_{2}{\mathrm{O}}_{3}$ alloys are wide-band-gap semiconductors with promising applications in power electronics. Although the physical properties of monoclinic ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ ($\ensuremath{\beta}$ phase) have been extensively explored, information is lacking about other phases ($\ensuremath{\alpha}, \ensuremath{\gamma}, \ensuremath{\kappa}$) of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and related alloys. Here we use density functional theory to assess the phase stability of different polymorphs of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and ${({\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x})}_{2}{\mathrm{O}}_{3}$ alloys at both zero and finite temperatures. Due to the preference of Al for the octahedral site, the $\ensuremath{\gamma}$ and $\ensuremath{\kappa}$ phases of ${({\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x})}_{2}{\mathrm{O}}_{3}$ exhibit a minimum enthalpy of formation at 62.5% and 50% Al concentrations, respectively. Relative to the other phases, the enthalpy of formation of the $\ensuremath{\gamma}$ phase is the highest over the entire range of alloy compositions. We examined the effect of strain arising from pseudomorphic growth of (010)-oriented ${({\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x})}_{2}{\mathrm{O}}_{3}$ films on $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ substrates and found that the alloys become less stable. At finite temperature we found that the lattice vibrations tend to stabilize the $\ensuremath{\kappa}$ phase and destabilize the $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$ phases, referenced to the monoclinic phase. This can be attributed to the greater phonon density of states of the $\ensuremath{\kappa}$ phase at low frequencies. A unique configurational entropy that is present in the $\ensuremath{\gamma}$ phase due to the cation vacancy disorder plays a substantial contribution in stabilizing the $\ensuremath{\gamma}$ phase at finite temperature, particularly at 50% Al concentration. Our study provides a comprehensive overview of stability of different phases of ${({\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x})}_{2}{\mathrm{O}}_{3}$, offering insights into the driving forces for polymorph formation that should prove useful for improved control over phase-pure growth of these important alloys.