Structure and thermodynamic stability of $β$-Ga$_2$O$_3$ surfaces

Abstract

We present a comprehensive first-principles investigation of all symmetrically inequivalent low-index surfaces of $β$-Ga$_2$O$_3$, examining their structural properties and thermodynamic stability across experimentally relevant growth conditions. Using density-functional theory with both the semi-local functional PBEsol and a modified PBE0 hybrid functional with 26% exact exchange, denoted PBE0(0.26), we calculate surface free energies for the (010), (100), (001), ($\bar{2}01$), (110), (111), and ($11\bar{1}$) orientations, including the effects of harmonic vibrational contributions and varying oxygen chemical potentials. We demonstrate that the energetic ordering remains consistent across computational approaches and that the vibrational contributions remain below 0.2 J/m$^2$ up to temperatures of 1000 K. A coordination-based model that correlates surface stability with the density of under-coordinated atoms reveals that under-coordinated oxygen atoms and tetrahedral Ga sites substantially destabilize surfaces, while exposed under-coordinated octahedral Ga atoms serve as indicators of surface stability. Our thermodynamic analysis shows that stoichiometric terminations dominate over nearly the entire range of chemical potentials relevant for $β$-Ga$_2$O$_3$ stability, while non-stoichiometric terminations emerge only under extreme reducing or oxidizing conditions. Notably, we predict the formation of stable Ga-rich terminations resembling Ga adlayers for the (100) and ($\bar{2}01$) surfaces under highly reducing conditions.