First-Principles Study of Mg-Induced Phase Stabilization in Ga$_2$O$_3$ polymorphs

TL;DR

This work addresses how Mg incorporation affects the relative phase stability of Ga$_2$O$_3$ polymorphs, motivated by experimental observations of γ-Ga$_2$O$_3$ stabilization during growth on Mg-containing substrates. Using first-principles density functional theory with PAW-PBE, it constructs $(\mathrm{Mg}_{x}\mathrm{Ga}_{1-x})_2\mathrm{O}_{3-x}$ alloys up to $x=0.25$ and evaluates formation enthalpies against $eta$-Ga$_2$O$_3$ and MgO, incorporating charge compensation by oxygen vacancies. The key findings are that Mg substitution narrows the enthalpy gaps between polymorphs, Mg shows a clear octahedral-site preference in the β phase, and γ-Ga$_2$O$_3$ exhibits no strong site preference yet benefits thermodynamically from configurational entropy in its disordered spinel-like framework, potentially enabling γ formation under high-temperature or non-equilibrium growth. These results provide a thermodynamic rationale for γ stabilization observed during epitaxial growth on Mg-containing substrates and suggest cation substitution as a viable strategy to tailor Ga$_2$O$_3$ polymorph stability in device-relevant contexts, with the data and workflows openly available on GitHub. The study provides a quantitative link between composition, site occupancy, and phase stability, highlighting the role of entropy in stabilizing metastable disordered phases at finite temperatures.

Abstract

In this study, we investigate the effect of Mg incorporation on the relative phase stability of the four primary Ga$_2$O$_3$ polymorphs using density functional theory (DFT) calculations, with the goal of rationalizing experimental observations suggesting that diffusion from MgAl$_2$O$_4$ substrates contributes to relative stabilization of the $γ$ phase. Mg incorporation is modeled up to 25% of Ga sites within supercells derived from fully relaxed unit cells of each polymorph. Our results show that while $β$-Ga$_2$O$_3$ remains the thermodynamically most stable phase, the enthalpic differences between polymorphs decrease with increasing Mg content. The inherently disordered $γ$ phase, with its high configurational entropy, becomes less energetically unfavorable under Mg substitution, suggesting that entropy-driven stabilization may facilitate its formation under high-temperature and/or nonequilibrium growth conditions such as those previously reported. These findings provide a thermodynamic rationale for the experimental observation of the $γ$ phase during epitaxial growth on MgAl$_2$O$_4$ spinel substrates.

Figures (5)

• Figure 1: Cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of films grown at (a) 470 ° C, (b) 750 ° C, and (c) 850 ° C, respectively and their corresponding integrated EDX composition profiles shown in (d-f). The red dashed rectangles with arrows indicate the regions and directions along which the EDX profiles were acquired.
• Figure 2: Illustration of structures for Ga2O3 polymorphs in decreasing order of stability as determined by DFT – (a) $\beta$-Ga2O3; (b) $\kappa$-Ga2O3; (c) $\alpha$-Ga2O3; (d) $\gamma$-Ga2O3. Red spheres denote O atoms and green spheres and polyhedra denote Ga atoms and their coordination. Cells (a) and (c) are primitive unit cells of the respective structures. Structural visualization was performed using VESTA. momma_vesta_2011
• Figure 3: Bulk enthalpy of formation ($\Delta H$) for $(\mathrm{Mg}_{x}\mathrm{Ga}_{1-x})_2\mathrm{O}_{3-x}$ alloys as a function of Mg concentration (% of Ga sites substituted) for the $\alpha$-, $\beta$-, and $\kappa$-polymorphs of Ga2O3. Filled symbols represent minimum values, while open symbols represent the values for enthalpy of formation of other structures in the selected sample of structures for each polymorph at a given concentration.
• Figure 4: Average and range of enthalpy of formation ($\Delta H$) for epitaxially strained Mg-substituted (a) $\beta$-Ga2O3 and (b) $\gamma$-Ga2O3 as a function of % Ga sites substituted, shown for three site occupancy configurations: octahedral-only (yellow), tetrahedral-only (blue), and random distribution (red).
• Figure 5: Atomic-scale HAADF-STEM images for the film grown at (a) 470 °C, (b) 750 °C and (c) 850 °C, respectively. (d) shows the atomic structure of cubic spinel structure along [010] zone. (e) shows the combined line profiles of the image intensity across three atomic rows from (a) to (c), showing the inversion in relative contrast between tetrahedral and octahedral sites.