Universal Stability of Ga Split Vacancies across \alpha-, \beta-, and \kappa-Ga2O3 Polymorphs: A Machine-Learning Accelerated Study

Split Ga vacancies are the dominant native acceptor in $\beta$-$Ga_2O_3$; however, their role in $\alpha$ and $\kappa$ phases has been largely overlooked or assumed to be unfavorable. A detailed understanding of these defects is critical for tailoring the electrical conductivity and optical properties and optimising $Ga_2O_3$-based devices. In this work, we used machine learning interatomic potentials (MLIPs) to accelerate the discovery of non-local defect reconstructions, followed by HSE06 hybrid DFT to accurately quantify defect properties of single vacancy $V_{\text{Ga}}$, split vacancy $V_{\text{Ga}}^{\text{i}}$ and substitutional donors ($\mathrm{Hf_{Ga}}$ and $\mathrm{Si_{Ga}}$) across a wide range of experimentally relevant conditions for the oxygen chemical potential. We find that split vacancies are the ground-state vacancy for all studied polymorphs ($\beta$, $\alpha$, and $\kappa$). Split vacancies are more stable than simple vacancies by ~0.75 eV ($\beta$), ~0.41 eV ($\alpha$), and ~0.14 eV ($\kappa$). Notably, MLIPs correctly identified the specific split-vacancy ground states and yielded an energetic ordering of symmetry-inequivalent defect configurations in excellent agreement with HSE06 results. While Hf and Si show low formation energy and act as shallow donors, especially under oxygen-poor conditions, their efficiency is limited by split-vacancy compensation. The growth under oxygen-poor conditions is a universal requirement to suppress these defects and achieve high n-type conductivity across the $Ga_2O_3$ polymorph.