$β$-Ga$_2$O$_3$(001) surface reconstructions from first principles and experiment

TL;DR

This work addresses the problem of understanding surface reconstructions on β-Ga₂O₃(001) under epitaxial growth conditions. It combines ab initio atomistic thermodynamics with replica-exchange grand-canonical MD and experimental HAADF-STEM validation to map phase stability as a function of oxygen and gallium chemical potentials. A key finding is the identification of a stable 1×2 reconstruction on the (001)-B termination comprising paired GaO₄ tetrahedra, which aligns with STEM observations, along with an In-substitution effect that depends on the oxygen environment. The study provides actionable insights for controlling surface structure during MEXCAT growth and highlights directions for investigating kinetics and alternative reconstructions at high temperatures.

Abstract

We present a comprehensive investigation of reconstructions on $β$-Ga$_2$O$_3$(001) combining first-principles calculations with experimental observations. Using {\it ab initio} atomistic thermodynamics and replica-exchange grand-canonical molecular dynamics simulations, we explore the configurational space of possible reconstructions under varying chemical potentials of oxygen and gallium. Our calculations reveal several stable surface reconstructions, most notably a previously unreported 1$\times$2 reconstruction consisting of paired GaO$_4$ tetrahedra that exhibits remarkable stability across a wide range of experimental growth conditions. In this reconstruction, two Ga atoms share one oxygen bond and are separated by a distance of \SI{2.64}{\angstrom} along the [010] direction. High-angle annular dark-field scanning transmission electron microscopy imaging of homoepitaxially grown (001) layers is consistent with the predicted structure. Additional investigations of possible indium substitution at the surface sites, which can occur during metal-exchange catalysis growth, reveal a cooperative effect in In incorporation, with distinct stability regions for In-substituted structures under O-rich conditions. Our findings provide an understanding for controlling surface properties during epitaxial growth of $β$-Ga$_2$O$_3$(001).

Figures (14)

• Figure 1: a) Conventional unit cell of $\beta$-Ga$_2$O$_3$ viewed along [010]. The octahedrally (tetrahedrally) coordinated gallium atoms, Ga1 (Ga2), are dark (light) green. The inequivalent oxygen atoms are shown in orange (O1), red (O2), and yellow (O3). The stoichiometric (001)-A and (001)-B terminations are indicated by colored lines. b) Overlays of the unrelaxed (gray) and relaxed (bright color) stoichiometric (001)-A and (001)-B surface terminations. Shown is a side view of the surface structures projected along [010].
• Figure 2: Unrelaxed bulk-truncated (001) surface terminations. The stoichiometric terminations are (001)-B (left) and (001)-A (right). The different terminations are numbered for easier referencing.
• Figure 3: Surface phase diagram of $\beta$-Ga$_2$O$_3$(001) obtained with the functional PBEsol, including only the bulk-truncated terminations from Fig. \ref{['fig:bulk_truncated_structures']}. The top four panels show the relaxed surface structures along [010], which have a region of stability in the phase diagram. At the top and right axes, the dependence of $\Delta \mu_{\text{O}}$ and $\Delta \mu_{\text{Ga}}$ is transformed into a pressure scale at a fixed temperature of 1000K. The dashed rectangles indicate the experimentally accessible pressure range of $10^{-10}$ to 1.
• Figure 4: Top view of the ideal (001)-A surface. The conventional unit cell is indicated by the black rectangle. Adsorption sites are marked with different symbols, i.e., atop sites with unfilled crosses and hollow sites with filled symbols.
• Figure 5: Surface phase diagrams of $\beta$-Ga$_2$O$_3$(001) in oxygen and gallium atmosphere obtained with different levels of theory: geometries relaxed with PBEsol (left) and with PBE0(0.26) at the PBEsol geometries (right). Shown are projections along [010] of the surface structures, which have a region of stability in the phase diagram. The chemical potentials $\Delta \mu_{\text{O}}$ and $\Delta \mu_{\text{Ga}}$ are transformed into a pressure scale at a fixed temperature of 1000K shown as top and right axes. The dashed rectangles indicate the experimentally accessible pressure range of $10^{-10}$ to 1.