Atomic signatures of local environment from core-level spectroscopy in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$

We present a joint theoretical and experimental study on core-level excitations from the oxygen $K$ edge of $\beta {\text{-Ga}}_2{\text{O}}_3$. A detailed analysis of the electronic structure reveals the importance of O-Ga hybridization effects in the conduction region. The spectrum from O 1 $s$ core electrons is dominated by excitonic effects, which overall redshift the absorption onset by 0.5 eV, and significantly redistribute the intensity to lower energies. Analysis of the spectra obtained within many-body perturbation theory reveals atomic fingerprints of the inequivalent O atoms. From the comparison of energy-loss near-edge fine-structure (ELNES) spectra computed with respect to different crystal planes, with measurements recorded under the corresponding diffraction conditions, we show how the spectral contributions of specific O atoms can be enhanced while quenching others. These results suggest ELNES, combined with ab initio many-body theory, as a very powerful technique to characterize complex systems, with sensitivity to individual atomic species and to their local environment.

Figure 1

Unit cell of $\beta \text{−}{\text{Ga}}_2{\text{O}}_3$. Tetrahedrally coordinated gallium atoms (Ga1) are depicted in green and octahedrally coordinated ones (Ga2) in gray. Inequivalent O atoms are indicated in red (O1), pink (O2), and maroon (O3).

Figure 2

$\beta \text{−}{\text{Ga}}_2{\text{O}}_3$ crystal in [010] direction. (200) and (001) crystal planes are highlighted. The unit cell of $\beta \text{−}{\text{Ga}}_2{\text{O}}_3$ is indicated by dashed lines.

Figure 3

Density of states (DOS) of $\beta \text{−}{\text{Ga}}_2{\text{O}}_3$, including the total contribution (TDOS) as well as the projections on Ga $s$, $p$, $d$, and O $p$ states. The Fermi energy is set to 0 eV.

Figure 4

Core-level absorption spectrum from the O $K$ edge of $\beta \text{−}{\text{Ga}}_2{\text{O}}_3$, given by the average of the diagonal components of Im ${\varepsilon }_M$. BSE results are indicated by solid lines, including contributions from the inequivalent O atoms, as well as from their sum. The independent-particle (IPA) spectrum is shown for comparison (shaded area). A Lorentzian broadening of 0.1 eV is applied to all spectra. Inset: Two-dimensional projection on the (010) plane of the electron distribution of the lowest-energy exciton from the 1 $s$ core state of O2, indicated by the arrow. The position of the hole is marked by a cross.

Figure 5

ELNES spectra of $\beta \text{−}{\text{Ga}}_2{\text{O}}_3$ along the (200) and (001) crystal planes, showing (a), (b) the total theoretical spectra (BSE, solid lines and IPA, shaded area), as well as the experimental ones (dots); (c), (d) oxygen-resolved contributions. The computed spectra are convolved with a Lorentzian broadening of 1.2 eV. The intensity of all the spectra is normalized to the height of their strongest peak.