【International Papers】Mapping primary crystallographic planes in β-Ga₂O₃ based on a pseudo-cubic oxygen sublattice

      Researchers from the National Institute for Materials Science have published a dissertation titled "Mapping primary crystallographic planes in β-Ga₂O₃ based on a pseudo-cubic oxygen sublattice" in Japanese Journal of Applied Physics.

Background

      Recently, β-Ga₂O₃ has attracted increasing attention as a promising semiconductor for ultraviolet optoelectronics and power electronics, owing to its large bandgap (≥4.43 eV) and the availability of scalable, melt-grown single crystals. In particular, the availability of low-defect native substrates provides a reproducible platform for the optimization of homoepitaxy and device processing, thereby enabling rapid device demonstration. However, establishing clear guidelines for substrate orientation selection and the associated process design remains challenging owing to its low-symmetry monoclinic structure, in contrast to conventional semiconductors with high-symmetry crystal structures (e.g. diamond, zinc blende, and wurtzite structures).

      β-Ga₂O₃ crystallizes in the monoclinic system (space group C2/m) and has lattice parameters of a = 12.214 Å, b = 3.0371 Å, c = 5.7981 Å, α = 90°, β = 103.83°, and γ = 90°. This monoclinic structure, unique to β-Ga₂O₃ and θ-Al₂O₃, hampers an intuitive understanding of crystal orientations. For example, the planes that are exactly and nearly perpendicular to (100) are {010} and {-112}/{-102}, respectively; however, such orientation relationships are not readily apparent from the monoclinic unit cell. Therefore, an alternative and more straightforward representation is required to facilitate understanding of this complex crystal structure.

Abstract

      Although β-Ga₂O₃ crystallizes in the monoclinic system, its structural complexity can be simplified by focusing on the oxygen framework. The oxygen sublattice forms a cubic close-packed arrangement, corresponding to a distorted face-centered cubic (fcc) structure defined by lattice vectors: afcc = b + 1/2 c, bfcc = −b + 1/2 c, cfcc = 1/3 a + 1/6 c, giving lattice parameters of a_fcc = b_fcc = 4.20 Å, c_fcc = 3.95 Å, α_fcc = β_fcc = 90.1°, γ_fcc = 92.7°. This pseudo-cubic representation provides a straightforward understanding of the crystal shape, thereby facilitating systematic exploration of its crystal orientations.

Conclusion

      In summary, we systematically investigated a pseudo-cubic description of monoclinic β-Ga₂O₃ based on its distorted fcc oxygen sublattice. By defining an averaged fcc unit cell and establishing the correspondence between fcc and monoclinic planes, the complex orientation relationships of β-Ga₂O₃ can be understood in an intuitive and straightforward manner. This approach identifies the primary planes constituting the oxygen sublattice, clarifies the orthogonal relationships among these planes, enables reasonable selection of substrate orientations suitable for vertical etching, and allows estimation of epitaxial relationships with cubic oxides such as NiO. The pseudo-cubic representation therefore provides a practical crystallographic basis for β-Ga₂O₃ and is useful for screening unexplored substrate orientations.

Fig. 1. Averaged pseudo-cubic unit cell of the distorted face-centered cubic (fcc) oxygen sublattice in β-Ga₂O₃. The unit cell is defined by the lattice vectors afcc, bfcc, and cfcc, giving lattice parameters of a_fcc, b_fcc, c_fcc, α_fcc, β_fcc, and γ_fcc. Oxygen atoms are placed at the fcc sites and are shown in the unit cell as open circles.

Fig. 2. Crystal shape faceted with the representative oxygen sublattice planes of β-Ga₂O₃. The Miller indices of the hidden (hkl) facets can be identified because they are crystallographically equivalent to their opposite (hkl) facets that are already labeled.

 

DOI：

doi.org/10.35848/1347-4065/ae42ac