Addendum: The role of oxygen vacancies in the electronic and optical properties of κ-Ga₂O₃

Addendum to: Communications Chemistry https://doi.org/10.1038/s42004-025-01843-1, published online 13 December 2025

After formal acceptance of our manuscript, we became aware of a previous study whose research topics and results partially overlap with our work^1,2. The present Addendum is devoted to clarifying nomenclature confusion and numerical consistency of calculation results related to ε/κ-Ga₂O₃, and the connections between the findings presented in our publication and those reported by the authors of the referenced study.

Nomenclature and structural relationship between ε-Ga₂O₃ and κ-Ga₂O₃

The confusion around the ε and κ phases stems from the historical evolution of structural characterization and nomenclature in the Ga₂O₃ field, which we clarify based on widely accepted crystallographic studies.

Historical nomenclature and structural correction

Prior to 2017, ε-Ga₂O₃ was initially assigned to a hexagonal crystal system with the space group P6₃mc due to its pseudo-hexagonal diffraction characteristics in conventional XRD measurements^3,4,5. However, theoretical studies consistently predicted that ε-Ga₂O₃ belongs to the orthorhombic crystal structure⁶. In 2017, Cora et al. resolved this ambiguity using high-resolution transmission electron microscopy (HRTEM), demonstrating that the so-called ε-Ga₂O₃ has an intrinsic orthorhombic crystal structure with the non-centrosymmetric space group Pna2₁⁷. The exact same structure defined as κ-Ga₂O₃. The macroscopically observed hexagonal symmetry of ε-Ga₂O₃ thin films arises entirely from 120° in-plane rotational twinning of orthorhombic κ-Ga₂O₃ domains, rather than an intrinsic hexagonal lattice⁸. Therefore, the term κ-Ga₂O₃ in our work refers to orthorhombic κ-Ga₂O₃, as characterized by microstructural analysis.  

Intrinsic structural unity

In both experimental and theoretical research, ε-Ga₂O₃ and κ-Ga₂O₃ are universally referred to as the ε/κ phase system, as they share an identical orthorhombic Pna2₁ crystal structure unit cell, with 4 crystallographically inequivalent Ga sites and 6 inequivalent O sites⁹. This is the only structurally stable lattice model for first-principles calculations of this polymorph, as multi-domain twinned ε-Ga₂O₃ cannot be accurately modeled via conventional periodic supercell calculations.

The only meaningful distinction between the two terms in the field lies in their microstructural morphology. ε-Ga₂O₃ typically refers to the experimentally common multi-domain, pseudo-hexagonal thin films, composed of three orthorhombic κ-Ga₂O₃ domains rotated by 120° relative to each other. In addition, κ-Ga₂O₃ specifically refers to the single-domain, intrinsic orthorhombic phase, which is the ideal lattice model for all first-principles calculations of this polymorph’s intrinsic physical and defect properties. In short, the ε and κ phases share the exact same intrinsic crystal structure at the unit cell, and the two nomenclatures describe the same polymorph from macroscopic morphological and microscopic crystallographic perspectives, respectively. Consequently, numerous researchers refer to orthorhombic Ga₂O₃ as either ε-Ga₂O₃ or κ-Ga₂O₃^10,11. This is the fundamental reason for the consistency in the physical trends of oxygen vacancy defects between the two studies^1,2.

Connections of the close numerical values between the two works

The close numerical values of the charge transition levels (CTLs) and formation energies of oxygen vacancies between Ref. ¹ on ε-Ga₂O₃ and our work in Ref. ² on κ-Ga₂O₃ constitute a scientifically rational result. Since the two studies are based on the same Pna2₁ orthorhombic unit cell (the only stable lattice model for this polymorph), the formation energy and CTLs of oxygen vacancies, as intrinsic point defects, are fundamentally determined by the local atomic coordination, electronic structure, and bonding characteristics of the lattice. The high consistency in the overall trend and numerical range of defect properties between the two works is direct evidence of the reproducibility of the physical laws of oxygen vacancies in the ε/κ-Ga₂O₃ system, which is a core feature of credible first-principles research in condensed matter physics.

Our work is completely independent in calculation methodology. Ref. ¹ employed the PBE0-TC-LRC hybrid functional with a 480-atom supercell for ε-Ga₂O₃ calculations. In contrast, our work used the HSE06 hybrid functional (the most widely used functional for Ga₂O₃ defect calculations in the field) and a 160-atom fully relaxed orthorhombic κ-Ga₂O₃ supercell. The differences in exchange-correlation functional selection, supercell size, and k-point sampling scheme determine that all numerical results in our work are independent calculation outputs. Although the trends in transition levels are in close concordance with the published results, minor numerical differences between the two works (e.g., the (+2/0) CTL of V_O6 is 1.84 eV relative to the calculated CBM in the ref. ¹ on ε-phase work, while we obtained 2.05 eV for the same site; the (+2/0) CTL of V_O1 is 0.95 eV relative to the calculated CBM in the ref. ¹ on work vs. 1.01 eV in ours) further verify the independence of our calculations by different functional. In summary, the close numerical values between the two works are a testament to the universality of the physical laws of oxygen vacancies in the ε/κ-Ga₂O₃ system, while our work provides independent calculation results and novel physical mechanism insights for this polymorph.

We acknowledge the contributions of Kaewmeechai et al. to the study of oxygen vacancies in Ga₂O₃ polymorphs; their systematic investigation of α-, β-, and ε-Ga₂O₃ provides a valuable reference for understanding the universal characteristics of V_O in Ga₂O₃ materials, and our work complements the research gap in κ-Ga₂O₃, enriching the academic community’s understanding of defect behaviors in metastable Ga₂O₃ phases^1,2.