# Fileset

[SUPPLEMENTARY_MATERIAL.pdf](https://mdr.nims.go.jp/filesets/857ee169-33cf-4976-85ed-695125d5f47b/download)

## Creator

[Yuki Fujishiro](https://orcid.org/0009-0006-7436-2911), [Tomoe Yayama](https://orcid.org/0000-0002-5708-8723), [Takahiro Nagata](https://orcid.org/0000-0002-8591-2943), [Toyohiro Chikyow](https://orcid.org/0000-0003-3860-4806), [Fumiko Akagi](https://orcid.org/0000-0003-4934-8465)

## Rights

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Yuki Fujishiro, Tomoe Yayama, Takahiro Nagata, Toyohiro Chikyow, Fumiko Akagi; Effectiveness of fluorine termination at nitrogen vacancies inside gallium nitride crystals based on first-principles calculations. J. Appl. Phys. 28 February 2026; 139 (8): 085703 and may be found at https://doi.org/10.1063/5.0303385.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Effectiveness of fluorine termination at nitrogen vacancies inside gallium nitride crystals based on first-principles calculations](https://mdr.nims.go.jp/datasets/798dbb5d-2857-4a03-8944-6b123db49dce)

## Fulltext

1  SUPPLEMENTARY MATERIAL Fig. S1 shows the initial and optimized structures of F-terminated 3 × 3 × 3 GaN supercell models with one to four F atoms placed around the N vacancy. Models are labeled according to the number of F atoms placed around the N vacancy (Fn). The F2 and F3 models have two types of patterns that are distinguished by their symmetry: p1 and p2. The total energies of the F-terminated models, defects (VN), and ideal GaN model (which was used as a reference) were calculated with considering various charged states of GaN models.    Fig. S1. Enlarged views of F-terminated models with one to four F atoms placed around the N vacancy: (a) F1, (b) F2p1, (c) F2p2, (d) F3p1, (e) F3p2, and (f) F4. The top row shows the initial structures, and the bottom row shows the optimized structures.  The formation energy ∆𝐸form is expressed as ∆𝐸form = 𝐸term − 𝐸ideal + 𝑛N𝜇N − 𝑛F𝜇F + 𝑞(𝐸F + 𝜀V) + ∆𝑣 (1) where 𝐸term and 𝐸ideal are the total energies of a F-terminated model and of the ideal GaN model, respectively. 𝑛N  is the number of missing N atoms, and 𝑛N    1 in this study. 𝜇N  is the chemical potential of N and calculated using the total energy difference between a Ga–N atom pair (𝜇GaN/2) and a Ga atom (𝜇Ga)  in the GaN crystal. 𝑛F  is the number of adsorbed F atoms, and 𝜇F  is the chemical potential of a F atom in the GaN crystal. 𝜇F is given by the sum of the chemical potential of F in the molecular state F2 (𝜇moleculeF2 /2) and the chemical potential parameter Δ𝜇F: 𝜇crystalF =𝜇moleculeF22+ Δ𝜇F. (2) Δ𝜇F is a correction term that is defined as the difference between 𝜇crystalF  and 𝜇moleculeF2 /2:  2  Δ𝜇F = 𝜇crystalF −𝜇moleculeF22≤ 0. (3) q denotes the charged states. Electrons added or removed from the supercell are expressed by the Fermi level (EF) of the semiconductor host, which is in reference to the valence band maximum (VBM) (εv). In this study, any potential correction is not employed; therefore, ∆𝑣 = 0. Based on Eqs. (2) and (3), Eq. (1) reduces to Eq. (4). Here, the case in which F is incorporated into the solid phase corresponds to 𝜇crystalF − 𝜇moleculeF2 /2 ≤ 0. Δ𝜇F → 0 corresponds to an F-rich environment. In this environment, 𝜇crystalF  and 𝜇moleculeF2 /2 are identical. ∆𝐸form = 𝐸term − 𝐸ideal + 𝑛N (12𝜇GaN − 𝜇Ga) − 𝑛F12𝜇moleculeF2 − 𝑛FΔ𝜇F + 𝑞(𝐸F + 𝜀V) (4) Fig. S2 shows the formation energy as a function of EF for various Δ𝜇F. The black lines indicate the formation energies of VN with various charged states. The results show good agreement with Ref. 32 at the GGA-PBE level. In an F-rich limit environment ( Δ𝜇F = 0 ), F4()) and F4(−) are thermodynamically stable. Eventually, the F4(−1), F3p2()), and F2(+) configurations emerge as stable phases depending on the fluorine concentration. These results are reasonable because they satisfy the electron counting rule except for F4()). Consequently, the F3p2 structure, which is the focus of this paper, is considered a realistic configuration that can exist stably. In addition, the tendency of fluorine atoms to be incorporated near the defect is revealed.   Fig. S2. The formation energy ∆𝐸form as a function of EF with various Δ𝜇F conditions.