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## 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)

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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/)

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[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)

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1  Effectiveness of fluorine termination at nitrogen vacancies inside 1 gallium nitride crystals based on first-principles calculations  2  3 Yuki Fujishiro1*, Tomoe Yayama2*, Takahiro Nagata3, Toyohiro Chikyow4, Fumiko 4 Akagi1, 2 5 1 Electrical Engineering and Electronics Program, Graduate School of Engineering, 6 Kogakuin University, Shinjuku-ku, Tokyo 163-8677, Japan 7 2 Department of Applied Physics, School of Advanced Engineering, University of 8 Kogakuin, 1-24-2, Nishi-shinjuku, Shinjuku-ku, Tokyo, Japan 9 3 Research Center for Electronic and Optical Materials, NIMS, 1-1 Namiki, Tsukuba, 10 Ibaraki 305-0044, Japan 11 4 Research Center for Materials Nanoarchitectonics (MANA) Center for Basic Research 12 on Materials, NIMS, Tsukuba, Japan 13 * Authors to whom correspondence should be addressed: cm24041@ns.kogakuin.ac.jp; 14 yayama.tomoe@cc.kogakuin.ac.jp 15   16 mailto:cm24041@ns.kogakuin.ac.jpmailto:yayama.tomoe@cc.kogakuin.ac.jp2  ABSTRACT 1 Nitrogen (N) vacancies inside gallium nitride (GaN) crystals can scatter carriers and 2 degrade the performance of GaN-based devices. Hydrogen (H) termination is an effective 3 approach for eliminating defect levels in Si crystals but is less effective for GaN because 4 the latter requires higher processing temperatures, which causes H to desorb more easily. 5 Fluorine (F) is a potential alternative to H owing to its high chemical reactivity and small 6 atomic radius. In this study, first-principles calculations were used to investigate the 7 effectiveness of F termination at N vacancies in GaN crystals. The calculated density of 8 states and band dispersion diagram indicated that F termination eliminated defect states 9 near the conduction band edge and made the electronic states near the band edges 10 resemble those of intrinsic GaN. These effects were attributed to the bonding of F atoms 11 with Ga dangling bonds. Although H termination also resulted in the bonding of H atoms 12 with Ga dangling bonds, the bonding states remained within the bandgap near the band 13 edges; therefore, defect levels were not eliminated as effectively as with F termination. 14 This behavior was attributed to the larger energy difference between the bonding and 15 antibonding states of Ga–F bonds compared with Ga–H bonds. These results suggest that 16 F termination can eliminate defect levels caused by N vacancies inside GaN crystals and 17 improve the performance of GaN-based devices. 18   19 3  I. INTRODUCTION 1 Gallium nitride (GaN) is a semiconductor with excellent carrier mobility and dielectric breakdown 2 strength.1,2 However, defects that form during the fabrication of a GaN-based device can result in 3 defect levels in the bandgap and near the band edges, which can cause problems such as current 4 collapse.3,4 Eliminating these defect levels can improve the reliability of GaN-based devices. Defect 5 levels in Si crystals5 and Si–SiO2 interfaces6 are typically eliminated by hydrogen (H) termination. 6 The effectiveness of annealing is determined by the annealing temperature, but annealing GaN 7 typically requires higher temperatures because of its higher melting point compared with Si. For 8 example, Si requires an annealing temperature of 800°C–1000°C to restore crystallinity after ion 9 implantation7,8 while GaN requires an annealing temperature of about 1100°C–1400°C.9,10 In addition, 10 a temperature that is approximately two-thirds the melting point (in Kelvin) is generally required for 11 recrystallization during annealing.11,12 At higher temperatures, adsorbed H desorbs more easily13,14 and 12 can passivate acceptors by forming complexes in Mg-doped p-type GaN.15-17 Therefore, a termination 13 element other than hydrogen, one that remains adsorbed even under high-temperature annealing, is 14 needed to eliminate defect levels in GaN crystals. 15 One potential alternative is fluorine (F). Jung et al.18 investigated the effectiveness of F termination 16 for Germanium (Ge) and confirmed a decrease in vacancy concentrations. F has the highest 17 electronegativity among all elements and thus has high chemical reactivity, which would help keep F 18 atoms bonded on Ga atoms. Furthermore, F atoms have a small atomic radius, which should allow 19 them to diffuse easily inside GaN crystals. To date, the incorporation of F into GaN crystals has been 20 achieved via ion implantation, and the stability of F atoms in GaN crystals and at AlGaN–GaN 21 interfaces has been investigated.19,20 Based on hard X-ray photoelectron spectroscopy measurements 22 at SPring-8, Nagata et al. reported that the Fermi level of GaN thin films annealed under various 23 fluoride atmospheres shifted to the valence band after fluorination unlike untreated samples. This shift 24 suggests that the incorporated fluorine compensates for the residual charges in GaN by reducing the 25 density of defects responsible for Fermi-level pinning.21,22 Gao et al. reported that F plasma treatment 26 of AlGaN/GaN high-electron-mobility transistors reduced the leakage current, which may be 27 attributed to a decrease in interface traps.23 Using first-principles calculations to determine the 28 electronic state of the GaN surface during the adsorption of several F atoms, we previously found that 29 F atoms effectively terminated the GaN (0001) surface.24 Thus, F termination was confirmed to 30 eliminate surface levels from the bandgap at the GaN surface. However, defects that are critical to 31 GaN-based device performance are not necessarily located at the surface but at the interfaces of nitride 32 heterojunctions or inside GaN crystals, where there is marginal space for adsorbed atoms. Therefore, 33 it is necessary to clarify the effects of F termination on defects inside GaN crystals. 34 In this study, we focused on N vacancies inside GaN crystals and used first-principles calculations to 35 investigate how F atoms are adsorbed onto Ga dangling bonds caused by N vacancies inside a GaN 36 4  crystal and to determine their stable atomic configurations. We then analyzed the electronic states of 1 the obtained adsorption structures to clarify whether and how defect levels were eliminated. We also 2 examined the differences between F and H terminations. 3  4  5 II. METHODS 6 The electronic states were obtained via first-principles calculations based on density functional theory 7 using the Vienna Ab initio Simulation Package.25-28 The generalized gradient approximation of 8 Perdew–Burke–Ernzerhof (GGA-PBE) was used as the exchange-correlation functional.29-31 For 9 structural optimization, the convergence criterion was set to 0.005 eV/Å. For the calculations, a cutoff 10 energy of 800 eV and 4 × 4 × 4 k-points mesh were applied. The lattice constants, c/a ratio, and atomic 11 positions were optimized for a GaN unit cell containing two N atoms and two Ga atoms. The optimized 12 lattice constants were a = b = 3.22 Å and c = 5.25 Å. Several types of 3 × 3 × 3 GaN supercell models 13 were created with this unit cell: a pristine model without any defects (i.e., defect-free model), a model 14 incorporating a single N vacancy (VN i.e., defect model), and defect-containing models in which the 15 vacancy was terminated by F or H atoms in various configurations. In this study, we focused on models 16 in which three F atoms were adsorbed (i.e., F-terminated). We also considered models in which three 17 H atoms were adsorbed for comparison (i.e., H-terminated). The metastable structures and electronic 18 states were then determined for each model. We validated the cell size dependency by visualizing the 19 charge density distribution for different supercell dimensions. The results confirmed that localized 20 bonding states in F-terminated model were effectively contained within both the 3 × 3 × 3 model and 21 larger models and that these models reproduced equivalent bonding states. 22 As a preliminary calculation, formation energies were calculated for models in which one to four F 23 atoms were placed around a N vacancy. The metastable structure with three F atoms placed around the 24 N vacancy had the lowest formation energy over a wide range of both the chemical potential 25 parameters of F and the Fermi level shift (Supplementary Materials). Furthermore, we confirmed that 26 the thermodynamic stability of the charged states of VN was consistent with the work reported the 27 formation energy of GaN with the various types of defect by Lyons and van de Walle.32 According to 28 the electron counting model,33 the stability of these F terminated models is because the number of 29 electron pairs derived from the bonding between the Ga dangling bonds and F atoms is an integer. 30  31  32 III. RESULTS AND DISCUSSION 33 A. Identification of metastable structures 34 5  The optimal structures of the defect-free, defect, F-terminated, and H-terminated models were 1 identified, and the stable positions of F and H atoms near the N vacancy were determined. 2  3 1. Defect-free and N-vacancy models 4 Figure 1(a) shows an overall view of the defect-free model, which is a GaN 3 × 3 × 3 supercell 5 containing 54 Ga atoms and 54 N atoms. Fig. 1(b) and (c) show enlarged views of a part of the defect-6 free model and the defect model in the area near a N vacancy. Both models were structurally optimized. 7 In the defect-free model, the bond lengths along the a–b plane and c-axis are 1.97 and 1.98 Å, 8 respectively. In the defect model, these bond lengths are 1.93 and 1.96 Å, respectively. Therefore, the 9 Ga atoms adjacent to the defect move toward the N vacancy. The defect model has dangling bonds on 10 the four Ga atoms adjacent to the N vacancy due to four broken Ga–N bonds that can interact with 11 exogenous species. 12  13  14 Fig. 1. Defect-free and defect models: (a) overall view of the defect-free model, (b) enlarged view of 15 the defect-free model, and (c) enlarged view of the N vacancy in the defect model. 16  17 2. Fluorine-terminated models 18 To determine the energetically stable positions for adsorption of F atoms onto Ga dangling bonds, our 19 approach involved a two-step geometry analysis. First, we detected the potential energy surface (PES) 20 via atomic probing with F and H atoms. Second, we optimized the geometry using the conjugate 21 gradient (CG) method. We employed this two-step analysis because simple geometry optimization 22 only yields results that converge to the local minimum nearest the initial atomic configuration. 23 Exploration of the PES is effective for determining the number and stability of various metastable 24 structures that may exist in the vicinity of the defect. To restrict the degrees of freedom in the 25 exploration, the atomic configuration was fixed during this procedure and the position of the probe 26 atom was varied one-dimensionally. As a first step, total energies were evaluated for F-terminated 27 models with three F atoms placed at various points near the N vacancy. As shown in Fig. 2(a), the line 28 connecting a Ga atom and the N vacancy can be defined as an 𝑟 -axis, where the N vacancy is 29 positioned at 𝑟 = 0. Because four Ga atoms neighbor the N vacancy, four corresponding 𝑟-axes can 30 6  be defined. As shown in Fig. 2(b), an axis connecting the N vacancy and atomic position A can be 1 defined as 𝑟A, and the other axes connecting the N vacancy to atomic positions B, C, and D can be 2 defined as 𝑟B , 𝑟C , and 𝑟D , respectively. The F atoms can then be placed along these axes. For 3 simplicity, the values of 𝑟i  ( i = A to D ) are set the same for all axes rather than setting each 4 independently. Accordingly, 𝑟i is denoted simply as 𝑟 hereafter. Positions with 𝑟 < 0 are closer to 5 the Ga atom, whereas those with 𝑟 > 0 lie in the direction opposite the Ga atom. The F-terminated 6 model with F atoms placed at three of these four positions is designated as the F3 model. In terms of 7 symmetry, two distinct patterns can be defined depending on which three of the four axes the F atoms 8 are placed along. For pattern 1 (p1), F atoms are placed along 𝑟B, 𝑟C, and 𝑟D. For pattern 2 (p2), F 9 atoms are placed along the axes 𝑟A, 𝑟C, and 𝑟D. Two additional configurations equivalent to p2 are 10 also possible, with F atoms located at A, B, and C or at A, B, and D. 11  12  13 Fig. 2. Definition of the axis 𝑟: (a) position of a F atom on axis 𝑟i (i = A–D), and (b) axis 𝑟i in real 14 space. 15  16 Fig. 3 shows the relationship between the total energy and F atom position 𝑟 for the F3p1 and F3p2 17 models, where the F atoms are placed at 0.1-Å intervals in the ranges −1.5 ≤ 𝑟 ≤ −0.5 and 0.5 ≤18 𝑟 ≤ 2.5 . Both the F3p1 and F3p2 models have two local minima in the negative and positive 𝑟 19 7  regions. The local minimum in the positive region (𝑟 = 1.3 Å) has a lower energy than the local 1 minimum in the negative region. In other words, a structure in which the F atoms are located away 2 from the Ga atoms rather than close to them is more stable. 3  4  5 Fig. 3. Relationship between the F atom position 𝑟 and total energy of F3 models: (a) F3p1 and (b) 6 F3p2. 7  8 As a second step of geometry analysis, we performed structural optimization using CG method for 9 F3p1 and F3p2 using the three lowest-energy structures in the positive r region as initial configurations. 10 The three initial structures of F3p1 relaxed to the same metastable configuration, referred to as 11 F3p1_opt. Similarly, the three initial structures of F3p2 relaxed to the same metastable configuration, 12 referred to as F3p2_opt. F3p2_opt had a lower total energy (−659.315 eV) than F3p1_opt 13 (−658.722 eV), indicating that F3p2_opt represents the most stable adsorption structure. Fig. 4 shows 14 the initial and optimized structures of F3p2_opt around the N vacancy. The F atom originally at point 15 A (Fig. 4(a) and 4(b)) moves away from the other F atoms (red arrow) to a position between the Ga 16 atoms in the optimized structure (Fig. 4(c) and 4(d)). These results indicate that the F atoms adsorb on 17 the Ga dangling bonds while maintaining distance from each other. F3p2_opt appears to represent a 18 stable configuration for terminating Ga dangling bonds with three F atoms. 19  20 8   1 Fig. 4. F3p2_opt model: (a) enlarged view (b) and parallel view along the c-axis of the initial structure; 2 (c) enlarged view and (d) parallel view along the c-axis of the optimized structure. 3  4 3. Hydrogen-terminated models 5 A stable structure was determined for H-terminated models in the same manner as for the F-terminated 6 models discussed in the previous section. Because H is a monovalent element similar to F, termination 7 by three H atoms (i.e., H3 model) also satisfies the electron counting model. As with the F3 model, 8 the H3 model also had two distinct patterns: H atoms placed along 𝑟B, 𝑟𝐶 , and 𝑟D (p1) and H atoms 9 placed along 𝑟A, 𝑟𝐶 , and 𝑟D (p2). For both patterns, H atoms were placed at 0.1-Å intervals in the 10 ranges of −1.5 ≤ 𝑟 ≤ −0.3 and 0.5 ≤ 𝑟 ≤ 2.5. Fig. 5 shows the relationship between the energy 11 and H atom position 𝑟. Both the H3p1 and H3p2 models exhibited local minima in the negative and 12 positive 𝑟 regions. However, the energy difference between the local minima in the negative and 13 positive regions was smaller for H than for F. 14  15 9   1 Fig. 5. Relationship between the H atom position r and total energy of H3 models: (a) H3p1 and (b) 2 H3p2. 3  4 For both the H3p1 and H3p2 models, as a second step of geometry analysis, CG geometry optimization 5 was performed using the three different structures near the minimum energy as initial configurations. 6 We confirmed that the same metastable structure was obtained at each energy minimum. Table I lists 7 the energies of the metastable structures. The most stable structure was generated when the H3p2 8 model with H atoms placed in the negative 𝑟 region was used as the initial configuration (H3p2_opt).  9  10 Table I. Total energies of metastable structures for the H3p1 and H3p2 models. 11  Negative 𝑟 Positive 𝑟 H3p1 −653.422 eV −654.146 eV H3p2 −654.667 eV −654.347 eV  12 Fig. 6 shows an enlarged view around the N vacancy for the H3p2_opt model. Two H atoms are 13 located on the upper side where the Ga atom density is higher, and one H atom is positioned on the 14 lower side. Throughout the two-step geometry analysis, we found that the PES exhibits one local 15 minimum on each side of the defect for F and H probe atoms. This finding was further confirmed via 16 CG geometry optimization starting from multiple initial configurations near these local minima, which 17 consistently converged to the same final structures. Furthermore, the stable configuration exhibited a 18 clear elemental dependence: the local minimum further away from the Ga atom is more stable for F 19 whereas the local minimum closer to the Ga atom is more stable for H. Although F and H are 20 monovalent elements, we found that their stable structures are different, which may due to their ionic 21 radii difference. 22  23 10   1 Fig. 6. H3p2_opt model: (a) enlarged view and (b) parallel view along the 𝑐-axis. 2  3  4 B. Electronic states 5 The electronic states for F3p2_opt and H3p2_opt were determined. Fig. 7 shows the band dispersion 6 diagrams and density of state (DOS) distributions for the (a) defect-free, (b) defect, (c) F3p2_opt, and 7 (d) H3p2_opt models. The highest occupied state was set to 0 eV. Both the total DOS and projected 8 DOS (PDOS) were determined for each model. The PDOS includes the outermost orbitals, which 9 include the 4p orbitals of the four Ga atoms adjacent to the N vacancy, the 2p orbitals of the F atoms, 10 and the 1s orbitals of the H atoms. The band dispersion diagrams of the defect-free and defect models 11 show that the latter has a band near the conduction band minimum (CBM) at approximately 0.5 eV 12 that does not appear in the former. This band has marginal energy dispersion, which indicates that it 13 is a localized state. Although the nearly flat defect-induced band exists within the conduction band, 14 the location is considerably shallow and likely serves as a trap level, such as for optical devices under 15 finite temperature and especially highly band-filling conditions. 34 The presence of defect-induced 16 level near the CBM is consistent with the results reported by Lewis et al., who analyzed the electronic 17 states using HSE06 and found defect levels located at CBM +0.2 eV to CBM +0.42 eV.35The PDOS 18 of the defect model also has a peak for Ga_4p near the CBM, which indicates that the previous 19 localized state derives from the Ga dangling bonds. The band dispersion diagram of the F3p2_opt 20 model has clear band edges and no defect levels near the valence band maximum (VBM) and CBM, 21 and it is more similar to the defect-free model than the defect model. In the PDOS of the F3p2_opt 22 model, the peak for Ga_4p no longer exists near the band edges. The lower panel of Fig. 7(c) shows 23 states consisting of Ga_4p and F_2p at approximately −7.5 eV below the VBM. This suggests that 24 three F atoms passivate the Ga dangling bonds and form bonding states, which consequently pushes 25 the corresponding defect levels far from the band edges. The bonding state at Γ point is further 26 discussed in the following section based on the charge density distribution.  27 11   1 Fig. 7. Band dispersion diagrams and density of state (DOS) distributions: (a) defect-free model, (b) 2 defect model, (c) F3p2_opt model, and (d) H3p2_opt model. 3 12   1 Figs. 8–11 show the charge density distributions for the defect-free, defect, F3p2_opt, and H3p2_opt 2 models, respectively. Fig. 8(a) shows that the charge density of the CBM in the defect-free model 3 forms an s-orbital-like isosurface enclosing the N atoms. Fig. 8(b) shows that the charge density of the 4 VBM in the defect-free model forms a p-orbital-like isosurface enclosing the N atoms. Fig. 9 shows 5 the charge density distribution of the defect model at the Γ point (red point in Fig. 7(b)), which is 6 considered to be a defect level. The charge density is localized around the Ga atoms adjacent to the N 7 vacancy, which confirms that the states observed near the CBM are due to Ga dangling bonds. 8  9  10 Fig. 8. Charge density distributions of the defect-free model: (a) CBM and (b) VBM. The isosurface 11 values were taken to be 0.001/bohr3. 12  13 13   1 Fig. 9. Defect level at the Γ point of the defect model. The isosurface values were taken as 0.001/bohr3. 2  3 Fig. 10 shows the charge density distributions of the F3p2_opt model at the Γ point (orange and blue 4 points in Fig. 7(c)), which correspond to the lowest unoccupied state and highest occupied state, 5 respectively. Fig. 10(a) shows that the charge density of the CBM is distributed around the N atoms 6 with an s-orbital-like shape, while Fig. 10(b) shows that the charge density of the VBM is distributed 7 around the N atoms with an p-orbital-like shape, similar to the defect-free model. In addition, no 8 localized states are observed in the lowest unoccupied state and highest occupied state, indicating that 9 placing three F atoms around the N vacancy terminates the Ga dangling bonds and results in a state 10 that closely resembles that of a defect-free GaN crystal. The peaks of the PDOS for the Ga 4p orbitals 11 and F 2p orbitals overlap near an energy of −7.5 eV (lower left panel in Fig 7(c)), which suggests a 12 bond between the Ga dangling bonds and F atoms. Fig. 10(c) shows that the charge density distribution 13 of the bonding state is localized around the F atoms and the Ga atoms adjacent to the N vacancy. This 14 indicates that the Ga atoms adjacent to the N vacancy bond with the F atoms, resulting in elimination 15 of the defect level. 16  17 14   1 Fig. 10. Charge density distributions of the F3p2_opt model: (a) lowest unoccupied state, (b) highest 2 occupied state, and (c) bonding state. The isosurface values were taken as 0.001/bohr3. 3  4 Unlike the band dispersion diagram of the defect-free model (Fig. 7(a)), the band dispersion diagram 5 of the H3p2_opt model (Fig. 7(d)) has a band near an energy of 0 eV. The PDOS of the H3pt_opt 6 model (Fig. 7(d)) also has an overlap between Ga atoms adjacent to the N vacancy and H atoms near 7 the VBM around an energy of 0 eV, which suggests bonding between the Ga dangling bonds and H 8 atoms. Fig. 11(b) shows that the charge density distribution of the highest occupied state at the Γ point 9 (pink point in Fig. 7(d)) is localized around the H atoms and Ga atoms adjacent to the N vacancy, 10 suggesting that this state corresponds to the bonding between the Ga dangling bonds and 1s orbitals 11 of the H atoms. These results indicate that similar to F termination, H termination leads to bonding 12 between Ga dangling bonds and H atoms. 13  14 15   1 Fig. 11. Charge density distributions of the H3p2_opt model: (a) lowest unoccupied state and (b) 2 highest occupied state. The isosurface values were taken to be 0.001/bohr3. 3  4 C. Difference between F and H termination 5 The results in the previous section indicated that F termination is more effective than H termination at 6 eliminating defect levels near the band edges because it shifts these defective states to energy levels 7 far from the band edges. This difference may be attributed to the larger energy difference between the 8 bonding and antibonding states induced by F termination compared to that induced by H termination. 9 The energy eigenvalues for the Ga 4p, F 2p, and H 1s orbitals were calculated to be −5.673573, 10 −19.86485 and −13.60569 eV, respectively, by Harada using the self-consistent field method within 11 the Hartree–Fock approximation.36 Thus the F 2p orbital has a lower energy than the H 1s orbital. Fig. 12 12 shows a schematic of how the energy difference between the bonding and antibonding states 13 induced by binding between the Ga dangling bonds primarily comprising Ga 4p orbitals and F 2p 14 16  orbital is larger than the case with the H 1s orbital. This energy difference means that the adsorption 1 of H onto Ga dangling bonds results in the bonding state remaining near the band edges. In contrast, 2 the adsorption of F onto Ga dangling bonds results in a bonding state that forms at an energy level far 3 from the band edges. This results in electronic states near the band edge resembling those of defect-4 free GaN. In other words, F termination eliminates defect levels more effectively and can improve the 5 performance of GaN-based devices. 6  7  8 Fig. 12. Schematic of the differences in energy of the bonding and antibonding states with (a) H 9 termination and (b) F termination. 10  11  12 IV. Conclusion 13 We used first-principles calculations to investigate the atomic configurations in which three F or H 14 atoms are adsorbed onto Ga dangling bonds inside GaN crystals and the electronic states. For F 15 termination, the most stable configuration corresponded to three F atoms adsorbed at low-symmetry 16 sites located farther from the Ga atoms. In contrast, the most stable atomic configuration for H 17 termination was with three H atoms at positions closer to the Ga atoms. F termination eliminated defect 18 levels near the band edges by forming bonds between the Ga dangling bonds and F atoms, resulting 19 in electronic states similar to those of defect-free GaN. In contrast, although H termination also formed 20 bonds between Ga dangling bonds and the H atoms, the resulting bonding state appeared near the 21 VBM. The localized states induced by H termination could affect the performance of GaN-based 22 devices. While this study does not address experimental methods of F incorporation, the findings 23 indicate that achieving an ideal fluorinated configuration could effectively eliminate defect levels. 24  25  26 SUPPLEMENTARY MATERIAL 27 17  The formation energies of F-terminated models with one to four F atoms placed around the N vacancy 1 are compared. 2  3 ACKNOWLEDGMENTS 4 This work was supported by JSPS KAKENHI Grant Number 25K08496 and used computational 5 resources of AOBA-S provided by Tohoku University through the HPCI System Research Project 6 (Project ID: hp250045). 7  8 AUTHOR DECLARATIONS 9 Conflict of interest 10 The authors have no conflicts to disclose. 11 Author contributions 12 Y. Fujishiro: Data Curation (lead). Formal Analysis (lead). Investigation (lead). Methodology (equal). 13 Visualization (lead). Writing–Original Draft Preparation (lead). T. Yayama: Conceptualization (lead). 14 Data Curation (support). Funding Acquisition (lead). Investigation (support). Methodology (equal). 15 Project Administration (support). Resources (equal). Software (equal). Validation (equal). Writing–16 Original Draft Preparation (support). T. Nagata: Conceptualization (equal). Validation (equal). 17 Writing–Review & Editing (equal). T. Chikyow: Conceptualization (equal). Validation (equal). 18 Writing–Review & Editing (equal). F. Akagi: Project Administration (lead). Resources (equal). 19 Software (equal). Supervision (lead). Validation (equal). Writing–Review & Editing (equal). 20 Data availability 21 The data that support the findings of this study are available within the article. 22  23 REFERENCES 24 1H. Amano, Y. Baines, E. Beam, M. Borga, T. Bouchet, P. R. Chalker, M. Charles, K. J. Chen, N. 25 Chowdhury, R. Chu, C. D. Santi, M. M. D. Souza, S. Decoutere, L. D. Cioccio, B. Eckardt, t. 26 Egawa, P. Gay, J. J. Freedsman, L. Guido, O. Häberlen, g. Haynes, T. Heckel, D. Hemakumara, P. 27 Houston, J. Hu, M. Hua, Q. Huang, A. Huang, S. Jiang, H. Kawai, D. 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