# Dynamics Studies of Nitrogen Interstitial in GaN from Ab Initio Calculations

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}(E

_{c}−0.60 eV) and H

_{1}(E

_{v}+0.87 eV) are dominating traps in n-type GaN, and they attributed H

_{1}trap to the gallium vacancy or C related defects. Sunay et.al [10] applied electron paramagnetic resonance (EPR) to find that the hole is around the Mg acceptor. In addition, by using positron annihilation spectroscopy (PAS), EPR, and density functional theory (DFT), Bardeleben et.al [11] found that the isolated N interstitial is unstable and prefers to form a split interstitial configuration, which is located at E

_{c}−1.0 eV. However, experimental devices have limitations, i.e., DLTS can only obtain the energy level but not the specific type of defect.

_{i}can occupy five charge states within the band gap. However, in some cases, such as under the doping process or radiation environment, the defects may move among the material and interact with other defects, instead of keeping as static ones. In contrast with abundant of calculations of static properties, less is known about the dynamics studies of defects [18,19], especially the interaction of defects.

_{i}). First, the most stable configurations of different charge states were calculated. Then, the migration of it was studied and a rotation process, which was not reported in previous researches, was included. Finally, its interaction with vacancy (V

_{N}) was systematically investigated.

## 2. Methods

^{2}2p

^{3}for N and 3d

^{10}4s

^{2}4p

^{1}for Ga were considered. The supercell method was applied with the periodic boundary conditions. Specifically, 4 × 4 × 2 supercell with 128 atoms was large enough to use in our simulations. The gamma k-point mesh was set to 2 × 2 × 2, and the cutoff energy was set as 500 eV. The convergence of force was less than 0.01 eV/Å for all the computations, while the criterion of energy was minimized to a value of 10

^{−5}eV. Climbing image nudged elastic band (CI-NEB) method [23] was used to investigate the migration processes and their corresponding possible minimum energy path, as well as the recombination process. Furthermore, in order to obtain an accurate transition state faster, DIMER method [24] was applied sometimes within CI-NEB method. The criterions of energy and force applied in these two methods were the same as the values in the optimization of structures.

_{i}is described as follows Equation (1) [27]:

## 3. Results

#### 3.1. Configurations of N_{i}

_{i}. Tens of (more than 50) possible sites were carried out assuming that N

_{i}could locate in any possible space in the crystal. The results revealed that wherever the initial N

_{i}is, even the O or T sites, it always prefers a split interstitial configuration. This configuration is a N-N dimer tilted bond as presented in Figure 2, and the calculated formation energy of the neutral state is 4.67 eV. These findings correspond to the previous researches [12,14,17] well. Furthermore, some new specific characteristics of these N

_{i}were concluded, and they could be directly applied in later simulations or experiments.

_{i}should be sixfold symmetry. However, due to the different orientations of N atom with its nearest Ga atoms, the tilted N

_{i}presents a threefold symmetry in each layer, respectively, not a true sixfold symmetry. These threefold symmetry configurations can transform to each other by rotating [0001] axis by multiples of 120°. The example of three configurations on A layer, named “A

_{1},” “A

_{2},” and “A

_{3}” is shown in Figure 2, and the following discussions are mainly based on this A

_{1}configuration. Note that the foreign atom can become either atom in this dimer bond. Due to the tilting characteristic, its direction’s projection on the c-plane is the same as that between the origin N atom with the nearest Ga atom, which is [1−10c] (parameter c is about 1.75). Additionally, its bond length is measured about 1.35 Å. This N-N bond length is a little larger than N

_{2}gas molecule (1.11 Å) and much less than normal Ga-N bond length (1.97 Å), which indicates that it may be a relatively stable bond. The schematics of configurations on B layer are included in Figure A1, Figure A2 and Figure A3 in Appendix A.

_{i}always occupies five charge states (−1 to 3) within the band gap. Therefore, the charge state of −1 to 3 was considered in our research. With regards to different charge states, the bond length of N

_{i}changes significantly, from 1.44 to 1.15 Å. However, the directions are like the neutral ones. The differences between them mainly reflect on the parameter c, and the corresponding results are listed in Table 1. Comparing the values in Table 1, the bond length of N

_{i}was found to increase as the charge state decreases, indicating that positive charge states may provide a more attractive force than negative charge states. On the other hand, our calculated bond length is consistent well with previous work [18,27].

#### 3.2. Migration of N_{i}

_{i}is one of the most common native defects in the GaN material. Therefore, its migration behavior influences the properties of material significantly. As shown in Figure 3a, there are two possible migration paths, in-plane and out-of-plane. Only the first nearest neighbor (1NN) atoms were considered here. With regards to six nearest atoms in-plane, determined by the orientation of N

_{i}, the migration could be divided into three categories, A, B, and C site, as shown in Figure 3b. Since C site is symmetrical with A site, only A and B site was taken into consideration. Furthermore, the upward one (N

_{up}) in N

_{i}was regarded as the atom to migrate.

#### 3.2.1. In-Plane Migration

_{i}are found. The first one is a direct migration, the N

_{up}atom first breaks the bond of interstitial and then directly migrates to the A site, forming a new type N

_{i}. The corresponding migration process is shown in Figure 4a. Note that the initial state (a-1) is different from the final state (a-3), which is another type of orientation in this layer. Furthermore, its related energy barrier is shown in Figure 4b, and the migration barrier is 2.34 eV, which is consistent well with previous studies, i.e., 2.33 eV [14] and 2.4 eV [17,18].

_{2}) in this layer. After the rotation process, the N atom starts to move and then migrates to A site. Compared with the direct migration, there are two different points. First, the final state (a-4) is the same as the initial state (a-1) before rotation. Second, the migrated atom transfers finally to the lower site after the whole migration. The whole process is presented in Figure 5b, and the migration barrier is 2.43 eV, slightly larger than the first type of migration path. And the animations of these two migration are included in Figures S1 and S2 in Supplementary Materials.

_{1}type’s orientation. Therefore, it must rotate first to A

_{2}or A

_{3}type, and then, it migrates directly to B site. When it starts to migrate from A

_{2}type, the migration barrier is 2.43 eV, the same as the indirect migration to A site. However, when it rotates first to A

_{3}type, this process only needs 2.34 eV, which is equivalent to the direct migration. This phenomenon, as shown in Figure 6, illustrates that the different migration barriers (2.43 vs. 2.34 eV) are not influenced by the rotation process. In addition to this, it also can be seen that when the N atom presents downward migration, the migration barrier is 2.43 eV, whereas when the N atom migrates upward, the value changes to 2.34 eV.

#### 3.2.2. Out-of-Plane Migration

_{i}, the results are like previous work [16,17] and show that it could be a direct migration as discussed above. All of the detailed values are also listed in Table 2.

_{i}did not observe the rotation behavior and concluded that it is an isotropic behavior with the same energy barriers from the in-plane to out-of-plane [18]. In our detailed researches, although the rotation barrier of 0.04–0.31 eV is very small compared with migration barriers of about 2 eV, its existence shows that the migration of N

_{i}is not the same, especially in the migration mechanisms. Additionally, under room temperature, according to the Arrhenius equation, the difference of 0.1 eV may cause several orders of magnitude difference of gigahertz, which cannot be neglected in the application of high frequency devices [28,29]. Due to this little barrier, the migration process of N

_{i}can present different possibilities, not merely a direct migration, and the rotation behavior provides a new perspective of the migration of N

_{i}by the theoretical work. Therefore, the migration barrier is concluded to be an anisotropic behavior by the calculations about different migration barriers.

#### 3.3. Stability of N_{i}-V_{N} Complex

_{i}-V

_{N}) was investigated here and the charge states of 0 to +3 were considered due to the possible charge states of isolated defects. Since N

_{i}is a tilted configuration, a range of initial distances (d

_{FP-id}) of N

_{i}-V

_{N}were considered for different charge states. Additionally, the separation distance (d

_{FP-sd}) is defined as the nearest distance of the final N

_{i}-V

_{N}.

_{i}, the recombination (annihilation of interstitial and vacancy, N

_{i}+ V

_{N}→N

_{N}) is not observed for variety of N

_{i}-V

_{N}, except the neutral one with the nearest d

_{FP-id}(2.75 Å) (in the following discussions, this specific condition is not considered). This phenomenon indicates that N

_{i}is a type of relatively stable defect since it cannot nearly recombine spontaneously. In addition, consequently, N

_{i}and V

_{N}remain to locate their site and the N

_{i}bond does not break itself. The bond lengths of N

_{i}in N

_{i}-V

_{N}are illustrated in Table 3. Compared with the values in Table 1, the bond length of N

_{i}in (N

_{i}-V

_{N})

^{q}(0 ≤ q ≤ 3) is found to be almost equal to it of (N

_{i})

^{q}

^{−1}. Accordingly, (N

_{i}-V

_{N})

^{q}is assumed to consist of (N

_{i})

^{q}

^{−1}and (V

_{N})

^{+1}. In order to verify this point more accurately, a more detailed charge analysis of these defects, containing N

_{i}-V

_{N}, isolated N

_{i}and V

_{N}, is required to be carried out.

_{i}defects, this value changes a lot. For the neutral one, the charges of two N

_{i}atoms are identical to become 0.87|e|, and other Ga and N atoms in this system almost do not change. This phenomenon shows that due to the introduction of N

_{i}, the charge of one original N atom decreases and this decrement mainly transfers to the foreign N atom. Since the charges of two N

_{i}atoms are identical, their average values are adopted in the comparison. As for V

_{N}, due to its special property without atoms, the average charges of the four nearest Ga atoms are considered instead. The comparisons between them are shown in Table 4.

_{i}-V

_{N}and isolated defects, the Bader charges of N

_{i}and V

_{N}in (N

_{i}-V

_{N})

^{q}are consistent well with the values of isolated ones, e.g., (N

_{i}-V

_{N})

^{+2}(0.67/1.21 |e|), (N

_{i})

^{+1}(0.66 |e|) and (V

_{N})

^{+1}(1.21 |e|). This accurate comparison suggests that for the N

_{i}-V

_{N}in the q charge state, this configuration could be associated with the reaction of (N

_{i})

^{q}

^{−1}and (V

_{N})

^{+1}, namely, (N

_{i}-V

_{N})

^{q}→(N

_{i})

^{q}

^{−1}+ (V

_{N})

^{+1}. The charge state of V

_{N}always remains the constant value of +1 in N

_{i}-V

_{N}pair. This similar relationship is also found in Si material [32], however, in their studies, they observed that Si interstitial is the defect that remains as constant charge. Additionally, this phenomenon may explain that why only the neutral nearest N

_{i}-V

_{N}recombine spontaneously, since the neutral N

_{i}-V

_{N}is consist of (N

_{i})

^{−1}and (V

_{N})

^{+1}and they are exactly opposite charge.

_{b}< 0 means attraction and E

_{b}> 0 means repulsion for this definition. By introducing different d

_{FP-id}of N

_{i}-V

_{N}, the binding energies with different d

_{FP-sd}were obtained in Figure 8. From this figure, the binding energy of N

_{i}-V

_{N}was observed to be influenced by the d

_{FP-sd}. As the d

_{FP-sd}increases, the binding energy increases first and then stays at about 0 eV from 3.9 Å, which indicates that the well-separated distance of N

_{i}-V

_{N}is 3.9 Å.

_{i}-V

_{N}(d

_{FP-sd}= 3.9 Å) is found to be 2.1 eV, which also verifies that this distance is a truly well separation distance from another perspective. It is worth noting that this recombination barrier is a little less than the migration barrier. Furthermore, the nearest neutral (d

_{FP-sd}= 1.89 Å) one is also calculated to be 0.15 eV. Such small barrier value indicates that this distance of N

_{i}-V

_{N}is a metastable defect complex with strong binding, and it is easier to annihilate under ambient temperature.

#### 3.4. Comparisons with the Experiments

_{i}starts to anneal at 673 K during the first annealing stage, and this process of annealing may relate to the migration process. Additionally, the experiments also showed that this N

_{i}locates at the Fermi level 1 eV below the conduction band minimum, indicating that it most likely corresponds to −1 charged state. Therefore, in order to verify our computation results, the reported experimental results were implemented to compare. According to the previous studies [33,34] of the correlation between activation energy and temperature, Arrhenius law was applied to the activation energy in most of cases. Thus, based on the Equation (3) of Arrhenius law, the activation energy, namely, the migration energy, is given by:

_{i}with −1 charge state is 1.80 eV, which is in good agreement with the experimental results and closer than other works [18,19]. In other words, this comparable result provides another perspective to prove our results.

## 4. Conclusions

_{i}) in GaN material. With regards to different N

_{i}configurations, it is found that the most stable configuration of N

_{i}presents a threefold symmetry in each layer and different charge states of N

_{i}show a similar orientation but different bond lengths.

_{i}, a rotation process which has not been reported is observed. Due to this process, the in-plane migration is found to be divided into two paths, upward and downward paths and the migration barriers of them differ at some charge states. Different from previous studies, our specific work shows that the migration of N atom is an anisotropic process, especially in the migration mechanisms. Furthermore, part of our results of migration of N

_{i}are consistent well with the existing experiments and the corresponding theories.

_{i}-V

_{N})

^{q}may consist of (N

_{i})

^{q}

^{−1}and (V

_{N})

^{+1}. Additionally, the calculations of binding energy and recombination barrier also reveal that the well separation distance of N

_{i}-V

_{N}is about 3.9 Å.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

- Li, Y.-C.; Chang, L.-B.; Chen, H.-J.; Yen, C.-Y.; Pan, K.-W.; Huang, B.-R.; Kuo, W.-Y.; Chow, L.; Zhou, D.; Popko, E. Phosphor-Free InGaN White Light Emitting Diodes Using Flip-Chip Technology. Materials
**2017**, 10, 432. [Google Scholar] [CrossRef] [PubMed] - Polyakov, A.Y.; Lee, I.-H. Deep traps in GaN-based structures as affecting the performance of GaN devices. Mater. Sci. Eng. R Rep.
**2015**, 94, 1–56. [Google Scholar] [CrossRef] - Nguyen, H.T.; Yamada, H.; Yamada, T.; Takahashi, T.; Shimizu, M. Fabrication and Evaluation of N-Channel GaN Metal–Oxide–Semiconductor Field-Effect Transistors Based on Regrown and Implantation Methods. Materials
**2020**, 13, 899. [Google Scholar] [CrossRef] [PubMed] [Green Version] - He, H.; He, C.; Zhang, J.; Liao, W.; Zang, H.; Li, Y.; Liu, W.-B. Primary damage of 10 keV Ga PKA in bulk GaN material under different temperatures. Nucl. Eng. Technol.
**2020**, 52, 1537–1544. [Google Scholar] [CrossRef] - Weaver, B.D.; Martin, P.A.; Boos, J.B.; Cress, C.D. Displacement Damage Effects in AlGaN/GaN High Electron Mobility Transistors. IEEE Trans. Nucl. Sci.
**2012**, 59, 3077–3080. [Google Scholar] [CrossRef] - Costanzo, F.; Giofre, R.; Massari, A.; Feudale, M.; Suriani, A.; Limiti, E. A MMIC power amplifier in GaN on Si technology for next generation Q band high throughput satellite systems. Integration
**2019**, 68, 139–146. [Google Scholar] [CrossRef] - Belabbas, I.; Chen, J.; Nouet, G. Electronic structure and metallization effects at threading dislocation cores in GaN. Comput. Mater. Sci.
**2014**, 90, 71–81. [Google Scholar] [CrossRef] - Ene, V.L.; Dinescu, D.; Zai, I.; Djourelov, N.; Vasile, B.S.; Serban, A.B.; Leca, V.; Andronescu, E. Study of Edge and Screw Dislocation Density in GaN/Al
_{2}O_{3}Heterostructure. Materials**2019**, 12, 42055. [Google Scholar] [CrossRef] [Green Version] - Kanegae, K.; Fujikura, H.; Otoki, Y.; Konno, T.; Yoshida, T.; Horita, M.; Kimoto, T.; Suda, J. Deep-level transient spectroscopy studies of electron and hole traps in n-type GaN homoepitaxial layers grown by quartz-free hydride-vapor-phase epitaxy. Appl. Phys. Lett.
**2019**, 115, 012103. [Google Scholar] [CrossRef] - Sunay, U.R.; E Zvanut, M.; Marbey, J.; Hill, S.; Leach, J.H.; Udwary, K. Small non-uniform basal crystal fields in HVPE free-standing GaN:Mg as evidenced by angular dependent and frequency-dependent EPR. J. Phys. Condens. Matter.
**2019**, 31, 345702. [Google Scholar] [CrossRef] - Van Bardeleben, H.J.; Cantin, J.-L.; Gerstmann, U.; Scholle, A.; Greulich-Weber, S.; Rauls, E.; Landmann, M.; Schmidt, W.G.; Gentils, A.; Botsoa, J.; et al. Identification of the Nitrogen Split Interstitial (N-N)
_{N}in GaN. Phys. Rev. Lett.**2012**, 109, 206402. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gao, F.; Bylaska, E.J.; Weber, W.J. Intrinsic Defect Properties in GaN Calculated by Ab Initio and Empirical Potential Methods. Phys. Rev. B
**2004**, 70, 245208. [Google Scholar] [CrossRef] - Lyons, J.L.; Van de Walle, C.G. Computationally predicted energies and properties of defects in GaN. NPJ Comput. Mater.
**2017**, 3, 180. [Google Scholar] [CrossRef] - Gao, Y.; Sun, D.; Jiang, X.; Zhao, J. Point defects in group III nitrides: A comparative first-principles study. J. Appl. Phys.
**2019**, 125, 215705. [Google Scholar] [CrossRef] - Matsubara, M.; Bellotti, E. A first-principles study of carbon-related energy levels in GaN: I. Complexes formed by substitutional/interstitial carbons and gallium/nitrogen vacancies. J. Appl. Phys.
**2017**, 121, 195701. [Google Scholar] [CrossRef] [Green Version] - Xie, Z.; Sui, Y.; Buckeridge, J.; A Catlow, C.R.; Keal, T.W.; Sherwood, P.; Walsh, A.; Farrow, M.R.; Scanlon, D.O.; Woodley, S.M.; et al. Donor and acceptor characteristics of native point defects in GaN. J. Phys. D Appl. Phys.
**2019**, 52, 335104. [Google Scholar] [CrossRef] [Green Version] - Diallo, I.C.; Demchenko, D.O. Native Point Defects in GaN: A Hybrid-Functional Study. Phys. Rev. Appl.
**2016**, 6, 064002. [Google Scholar] [CrossRef] [Green Version] - Kyrtsos, A.; Matsubara, M.; Bellotti, E. Migration mechanisms and diffusion barriers of carbon and native point defects in GaN. Phys. Rev. B
**2016**, 93, 245201. [Google Scholar] [CrossRef] [Green Version] - Limpijumnong, S.; Van de Walle, C.G. Diffusivity of native defects in GaN. Phys. Rev. B
**2004**, 69, 035207. [Google Scholar] [CrossRef] - Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B
**1996**, 54, 11169–11186. [Google Scholar] [CrossRef] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B
**1999**, 59, 1758–1775. [Google Scholar] [CrossRef] - Henkelman, G.; Uberuaga, B.P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys.
**2000**, 113, 9901–9904. [Google Scholar] [CrossRef] [Green Version] - Henkelman, G.; Jónsson, H. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys.
**1999**, 111, 7010–7022. [Google Scholar] [CrossRef] - Jain, A.; Ong, S.P.; Hautier, G.; Chen, W.; Richards, W.D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; et al. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Mater.
**2013**, 1, 11002. [Google Scholar] [CrossRef] [Green Version] - Schulz, H.; Thiemann, K. Crystal structure refinement of AlN and GaN. Solid State Commun.
**1977**, 23, 815–819. [Google Scholar] [CrossRef] - Freysoldt, C.; Neugebauer, J.; Van De Walle, C.G. Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations. Phys. Rev. Lett.
**2009**, 102, 016402. [Google Scholar] [CrossRef] [Green Version] - Chung, J.W.; Hoke, W.; Chumbes, E.; Palacios, T. AlGaN/GaN Hemt with 300-Ghz Fmax. IEEE Electron. Device Lett.
**2010**, 31, 195–197. [Google Scholar] [CrossRef] - Weichuan, X.; Liu, Z.; Qiu, H.; Ranjan, K.; Palacios, T. Inaln/Gan Hemts on Si with High f
_{T}of 250 Ghz. IEEE Electron. Device Lett.**2017**, 39, 75–78. [Google Scholar] - Tang, W.; Sanville, E.; Henkelman, G. A grid-based Bader analysis algorithm without lattice bias. J. Phys. Condens. Matter
**2009**, 21, 084204. [Google Scholar] [CrossRef] - Henkelman, G.; Arnaldsson, A.; Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci.
**2006**, 36, 354–360. [Google Scholar] [CrossRef] - Beck, M.J.; Tsetseris, L.; Pantelides, S.T. Stability and Dynamics of Frenkel Pairs in Si. Phys. Rev. Lett.
**2007**, 99, 215503. [Google Scholar] [CrossRef] [PubMed] - Dippong, T.; Levei, E.A.; Cadar, O.; Goga, F.; Toloman, D.; Borodi, G. Thermal behavior of Ni, Co and Fe succinates embedded in silica matrix. J. Therm. Anal. Calorim.
**2019**, 136, 1587–1596. [Google Scholar] [CrossRef] - Gerstmann, U.; Rauls, E.; Frauenheim, T.; Overhof, H. Formation and annealing of nitrogen-related complexes in SiC. Phys. Rev. B
**2003**, 67, 205202. [Google Scholar] [CrossRef] - Sahoo, B.K.; Sahoo, S.K.; Sahoo, S. Macroscopic polarization and thermal conductivity of GaN. J. Phys. Chem. Solids
**2013**, 74, 1669–1671. [Google Scholar] [CrossRef]

**Figure 1.**Different view of the structure of wurtzite GaN material: (

**a**) side view and (

**b**) top view of A layer and B layer.

**Figure 2.**Configurations of split interstitial: (

**a**) side view of A

_{1}, (

**b**) top view of A

_{1}, (

**c**) side view of A

_{2}, and (

**d**) side view of A

_{3}(N

_{i}atoms are denoted by yellow spheres, the same below).

**Figure 3.**The migration mechanism of A

_{1}type N

_{i}atom (the yellow atom is migrated N atom, the same as below): (

**a**) two possible paths and (

**b**) the top view of the in-plane migration.

**Figure 4.**The direct in-plane migration for A site: (

**a**) the process of direct migration. (

**b**) The corresponding energy barrier (the solid dots are interpolated points and the solid line show the energy path obtained from CI-NEB methods).

**Figure 5.**The indirect in-plane migration for A site: (

**a**) the process of indirect migration and (

**b**) the corresponding energy barrier.

**Figure 6.**Two rotation-migration mechanisms to B site: (

**a**) A

_{1}rotates to A

_{2}and (

**b**) A

_{1}rotates to A

_{3}.

**Figure 7.**(

**a**) Upward and (

**b**) downward migration (the left yellow atom migrates to the right yellow atom).

Charge State | d_{N-N} (Å) | Parameter c | ||
---|---|---|---|---|

This Work | Other Work | Other Work (%) | ||

3 | 1.15 | 1.12 ^{a} 1.11 ^{b} | 2.61 ^{a} 3.48 ^{b} | 1.50 |

2 | 1.20 | 1.18 ^{a} | 1.67 ^{a} | 1.51 |

1 | 1.27 | 1.25 ^{a} | 1.57 ^{a} | 1.55 |

0 | 1.35 | 1.34 ^{a} | 0.74 ^{a} | 1.75 |

−1 | 1.44 | 1.45 ^{a} 1.41 ^{b} | 0.69 ^{a} 2.08 ^{b} | 2.27 |

Charge State | Rotation Barrier/eV | In/eV(upward/downward) | Out/eV | In/eV | Out/eV |
---|---|---|---|---|---|

−1 | 0.33 | 1.80/1.80 | 1.87 | 1.9 ^{a}, 1.6 ^{b} | 1.9 ^{a}, 1.6 ^{b} |

0 | 0.35 | 2.34/2.43 | 2.40 | 2.4 ^{a}, 2.4 ^{b}, 2.33 ^{c} | 2.4 ^{a}, 2.4 ^{b} |

1 | 0.27 | 2.48/2.52 | 2.18 | 2.2 ^{a}, 2.1 ^{b} | 2.1 ^{a}, 2.1 ^{b} |

2 | 0.24 | 1.98/2.08 | 2.13 | 2.1 ^{a}, 2.5 ^{b} | 2.2 ^{a}, 2.5 ^{b} |

3 | 0.23 | 1.57/1.26 | 2.13 | 2.1 ^{a}, 1.4 ^{b} | 1.7 ^{a}, 1.4 ^{b} |

Defect Type | Charge State | Bond Length/Å |
---|---|---|

N_{i}-V_{N} | +3 | 1.21 |

+2 | 1.26 | |

+1 | 1.34 | |

0 | 1.44 |

Defect Type | Charge State | N_{i}-V_{N} (N_{i}/V_{N}) | Isolated One (N_{i}/V_{N}) |
---|---|---|---|

Bader Charge(|e|) | 3 | 0.51/1.23 | 0.21/1.43 |

2 | 0.67/1.21 | 0.44/1.28 | |

1 | 0.84/1.19 | 0.66/1.21 | |

0 | 1.04/1.22 | 0.87/1.15 | |

−1 | – | 1.05/1.07 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

He, H.; Liu, W.; Zhang, P.; Liao, W.; Tong, D.; Yang, L.; He, C.; Zang, H.; Zong, H.
Dynamics Studies of Nitrogen Interstitial in GaN from Ab Initio Calculations. *Materials* **2020**, *13*, 3627.
https://doi.org/10.3390/ma13163627

**AMA Style**

He H, Liu W, Zhang P, Liao W, Tong D, Yang L, He C, Zang H, Zong H.
Dynamics Studies of Nitrogen Interstitial in GaN from Ab Initio Calculations. *Materials*. 2020; 13(16):3627.
https://doi.org/10.3390/ma13163627

**Chicago/Turabian Style**

He, Huan, Wenbo Liu, Pengbo Zhang, Wenlong Liao, Dayin Tong, Lin Yang, Chaohui He, Hang Zang, and Hongxiang Zong.
2020. "Dynamics Studies of Nitrogen Interstitial in GaN from Ab Initio Calculations" *Materials* 13, no. 16: 3627.
https://doi.org/10.3390/ma13163627