Repairing the N-vacancy in an InN monolayer using NO molecules: a first-principles study

The synthesis of a perfect InN monolayer is important to achieve desirable properties for the further investigation and application of InN monolayers. However, the inevitably existing defects, such as an N-vacancy, in the synthesized InN nanomaterials would significantly impair their geometric and electronic behaviors. In this study, we proposed to repair the N-vacancy in the InN monolayer using NO molecules through NO disproportionation, which was verified to be energetically favorable according to our first-principles calculations. The repaired InN monolayer was similar to the perfect counterpart in terms of the geometric and electronic aspects. In this study, a promising strategy is presented for repairing the N-vacancy in the InN monolayer to perfect its physicochemical properties effectively, which may also be used to repair N-vacancies in other materials.


Introduction
Two-dimensional (2D) materials are always the focus of attention due to their unique electronic behavior, high charge-carrier mobility, large specic surface area and excellent optical property, 1,2 which enable their applications in many elds. The rst real 2D material with one-atom thickness is graphene; however, its gapless nature limits its application in logic and high-speed switching devices. 3 Thus, other candidate materials with a graphene-like structure, tunable band gap and similar or even better properties for specic applications need to be explored. [4][5][6][7] Ultrathin III-V compounds with graphene-like microscopic structures and direct-bandgaps have recently received signicant attention. [8][9][10][11][12][13] Among them, aer the remarkable breakthrough in the synthesis of nano-scaled InN, InN monolayers have been widely studied for potential application as gas nanosensors [14][15][16] and optical coatings. 17,18 However, there are some inevitable defects in the synthesized InN nanomaterials; for example, the N vacancies have low formation energy and can become more stabilized upon the incorporation of In vacancies; this leads to the formation of vacancy-complexes. 19,20 Hence, the existence of N vacancies is harmful to the chemical stability and electronic behavior of the InN monolayer. It has been reported that unlike the case of multilayer InN, the electron mobility of the InN monolayer can be impaired pronouncedly as the number of vacancies increases; 21 this largely deteriorates its physicochemical behavior. In this regard, the possible N vacancies should be repaired aer the synthesis of the InN monolayer to obtain a perfect conguration with high material quality.
A novel method to perfect the InN monolayer was introduced in this study, wherein gaseous NO was proposed as the N source through NO disproportionation, specied as NO(g) + NO(g) / N(s) + NO 2 (g). This is an intriguing approach as it does not require metal catalysts, and the N-defected InN (Vac-InN) monolayer thus obtained behaves as a catalytic support, which heals itself by the N atom produced from the reaction. In fact, the repairing of vacancy using gas molecules has been investigated in the last several years. Liu proposed to heal the C-vacancy in graphene by the CO molecule based on an electric eld method. 22 Divacancy in graphene or carbon nanotubes could also be healed using C 2 H 2 or C 2 H 4 molecules. 23,24 In the C 3 N monolayer, the C or N vacancies were also repaired using CO or NO molecules. 25 Moreover, the interaction between gas molecules used to repair the vacancy and the 2D nanomaterials could exert signicant effects on the electronic behavior of the substrates, such as the case of MoS 2 and WSe 2 monolayers in which an effective p-doping was achieved aer gas adsorption on the vacancy sites. 26,27 In this study, our calculations indicated that the processes of repairing the Nvacancy InN monolayer using the NO molecules were energetically favorable due to the small energy barrier and large energy drop in each reaction. These results, in line with the previous reports, veried the feasibility and efficiency of repairing 2D nanomaterials by related gaseous molecules. Thus, we are hopeful that our study can provide some guidance to synthesize a perfect InN monolayer for application in many elds.

Computational details
The whole structural relaxation and electronic calculations were performed within the dispersion-corrected density functional theory (DFT) of DMol 3 package. 28 Perdew-Burke-Ernzerhof (PBE) function within the generalized gradient approximation (GGA) 29,30 was adopted to describe the electron exchangecorrelation interaction. The DFT-D2 method developed by Grimme was employed to better understand the Van der Waals force and long-range interactions. 31 Double numerical plus polarization (DNP) was selected as the atomic orbital basis set, 32 with global orbital cut-off radius of 5.0Å and smearing of 0.005 Ha to ensure a high computational quality. The Monkhorst-Pack k-point mesh of 10 Â 10 Â 1 was determined for all supercell geometry optimizations and electronic structure calculations. Complete linear synchronous transit (LST)/quadratic synchronous transit (QST) calculations were performed to locate transition states (TS). 33 We established a 4 Â 4 Â 1 intrinsic InN monolayer supercell with a vacuum region of 15Å to prevent the interaction between adjacent units. The lattice constant of the fully optimized InN monolayer was 3.62Å, which is in agreement with other theoretical work (3.63Å (ref. 34)). The adsorption energy (E ad ) was calculated as: where E Surf and E Surf/NO represent a total energy of the analyzed monolayer before and aer NO adsorption, and E NO is the energy for isolated NO molecule. Hirshfeld method was considered to analyze the atomic and molecular charge behaviors.  Fig. 1(a) that the vacancy-In distances are 2.09Å, which is equal to the length of In-N bond in the perfect InN monolayer. This reveals that the N defect causes slight deformation in the plane morphology of the InN monolayer. However, the electronic behavior of the InN monolayer undergoes signicant changes within the N vacancy, as veried from the distributions of density of state (DOS) in Fig. 1(b). It can be seen that the DOS curves of the Vac-InN monolayer are le-shied when compared with those of the intrinsic counterpart due to the strong donator-like states caused by the nonbonding electrons. It has been reported that these states can trap electrons and scatter other charge carriers in the InN monolayer, 35 by which the carrier mobility would be reduced. Thus, repairing of the N vacancy is essential to guarantee the desirable property of the InN monolayer.

Adsorption of the NO molecule on the N-vacancy InN monolayer
Before conducting the repairing processes of N-vacancy in the InN monolayer, we investigated its adsorption behavior upon NO molecule, where two adsorption sites were considered, namely N-vacancy site and In-above site neighboring the Nvacancy. Moreover, in the abovementioned two sites, the NO molecule was placed at the N-end, O-end and molecule-parallel positions to the plane, in which the stability of each adsorbed conguration was determined by E ad .
The geometries of adsorption congurations aer full optimization are shown in Fig. 2. It could be found that regardless of the N-vacancy site or the In-above site, the N-end position is the most energetically favorable structure with the calculated E ad of À1.11 and À1.01 eV, respectively. Interestingly, at the Inabove site with the N-end position, the NO molecule experiences a dramatic displacement and moves to the N-vacancy site with N atom captured by two dangling In atoms, similar to the structure of N-end position at the N-vacancy site. In practice, the conguration of the N-end position at the N-vacancy site is  indeed most energetically favorable among all the structures. Thus, it was dened as the specic model for NO chemisorption, which has been analyzed in detail in the next section. Moreover, it shed light on the possibility of reparation of the Nvacancy InN monolayer using NO, where the adsorption of NO is the rst step.
To further understand the chemisorption of the NO molecule, the band structure (BS) and density of state (DOS) are plotted in Fig. 3. For better comparison, the band structure of the pure N-vacancy InN monolayer is also exhibited. It can be seen from Fig. 3(a) that there is a state at the bottom of the conduction band crossing the Fermi level; this indicates that the existence of N-vacancy signicantly changes the semiconducting property of the InN monolayer. However, aer the adsorption of the NO molecule on the N-vacancy InN monolayer, we can see from the BS in Fig. 3(b) that there is no impurity state crossing the Fermi level. That is, the adsorption of NO molecule is p-doping for the N-vacancy InN monolayer. 25 On the other hand, two novel states emerge at the top of the valence band, which result from the adsorbed NO molecule based on the molecule DOS of NO shown in Fig. 3(c). From this gure, we can infer that the NO molecule is strongly activated during adsorption: the 1p and 5s orbitals are shied to a higher level and spilt into several small states; the spin-down of 2p* orbital becomes occupied even aer adsorption and shis to a level higher than the Fermi level. These ndings verify the chemisorption of NO at the N-vacancy site with the N-end position. Moreover, the atomic DOS of the N 2p and In 5p orbitals in Fig. 3(d) exhibits a strong hybridization between the N and the In atoms given the obvious overlaps around À6, À4 and 0 eV, supporting the chemisorption of the NO molecule on the N-vacancy InN monolayer and the formation of stable chemical bonds of In-N.

Repairing processes of the N-vacancy in InN monolayer
To heal the N-vacancy in the InN monolayer, two processes are required, i.e. a repairing process and a removal process. The repairing process begins with the physisorption of one NO molecule on the defected InN monolayer, as depicted in Fig. 4(a). The distance between the N 1 atom and the plane is measured to be 2.06Å, indicating a large distance of at least 3Å between the candidate N 1 and any neighboring In atom. The calculated E ad of À0.66 eV and the negative charge of the NO molecule (À0.091e) ( Table 1) also verify the physisorption nature of the Vac-InN/NO interaction. In Fig. 4(b), we can nd that the energy barrier of 0.44 eV must be overcome to reach the transition state (TS) and then ll the N-vacancy using the NO molecule. In the TS, the N 1 -O 1 bond is elongated to 1.24Å from 1.16Å in the initial state (IS), and the N atom is captured by the Vac-InN monolayer with the atom-to-plane distance of 1.20Å.   Moreover, the NO is negatively charged by À0.287e, wherein the N 1 and O 1 atoms gain 0.074 and 0.122e (Table 1) from the Vac-InN monolayer, respectively. In the nal state (FS) shown in Fig. 4(c), the atom-to-plane distance becomes further smaller; this indicates that the pioneer NO is stably adsorbed on the Vac-InN monolayer with strong bonds formed between the N 1 candidate and the neighboring In atoms. The short In-N 1 bond length of 2.23Å can conrm this as well, which becomes further shortened when compared with 2.45Å in TS. For the adsorbed NO molecule, differences occur not only in the N 1 -O 1 bond length, which elongates up to 1.36Å, but also in the atomic charges wherein the N 1 and O 1 atoms are much more negatively charged by À0.186 and À0.308e (Table 1), respectively. Based on the calculated E ad of À1.11 eV, chemisorption could be identi-ed for this system. Note that the N 1 -O 1 bond in NO was weakened to some degree during the repairing process according to the dramatic deformation in its molecular morphology, it is hopeful that the N 1 -O 1 bond would be workably dissociated by further interacting with another reducing molecule. In this case, the O 1 atom could be removed, and the Vac-InN monolayer could be repaired. Aer the repairing process, one more NO molecule was introduced as a reducing species to interact with the extra O 1 atom; this facilitated the dissociation of the N 1 -O 1 bond in the NO precursor and formation of the separated NO 2 molecule instead. Then, the repaired InN monolayer could be obtained aer the release of the formed NO 2 . Fig. 5(a) demonstrates the initial state (IS) of the removal process. We can see that aer interaction, the second NO is located at the le-top above the adsorbed NO, with the distance of 2.77Å. The N 1 -O 1 bond length is slightly elongated to 1.38Å; however, there are no obvious deformations in the structures of the Vac-InN monolayer and the second NO molecule. Moreover, both the N 2 and the O 2 atoms are positively charged, donating 0.028e to the surroundings, from a molecular point of view; this denitely would lead to electron redistribution in the new system. These ndings indicate a weak physisorption for this IS, as further suggested by a small E ad of À0.28 eV. With the negatively charged N 1 and O 1 atoms (À0.189 and À0.289e) as well as positively charged N 2 atom (0.023e) seen in Table 1, there should be electrostatic repulsion between N 1 and O 1 and electrostatic attraction between N 2 and O 1 at this stage. These forces would enhance the O 1 -removing process signicantly. By overcoming the energy barrier of 0.66 eV, the reaction will pass through the TS. As described in Fig. 5(b), the O 1 atom is trapped by the N 2 atom with the bond length of 1.81Å, and the N 1 -O 1 bond elongates to 1.89Å, whereas the In-N 1 bond further shortens to 2.16Å. These deformations manifest the strong potential for the dissociation of N 1 -O 1 bond and the formation of a new NO 2 molecule. Furthermore, electron localization in this TS becomes more evident for the N 1 , O 1 and N 2 atoms, which are charged by À0.262, À0.308 and 0.057e (Table 1), respectively. These allow the further deformations of the two NO molecules under electrostatic forces towards FS. When to the reaction reaches FS, as portrayed in Fig. 5(c), the formed NO 2 is desorbed from the repaired InN monolayer, with the N 1 -O 1 bond length of 2.98Å. The N 2 -O 1 bond and In-N 1 bonds are shortened to 1.23 and 2.12Å, which are quite close to the lengths of 1.16 and 2.09Å in the isolated NO and perfect InN monolayer, respectively. The N 1 atom is negatively charged by À0.373e (Table 1), which is a little lower than that of the Nvacancy (À0.421e) in the perfect InN monolayer. Upon the release of NO 2 , the N 2 , O 1 , and O 2 are charged by 0.075, À0.173 and À0.187e, respectively. This means that NO 2 in total accepts 0.279e from the repaired InN monolayer, which corroborates with its strong electron-withdrawing capacity when it interacts with certain substrates. 36,37 In addition, the calculated E ad of À1.18 eV in the FS implies a geometrically stable conguration for the NO 2 removal and InN monolayer reparation.
As a supplement, we also optimized the conguration wherein the NO 2 was released from the repaired InN monolayer, keeping a long distance (5.93Å) with the plane, as exhibited in Fig. 6(a). The In-N 1 bond recovers to 2.09Å making the repaired InN monolayer a complete plane and the N 1 is negatively charged by 0.413e indicating the good compatibility of candidate N with the Vac-InN monolayer. At the same time,  through the DOS comparison between the intrinsic InN monolayer and repaired counterpart in Fig. 6(b), one can see that the DOS curves of such two systems are completely overlapped at every region, manifesting the recovered electronic behavior for the repaired InN monolayer. In addition, the geometric stability of repaired InN monolayer is further conrmed by the vibrational analysis where the frequency ranging from 113.97 to 1352.98 cm À1 is obtained. Based on these results, we presumed that the reparation for Vac-InN monolayer was successfully accomplished.
To further comprehend the charge-transfer behavior in different states, we implement the electron localization function analysis (ELF), as displayed in Fig. 7. It was found that during the repairing process, the N 1 -O 1 bond is gradually weakened according to the declined electron accumulation region on the bond, whereas the In-N 1 bond becomes gradually rmed due to the improved overlaps in electron localizations. Apart from that, the N 1 and O 1 atoms maintain negatively charged, which is in accordance with the Hirshfeld method analysis. In the IS of removing process, the N 2 and O 2 atoms are slightly positive-charged under the weak physisorption. However, the condition changes remarkably when the reaction reaches the TS, where the electrostatic interactions between N 1 and O 1 atoms as well as between N 2 and O 1 seem to be visible, given the electron localization distribution. These forces facilitate the dissociation of N 1 -O 1 bond and formation of novel NO 2 molecule. In the FS, the N 2 -O 1 bond becomes further tightened according to the electron accumulation on this bond; while the negatively charged N 1 atom presents a similar electron accumulation with respect to another native N atom in the InN monolayer. These ndings conrmed the feasibility of O 1removing by another NO and a good suitability of N 1 product at the N-vacancy.
Additionally, the energy barrier of 0.44 eV in repairing process could be easily realized at room temperature since a surface reaction at ambient temperature could occur when the energy barrier was smaller than the critical barrier of 0.91 eV. [38][39][40] Moreover, the drop energy of 0.45 eV in repairing process could substantially supply for the removal process to overcome the energy barrier of 0.66 eV. Additionally, the strong exothermicity of 0.91 eV in removal process was capable to proceed another repairing-removing cycle to heal any other Nvacancies in InN monolayer. Therefore, we considered that the proposed approach was energetically favorable with good spontaneity.

Conclusions
In this study, we investigated the reparation of the N-defected InN monolayer by NO molecules; this was theoretically conducted by the rst-principles theory. The repairing processes included the adsorption of one NO molecule, lling of the vacancy by the candidate N 1 and the removal of extra O 1 by another NO molecule through NO disproportionation. The results obtained herein indicated that the processes were energetically favorable due to the small energy barrier and large energy drop in each reaction. The ELF was also analyzed to further comprehend the charge-transfer behavior in various states. Our study would be meaningful to provide some guidance for the synthesis of a perfect InN monolayer with desirable physicochemical properties, which may also be applied to repair the N-vacancy in other materials.