Controlling Structural and Electronic Properties of ZnO NPs: Density-Functional Tight-Binding Method

We carried out a thorough examination of the structural and electronic features of undoped and Nitrogen (N)-doped ZnO nanoparticles (NPs) by the density-functional tight-binding (DFTB) method. By increasing the percent of N atoms in undoped ZnO NPs, the number of bonds (n), order parameter (R) and radial distribution function (RDF) of two-body interactions such as Zn-Zn, N-N, O-O, N-O, etc. were investigated using novel algorithms. Our results show that the total n of Zn-Zn interactions is greater than that of Zn-Zn, N-N, N-O, and O-O; thus, it means that Zn atoms have a greater preference for N or O atoms. The RDFs of Zn and O atoms increase based on the increase in the content of N atoms. The R of Zn, O and N atoms demonstrate that O and N atoms tend to locate at the center, whereas Zn atoms tend to reside on the surface. The density of state (DOS) indicates that the undoped and N-doped ZnO NPs demonstrate a semiconductor-like behavior that is coherent with measured data. The HOMO-LUMO energy gap decreases from -4.717 to -0.853 eV. n increase in the content of N atoms contributes to the destabilization of ZnO NPs due to a decrease in the energy gap.


Introduction
Nanoparticles (NPs), tiny objects whose sizes are lay between 1 and 100 nanometers, are finding use in diverse areas including energy, electronics, biomedical and optical fields due to their shape dependence properties as opposed to their bulk structure. More specifically, metallic NPs exhibit properties useful as both insulators and semiconductors and have been widely investigated (Wang, 2007;Yang, et al. 2008;Kushwaha, 2012). ZnO and its NPs, in particular, have been an area of intense scrutiny (Koç, et al. 2019;Rezkallah, et al. 2017;Caglar, et al. 2019;Coşkun, et al. 2018), because they have a wide bandgap and excellent optical properties for optoelectronics applications, being widely studied in various fields as photodetectors (Chang, et al. 2012), energetic materials (Barziniy, et al. 2019), and biomedical agents (Zhang, 2013). This study aims at investigating the effect of Nitrogen (N) on ZnO NPs using the density-functional tight-binding (DFTB) method. Among the analyses, we conduct are studies of the HOMO, LUMO and HOMO-LUMO gap ( ), total energies, density of states (DOS), as well as, the structural analysis such as radial distribution functions (RDFs), order parameter (R) to learn about how behave Zinc (Zn), Oxygen (O) and N atoms and the number of bonds ( ) of two-body interactions in the undoped and doped ZnO NPs. To supplement our work on structural changes, we implemented programs in R code (https://github.com/hasankurban/Structural-Analysis-NanoParticles) to analyze the RDF, n and R.

Material and Method
We used the DFTB+ code (Aradi, et al. 2007), which is an implementation of DFTB method, with the 3ob/3ob-3-1 (Gaus, et al. 2013;Kubillus, et al. 2015) set of Slater Koster parameters to compare the structural features and electronic structure of studied ZnO NPs. To make the program more accessible to noncomputational scientists, we have also ensured that the programs are simple to use. Additionally, we have added functionality to include analysis of the n, R, and RDF of the ZnO NPs in terms of an increase in the N content. The code is open source and it is freely available online, thus, researchers can visualize their data using the code.

Structural analysis
The initial structure of undoped ZnO NP with n = 258 atoms is indicated in Fig. 1. All of the ZnO NPs were characterized by 30×30×30 supercells of the hexagonal crystal structure (wurtzite, space group P6 3 mc). We carved a spherical ZnO NP from this bulk hexagonal supercell. The radius of the NP is set to the desired value (0.9 nm) and only atoms within that sphere are considered, whereas those outside the sphere are removed. All calculations are carried out at constant volume.

The
represents the nearest neighbor contacts number, which is also the number of bonds, and usually used to distinguish the degree of packing, a significant property of NP. The (Wu, et al. 2016) for the NPs is given by is the distance between and atoms and (0) is obtained by fitting the experimental data and represents a nearest neighbor criterion (NIST, 2019;Czajkowski, et al. 1999). Fig. 2 indicates the total n in the ZnO NP with 258 atoms. The curve of ZnO NP in Fig. 2 reveals that the of N-N and N-O interactions increases gradually in terms of increase in the content of N. Moreover, the total of Zn-Zn interactions is comparatively smaller than the total , while the of N-N is the smallest. These results show that N atoms incline to make more bonds with O atoms: that Zn 2 tends to locate at the surface. Additionally, the total of Zn-Zn bonds is larger than that of N-N, N-O, O-O and Zn-Zn. it means that Zn atoms have a higher priority for N or O atoms than for Zn atoms based on the increase of N content. Here, it is interesting to note that there is no experimental data on the Zn-O and Zn-N two-body interactions, thus, Zn atoms probably adhere to N or O atoms. represents the order parameter and is used to find a stable structure in the NP. One needs to calculate (Kurban, et al. 2016) which helps to investigate the segregation of atoms in the NP. R T i is the average distance of a type atoms according to a center of a NP, where is the number of type atoms, and is the distance of the atoms to the coordinate center . We define a distance from the center of NP to a reference point as to indicate the location of atoms; if < (a "small" value), the type atoms are assumed to be at the center, and if > (a "large" value), the type atoms are assumed to be at the surface region of NP. If neither is true, i.e., if ≤ ≤ (a "medium" value), it is assumed a well-mixed NP.   Here, the R shows the changes in the structural properties of ZnO NP with a change N-doped ZnO NPs. The R of Zn, O and N atoms indicate that N atoms incline to locate at the center, while Zn atoms tend to occupy the surface. The R of N atoms to the surface is related to its lower cohesive energy. Besides, the demonstrates different features when it comes to an increase in the content of N atoms. For example, values sharply increase after doping 35% N, and smoothly decrease. The Radial Distribution Function (RDF), a significant parameter, is known as the probability of finding a particle at a distance r from another tagged particle. The RDF is mathematically shown as follows: represents the mean number of atoms in a shell of width at distance , |∆| is the total atom number and is the volume of the spherical shell and is the mean atom density.

Electronic structure
In Fig. 5, we demonstrate the results of the HOMO, LUMO and Fermi levels with respect to N content to acquire detailed information on electronic states in the undoped and N-doped ZnO NPs. When it comes to an increase in the content of N, the density of localized states concomitantly decreases, thus the greatest contribution comes from the undoped ZnO NPs and then these fluctuations progressively also disappear. It has a sharply increasing tendency to occur in the region of between -10 and -15 eV. The DOS figures also demonstrate that the studied ZnO NPs have the energy gap, so, all the NPs indicate semiconductor character. With increasing the content of N, the changes in HOMO, LUMO and Fermi energy were predicted in a different manner like an increase and a decrease.
The HOMO energy level for undoped ZnO NP is -7.89 eV, i.e., about 0.97 eV higher than that of the 50% N-doped NP (-6.91 eV) which is the lowest HOMO level among the other NPs models and thus it is less reactive, but more stable (see Fig. 6, Table 1). On the other hand, Fermi energies are in the middle of the valence and conduction band. The HOMO-LUMO energy gap of undoped ZnO NP is 4.71 eV, which decreases from -4.717 to -0.853 eV. It is clear then that an increase in the content of N atoms contributes to the destabilization of ZnO NPs due to a decrease in the energy gap.

Discussion and Conclusions
In this study, we use the DFTB method and study electronic structural features of undoped and Nitrogen (N)-doped ZnO NPs with 258 atoms.
To carry out structural analysis, we developed a new code in R code to conduct structural analysis, i.e., analyzing the RDF, n and R of two-body interactions of atoms in the ZnO NPs. Our results show that the total n of Zn-Zn two-body interactions is larger than that of N-N,