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	�:			
        Ab-initio Study of the Structural Stability and Electronic Properties of ZnO Nanowires
Satyendra Singh1* and Pankaj Srivastava2
1Department of Physics, Shri Ram College of Engineering & Management, Banmore, Morena, 476444, India
       2Applied Physics Group, ABV-Indian Institute of Information Technology & Management (ABV-IIITM), Gwalior,474010, India.
* Corresponding author. Mobile No. +919685067178
Corresponding author email address:  HYPERLINK "mailto:satyendra7171@yahoo.co.in" satyendra7171@yahoo.co.in 

Abstract
Four different thin ZnO nanowires were studied by pseudopotential density functional electronic structure calculation using the generalized gradient approximations. The different structures were two atom linear wire, two atom zigzag wire, four atom square wire and six atom hexagonal wire. The geometry and the stability of all nanowires were investigated. We have also investigated the density of states and band structure of nanowires. We predict that two atom zigzag wire cross section have greater stability in comparison to other structures and thus energetically more favorable. 
Keywords:  ZnO nanowires, electronic band structure, density of states, total energy.


Introduction  
 It is well known that zinc oxide (ZnO) is a wide band gap (Eg = 3.37 eV) semiconductor with interesting electronic, piezoelectric, and photoconduting properties. It has a wide range of applications in electronics, optoelectronics, photovollaic, and sensors [1, 2]. One-dimensional (1D) zinc oxide (ZnO) nanostructures have been synthesized in various morphologies like nanorods, nanowires [3], nanobelts [4] nanorings [5] and nanohelices [6]. The extraordinary combination of semiconducting and electromechanical properties of ZnO nanostructures makes them potential building blocks for future nanodevices. For example, optoelectronic devices [3] logic circuits [7] and piezoelectric devices like nanogenerators [8, 9] nanoresonators, and electromechanically coupled nanocantilever sensors [10] have already been conceptualized. Size-dependent surface luminescence in ZnO nanowires is studied by Ilan et al. [11] Zhang et al. [12] investigated optical properties of ZnO nanowires by electron energy�loss spectroscopy. Ab-initio study of energetic stability and electronic confinement for different structural phases of ZnO nanowires is done by Schmidt et al. [13] Experimental-computational investigation of ZnO nanowires strength and fracture is done by Agrawal et al. [14]  Xu et al. [15] studied the hydrogen and oxygen adsorption on ZnO nanowires. First principle study of the electronic and optical properties of ZnO nanowires is done by Zhang et al. [16] Gao et al. [17] studied the structural transition of ZnO nanowires at high pressure. The study of tuning electronic structure of ZnO nanowires by suface functionalization is done by Huang et al. [18] Zhang et al. [19] synthesized the well-aligned ZnO nanowires without catalysts. Growth and replication of ordered ZnO nanowire array on general flexible substrates is done by Zhang et al. [20]  

 Computational Details
Ab-initio DFT calculations [21, 22] within the plane wave pseduopotential method was employed to investigate the structure of ZnO nanowires. For exploring the structural and electronic properties of various materials, the pseudopotential method is found very successful [23]. In this study we have used ABINIT code [24]. The generalized gradient approximation and the exchange correlation function of Perdew, Burk and Ernzerhof were applied in these calculations [25]. The exchange correlation potential of Troullier and Martins [26] was used in this study.  These pseudopotentials were taken from ABINIT web page [24]. The potentials were tested by doing calculations on bulk ZnO material and the results were found to be consistent with the experimental ones.
	All the calculations were performed in a self consistent manner. The studied structures have been optimized for Hellmann-Feynman forces as small as 10-3 eV/� on each atom. The calculations were performed with a kinetic energy cut off of 30 Hartee. The wires were positioned in a supercell of side 20 a.u. along the x and y directions. The axis of the wire was taken along the z � direction and the periodic boundary conditions were applied.  In the integration of the Brillouin zone, the Monkhorst-pack method [27] with 15k-points sampling along the z-direction was used. All atoms were allowed to relax without any imposed constraint. We have determined the self-consistent optimized value for lattice parameter of bulk ZnO to check the self consistent calculations. Our calculated value of 4.52 � is very close to the experimental value of 4.58 �. All the structures have been optimized to achieve minimum energy by relaxing the atomic positions in the unit cell. The magnitude of atomic relaxation depends on the plane cut-off energy and one should obtain convergence with respect to cut-off energy too.


Results and Discussion
In this study four different geometric structures of ZnO nanowires were investigated. The details about geometric structures have been given in our earlier published papers [28-32]. The considered geometrical structures of ZnO nanowires are shown in Figure 1. For the stability of the structure of a ZnO nanowire it is mandatory to get minimum energy configuration at particular structure geometry. Variation of energy with interatomic distance for various structure geometries have been depicted in table 1 and the interatomic distances at which the minimum energy state is achieved are highlighted in bold letters in the table. The optimized interatomic distances and the energies corresponding to stability of nanowire structure are presented in table 2.
All the structural parameters were optimized independently in the case each structure to explore the minimum energy configuration. The total energy as a function of x = �a� for an infinite linear wire has been calculated , where �a� is the Zn-O distance of the order of 0.01 nm and then the effect of total energy is investigated. The two atom linear wire shows minimum energy at an inter atomic distance of 0.64 nm, the wire becomes stable at �1056.56 eV. In two atom zigzag wire the minimum energy is obtained at 0.22 nm distance, i.e. -1058.29 eV. The zigzag wire has slightly lower energy in comparison to a linear wire. In the case of four atom square wire, the energy is minimum at 0.22 nm as that of zigzag wire, but its energy i.e. �1057.89 eV. The minimum energy configuration for a six atom hexagonal wire predicts again the interatomic distance of 0.22 nm but its total energy is found to be -1050.37 eV. The detailed investigation of all the structures reveals that two atom zigzag cross sectional wire has the minimum energy configuration in comparison to other all the structures and therefore analyzed so far is treated to be the most stable structure, the variation of inter atomic distance with energy are shown in Figure 2, for all the structures taken under consideration.
The variation of energy with DOS has been shown in Figure 3. The nature of density of states (DOS) that corresponds to optimized inter atomic distance for all structures is analyzed and it is observed that DOS is higher for two atom linear and four atom square wire near the Fermi level, whereas the DOS is lower for two atom zigzag wire and it is already predicted to be the most stable structure in our analysis. As a matter of fact the DOS is negligible/lower in case of nanowires near the Fermi level because of confinement of states. The Fermi level of DOS lies between �4.71 eV to �17.77 eV, it is a universally accepted fact that the band structure of a nanowire is different from that of the bulk material. 
The band structure of all ZnO nanowires is shown in Figures 4-7. The bulk material of ZnO semiconductor has Td point group symmetry, when a nanowire is formed the symmetry of the structure will be lowered, due to the confinement of states. The 3-fold degenerate states in the bulk tend to split into other symmetric states in the nanowire. The splitting of states have interesting physics on the band structure of the nanowires. Some interesting features have been observed here. The band structure of a two atom linear wire in Figure 4 clearly depicts the semiconducting behaviour of the wire, as the one band crosses the Fermi level. The band structure of two atom zigzag wire exhibit metallic character as is evident from the Figure 5, as the band crosses the zero Fermi level. In the case of four atom square wire there are no crossings of bands across the zero Fermi level as is evident in Figure 6, this structure seems to be insulating. Thus, it can be conclude that the band states get shifted towards the lower energy values for the most stable structure in case of nanowires. This may be due to the quantum confinement effect in one dimensional structure. In six atom hexagonal wire the bands are again much below the Fermi level as shown in Figure 7, which exhibit insulating behavior, thus, the geometrical shape plays very important role in predicting the ground state properties of nanowires, initially taken semiconducting nanowires may be metallic or semiconducting which entirely depends upon the size and shape of the structure. The electronic properties change drastically as is evident from the studies so for in the research work. 
	One of the workers [33] studied the electronic properties of silica nanowires who predict that linear wire is metallic and zigzag chain is insulator, whereas our prediction regarding ZnO nanowires are just opposite to their findings. Thus the properties are going to be changed at nanolevel, not only due to geometrical consideration but also the materials taken into consideration viz metallic or semiconductor or amorphous or ceramics.

 Conclusions
We have investigated four different nanowires of ZnO by employing ab-initio DFT calculations in the pseudopotential approximations. The stability and electronic properties were analyzed in detail. It was found that two atom zigzag nanowire have greater stability and energetically more favorable, in comparison to others. The DOS in case of two atom zigzag wire are found to be lower near the Fermi level as compared to others. The band structure investigation reveals remarkable features at nano dimensions. It was found that two atom linear wire is semiconducting, two atom zigzag wire is metallic, four atom square wire and six atom hexagonal wire are an insulator. Thus, the choice of material as well as size and shape of the structure plays an important role in deciding nanowires for optoelectronic and photonic applications. Our predictions may help the experimental workers to fabricate semiconducting nanowires for device application.

Acknowledgement 
The authors are thankful to Shri Ram College of Engg. & Management, Banmore (M.P.) and ABV-Indian Institute of Information Technology and Management (ABV-IIITM), Gwalior (M.P.) for providing the infrastructural facilities for computational work.

 

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