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2007, 111, 1556-1559 Published on Web 01/05/2007
Theoretical Study on the Structural, Energetic, and Optical Properties of ZnS Nanotube Sougata Pal, Biplab Goswami, and Pranab Sarkar* Department of Chemistry, VisVa-Bharati UniVersity, Santiniketan- 731235, India ReceiVed: October 14, 2006; In Final Form: December 7, 2006
We present results of our theoretical investigation on structural, energetic, and optical properties of ZnS nanotube. The calculations are performed by using density functional tight-binding method. Our results include the variation of radial distribution, buckling, strain energy, and band gap as a function of the tube radius. The band gap of the ZnS nanotube depends on the helicity of the tube and is always smaller for zigzag (n,0) tubes than tubes with armchair (n,n) symmetry. The other interesting and characteristic observation of ZnS nanotube is that for the zigzag tube, the band gap decreases with increasing radius and it passes through a broad maximum for armchair nanotubes.
In the past decade, the studies on one-dimensional (1D) nanostructures such as nanowires or nanotubes has attracted considerable attention because of their potential use in both nanoscale engineering and nanotechnology.1,2 Because of quantum confinement, 1D nanostructures possess unique properties compared to corresponding bulk materials. The particular physical and chemical properties of 1D solids promise new inventions, new materials with new properties, and fresh contribution to human knowledge.3 The discovery of carbon nanotubes in 19914 has stimulated extensive experimental and theoretical research concerning structures based on hexagon networks. The physical properties of carbon nanotube depends on the diameter as well as the helicity of the nanotube. Thus, the carbon nanotubes can be either metallic or semiconducting5-8 depending upon the tube diameter and chirality. The fact that the band gap can be controlled by varying diameter of the tube allows one the engineering of the band gap. The spherical geometry of C60, and especially of carbon onions, find some analogy in inorganic fullerenes, whereas the cylindrical geometry of carbon nanotubes is paralleled by the structure of numerous inorganic nanotubes. From the very beginning, the concept of inorganic nanotube was developed because of combined efforts of experimentalists (synthesis and studies of their functional characteristics) and theoreticians (simulation of new nanotube forms, prediction of their structure and properties). The first successful reports on inorganic (WS2) nanotubes by Tenne et al.9 in 1992 was followed by intense experimental and theoretical research on hollow cylindrical structures that led to the development and prediction of several inorganic nanotubes like GaSe, BN, AlN, GaN, SiC, and CdSe nanotubes and several others.10-18 As an important II-IV semiconductor, zinc sulfide has a wide band gap energy of 3.66 eV. ZnS nanocrystals have attracted tremendous attention because of their application in diverse fields. Thus, they can be used as a key material for ultraviolet light-emitting diodes and injection lasers, as phosphors in cathode-ray tubes and flat panel displays, for thin film electro* Corresponding author. E. Mail:
[email protected].
10.1021/jp066753a CCC: $37.00
luminescence, and for IR windows.19-21 ZnS nanocrsytals also have been investigated for use in fuel cells, solar energy conversion, catalysts, and nonlinear optical devices. Much effort has gone into the synthesis and characterization of 1D nanocrystals and nanoparticles of ZnS. Wang et al.22 has used ZnO nanobelts as templates to fabricate ZnS nanotubes by chemical reaction between ZnO supports and H2S. Recently, Zhu et al.23 also have reported the synthesis of a ZnS nanotube. Jiang et al.24 reported the ZnS nanowire with a wurtzite polytype modulated structure. Zhang et al.25 described a synthetic method for the preparation of ZnS nanotube assisted by carbon nanotubes. They have shown that the UV-vis absorption spectra of these nanotubes exhibit large blue shifts because of quantum size effects. These 1D nanostructures of ZnS may have potential applications in high H2 storage, drug delivery, and second-order template because of their large capacity and high solubility. Although, there are a number of experimental studies on the synthesis and characterization of ZnS nanotubes, theoretical research addressing the electronic structure of ZnS nanotubes and their dependence on the chirality and radius are scarce and are therefore highly desirable. In the present letter, we propose to study the electronic structure of the ZnS nanotube by using the density functional tight-binding (DFTB) method.26 We will address the radial distribution, buckling, strain energy, and band gap as a function of the tube radius and also as helicity of the tube. We have employed the parametrized density functional tightbinding method of Porezag et al.,26 which has been described in detail elsewhere, and therefore shall be only briefly outlined here. In this method, the hopping integrals used to construct the Hamiltonian and overlap matrices are tabulated as a function of internuclear distance on the basis of first principles density functional theory with local density approximation. The method employs the localized basis sets, retaining only one and twocenter contributions to the Hamiltonian matrix elements. A minimal basis set corresponding to a single atomic like orbital per atomic valence state is used. This approach has been shown to be a good compromise between the more accurate but more © 2007 American Chemical Society
Letters
J. Phys. Chem. C, Vol. 111, No. 4, 2007 1557
rj ) |R Bj - bR0|, j ) 1, 2, ...n + m
Figure 1. Optimized geometry of ZnS nanotubes (a) (8,8) armchair nanotube and (b) (14,0) zigzag nanotube.
costly ab initio techniques and computationally less expensive but less accurate empirical potentials. Its applicability to the study of the electronic structure of nanotubes already has been shown for several tubular systems.11-13,15 For each ZnS tubular structure having a different radius and helicity, a series of calculations were carried out in which the initial structure was fully relaxed with respect to both the atomic positions and the tube cell length using conjugated gradient technique. Using the nonorthogonal tight-binding (TB) scheme briefly outlined above, we have performed a series of calculations aimed at characterizing the properties of single-wall ZnS nanotubes. In particular, we have considered zigzag (n,0) and armchair (n,n) nanotubes. The structure of a single-wall nanotube can be conceptualized by wrapping a one-atom-thick layer of graphite called graphene into a seamless cylinder. The way the graphite sheet is wrapped is represented by a pair of indices (n,m) called chiral vector. The integers n and m denote the number of unit vectors along two directions in the honeycomb crystal lattice of graphene. If m ) 0, the nanotubes are called zigzag, and if n ) m, the nanotubes are called armchair. The optimized geometry of (8,8) and (14,0) ZnS nanotubes are shown in Figure 1. The average Zn-S bond length in zigzag and armchair nanotubes are 2.33 and 2.30 Å, respectively. These bondlengths are slightly shorter than in bulk ZnS () 2.34 Å) but are slightly larger than in bubble spheroid structures () 2.25 Å).27 The average Zn-S bond length in the double bubbles are 2.36 Å for the innermost bubble and 2.31 Å for the outermost bubble.28 So the average Zn-S bond length in nanotubes is comparable with that of the outermost bubble and is smaller than that of the innermost bubble of the double-bubble structures. In describing the structural properties of the nanotubes, we first define a line passing through the center of the ZnS nanotube through
B R0 )
1 n+m
n+m
B Rj ∑ j)1
(1)
where n and m are number of Zn and S atoms in the nanotube, respectively. Subsequently, the radial distance for the jth atom is defined as
(2)
Figure 2 shows the radial distributions of eight different ZnS nanotubes with either zigzag (right panel) or armchair (left panel) symmetry. We have shown the radial distribution of Zn and S atoms both for initial (lower half) and relaxed (upper half) geometries. In Figure 2, it is seen that during relaxation the diameter of the tube is considerably reduced. The Zn and S atoms, which are at same distance from the center of the tube in the initial geometry, have split into two groups in the optimized geometry. The inspection of individual radial distribution shows that Zn atoms move inward from the surface whereas the S atoms move outward. This feature is exactly the same as that that had been observed in ZnS quantum dots.29 Another structural feature of the nanotube that is closely related to the radial distribution is the certain degree of buckling on the tube surface that results from the Zn atoms displacing toward the tube axis while the S atoms move in the opposite direction. The buckling decreases rapidly with increasing tube radius (Figure 3) and the amount of buckling is slightly dependent on the tube helicity, being smaller for armchair nanotubes compared to the zigzag tube of similar size. This observation is also evident from the radial distribution. As the radius of the tube increases, the separation between the Zn and S atoms continues to decrease both for zigzag and armchair nanotubes (Figure 2). When compared to those of BN and GaN tubes with similar radius, the buckling is more significant in ZnS nanotubes. This tendency of buckling of ZnS nanotubes is the result of the slightly different hybridizations of the Zn and S atom in the curved hexagonal layer. Hernandez et al.13 also have found the same kind of buckling effect in BN nanotubes. The presence of buckling of these nanotubes may have the effect of forming a surface dipole and hence be highly relevant for potential applications of these nanotubes. In Figure 4(a) we have shown the strain energy that may be defined as the difference of the energy per atom in the tube and that in the corresponding flat sheet as a function of the tube radius both for zigzag and armchair nanotubes. In Figure 4, it is evident that the characteristic behavior Es ∝ 1/D2 in which D is the tube diameter, as it is obtained for other nanotubes, is recovered. We note that similar to the results of BN,13 AlN14, and GaN,16 the strain energy in ZnS nanotubes is relatively insensitive to the detailed structures of the tube, which is in sharp contrast with the fact that carbon armchair nanotubes are more stable than the zigzag nanotubes. The other point is that the magnitude of the strain energies for ZnS nanotubes are smaller compared to those of carbon nanotubes, which ensures a possibility for the synthesis of these nanostructures. We also have investigated the band gap of the nanotube as a function of the radius for both zigzag and armchair nanotubes. The evolution of the band gap of these nanotubes as a function of the radius is plotted in Figure 4(b). The calculated band gap is higher for the armchair than the corresponding zigzag nanotubes. This feature is the same as those of SiC,18 BN,12 AlN13 and GaN16 nanotubes. The magnitudes of the band gap are higher than that of the bulk solid. The high theoretical values are in good agreement with that of the experimentally observed values for the ZnS nanotube by Zhang et al.25 The interesting point to note is that for zigzag nanotubes, the band gap decreases with increasing tube radius, while for armchair nanotubes it first increases and then decreases. There are two factors responsible for increase or decrease in band gap with tube radius. One is quantum confinement effects that result in the decrease of band gap with increasing tube radius, and the other factor may be related to curvature induced σ-π hybridization in the ZnS
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Figure 4. (a) Strain energies per atom as a function of radius for ZnS armchair and zigzag nanotubes. Circles (O) for zigzag and crosses (×) for armchair nanotubes. (b) Band gaps of ZnS armchair and zigzag nanotubes as a function of the tube radius. Circles (O) for zigzag and crosses (×) for armchair nanotubes.
Figure 2. Radial distribution of zinc and sulfur atoms for armchair (left panel) and zigzag (right panel) ZnS nanotubes of different sizes: (a) (5,5), (b) (6,6), (c) (7,7), (d) (8,8) ZnS armchair nanotubes and (e) (8,0), (f) (10,0), (g) (12,0), (h) (14,0) ZnS zigzag nanotubes. In each panel, the upper and lower parts represent the relaxed and unrelaxed structures, respectively.
degree of buckling upon relaxation. The buckling is slightly dependent on the helicity of the tube. While the band gap decreases with increasing tube radius for the zigzag ZnS nanotube, it passes through a broad maximum for armchair nanotubes. We hope that our results will stimulate the experimentalist to validate our theoretical prediction. Acknowledgment. The financial support from UGC, New Delhi, [F-12.30/SR(2003)], CSIR, Government of India [01(1908)-EMR-II/2003], DST, Government of India through research grants are gratefully acknowledged. References and Notes
Figure 3. Buckling in the ZnS nanotube equilibrium structures vs tube radius. Buckling is defined as the mean radius of zinc atoms minus the mean radius of the sulfur atoms. Circles (O) for zigzag and crosses (×) for armchair nanotubes.
nanotube with a different radius. These results imply that the curvature induced σ-π hybridization has the most pronounced effect for smaller armchair nanotubes resulting in increasing band gap with increasing radius. And for the zigzag nanotube, it is the quantum size effects that predominate over curvature induced σ-π hybridization. To summarize, by using DFTB scheme we have carried out an extensive study of the energetic, structural, and optical properties of both zigzag and armchair ZnS nanotubes. To the best of our knowledge, this is the first theoretical study addressing the electronic structure of the ZnS nanotube. Our results indicate that the strain energy of the ZnS nanotube is smaller than the carbon nanotubes, and it decreases with increasing tube radius and is insensitive to the tube helicity. Because of the difference in hybridization of Zn and S atoms in the curved hexagonal layer, these nanotubes show a certain
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