Theoretical Insight into Faceted ZnS Nanowires and Nanotubes from

School of Physics and Microelectronics, Shandong UniVersity, Jinan 250100, China, ... Engineering, School of Engineering, UniVersity of Queensland, Br...
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J. Phys. Chem. C 2008, 112, 3509-3514

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Theoretical Insight into Faceted ZnS Nanowires and Nanotubes from Interatomic Potential and First-Principles Calculations Lijuan Li,† Mingwen Zhao,*,†,‡ Xuejuan Zhang,† Zhonghua Zhu,‡ Feng Li,‡,§ Jiling Li,† Chen Song,† Xiangdong Liu,† and Yueyuan Xia*,† School of Physics and Microelectronics, Shandong UniVersity, Jinan 250100, China, DiVision of Chemical Engineering, School of Engineering, UniVersity of Queensland, Brisbane 4072, Australia, and Department of Physics, Taishan UniVersity, Taian, Shandong 27102, China ReceiVed: September 3, 2007; In Final Form: December 30, 2007

The geometric, energetic, and electronic structures of zinc sulfide (ZnS) nanowires (NWs) and nanotubes (NTs) with hexagonal cross sections were explored using interatomic potential (IP) and first-principles calculations. The size-dependent surface structures, energetic evolution, and electronic properties of these nanomaterials were addressed. The formation energy of the NWs with respect to wurtzite ZnS crystal decreases monotonously with the increase in wire radius, whereas that of the multiwalled ZnS-NTs decreases with the increasing wall thickness, irrespective of the tube radius. The faceted ZnS-NTs with thick walls have energetic superiority over the cylindrical tubes built analogously to the boron nitride (BN) nanotubes. Both the ZnSNWs and NTs are wide-band gap semiconductors with a direct band gap at Γ point. The results provide vital information for the fabrication and utilization of ZnS nanomaterials, for example, for building nanoscale optical and photonic devices.

I. Introduction Low-dimensional semiconductor nanomaterials, such as clusters, nanotubes, and nanowires, have been attracting growing attention because of their unusual properties resulting from large surface-to-volume ratios, quantum size-confinement effects, and, accordingly, potential applications in building optoelectronic nanodevices. Zinc sulfide (ZnS) is of particular interest as an important phosphor host material1 and an attractive candidate for applications in novel photonic crystals.2 ZnS is naturally observed in two polymorphs, zinc blende (cubic) and wurtzite (hexagonal), with atoms in the bulk of both polymorphs being fourfold-coordinated, having a tetrahedral coordination. The wurtzite (w-) ZnS is less stable than zinc blende, but can be formed at high temperature.3-5 Until now, diverse forms of ZnS nanostructures have been fabricated, such as nanoparticles,6 nanowires,7,8 nanotubes,9 nanobelts,10,11 and nanosheets.3 ZnS nanowires synthesized by pulsed laser vaporization have wurtzite structures with rectangular or hexagonal cross sections and axes orientated along the [0001] or [1000] direction.8 The hexagonalfaceted ZnS nanotubes produced by a thermochemistry process can be characterized as [0001]-orientated prisms enclosed by low-index planes.9 The photoluminescence (PL) spectrum of the single-crystalline ZnS nanotubes exhibits a weak blue emission centered at 439 nm and a strong green emission centered at about 538 nm.9 The observation of a 439 nm emission peak was attributed to a large surface-to-volume ratio in the nanotubes. Such emission bands have also been reported for ZnS nanowires7 and nanobelts.8,9 Akiyama et al. investigated the structural trends of ZnS-NWs with zinc blende and wurtzite structures using an efficient * Corresponding authors. E-mail: [email protected]; [email protected]. † Shandong University. ‡ University of Queensland. § Taishan University.

empirical interatomic potential that incorporates electrostatic energies due to bond and ionic charges.12 They found that the wurtzite structure is stable for diameters less than 4 nm while the zinc blende structure is energetically favorable for diameters larger than 24 nm. This gives a good explanation to the experimental findings that the synthesized ZnS-NWs always have a wurtzite structure. Wang et al. calculated the energy band gaps of ZnS-NWs using DFT under the local density approximation (LDA).13 They showed that the band gap of ZnSNWs is wider than that of bulk w-ZnS crystal and decreases with the increasing diameter. The size-dependent band gap of low-dimensional semiconductor compounds including ZnS has also been predicted on the basis of a thermodynamic model.14 Alternatively, considerable theoretical efforts have been devoted to the study of ZnS clusters. The geometric evolution of the stable ZnS clusters has been predicted in a relatively wide range of sizes by using first-principles calculations. It was shown that the small-size (ZnS)n clusters (n e 5) favor the formation of ring-like configurations.15 The stable configurations of largersize clusters (n e 47) have hollow bubble-like structures formed by four-, six-, and eight-atom rings in a shell-like arrangement, whereas for n g 50, onion-like configurations, in which one bubble encloses another, become energetically favorable.16,17 These ZnS bubbles resemble the already-synthesized boron nitride (BN) nanocages in atomic arrangement.18,19 Another calculation based on the density-functional tight-binding method (DFTB) also indicated that the small-size clusters (n e 16) prefer hollow bubble-like structures to solid wurtzite-like configurations, but for large-size clusters (e.g., n ) 58 and 68) the later ones become more stable.20 All of these results suggest that ZnS clusters, within an appropriate range of size, have the tendency to form hollow bubble-like configurations. The close structural resemblance between the ZnS bubbles and BN nanocages reminds us of the manufacturability of single-walled ZnS nanotubes (ZnS-SWNTs) with atomic arrangements similar

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to those of single-walled BN nanotubes. Indeed, Pal et al. studied the structural, energetic, and optical properties of the ZnSSWNTs built analogously to BN nanotubes, using DFTB calculations.21 Although, the strain energy of the ZnS-SWNTs with respect to the ZnS graphene-like sheet was revealed to be lower than that of carbon nanotubes, the manufacturability of these tubes is still an open question because the ZnS graphenelike sheet is not the stable form of ZnS materials. More extensive works regarding this issue are desirable. The already-grown ZnS nanotubes possess faceted configurations with rectangular or hexagonal cross sections9 and bear no resemblance to the hypothetic ZnS-SWNTs with cylindrical morphologies presented by Pal et al.21 The further development in utilizing the faceted ZnS nanotubes will require theoretical knowledge. However, in contrast to the abundant theoretical works on ZnS clusters, no theoretical study of the geometric and electronic properties of these faceted ZnS nanotubes has been reported so far. Additionally, although the structural trends and the sizedependent band gaps of ZnS-NWs have been studied theoretically,12-14 some important issues remain unclear from the published works. For instance, the formation energy evolution of ZnS-NWs as a function of wire radius has not been modeled. The surface states corresponding to the undercoordinated atoms on the facets and the band structures of ZnS-NWs were not reported. Theoretical studies of these questions are expected to provide useful guidance to experimental progresses, for example, in building nanoscale optical and photonic devices. In this contribution, we explore the energetics, geometrics, and electronic structures of faceted ZnS-NWs and NTs using interatomic potential (IP) and first-principles calculations within density functional theory (DFT). The faceted ZnS-NTs were modeled by hollow hexagonal prisms, which resemble the already-synthesized nanowires and nanotubes. The configurations under study have radii varying between 0.6 and 2.5 nm and wurtzite structures. The energetic evolution and surface relaxation of these nanostructures were investigated. The formation energies (Eform) of these configurations with respect to the stable w-ZnS crystal were calculated and addressed on the basis of a simple model. The possibility of growing ZnSSWNTs was discussed via comparing its Eform with those of the already-synthesized ZnS-NWs and NTs with faceted morphology. The electronic properties of these nanomaterials were also predicted from the electronic band structure calculations using DFT. The surface states were determined by projecting the total electron density of states (TDOS) onto the undercoordinated and fully coordinated atoms, respectively. II. Method and Computational Details IP Calculations. The IP between the atoms employed in this work was calculated by the Born model of solids involving two main contributions, namely, long-range and short-range interactions, respectively. The long-range term arises from the electrostatic interaction between the charges of all of the ions. Both the repulsive interactions due to Pauli forces and the attractive interactions due to the van der Waals dispersion forces are included in the short-range term, which is described by a mixed Buckingham and Lennard-Jones 9-6 potential model

) A exp(-rij /F) + B/rij9 - C/ij6 V short ij

(1)

where A, B, C, and F are the fitted parameters. A three-body potential was introduced to represent the semicovalent nature of the Zn-S bonds

Vijk ) (1/2)KTB(θijk - θ0)2

(2)

where θ0 is the equilibrium angle between Zn-S-Zn, and KTB is a fitted force datum. Additionally, in order to model the polarization of the S anions, the charges on the S atoms are split into a core and a massless shell, according to the Dick-Overhauser approximation.19 The core and the shell of the same atom interact with a harmonic potential

V core-shell ) (1/2)Krij2 ij

(3)

where rij is the core-shell separation. The spring constant, K, and the shell charges are fitted. The IP calculations in the work were preformed by using the GULP code23 with the parameters presented by Hamad et al.24 DFT Calculations. We performed DFT calculations by using the SIESTA code25-27 adopting norm-conserving pseudopotentials28,29 and the generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof (PBE) for the exchange-correlation functional.30 The Zn 3d and 4s states and S 3s and 3p states are treated as valence electrons. The valence electron wavefunctions were expanded by a double-ζ basis set plus polarization functions (DZP), which was optimized for w-ZnS. The numerical integrals were performed on a real space grid with an equivalent energy cutoff of 250 Ry. For the ZnSNWs and NTs, the periodic boundary conditions were applied to the axial direction, and a sufficient vacuum space larger than 15 Å was kept along the radial direction to decouple the interactions between adjacent NWs or NTs to ensure an isolated one-dimensional structure being considered. The Brillouin zone integrations were carried out by using a 1 × 1 × 8 k-mesh according to the Monkhorst-Pack scheme.31 All of the atomic positions and the lattice vectors were optimized using a conjugate gradient (CG) algorithm, until each component of the stress tensor was below 0.02 GPa and the maximum atomic force was less than 0.01 eV/Å. Moreover, we calculated the optimized configurations and formation energies of some selected ZnS-NWs and ZnS-NTs using the plane wave basis Vienna ab initio simulation package (VASP),32,33 implementing DFT and GGA. Projected augmented wave potentials34 (PAW) were employed to describe the core electrons of Zn and S atoms. A kinetic energy cutoff of 350 eV and a 1 × 1 × 4 k-point sampling of the Brillouin zone were adopted. The DFT calculations based on the pseudopotential approximation have been used widely to investigate the geometric and electronic structures of ZnO and ZnS nanostructures, and their validity has been confirmed and commonly accepted.35-37 However, the size of these nanostructures that the DFT calculations can deal with is quite limited because of the heavy computational load. The combination of efficient IP and accurate DFT calculations gives a powerful method to study the ZnS nanostructures with a wide range of size that are more comparable to the real materials. III. Results and Discussion We first calculated the equilibrium configuration of the w-ZnS crystal to test the reliability of the IP by comparing the IP results with those of DFT calculations and experiments. The optimized lattice constants are a ) 3.88 Å and c ) 6.09 Å from IP calculations, which agree well with the DFT results, a ) 3.83 Å and c ) 6.33 Å (SIESTA) and a ) 3.86 Å and c ) 6.31 Å (VASP), and experimental data, a ) 3.85 Å and c ) 6.29 Å. The validity of the IP in predicting other bulk properties of

Insight into Faceted ZnS Nanowires and Nanotubes

Figure 1. Side (left column) and top views (right column) of (a) ZnS nanowire; (b) faceted double-walled ZnS nanotube; (c) (9,0) singlewalled ZnS nanotube. The structural parameters (d1, d2, d3, θ) representing the surface relaxations are indicated in the inset of this figure.

w-ZnS crystal has also been confirmed.24 The reliability of the IP in dealing with ZnS nanostructures will be discussed in the following parts of this paper. Several experiments have shown that the synthesized ZnSNWs and NTs possess wurtzite structures with rectangular or hexagonal cross sections and axes orientating along the [0001] or [1000] direction.8,9 In this work, we characterize the morphology of ZnS-NWs and NTs using hexagonal prisms with [0001]-orientated axes enclosed by six facets belonging to the {101h0} plane group of w-ZnS crystal, as shown in Figure 1a. Another type of configuration, triangular prisms, was also calculated but found to be less stable than hexagonal prisms with the same volume. This is consistent with the experimental findings that ZnS-NWs prefer a hexagonal morphology to a triangular one. The configurations of the multiwalled ZnS-NTs were derived from the ZnS-NWs through removing hexagonal cores of different sizes from the ZnS-NWs. As a result, both the inner and outer facets belong to the {101h0} plane group, as shown in Figure 1b. This morphology resembles the alreadysynthesized ZnS-NTs.9 The ZnS-NWs and NTs under study have radii varying between 0.6 and 2.5 nm, as shown in Figure 3. Their equilibrium configurations and energetics were calculated by using IP calculations. Figure 1a and b gives the thinnest ZnSNW and ZnS-NT studied in this work. The ZnS-SWNTs built analogously to BN nanotubes were also considered. The armchair (n,n) tubes with n ) 1-10 and zigzag (m,0) tubes with m ) 6-16 were calculated. The equilibrium configuration of (9,0) ZnS-SWNT is shown in Figure 1c. To evaluate the reliability of the IP calculations in dealing with these ZnS nanostructures, the equilibrium configurations and energetics of the smallest ZnS-NW and NTs and the (9,0) ZnS-SWNT (shown in Figure 1) were also studied by using DFT calculations. The structural parameters as indicated in the inset of Figure 1a and the formation energies of these nano-

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Figure 2. Top views of multiwalled ZnS-NTs and ZnS-NWs with faceted morphologies. The definitions of the inner (Rin) and outer (Rout) radii and wall thickness (d) are also presented in the inset of this figure.

Figure 3. Evolution of formation energy (Eform) of ZnS-NWs (red solid circles), multiwalled ZnS-NTs (open up triangles, down triangles, squares, and diamonds), and ZnS-SWNTs (crosses) as a function of radius. The red solid line represents the fitting data of ZnS-NWs given by the expression Eform ) 0.689/R0.78. The radii of the multiwalled ZnSNTs are the outer radii.

structures are listed in Table 1. The {101h0} planes in bulk w-ZnS crystal are nonpolar with the anions and cations lying on the same plane. However, surface relaxations occur on the facets of the ZnS-NW and NT. Anions displace outward from the surface while cations move inward, giving rise to surface dipoles, as shown in Figure 1a and b. The atom displacements on the inner walls of the ZnS-NT are opposite to those on the outer walls (Figure 1b). Similar relaxation behavior was also found for the ZnS-SWNT. Obviously, the structural parameters of these facets obtained from IP calculations agree well with the DFT results. The formation energy (Eform) with respect to the stable w-ZnS crystal was calculated to estimate the stability and manufacturability of these nanostructures. It can be seen from Table 1 that although the energetic orders of the nanostructures are the same, the Eform values obtained from these

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TABLE 1: Structural Parameters and Energetics of Selected ZnS Nanostructures Obtained by Using Different Theoretical Approachesa configurations NW MWNT SWNT

IP DFT IP DFT IP DFT

d1

d2

d3

θ

Eform (eV/ZnS)

2.27 2.25 2.27 2.23 2.23 2.25

2.32 2.32 2.30 2.31 2.24 2.24

2.31 2.31 2.28 2.30 2.23 2.25

12.2° 19.3° 11.7° 15.8° 10.0° 9.4°

0.330 0.472 (0.246) 0.338 0.480 (0.252) 0.468 0.788 (0.404)

a The equilibrium configurations of these nanostructures are shown in Figure 1. The definitions of the structural parameters are indicated in the inset of Figure 1. The distances (d1, d2, d3) are in angstroms. For the DFT data, the values in parentheses were obtained using the VASP package, while others are from SIESTA calculations.

calculations are different. It has been widely accepted that the DFT calculations within the VASP package are more reliable than those within SIESTA package. The present IP results are between the results of the VASP and SIESTA calculations (Table 1) but relatively closer to the VASP results. The above results indicate that the present IP calculations can give geometrics and energetics of ZnS nanostructures that compare well to the DFT calculations and thus can be employed safely to study the large-size ZnS nanostructures that are difficult for DFT calculations because of the heavy computational load. In the following calculations, we optimized the configurations of the ZnS nanostructures and calculated the Eform using the IP. Six ZnS-NWs with radii varying between 0.6 and 2.5 nm, as shown in the last row of Figure 2, were then calculated. The Eform values of these NWs decrease monotonously with the increase of the wire radius (R), as shown by the solid circles in Figure 3. These data can be fitted by the expression Eform ) 0.689/R0.78 (eV/ZnS), represented by the red line in Figure 3. It is understandable that the larger the wire radius, the more stable the wire. For the largest ZnS-NW under study (R ) 2.5 nm), the Eform is only 0.109 eV/ZnS. Considering that the cohesive energy of the w-ZnS crystal with respect to isolated Zn and Si atoms is -5.93 eV/ZnS obtained from the DFT calculations within the VASP package, the cohesive energy of this ZnSNW is about 98% of that of the w-ZnS crystal, indicating its high manufacturability. Indeed, the ultrafine ZnS-NW with the radius of 2.5 nm has been grown successfully through a thermal evaporation method.38 The as-synthesized ZnS-NW is of wurtzite structure with the axis orientated along the [0001] direction, which agrees well with the configuration modeled in the present work. The ZnS-NTs with thick walls were built by removing hexagonal cores of different sizes from the faceted ZnS-NWs, as shown in Figure 2. These faceted NTs differ significantly from either the ZnS-SWNTs as shown in Figure 1c or the multiwalled nanotubes constructed analogously to multiwalled BN nanotubes of coaxial cylindrical configurations. The atomic arrangement in these faceted tubes displays wurtzite-like characters and bears no resemblance to the graphene-like features of BN nanotubes. It is interesting to see that the Eform of these tubes decreases with the increase of wall thickness (d), irrespective of the tube radius, as shown in Figure 3. The doublewalled nanotube (2WNTs) with a wall thickness of 4.4 Å has an Eform of about 0.34 eV/ZnS, close to that of the thinnest ZnSNW shown in Figure 1a, 0.33 eV/ZnS. The Eform of the triplewalled nanotubes (3WNTs) is close to that of the nanowire (NW2) of radius of 13.7 Å, and this trend can be kept for all of the faceted ZnS-NTs, as shown in Figure 3. It can be naturally deduced that the septuple-walled nanotube (7WNTs) with a wall

Figure 4. Evolution of formation energy (Eform) of (a) ZnS-NWs and (b) multiwalled ZnS-NTs as a function of the reverse of wire radius (1/R) and walled thickness (1/d). The dashed line in a represents the data given by the expression: Eform ) 2.98/R, while the dashed line in b corresponds to the expression Eform ) 2.58/d.

thickness of about 2.1 nm will have an Eform comparable to that of the already-synthesized ZnS-NW of 2.5 nm radius, and thus high manufacturability. Although the growth of such ultrathin ZnS-NTs has not been achieved experimentally so far, it is expected in the near future because of the energetic advantage of these tubes.40 The Eform evolution of the ZnS-NWs and NTs as a function of wire radius or wall thickness is understandable, in term of a simple model. If we suppose that the Eform values of the ZnSNWs and NTs arise totally from the surface energy then it can be determined by the following expression39

Eform )

4 × Esurf

x3 × n × (Rout - Rin)

(4)

where Esurf is the surface energy density of the facets (eV/Å2), n is the atomic density (ZnS units per volume), and Rout and Rin are the inner and outer radii of the faceted ZnS-NTs, respectively, as indicated in the inset of Figure 2. For the ZnSNWs, Rin becomes zero, and the Eform can be written as

Eform ) Dwire/R,

Dwire )

4 × Esurf

x3 × n

(5)

From these expressions, it is clear that the Eform values of the ZnS-NWs decrease with the increase of wire radius, R, and have a proportional relationship to the inverse of tube radius (1/R). If we take the surface energy of the {101h0} surfaces as 0.52 J/m2 reported by Hamad et al.,24 and n ) 0.0252 ZnS/Å2, then the proportional coefficient, Dwire, will be 2.98 eV‚Å/ZnS. The data of this formula are represented by the dashed line in Figure 4a. However, the Eform values obtained from the IP calculations (represented by the solid uptriangles in Figure 4a) deviate from this expression, especially for the ZnS-NWs of small radii. We attribute it to the size-effect of these nanowires because the surface relaxations of these ZnS-NWs are size-dependent. The

Insight into Faceted ZnS Nanowires and Nanotubes

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value of θ decreases with the increase of wire radius and saturates to a value corresponding to an infinite surface. The θ of the thinnest ZnS-NW under study is 12.2°, as shown in Figure 1a. For the thickest wire (NW6), θ is decreased to 10.9°, close to the value of an infinite (101h0) surface, 10.8°.24 This means that the surface energy density, Esurf, of these ZnS-NWs, especially for those of small radii, cannot be treated as a constant value for all of the wires. However, for the large-size ZnSNWs, the Eform evolution as a function of wire radius tends to follow eq 5, as shown in Figure 4a. For the faceted ZnS-NTs, as shown in Figure 2, the wall thickness d can be expressed as d ) x3 × (Rout - Rin)/2, and the Eform can be written as

Eform ) Dtube/d,

Dtube ) 2 × Esurf/n

(6)

Obviously, the Eform values of these ZnS-NTs decrease with the increase of wall thickness, irrespective of the tube radius. Therefore, the multiwalled ZnS-NTs with the same wall thicknesses but different radii would have the same values of Eform. This is consistent with the IP results, as shown in Figures 3 and 4b. According to eq 6, Eform has a proportional relationship to the inverse of wall thickness, 1/d. The coefficient Dtube was calculated to be 2.58 eV‚Å/ZnS by using the data mentioned above. Because of the size-effect, the Eform evolution of these tubes as a function of wall thickness deviates from the trend predicted by eq 6, as shown in Figure 4b, especially for the tubes of thin walls. For the tubes of thick walls, however, the variational trend of Eform exhibits the tendency to follow the eq 6. From this simple model, the relationship between the Eform values of ZnS-NWs and NTs described above is also understandable. If the differences between the outer radii and the inner radii, Rout - Rin, of multiwalled ZnS-NTs are close to the radius of a ZnS-NW, then according to the eq 4 they will have close Eform values. The IP calculations indicate that the ZnS-NWs and NTs with close Eform values satisfy such a condition. The possibility of synthesizing ZnS-SWNTs designed analogously to BN nanotubes is an interesting issue. Although, the DFTB calculations have shown that the strain energy of ZnSSWNTs with respect to a graphene-like sheet is lower than that of carbon nanotubes, their manufacturability is still questionable because the graphene-like ZnS sheet is not the stable form of ZnS materials. We evaluated the formation energies of ZnSSWNTs with respect to the stable w-ZnS crystal using IP calculations and plotted them in Figure 3. Armchair (n,n) and zigzag (m,0) tubes with n ) 1-10, m ) 6, 16, were studied. Both IP and DFT calculations showed that the Eform values of these ZnS-SWNTs are around 0.46 eV/ZnS, which are higher than those of ZnS-NWs and multiwalled ZnS-NTs with faceted configurations (Table 1). The cohesive energies of these ZnSSWNTs are therefore about 91% of that of the stable w-ZnS crystal, which is lower than that of the already-synthesized smallest ZnS-NW with a radius of 2.5 nm, 98%. An alternative configuration to these ZnS-SWNTs was built by coaxially arranging two ZnS-SWNTs with appropriate radii. These cylindrical double-walled ZnS-NTs resemble the double-walled BN nanotubes, but differ significantly from the faceted ZnS nanotubes studied in the previous parts of this paper. Molecular dynamic simulations based on the IP calculations indicate that these cylindrical double-walled nanotubes are quite unstable and undergo severe structural distortion even at room temperature. Zn-S bonds were formed between the inner and outer walls, and the cylindrical morphology deforms to a faceted configuration, during the simulations. When the double-walled nanotube

Figure 5. Band structures of (a) ZnS-NW; (b) double-walled ZnSNT with faceted morphology; (c) (9,0) ZnS-SWNT; (d) w-ZnS crystal along the Γ(0,0,0) 2π/c f A(0,0,1/2) 2π/c direction, where c is the lattice constant along the axial direction. The equilibrium configurations of these ZnS nanostructures are shown in Figure 1. The energies at the Fermi levels are set to zero.

built by placing a (9,0) SWNT inside a (15,0) SWNT is heated, it transforms to a hexagonal-faceted tube as shown in Figure 1b. This is consistent with the energetic advantage of the faceted nanotubes against the SWNTs. Therefore, we can deduce that multiwalled ZnS-NTs prefer the hexagonal-faceted morphology to the coaxial cylindrical configurations. These results clearly imply the complication of the growth of ZnS-SWNTs. The study of the electronic structures of ZnS nanomaterials is another important issue, which would promote the applications of these materials in building nanoscale optoelectronic devices. The band structure calculations of the w-ZnS crystal using the DFT-GGA scheme gives a direction band gap of 2.0 eV at Γ point, which underestimates the band gap by about 1.7 eV, as compared to the experimental value, 3.7 eV. It is well known that the Kohn-Sham energy gaps differ from the quasiparticle gaps and are always smaller than the observed values. This can be corrected by evaluating the self-energy operator in the GW approximation. In this work, we simply assume that the band gap shift is constant for all of the ZnS nanostructures under study and add a correction of 1.7 eV to the calculated band gaps. The electronic band structures of the ZnS-NW (Figure 1a), faceted ZnS-NT (Figure 1b), and ZnS-SWNT (Figure 1c) indicated that they have direct band gaps of about 4.0, 4.1, and 4.4 eV, respectively, at the Γ point, as shown in Figure 5. The wider band gaps of these nanostructures as compared to bulk w-ZnS crystal are consistent with other DFT calculations13 and can be attributed to the quantum size-confinement effects in these low-dimensional nanostructures.41 The direct band gaps of these nanomaterials are quite important for building nanoscale optoelectronic devices. It is noteworthy that both the highest valence band (HVB) and the lowest conduction band (LCB) of the faceted ZnS-NT and ZnS-NW have relatively high dispersion along the Γ(0,0,0) 2π/c f A(0,0,1/2) 2π/c direction, similar to the feature of w-ZnS crystal. No flat band corresponding to the states of the threefold coordinated atoms on the facets appears in the band gap of the ZnS-NW and ZnS-NT, in good contrast to the case of AlN nanostructures.42 We then calculated the partial electron density of states (PDOS) of the ZnS-NW by projecting the total density of states onto the surface atoms (Zn′ and S′) and bulk atoms (Zn and S), respectively, as shown in Figure 6. It can be seen that the both the S(3p) states of bulk atoms and the S′ (3p) states of surface atoms contribute to the HVB of the ZnS-NW, whereas the LCB arises mainly from the Zn(4s) states of bulk

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Figure 6. Partial electronic density of states (PDOS) of the ZnS-NW (Figure 1a) obtained by projecting the total density of states onto the surface atoms (S′, Zn′) and bulk atoms (S, Zn). Red and blue lines represent the data of S (or S′) and Zn (or Zn′) atoms, respectively. The energies at the Fermi levels are set to zero. The arrows indicate the positions of the peak of the 3p states of the S (or S′) atoms.

atoms. There is a shift (0.57 eV) of the peak of the S′(3p) states of the surface S atom with respect to the S(3p) orbitals of the bulk S atom. Interestingly, this shift is close to that of the 439 nm emission peak relative to the 538 nm emission in the photoluminescence spectrum of ZnS single-crystalline nanotubes, which is 0.55 eV.9 The 439 nm emission peak was expected to have a close relationship to the large surface-tovolume ratio in the nanotubes. However, no theoretical support has been proposed so far. Although the photoluminescence of ZnS materials is intricate because of its sensitivity to the synthetic conditions, crystal size, and shape, the blue shift of the 3p orbitals of the surface S′ atom relative to that of the bulk S atom revealed from our DFT calculations may be helpful for understanding the origination of the ∼439 nm emission peak in ZnS nanomaterials. IV. Conclusions Our IP and DFT calculations show that the ZnS-NWs prefer hexagonal prism morphology with the Eform decreasing with increase of wire diameter. The multiwalled ZnS-NTs with faceted configurations have an energetic advantage over either single-walled or double-walled ZnS-NTs built analogously to BN nanotubes. The Eform values of these hexagonal-faceted nanotubes decrease with the increase of wall thickness, irrespective of the tube radius. The surface relaxations and surface energy density are size-dependent, especially for the small-size ZnS-NWs and ZnS-NTs. Both of the ZnS-NWs and ZnS-NTs are wide-band gap semiconductors with a direct band gap at the Γ point. The band gaps of these nanostructures are slightly wider than that of bulk w-ZnS crystal. No flat band corresponding to the states of surface atoms appear in the band gaps of these nanostructures. Acknowledgment. This work described in this paper is supported by the National Natural Science Foundation of China under grant nos. 50402017 and 10675075, and the National Basic Research 973 Program of China (grant no. 2005CB623602). M.W.Z. and Z.H.Z. thank the support from an Australian Research Council (ARC) linkage international fellowship. M.W.Z. thanks the Program for New Century Excellent Talents for the Universities in China. M.W.Z. also thanks Prof. J. D. Gale for providing us the GULP package.

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