J. Phys. Chem. C 2008, 112, 20291–20294
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First-Principles Study of the Structural Stability and Electronic Properties of ZnS Nanowires Hu Xu,†,‡ Yu Li,† A. L. Rosa,§ Th. Frauenheim,§ and R. Q. Zhang*,†,| Nano-organic Photoelectronic Laboratory, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100101, China, Graduate UniVersity of Chinese Academy of Sciences, Beijing, China, BCCMS, UniVersita¨t Bremen, FB1/NW1, 28359, Bremen, Germany, and Center of Super-Diamond and AdVanced Films and Department of Physics and Materials Science, City UniVersity of Hong Kong SAR, China ReceiVed: August 30, 2008; ReVised Manuscript ReceiVed: October 24, 2008
The structural stability and electronic properties of [0001] ZnS nanowires were investigated using density functional theory within the generalized gradient approximation. This paper focuses on the atomic relaxations, formation energies, and electronic structure of ZnS nanowires with triangular and hexagonal cross sections. It was found that the structural stability of nanowires mainly depends on the surface ZnS pair ratio. The bare and hydrogen-passivated wires were semiconducting, with band gaps larger than those in bulk ZnS. Hydrogen passivation had a significant influence on the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). I. Introduction 1
Since the discovery of carbon nanotubes, a number of onedimensional nanostructures have become the focus of intensive research owing to their unique physical and chemical properties. Recent successful growths of II-VI semiconductor nanowires, such as ZnS nanowires, have expanded the list of potential applications for nanomaterials. ZnS is an important II-VI semiconductor that presents in two types of crystal structures, wurtzite (hexagonal) and zinc blende (cubic). The most stable bulk form of ZnS at room temperature is the zinc blende structure, which can transfer to the wurtzite structure after heating to 1020 °C in ambient pressure.2 The wurtzite ZnS presents a wide direct band gap of 3.7 eV and a large excitonic binding energy of 40 meV at room temperature, so it is expected to offer unique optical, electrical, and piezoelectric properties.3-8 The wurtzite ZnS nanowires have been synthesized successfully by employing various methods such as the vapor-liquid-solid process,9 thermal evaporation,10 and pulsed laser vaporization.11 In particular, Zhang et al.12 have successfully grown ZnS nanowires with diameters of 5-12 nm, and quantum size effects are expected to have a pronounced influence on the application of small nanowires. To promote the growth and application of scientifically and technologically important nanomaterial, intensive theoretical studies on the structural and physical properties of ZnS nanowires are desirable at this time. Among the few previous theoretical attempts to study ZnS nanowires, Li et al.13 compared ZnS wires and tubes with hexagonal cross sections using interatomic potential and first-principles calculations, and they found the size dependency of the surface relaxations and surface energy density for both ZnS wires and ZnS tubes. However, a detailed understanding of the structural stability and electronic properties of ZnS nanowires is still needed. In this work, we investigated ZnS nanowires enclosed * Corresponding author. E-mail:
[email protected]. † Technical Institute of Physics and Chemistry, Chinese Academy of Sciences. ‡ Graduate University of Chinese Academy of Sciences. § Universita¨t Bremen. | City University of Hong Kong.
by different facets and explored the influence of hydrogen passivation on the electronic structure of the ZnS wires. II. Theoretical Method Our calculations were performed based on density functional theory within the generalized gradient approximation (GGA)14 for the electronic exchange correlation functional. We employed the projected augmented wave (PAW) method15 as implemented in VASP (Vienna Ab-initio Simulation Package)16 to investigate ZnS nanowires with diameters up to 1.8 nm. The Zn 3d electrons were treated as part of the valence band. The cutoff energy of 500 eV was used throughout the calculations. We also made a comparative study between the ZnS nanowires with the ZnS(101j0) surfaces which were modeled using periodic slabs, with 10 ZnS double layers and the ZnS(112j0) surfaces with 12 ZnS layers. The nanowires were infinite along the [0001] direction (c-axis) enclosed by (101j0) facets and (112j0) facets, respectively. The surfaces and nanowires were separated by a vacuum region of 15 Å. We used (4 × 6 × 1), (4 × 4 × 1), and (1 × 1 × 4) k-point Monkhorst-Pack meshes17 for the (101j0) surfaces, (112j0) surfaces, and nanowires, respectively. All atoms were allowed to relax until the forces were smaller than 0.02 eV/Å. III. Results and Discussion Our optimized lattice parameters of bulk ZnS are a ) 3.85 Å, c ) 6.31 Å, and u ) 0.375, which are in good agreement with the experimental values, a ) 3.82 Å and c ) 6.26 Å.18 The initial structures of surfaces and nanowires were constructed from wurtzite ZnS with optimized lattice parameters. The atomic relaxations for the (101j0) surface and the (112j0) surface (not shown) were examined briefly first to set a reference point for presenting our results for the nanowires. The Zn and S atoms form an array of ZnS dimers on the (101j0) surface. The (112j0) surface layers are made up of two ZnS dimers, which form zigzag lines along the surface. Zn atoms located in the first layer relax toward the bulk region, whereas the outermost S atoms remain close to their original positions for both nonpolar
10.1021/jp807718j CCC: $40.75 2008 American Chemical Society Published on Web 12/02/2008
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Xu et al.
Figure 1. Relaxed nanowires: top view of the smallest wire A, triangular wire B with (101j0) facets, hexagonal wire C with (101j0) facets, triangular wire D with (112j0) facets, and hexagonal wire E with (112j0) facets. Gray and yellow spheres denote Zn and S, respectively.
TABLE 1: Diameters (d), Formation Energies per ZnS Pair of Hydrogen-Passivated Wires (EfH), Lattice Constants (c), Band Gaps of Bare Wires (Eg), Band Gaps of Hydrogen-Passivated Wires (EgH), and the Buckling Anglesa bulk d (Å) EfH (eV) c (Å) Eg (eV) EgH (eV) ω (deg) a
6.31 1.94
(101j0)
2.13 2.20 17.21
(112j0)
A
B
C
D
E
2.22 2.39 17.67
4.73 -0.57 6.17 3.00 4.38 15.10
9.09 -0.89 6.27 2.79 3.68 15.49
11.79 -1.10 6.29 2.69 3.17 18.30
11.83 -0.94 6.25 2.76 3.64 16.54
17.95 -1.20 6.26 2.53 2.95 15.94
The nanowires are put in different circles, and the diameters of the circles are the diameters for the nanowires.
Figure 2. Formation energy as a function of the number of surface ZnS pairs divided by the total number of ZnS pairs in the system. The zero of energy is set to the formation enthalpy of ZnS bulk.
surfaces, forming a buckled Zn-S dimer. The buckling angles ω are 17.21° for the (101j0) surface and 17.67° for the (112j0) surface. The Zn-S bond lengths are 2.22 Å on the (101j0) surface and 2.26 Å on the (112j0) surface, which are smaller than that in bulk ZnS (2.36 Å). Rotation is associated with a decreasing energy of the occupied S dangling bond and an energy increment of the Zn empty state. In each surface dimer, the cation shifts downward until it lies nearly in the plane of its three anion neighbors to rehybridize toward a Zn sp2-like configuration. ZnS nonpolar surfaces have stronger rotations compared with those of ZnO,19,20 because materials with low cohesive energies and ionicities tend to have strong rotations.21 The relaxations of the atoms in the second layer are much smaller for both nonpolar surfaces. The optimized structures of ZnS nanowires with different lateral facets are shown in Figure 1: surface relaxation evidently plays an important role for the bare wires. The surface Zn atoms Zn(s) show remarkable relaxations, which have the same trend as the relaxations of the ZnO nanowires.19,22 On the surface, the Zn(s)-Zn(s) distance is 3.00 Å, much smaller than that in bulk ZnS (3.85 Å). The distances between the surface S atoms range from 4.08 to 4.11 Å, which are bigger than the distance in bulk ZnS (3.85 Å). Similar to the nonpolar (101j0) and (112j0) surfaces, the buckle of the Zn-S dimer results in a slight distortion near the surfaces because Zn atoms move toward the axis and the S atoms move away from the axis. The tilt angles of the surface Zn-S dimers are 15.10°, 15.49°, 18.30°, 16.54°,
and 15.94° for the nanowires A, B, C, D, and E, respectively. Along with the shrinkage of the surface atoms, the lattice constant c of the ZnS nanowires is reduced compared with that of bulk ZnS, as shown in Table 1. The lattice constants of the large nanowires tend to approach that of bulk ZnS. The Zn-S bond lengths relaxed significantly on the facets; however, those in the core region of the nanowires were much less affected by relaxation and were close to the bulk ZnS values. This trend was similar for all of the nanowires that we investigated. Recently, Zhang and Huang23 suggested that infinitely long ZnO hexagonal nanowires show a phase transformation from the wurtzite to graphite-like structure below a critical diameter of 13 Å. We checked the ZnS nanowires and confirm that there is no such region where the graphite-like structure is energetically more stable than the wurtzite one. Therefore, bare wires with small diameters do not undergo a phase transformation. In order to verify the energetic stability of ZnS nanowires, we calculated their formation energies according to
Ef ) Etot - nSµS - nZnµZn - nHµH
(1)
where Etot is the total energy of the wire, and nS, nZn, and nH are the numbers of S, Zn, and H atoms. µS, µZn, and nH are the chemical potentials of S, Zn, and H. These values are equal to the energies of the bulk Zn, bulk S, and H2 molecule, respectively. In Figure 2, we plot the formation energies of the surfaces and wires as a function of the surface pair ratio. Structural stability is mainly determined by the dangling bonds on the nanowire facets, which cause a large loss of formation energy. The ratio of the number of surface dangling bonds to the total number of atoms (equivalent to the surface to volume ratio24) in each diameter is low in hexagonal nanowires and high in triangular ones. So the hexagonal nanowires with a lower ratio of surface dangling bonds have much lower formation energies; hence, these nanowires have higher stability, and the high dangling bond ratio results in destabilization of the triangular nanowires. Ef converges into the calculated bulk formation energy as the surface pair ratio decreases. The linear behavior is an indication that the edge effects are small and the surface effects are dominant for ZnS wires. In addition to bare wires, we also investigated hydrogenpassivated ZnS nanowires (not shown). The Zn and S atoms on the side facets of bare ZnS nanowires are threefold coordinated, and all the dangling bonds can be passivated by H atoms. In spite of the notable Zn atom displacement, the S atom
First-Principles Study of ZnS Nanowires
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Figure 3. Band gaps of ZnS bulk, hydrogen-passivated ZnS surfaces, and nanowires as a function of the H/ZnS ratio.
remains close to the unrelaxed position. The surface Zn(s)-Zn(s) distances range from 4.42 to 4.47 Å, which are much larger than the distance in bulk ZnS (3.85 Å). The distances between the S surface atoms range from 3.56 to 3.59 Å, which are smaller than the distance in bulk ZnS (3.85 Å). The Zn-H (S-H) bond length is found to be 1.55 (1.35) Å. The structural relaxation of the outermost surface layer shows notable changes in comparison with the bare wires. The surface Zn (S) atoms are displaced outward (inward) and share larger bond lengths. The band gaps are 3.00, 2.79, 2.69, 2.76, and 2.53 eV for the wires A, B, C, D, and E, respectively. These values are much larger than the calculated GGA band gap for ZnS of 1.94 eV, indicating strong quantum confinement effects. The band gaps mainly depend on surface pair ratio, and the band gap increases as the surface pair ratio increases. The band structures for all bare nanowires are similar, showing a semiconducting character and a direct band gap at the Γ point. The band gaps of the hydrogen-passivated wires are much higher than those of bare nanowires. There is an increase in the band gaps to 4.38, 3.68, 3.17, 3.64, and 2.95 eV for the hydrogen-passivated wires A, B, C, D, and E, respectively. To identify the influence of the electronic properties of ZnS wires under hydrogen passivation, we examine the band gaps of hydrogen-passivated ZnS surfaces and nanowires as a function of the H/ZnS ratio, as shown in Figure 3. For wurtzite bulk ZnS, the band gap (Egbulk) is 1.94 eV. The dependence of band gaps of ZnS surfaces and nanowires on the H/ZnS ratio (R) can be described by
Eg ) Egbulk + 2.455R
(2)
According to this expression, the band gap of ZnS nanowires is proportional to the H/ZnS ratio, and we can evaluate the band gap of other hydrogen-passivated wires using this expression. Furthermore, the formation energies of the hydrogen-passivated wires were calculated and are listed in Table 1. The results indicate that these formation energies mainly depend on the H/ZnS ratio. The wire of a larger diameter with a lower H/ZnS ratio gives lower formation energy. The electronic band structures along the growth direction of the bare wire C and the hydrogen-passivated wire C are shown in Figures 4a and 5a, respectively. Although some bands are shifted, the shapes of the band edges are not significantly affected. For bare and hydrogen-passivated nanowires, the change in the band gap is due entirely to the confinement of the conduction band (CB) states. It is significant for small wires that the quantum confinement effect on the valence band maximum (VBM) is greater than that on the conduction band minimum (CBM). For large wires, the VBM is less affected by the wire’s diameter and the changes in the band gap are mainly
Figure 4. (a) Electronic band structure of bare wire C along the [0001] direction. (b) LUMO (blue) charge density at for the wire C. (c) HOMO (purple) charge density at for the wire C. The isosurface value used was 0.006 e Å-3.
Figure 5. (a) Electronic band structure of hydrogen-passivated wire C along the [0001] direction. (b) LUMO (blue) charge density at for the hydrogen-passivated wire C. (c) HOMO (purple) charge density at for the hydrogen-passivated wire C. The isosurface value used was 0.006 e Å-3.
due to changes in the CBM. Although the CBM is more sensitive to the diameter than the VBM, the valence states are still strongly affected by quantum confinement. We show the isosurfaces of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) at the Γ point of bare wire C and hydrogen-passivated wire C in Figures 4 and 5, respectively. The LUMO of the bare nanowire is more delocalized and has a large dispersion along the direction of growth, which is consistent with the character of the conduction band. Due to the delocalized character, the LUMO energy will decrease as the diameter of the nanowires increases, and the delocalized distribution is also responsible for the large dispersion of the LUMO from the Γ point to the A point. The HOMO density for the bare wire C is delocalized in the whole nanowire, which is different from that of ZnO
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Xu et al. semiconductors. The band gap of hydrogen-passivated wires can be predicted by the H/ZnS ratio. Moreover, the band gap of ZnS nanowires can be tuned by controlling the thickness of the nanowires and by hydrogen adsorption. The LUMO mainly localizes in the center, and the HOMO distributes from the center to the surface for the hydrogen-passivated nanowires, whereas the LUMO and the HOMO of bare wires are less localized throughout the whole nanowire. Acknowledgment. We thank Wei Fan and Lei Chen for fruitful discussions. The work described in this paper is supported by the National Basic Research Program of China (Grant No. 2006CB933000), the Research Grants Council of Hong Kong SAR (project no. CityU 103106), and the Centre for Applied Computing and Interactive Media (ACIM) of the City University of Hong Kong. A.L.R thanks DFG/SPP-1165 for financial support. We thank the Supercomputer Center of the Chinese Academy of Science (SCCAS) for computational facilities. References and Notes
Figure 6. Charge density difference distribution for the hydrogenpassivated wire C. The green indicates an increase in charge density. The isosurface value used was 0.12 e Å-3.
nanowires.25 For ZnO nanowire, the HOMO is mainly composed of surface O 2p-like dangling bonds. The three-coordinated surface atoms would not have a strong influence on the gapforming states; thus, the surface states involve less contributions to bare ZnS nanowires. Hydrogen passivation is shown to have a significant influence on the HOMO and the LUMO. The LUMO of hydrogen-passivated nanowire is localized mostly on the core of the nanowire and has a large dispersion along the direction of growth, whereas the HOMO is more delocalized and distributes from the center to the surface. To understand how hydrogen passivation affects the electronic properties of ZnS wires, we calculated the charge density difference of hydrogen-passivated wire C. The charge density difference is defined as the difference between the total charge density and the atomic charge density. The positive value of the charge density difference is shown in Figure 6 and indicates that H atoms gain more electrons as bonds are formed. This difference describes the effect of electron migration upon the formation of the bond between H atoms and ZnS wire. One can clearly see a substantial charge transfer from ZnS wire to passivated H atoms, and this charge transfer can evidently affect the characteristics of the HOMO and the LUMO. IV. Conclusions In conclusion, we have carried out first-principles density functional calculations on [0001] ZnS nanowires. The stability of wires mainly depends on the surface ZnS pair ratio. Both bare nanowires and hydrogen-passivated nanowires behave like
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