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First-Principles Study of the Relaxed Structures and Electronic Properties of Au Nanowires Jian-Min Zhang,*,† Xiu-Juan Du,† Su-Fang Wang,† and Ke-Wei Xu‡ College of Physics and Information Technology, Shaanxi Normal UniVersity, Xian 710062, Shaanxi, People’s Republic of China, and State Key Laboratory for Mechanical BehaVior of Materials, Xian Jiaotong UniVersity, Xian 710049, Shaanxi, People’s Republic of China ReceiVed: June 3, 2009; ReVised Manuscript ReceiVed: August 22, 2009

Under the generalized gradient approximation, the relaxed structures and electronic properties have been investigated for Au nanowires with cross sections of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 atom layers using the first-principles projector-augmented wave potential within the density functional theory. For all five-sized nanowires, the relaxed structures still have tetragonal symmetry and show a “round corner” phenomenon. The vanishing of the neighbor atoms outside the nanowire after being cleaved from bulk crystal not only causes the structure relaxation above but also affects the electronic properties in the following three aspects. (1) The total charges of the surface and near surface atoms are reduced. (2) The enhanced interactions appear between the surface atoms as well as the surface atoms and their first nearest neighbor atoms; we term this phenomenon the “skin effect”, which enhances the mechanical and the electronic transport properties of the nanowire compared to bulk. (3) The farther the atoms are from the central axis of the nanowires, the more the electrons fall in the higher energy region of the occupancy state due to the lower coordination number and thus fewer restrictions. In fact, the conclusions drawn here are applicable to not only the nanowires but also the other surface cases, such as nanobelts, nanotubes, nanocables, clusters, thin films, and so on. 1. Introduction When at least one of the dimensions of materials is reduced to the nanometer scale, they usually exhibit unique structural, mechanical, electrical, optical, and chemical properties. Nanowires (NWs) have attracted much attention because of their potential applications as next generation structural materials in biosensors, nanoelectromechanical systems, and miniaturized optic-electronic devices.1-6 Many experimental and theoretical methods have been used to investigate the structural and functional properties of the NWs.7-15 Due to the computer capability of present computers as well as the improvement of algorithms, it is possible to simulate the formation of very thin metal nanowires by computer. These new simulation methods, implemented at levels ranging from effective potentials to tight binding based up to ab initio electronic structure, help one to understand the experiments as well as stimulate new experiments, since these techniques now have predictive power.16 In particular, Au nanowires have attracted a great deal of attention in recent years because of their potential applications as junctions in circuits, as structural reinforcements in composite materials, and as sensors to detect airborne biological and chemical toxins.17,18 Recently, several experimental19-21 and theoretical22-25 studies have been published on structural and physical properties of different Au nanowires. Little research on the size-dependent relaxed structures and electronic properties of Au nanowires have been reported in detail. In the present work, under the generalized gradient approximation (GGA), the relaxed structures and electronic properties have been investigated for Au nanowires with cross sections of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 atom layers using the first-principles projector-augmented wave (PAW) potential within the frame* Corresponding author. Tel.: +86 29 85308456. E-mail address: [email protected]. † Shaanxi Normal University. ‡ Xian Jiaotong University.

Figure 1. [001] oriented Au nanowire with a cross section of 3 × 3 atom layers.

work of the density function theory (DFT).26 We use GGA since it considers not only the charge density as in LDA but also the gradient of the charge density which is more important for the cases of the nanowires with edges and thus large gradient of the charge density. Two phenomena, the “round corner” of the relaxed structures and the “skin effect” of the interactions between atoms, are attributed to the vanishing of the neighbor atoms outside nanowires. The paper is organized as follows. In section 2, the structure model and the calculation method of Au nanowires are given in detail. In section 3, the relaxed structures, charge-density analysis, and electronic structure of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires are analyzed. Finally, the conclusions of the work are drawn in section 4. 2. Calculation Model and Method In a top-down fabrication process, it is usual to cleave a foursquare fcc or bcc metal nanowire from the bulk crystal. As an example, Figure 1 schematically shows an fcc metal Au nanowire with a cross section of 3 × 3 atom layers. The wire

10.1021/jp905225h CCC: $40.75  2009 American Chemical Society Published on Web 09/18/2009

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Figure 2. Positions of the atoms on adjacent A (triangles) and B (circles) (001) layers before (open symbols) and after (closed symbols) relaxation for the 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires.

is assumed along the [001] direction with two (100) and two (010) lateral surfaces and as infinite in length to avoid end effects. Wider wires 5 × 5, 7 × 7, 9 × 9, and 11 × 11 can be obtained by adding two more atomic layers successively

perpendicular to the [100] and [010] transverse directions simultaneously. The calculations are performed within the framework of DFT using the PAW potential26 and a plane-wave basis set, as

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Figure 3. Relaxation amount of the representative atoms Ai on A layer of the 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires (a) and Bi on B layer of the 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires (b) as a function of the initial distance of the atoms away from the center of the nanowire.

implemented in the Vienna ab-initio simulation package (VASP) computer code.27-30 The 5d106s1 electrons of Au are taken as the valence electrons. The electron exchange and correlation are treated by using the Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA).31 We choose a conjugate-gradient algorithm to relax the ions into their ground states, and the energies and the forces on each ion are converged to less than 10-4eV/atom and 0.02 eV/Å, respectively. The Brillouin zone (BZ) integration is performed within the Monkhorst-Pack scheme32 using (1 × 1 × 5), (1 × 1 × 7), (1 × 1 × 9), (1 × 1 × 11), and (1 × 1 × 13) k points for 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires, respectively. A plane-wave cutoff of 230 eV is used. The optimized lattice parameter of 4.0796 Å for Au bulk is a little larger than the experimental value of 4.0783 Å. The theoretical lattice constant is used in all Au nanowires calculations. The large enough vacuum layers (16 Å) are added to two lateral directions [100] and [010] to make sure that the interactions between a wire and its periodic images are negligible. 3. Results and Discussion 3.1. The Relaxed Structures. The positions of the atoms on adjacent A (triangles) and B (circles) (001) layers, which are represented on one plane for convenience, before (open symbols) and after (closed symbols) relaxation are shown in

Figure 2 for the 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 nanowires due to no perpendicular to (001) plane movement. It is noted that for all five-sized nanowires, the relaxed structures still have tetragonal symmetry so that only the representative atoms Ai and Bi on A and B layers within the dashed line triangle should be considered. Second, the relaxation direction changes from inward for the atoms on the symmetrical diagonals (dashed hypotenuses) to outward for the atoms on the symmetrical medians (dashed right-angle sides), although the relaxation direction of the remaining atoms on unsymmetrical lines deviates slightly from the connected lines between the original positions of the remaining atoms and the center of the nanowires. This implies there is a “round corner” phenomenon. Such a phenomenon was also observed by Gall et al.24 with the modified embedded atom method (MEAM) and tight-binding (TB) simulations and by Gonza´lez et al.33 with time-resolved high resolution transmission electron microscopy (HRTEM) and will make a prism tend to be a cylinder for 1D structure as well as making a polyhedron tend to be a sphere for 0D structure. For a totally cylindrical or spherical nanostructure, however, additional symmetry in the radial direction is going to change the atom relaxation direction to be more isotropic along only the negative direction of the radial direction, thereby contracting these nanostructures uniformly. A single crystal cylinder (pillar) was obtained by Uchic et al.34 and Greer et

First-Principles Study of Au Nanowires al.35,36 with a focused ion beam microscope (FIBM). Third, as can be seen also in Figure 3 for the relaxation amount of the representative atoms Ai on A layer of the 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 nanowires (a) and Bi on B layer of the 5 × 5, 7 × 7, 9 × 9, and 11 × 11 nanowires (b) as a function of the initial distance of the atoms away from the center of the nanowire, with increasing the distance, the relaxation amount has an increasing trend. Fourthly, except that the atoms on each of four symmetry lines (two diagonals and two medians) are still on the same line after relaxation, the atoms on the same line originally are not on the same line after relaxation; i.e., so-called rumple phenomenon exits. Fifthly, the relaxation amount of the apex atoms increases with increasing nanowire size. 3.2. Charge Density Analysis. While a nanowire is cleaved from a bulk crystal, four new surfaces are created, where the atomic coordinations are reduced significantly. The neighbor atoms outside the nanowires vanish, and thus asymmetrical Coulomb electrostatic forces are applied to the electrons near the surfaces. In such a case, the electrons must redistribute in three-dimensional space to smooth the differences of electron density. Many surface phenomena, such as surface thermionic emission, surface reconstruction, surface relaxation, surface adsorption, surface catalysis, crystal epitaxial growth, and so on, are related to the surface charge redistribution. Figure 4 shows the charge density contours of adjacent A layer (a) and B layer (b) of the (001) cross section, the first layer (c) and the second layer (d) of the (100) lateral face, and the (110) plane including wire axis (f) in 3 × 3 Au nanowire (for example) together with those on the (100) plane (e) and (110) plane (g) of Au bulk crystal for comparison. An enhanced interaction appears between the surface atoms as well as the surface atoms and their first nearest neighbor atoms, compared with the (100) (e) and (110) (g) plane of Au bulk crystal. We term this phenomenon a “skin effect”. Such a phenomenon was also observed by da Silva et al. and was termed as a metallic (delocalized) bonding character.37 This resulted from the vanishing of the near neighbor atoms outside the wire; the surface atoms will contribute their partial electrons, which are originally given to (or shared with) the vanishing neighbors, to remaining neighbors. Considering that the surface-to-volume ratio increases with decreasing cross-sectional area of the nanowire, we know that both the strength and the elastic modulus of the nanowire are not only larger than the bulk but also increase with decreasing cross-sectional area of the nanowire. In fact, RubioBollinger et al.38 and Nautiyal et al.10 already found that interatomic interactions of the Au nanowire were much stronger than that of the Au bulk. Ma et al.39 have found that both the theoretical tensile strength and the elastic modulus increase with decreasing cross-sectional area of the Au nanowire, and Diao et al.25 also found Young’s modulus increases with decreasing cross-sectional area of the Au nanowire. 3.3. Electronic Structure. Better insight into the distribution of the electrons with energy can be gained from an analysis of the band structure and density of states (DOS). Figure 5 shows the band structure of a 3 × 3 Au nanowire as one example. The band structure is determined by the s-d electrons. The d bands are occupied as expected from the Au bulk. The states near the Fermi level are nearly free electron (NFE) like states with a parabola shape and a large energy range. Similar results were also observed in Cu nanowires.9 This is because the Au and Cu are both noble metals with similar valence electronic structure (5d106s1 for Au and 3d104s1 for Cu). These NFE states crossing the Fermi level also indicate the delocalized

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Figure 4. Charge density contours of adjacent A layer (a) and B layer (b) of the (001) cross section, the first layer (c) and the second layer (d) of the (100) lateral face, and the (110) plane including wire axis (f) in 3 × 3 Au nanowire together with those on the (100) plane (e) and (110) plane (g) of Au bulk crystal for comparison. All contours start from 0.025 and change successively by a factor of 0.025 as is labeled in the A layer of the (001) plane (a).

character of the electrons near the surface as shown in Figure 4 and will enhance the conductance of the nanowires. Figure 6 presents the s, p, d partial and total DOS projected onto the representative atoms A1 and A2 on A layer as well as atom B1 on B layer of a 3 × 3 Au nanowire. Energy reference is with respect to the Fermi level EF (vertical dashed line). It can be seen that, first for each representative atom, the total DOS curve almost overlaps with the d curve indicating the total DOS is contributed mainly by the d state. This is caused by the valence electrons 5d106s1 of Au atom. Second, a similar total DOS curve is obtained for each representative atom above EF. Below EF, it is interesting to note the driving down of the DOS

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Figure 5. Band structure of a 3 × 3 Au nanowire. The Fermi level EF is set to zero energy and indicated by the solid line.

Figure 6. s, p, d partial DOS and total DOS of the representative atoms A1 and A2 as well as atom B1 on adjacent A layer as well as B layer of the (001) cross section in 3 × 3 Au nanowire. The Fermi level EF is set to zero energy and indicated by the dashed line.

in the lower energy region and driving up of the DOS in the higher energy region for A1, B1, and A2 atoms successively. This results from the decrease in the number of the near neighbors (12 and 2, 8 and 3, and 5 and 4 for the first and the second neighbors of the A1, B1, and A2 atom, respectively) and thus the decrease in the restrictions coming from near neighbor atoms, so most electrons occupy the higher energy states. Therefore, we conclude that the lower coordination

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Figure 7. Total DOS for Au nanowires with cross sections of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 atom layers. The Fermi level EF is set to zero energy and indicated by the dashed line.

number will lead the most electrons to range in the higher energy region of the occupancy state. The total DOSs are compared in Figure 7 for the Au nanowires with cross sections of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 atom layers. The main structure below the Fermi level EF for each case is due to the d states, whereas the charges outside its shoulders have significant s character. The increase in the d bandwidth can be attributed to the increased radial extent of the d electrons and to the increase in the averaged coordination number per atom due to the increase in the cross-sectional area. Such an increased trend was also observed in the Cu nanowires.9 In the ballistic transport regime, the number of conducting channels increases with increasing DOS value at the Fermi level.15 The increase in the DOS value at the Fermi level with increasing the cross-sectional area here shows that the electronic transport property of the Au nanowire increases with increasing cross-sectional area of the nanowire. This can be attributed to the increased surface area with delocalized electrons and to the increase of available conducting states as the number of atoms in the nanowire increases. Previous conductance calculations on jellium wires and quantum constriction showed a stepwise increase of conductance with a continuous increase of the cross-sectional area.15,40,41 Figure 8 shows both the s, p, d orbital charge and total charge projected to each of the representative atoms Ai on A layer of the (001) cross section of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires (a) and Bi on B layer of the (001) cross section of 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires (b) as a function of the initial distance of the atoms away from the center of the nanowire. It is found that first the total charge of each representative atom is mainly contributed by the d orbital charges; this is also attributed to the valence electron configuration of 5d106s1 for Au atom. Second, it is well-known that the quantum confinement effects in 1D nanowires will lead to electron confinement away from the surface. Figure 8 distinctly shows that the s and d orbital charges keep almost constant while the p orbital and thus the total charge decrease with increasing initial distance of the atom away from the center of the nanowire. This also results from the fact that the coordination numbers of the atom decrease with increasing initial distance of the atom away from the center of the nanowire. Although surface charge depletion resulted mainly from the vanished contributions accompanying the vanishing of the neighbor atoms outside the nanowire reducing the electronic transport property

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Figure 8. s, p, d orbital charge and total charge projected to each of the representative atoms Ai on A layer of the (001) cross section of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires (a) and Bi on B layer of the (001) cross section of 5 × 5, 7 × 7, 9 × 9, and 11 × 11 Au nanowires (b) as a function of the initial distance of the atoms away from the center of the nanowire.

of the nanowire, the appearance of the metallic (delocalized) surface electrons will enhance the electronic transport property of the nanowire. So this is a competitive process. Furthermore, the structural relaxation plays an additional role in the electrons redistribution in three-dimensional space; that is, an inward (outward) relaxation of the atoms will be accompanied by the electrons inward (outward) of the nanowire core. 4. Conclusions In summary, under GGA, the relaxed structures and electronic properties have been investigated for Au nanowires with cross sections of 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 atomic layers by using the first-principles PAW potential within the DFT framework. The following conclusions are obtained. For all five-sized nanowires, the relaxed structures still have tetragonal symmetry and with increasing initial distance of the atoms away from the central axis of the nanowires, the relaxation amount has an increasing trend. Furthermore, the relaxation direction changes from inward for diagonal atoms to outward for median atoms showing there is a “round corner” phenomenon. The vanishing of the neighbor atoms outside the nanowire, on the one hand, accompanies the vanishing of their electrons which are originally shared with the surface atoms, so the total

charge of the surface atoms is reduced. On the other hand, the surface atoms will contribute themselves electrons which are originally shared with the vanishing neighbors to remaining neighbor atoms, so an enhanced interaction presents between the surface atoms as well as the surface atoms and their first nearest neighbor atoms. We term this phenomenon “skin effect”, which enhances the mechanical and the electronic transport properties of the nanowire compared to bulk. Furthermore, the vanishing of the neighbor atoms outside the nanowire accompanies also the vanishing of their restrictions onto the electrons of the surface atoms so most of them range in the higher energy region of the occupancy state. In fact, the conclusions drawn here are applicable to not only the nanowires but also the other surface cases, such as nanobelts, nanotubes, nanocables, clusters, thin films, and so on. Acknowledgment. The authors acknowledge the State Key Development for Basic Research of China (Grant No 2004CB619302) for providing financial support for this research. References and Notes (1) Beckman, R.; Johnston, E.-H.; Luo, Y.; Green, J. E.; Heath, J. R. Science 2005, 310, 465.

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