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J. Phys. Chem. C 2007, 111, 2942-2946
Stabilizing Zigzag Single-Walled Silicon Nanotubes and Tailoring the Electronic Structures by Oxygen Atoms: First-Principles Studies Mingwen Zhao,*,†,‡ John Zhonghua Zhu,‡ Yueyuan Xia,† and Max Lu‡ School of Physics and Microelectronics, Shandong UniVersity, Jinan, P.R. China, and ARC Centre of Functional Nanomaterials, School of Engineering, UniVersity of Queensland, Brisbane 4072, Australia ReceiVed: NoVember 10, 2006
The effects of oxygen atoms in stabilizing zigzag single-walled silicon nanotubes (SWSiNTs) have been studied by using first-principles calculations within density functional theory. The incorporation of oxygen atoms in the form of silicon monoxides into the (8,0)SWSiNT are found to not only stabilize the SWSiNT but also tailor the electronic structures from semiconducting to metallic. These findings will promote the fabrication and the utilization of silicon suboxide nanotubes which may find potential applications in nanoscale electronics and optoelectronics.
I. Introduction Silicon nanowires and nanotubes have been the focus of extensive research,1-4 among which single-walled silicon nanotubes (SWSiNTs) are of particular interest, spurred by the great success of carbon nanotubes in nanoscale electronics and optoelectronics. However, silicon atoms favor the formation of sp3 hybridization and, accordingly, promote the formation of silicon nanowires and thick-walled single-crystalline nanotubes.5-7 The pristine SWSiNTs built analogously to carbon nanotubes consist of threefold coordinated silicon atoms along with dangling bonds and are thus less stable. This has been confirmed by various theoretical works.8-13 Hydrogen atoms or metal cations were used to stabilize the SWSiNTs by saturating the dangling bonds on the tube walls.14,15 It has been found that oxygen atoms are crucial not only in the growth of silicon nanowires but also in the stabilization of silicon-based nanomaterials.16-19 Different from O-Si-O bond angles, the Si-O-Si bond angles are less rigid and can vary widely in different phases of silicon oxides to ensure that the O-Si-O angles are close to the standard sp3 hybridization value (109.5°). For example, the Si-O-Si bond angles in R-quartz and R-cristobalite are ∼146° but become 180° in β-cristobalite. The incorporation of oxygen atoms as silicon oxide sheaths stabilizes the sp3 silicon cores in silicon monoxide clusters and facilitates the nucleation and growth of silicon nanostructures.18 Moreover, the single-crystalline silicon nanotubes synthesized by using different methods are always embedded in amorphous silicon dioxide layers.5-7 This indicates that the incorporation of oxygen atoms into SWCNTs may give rise to the formation of stable silicon oxide nanotubes. The energetic favorability and thermal stability of the well-ordered ultrathin silica nanotubes, as well as the possible synthetic way toward these tubes, have been proposed on the basis of first-principles calculations.20-23 However, due to the ionic-like character of the Si-O bonds, all of these tubes are insulators with the band gap wider than ∼6.0 eV, which differ from the semiconducting silicon nanowires and nanotubes. Tailoring the electronic structures of the * To whom correspondence should be addressed. † Shandong University. ‡ University of Queensland.
silicon suboxide nanotubes from semiconducting to metallic by controlling the stoichiometry would be useful for building nanoscale devices. First-principles studies on these systems can provide vital information on the stable configurations and electronic structures, which would be decisive for further development of these nanomaterials. Silicon monoxide nanomaterials are of special interest due totheimportantfunctionsinthegrowthofsiliconnanostructures.16-19 The stable configurations and relevant stoichiometry-dependent electronic properties have been reported for the very thin silicon monoxide nanotubes (SiONTs).22 It was predicted that the most stable pentagonal SiONT is a semiconductor with a band gap of ∼0.9 eV, in contrast to the insulating pentagonal silica nanotube. However, the SiONTs studied in that work are thinner than 6.1 Å in diameter; neither surface reconstruction nor other incorporating ways of oxygen atoms was taken into account, which are crucial for the large size silicon oxide nanotubes.23 In this work, we focus on the stable configurations of the SiONTs designed by incorporating oxygen atoms into the (8,0)SWSiNT in different ways with the consideration of the possible surface reconstructions on the tube walls. The electronic structures of the SiONTs with different configurations are also investigated. The theoretical scheme used in this work is also valid for the investigation of the SiONTs built from other SWSiNTs, which is currently an ongoing project in our group. II. Method and Computational Details The calculations were performed with the SIESTA code24-26 adopting norm-conserving pseudopotentials27,28 and the generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof (PBE) for the exchange-correlation functional.29 The valence electron wave functions were expanded by a double-ζ basis set plus polarization functions (DZP). The periodic boundary conditions were applied along the axial direction of the tubes (taken as z-axis), and a sufficient vacuum space larger than 10 Å was kept along the radial direction (x and y directions) to decouple the interactions between adjacent tubes to ensure an isolated one-dimensional nanotube being considered. The Brillouin zone integrations were carried out by using a 1 × 1 × 8 k-mesh according to the Monkhorst-Pack
10.1021/jp067434m CCC: $37.00 © 2007 American Chemical Society Published on Web 02/01/2007
Stabilizing Zigzag SWSiNTs
J. Phys. Chem. C, Vol. 111, No. 7, 2007 2943
Figure 1. Stable configurations of (a) the pristine (8,0)SWSiNT, (b) the hydrogenated (8,0)SWSiNT, (c)-(e) the SiONTs built by incorporating oxygen atoms into the network of the (8,0)SWSiNT in different ways; and (f) the SiO3-coated (8,0)SWSiNT. The dashed rectangles indicate the sizes of the supercells.
TABLE 1: Structural Parameters, Formation Energy (∆Eform), and Energy Band Gap (Egap) of the Pristine (p-) and Hydrogenated (8,0) Single-Walled Silicon Nanotubes ((8,0)SiH Nanotubes) and Silicon Monoxide Nanotubes (SiONTs)a Si-Si
-Si-Si-O
-O-Si-O
-Si-Si-Si
∆Eform
Egap
SiONT(I) SiONT(II) SiONT(III) SiONT(IV)
2.417 2.442 2.219 2.410
105.0, 119.8 98.9, 121.3 105.5,111. 7 94.1, 99.3
90.2 112.7 111.3 128.0
111.9 95.5, 141.2 97.9, 122.6 116.7, 122.4
-1.787 -2.005 -2.040 -1.630
0.227 0.194 0.537 1.610
p-(8,0)SW SiNT
2.312
configurations
99.8, 110.3
0.846b
0.0
configuration
Si-Si
-Si-Si-H
-Si-Si-Si
∆Eform
Egap
(8,0)SiH nanotube
2.361, 2.377
102.0, 114.4
98.1, 113.6
0.064c
2.286
a The bond lengths and bond angles are in angstroms and degrees, respectively. The ∆E b form and Egap are in eV/atom and eV. The ∆Eform of the p-(8,0)SWSiNT was determined by the difference between the energy per atom of the SWSiNT and that of the bulk silicon in diamond structure. c The ∆E form of the (8,0)SiH nanotube was evaluated by using the expression: ∆Eform ) Etotal(H-SiNT)/n - (µSi + µH)/2, where Etotal(H-SiNT) is the total energy of the (8,0)SiH nanotube, n is the number of atoms per supercell in the tube, µSi is the chemical potential of silicon atom in bulk silicon, and µH is the chemical potential of hydrogen atom in H2 molecule at 0 K.
scheme.30 All 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. The differences of total energies were converged to within 10 meV. The formation energy (∆Eform) of the SiONTs is defined by the expression ∆Eform ) Etotal(SiONT)/n - (µSi + µO)/2, where Etotal(SiONT) is the total energy of the SiONT, n is the number of atoms per supercell in the tube, µSi is the chemical potential of silicon atom in bulk silicon, and µO is the chemical potential of oxygen atom in O2 molecule at 0 K.
III. Results and Discussion Single-walled silicon nanotubes (SWSiNTs) can be built analogously to carbon nanotubes by rolling a (111) sheet. However, different from the smooth surfaces of carbon nanotubes, these SWSiNTs have gearlike tube walls on which the silicon atoms extrude inward and outward alternatively (Figure 1a). The Si-Si bond length in the (8,0)SWSiNT is 2.31 Å, slightly shorter than that (2.35 Å) of the bulk silicon in diamond structure (Table 1). The Si-Si-Si bond angles are 99.8° and 110.3°, which are close to the standard value of sp3 hybridization (109.5°). These sp3-hybridized silicon atoms are threefold
2944 J. Phys. Chem. C, Vol. 111, No. 7, 2007 coordinated, forming dangling bonds, which is a disadvantage for the stabilization of the tube. This is also consistent with the high ∆Eform of the (8,0)SWSiNT, which is calculated as 0.846 eV/atom with respect to the bulk silicon. Hydrogen atoms were used to saturate the dangling bonds of these tubes, forming hydrogenated silicon (SiH) nanotubes.14 The preferable Si-H bonds are alternately oriented inward and outward rather than point outward in the stable (8,0)SiH nanotube (Figure 1b). Both the Si-Si bond lengths and the bond angles are close to the corresponding values in bulk silicon (Table 1). The ∆Eform determined by the difference between the total energy of the SiH nanotube and the sum of the chemical potential of silicon atom in bulk silicon and that of hydrogen atom in H2 molecule is 0.064 eV/atom. The incorporation of oxygen atoms into SWSiNTs is another method for avoiding the formation of dangling bonds and thus stabilizes the tubes. However, the binding aspect of oxygen atoms differs significantly from that of hydrogen atoms. The incorporation method of oxygen atoms into SWSiNTs is therefore quite different from that of the hydrogen atoms. Two typical situations were considered in this work: (1) oxygen atoms are involved in the network of SWSiNTs by replacing each of the axial-orientated Si-Si bonds with either two SiO-Si bonds (Figure 1c) or a single Si-O-Si. In the latter case, additional oxygen atoms are subsequently introduced to bridge the under-coordinated silicon atoms along the axial direction, forming the SiONTs as shown in Figures 1d and 1e; (2) the SWSiNTs are covered by a silicon oxide sheath in the form of SiO3 clusters (Figure 1f). All of these SiONTs are free from dangling bonds, but their detailed structures and the relevant electronic properties are quite different. There are two types of Si-Si bonds in the pristine (8,0)SWSiNT. One forms zigzag rings and another connects these rings along the axial direction (Figure 1a). Our calculations show that replacing the Si-Si bonds of the zigzag rings with SiO-Si bonds always gives rise to a configuration with a high ∆Eform and a severe distortion. In the following discussion, we focus on the axial-orientated Si-Si bonds. The SiONT shown in Figure 1c can be characterized by replacing each axialorientated Si-Si bond of a (8,0)SWSiNT with two Si-O-Si bonds, which are labeled as SiONT(I). The silicon zigzag rings in this configuration are connected by two-membered rings (2MRs) of SiO units which widely exist in small silica clusters.31 Each silicon atom of this tube is fourfold coordinated by two silicon atoms and two oxygen atoms. The average bond length of the Si-Si bonds is 2.417 Å, slightly longer than that of bulk silicon. The Si-Si-O and Si-Si-Si bond angles are close to the value of standard sp3 hybridization (109.5°), except that the O-Si-O bond angles in the 2MRs deviate notably from 109.5° (Table 1), which would give rise to a high ∆Eform. However, the energetic disadvantage of forming 2MRs can be compensated by the energy decrease resulting from avoiding the formation of dangling bonds. The ∆Eform of this tube is -1.787 eV/atom. To avoid the formation of 2MRs, we designed another kind of SiONTs by replacing each of the axial-orientated Si-Si bonds of a (8,0)SWSiNT with a single Si-O-Si bond and bridging the under-coordinated silicon atom with oxygen atoms along the axial direction (Figures 1d and 1e). The stable configurations of these SiONTs can be characterized by the axial stacking silicon hexadecagons via Si-O-Si bindings. Silicon and oxygen atoms of these tubes locate on different planes (Si- and O-plane) perpendicular to the tube axis. The surface reconstructions represented by different arrangements of oxygen atoms on the
Zhao et al. O-plane result in polytypic structures of the SiONTs. Two stable configurations with a low ∆Eform are shown in Figures 1d and 1e and labeled as SiONT(II) and SiONT(III), respectively. The oxygen atoms of the SiONT(II) extrude inward and outward, alternatively (Figure 1c). For the SiONT(III), however, a quarter of oxygen atoms locate in the interior of the tube, forming a cross section with fourfold symmetry (Figure 1e). The SiONT(III) is energetically more favorable than the SiONT(II) and SiONT(III) by about 0.035 and 0.218 eV/atom, respectively. This is related to the smaller deviation of bond angles of the SiONT(III) from the corresponding value of the standard sp3 hybridization (109.5°), as compared to that of either the SiONT(I) or the SiONT(II) (Table 1). Moreover, the SiONT(III) is also energetically more favorable than the pentagonal SiONT which was proposed as the most stable configuration of very thin SiONTs22 by about 0.013 eV/atom. This clearly indicates that surface reconstruction should be taken into account in searching for the stable configurations of SiONTs. Another type of SiONTs is characterized by coating SWSiNTs with silicon oxide sheaths. In real materials, silicon oxide sheaths always have amorphous structures. Modeling an amorphous layer is a great challenge for the first-principles calculations. In this work, the sheath is represented by SiO3 clusters binding to the exterior wall of a (8,0)SWSiNT, which forms a SiONT labeled as SiONT(IV) (Figure 1f). The dangling bonds of the SWSiNT are saturated by the oxygen atoms of the adsorbed clusters. Each silicon atom of the SWSiNT is fourfold coordinated by three silicon atoms and one oxygen atom with bond angles significantly deviating from the value of sp3 hybridization (Table 1). Although this model is quite simple, the binding aspect of the interface between the SWSiNT and the silicon oxide sheath can represent well the actual interfaces. It is noteworthy that threefold coordinated silicon atoms and nonbridging oxygen atoms (NBOs) are involved in this model, which is a disadvantage for the stabilization.31 This is the main reason why the SiONT(IV) is energetically most unfavorable among the SiONTs under study (Table 1). However, with the increase in the thickness of the silicon oxide sheath model, the ratios of the under-coordinated silicon atoms and the NBOs decrease, and a configuration with a lower ∆Eform can be obtained. To the best of our knowledge, this is the first theoretical attempt to model the SWSiNT coated by silicon oxide layer and, more importantly, the effect of the sheath on the electronic structures of the SWSiNTs can thus be investigated. The relationship between the electronic and the atomic structures of nanomaterials is of particular interest in nanoscience and nanotechnology. Our calculations show that the pristine (8,0)SWSiNT (Figure 1a) is metallic, in agreement with the results from Yang and Ni.12 The hydrogen atoms saturate the dangling bonds of the pristine SWSiNT and, thus, open a band gap of about 2.286 eV in the SiH nanotube, which exhibits the characteristics of direct band gap semiconductors (Figure 2a). This is also consistent with the results from Seifert et al.14 The incorporation of oxygen atoms into the network of (8,0)SWSiNT as SiONTs (Figures 1c-1e) modifies the electronic structures in different ways. The SiONT(I) and SiONT(II) (Figures 1c and 1d) have direct band gaps of 0.227 and 0.194 eV, respectively, at the Γ(0,0,0) π/a point (Figure 2b), which may display the characteristics of semimetals. The most stable configuration, SiONT(III) (Figure 1e), is a narrow band gap semiconductor with a direct band gap of 0.537 eV at the Γ point (Figure 2c). These characteristics are quite different from the insulating aspect of silica nanotubes.23 The SiONT(IV) has a direct band gap of 1.610 eV at the Γ point (Figure 2d). The band structures of the SiONT(IV) and
Stabilizing Zigzag SWSiNTs
J. Phys. Chem. C, Vol. 111, No. 7, 2007 2945 the adsorbed SiO3 clusters, as revealed by the partial electronic density of states (PDOS) projected onto different atoms (Figure 3). Both the highest valence band and the lowest conduction band of the SiONT(IV) mainly originate from the states of the silicon atoms of the (8,0)SWSiNT (Figure 3). The narrower band gap of the SiONT(IV) as compared to that of the SiH nanotubes can be attributed to the different chemical environment of the silicon atoms in these tubes.
Figure 2. Band structures along the Γ(0,0,0) π/a - X(0, 0, 1) π/a direction of (a) the hydrogenated (8,0)SWSiNT (Figure 1a), (b) and (c) the SiONTs corresponding to the configurations shown in Figures 1c and 1e, respectively, and (d) the SiO3-coated (8,0)SWSiNT (Figure 1f). The dashed lines indicate the position of the Fermi level (EF).
Figure 3. Partial electronic density of states (PDOS) projected onto the silicon and oxygen atoms at different locations (as shown in the inset of this figure) of the SiO3-coated (8,0)SWSiNT.
the (8,0)SiH nanotubes are similar near the Fermi surface, except the narrower band gap and the abundant local electronic states of the SiONT(IV) (Figures 2a and 2d). These local electronic states arise from the 2p orbitals of oxygen atoms of
The ionic-like Si-O bonds in silicon oxides always give rise to localized electronic states and, accordingly, isolatingcharacterized electronic structures, as revealed in R-quartz.22,23 However, the band structures of these SiONTs exhibit the features of semiconductors or semimetals with highly dispersed energy bands near the Fermi level (Figures 2b-2d). To understand this result, we plotted the wave functions of the highest valence band orbital (HVBO) and the lowest conduction band orbital (LCBO) of these SiONTs at the Γ point (Figures 4a-4d). Obviously, the HVBO and the LCBO mainly arise from the orbitals of silicon atoms rather than those of oxygen atoms. The wavefunctions of these tubes are localized in the regions of O-Si-O bonds, but are rather dispersed in the regions of Si-Si covalent bonds, dominating the semiconducting or semimetallic electronic structures of these tubes. Interestingly, the HVBO and the LCBO of these SiONTs exhibit different features. The lobes of the wave function isosurfaces of the HVBO are separated in the silicon polygons by the ionic-like Si-O bonds. However, the overlap of the wave functions between the adjacent silicon polygons is remarkable along the axial direction (Figure 4a). These dispersed wave functions would facilitate the electron transportation along the axial direction. For the LCBO, however, the hybridization of the atomic orbitals in the silicon polygons is greatly enhanced, forming closed isosurfaces of wave functions (Figures 4b and 4d). Such LCBO allows the electrons added into the conduction bands to move in a circle around the tube axis under a certain condition, i.e., electromagnetic field. These HVBO and LCBO could dominate the different response of the SiONTs to the external electromagnetic field, which may find potential applications in nanoscale electronics.
Figure 4. Isosurfaces of the wavefunctions of (a), (b) SiONT(I) and (c), (d) SiONT(III) at the Γ(0,0,0) π/a point. The highest valence band orbital (HVBO) and the lowest conduction band orbital (LCBO) are presented in the left and right columns, respectively.
2946 J. Phys. Chem. C, Vol. 111, No. 7, 2007 IV. Conclusions In summary, our first-principles calculations indicate that the incorporation of oxygen atoms into the (8,0)SWSiNT in the form of SiONTs can stabilize the tube by avoiding the formation of dangling bonds. The electronic structures of these SiONTs depend on the ways of incorporating oxygen atoms and exhibit diverse characteristics from semiconductors to semimetals. The (8,0)SWSiNT coated by silicon oxide clusters is a direct band gap semiconductor with the band gap narrower than that of the hydrogenated (8,0)SWSiNT. The direct band gaps in these stable SiONTs are crucial for building nanoscale optical and photonic devices that are impossible for bulk silicon. Acknowledgment. The work described in this paper is supported by the Australia Research Council (ARC) linkage international fellowship, the National Natural Science Foundation of China under Grant Nos. 50402017 and 10374059, and the National Basic Research 973 Program of China (Grant No. 2005CB623602). M. Zhao is thankful for the support from the Program for New Century Excellent Talents in University of China. References and Notes (1) Cui, Y.; Wei, Q. Q.; Park, H. K.; Lieber, C. M. Science 2001, 293, 1289. (2) Cui, Y.; Zhong, Z. H.; Wang, D. L.; Wang, W. U.; Lieber, C. M. Nano Lett. 2003, 3, 149. (3) Zheng, G.; Lu, W.; Jin, S.; Lieber, C. M. AdV. Mater. 2004, 6, 1890. (4) Gudiksen, M. S.; Lauhon, L. J.; Wang, J.; Smith, D. C.; Lieber, C. M. Nature (London) 2002, 415, 617. (5) Sha, J.; Niu, J.; Ma, X.; Xu, J.; Zhang, X.; Yang, Q.; Yang, D. AdV. Mater. 2002, 14, 1219. (6) Jeong, S. Y.; Kim, J. Y.; Yang, H. D.; Yoon, B. N.; Choi, S.-H.; Kang, H. K.; Yang, C. W.; Lee, Y. H. AdV. Mater. 2003, 15, 1172. (7) Tang, Y. H.; Pei, L. Z.; Chen, Y. W.; Guo, C. Phys. ReV. Lett. 2005, 95, 116102.
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