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J. Phys. Chem. C 2007, 111, 1234-1238
Faceted Silicon Nanotubes: Structure, Energetic, and Passivation Effects Mingwen Zhao,*,† R. Q. Zhang,‡ Yueyuan Xia,† Chen Song,† and S.-T. Lee‡ School of Physics and Microelectronics, Shandong UniVersity, Jinan 250100, China, and Centre of Super-Diamond and AdVanced Films (COSDAF) & Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, China ReceiVed: September 20, 2006
We report the favorable configurations of double-walled silicon nanotubes (DWSiNTs) with faceted wall surfaces, determined from first-principles calculations. These tubes have higher energetic favorability than the conventionally adopted cylindrical configurations of single-walled silicon nanotubes (SWSiNTs) and compare well with the synthesized silicon nanowires. The hexagonal (h-) and tetrahedral (t-) like structures of these DWSiNTs are almost energetically equivalent, but quite different in their electronic structures. The hydrogen passivation effects on the geometrics and electronic structures of these DWSiNTs are also investigated.
Introduction Quasi-one-dimensional (Q1D) silicon nanostructures, i.e., silicon nanowires (SiNWs) and silicon nanotubes (SiNTs), are currently attracting great interest1-6 as promising building blocks for the “bottom-up” approach to future nanoscale devices.7-9 Particularly exciting are their potential applications in optical and photonic devices10 that are impossible for bulk silicon. Different from carbon atom, the favorable formation of sp3 hybridization in silicon atoms promotes the formation of SiNWs rather than single-walled silicon nanotubes (SWSiNTs).11-13 This was also confirmed by the high formation energies of the cylindrical SWSiNTs characterized analogously as carbon nanotubes (CNTs)14,15 or rolling Si(111) sheets12-16 with respect to the bulk silicon in diamond structure. In the conventionally used models of pristine SWSiNTs, each silicon atom is threefold coordinated, facilitating the formation of a dangling bond. The incorporation of hydrogen atoms or metal cations in the form of SiH or silicide is always necessary to stabilize the SWSiNTs.17,18 Experimentally, several kinds of SiNTs have been synthesized by using nanochannel arrays with1 or without the assistance of catalysis2 or by using a hydrothermal method.3,4 These SiNTs are typically tens of nanometers in diameter and several nanometers in wall thickness. The tube wall consists mostly of crystalline silicon and a little amorphous silicon embedded in amorphous SiO2 layers. Obviously, this atomic arrangement bears no resemblance to the theoretical models of either SWSiNTs or multiwalled CNTs. Although the fabrication of an ultrathin SiNT having an atomic arrangement comparable with a puckered structure and different chiralities has been reported,5 the electronic structure dependent on the tube chirality revealed in that experiment is inconsistent with the theoretical prediction based on cylindrical SWSiNTs.14,16 The synthesis of SWSiNTs still remains an open challenge. The wide gap between the hypothetical structures and the real materials makes a novel model of SiNTs beyond cylindrical configurations highly desirable, which is obviously needed for experimental progress * To whom correspondence may be addressed. E-mail:
[email protected]. † Shandong University. ‡ City University of Hong Kong.
toward understanding the atomic structures and growth mechanisms of these nanomaterials. The structural characteristics of Q1D silicon nanostructures beyond the diamond structure in bulk silicon and hydrogenpassivated SiNWs have been presented recently, by considering possible surface reconstructions with the tendency to reduce the surface energy. Menon and Richter proposed a Q1D silicon nanostructure with fourfold coordinated cores and threefold coordinated surface characterized by one of the most stable reconstructions of bulk silicon.19 Ponomareva et al. have compared the cohesive energies and thermal stability of very thin (e6 nm) SiNWs in tetrahedral, cagelike, and polycrystalline forms and predicted that tetrahedral-type nanowire is the most stable, whereas cagelike nanowire has great thermal stability.20 Kagimura et al. considered several configurations of SiNWs with different diameters and found that filled-fullerene wires are the most stable for diameters between 0.8 and 1.0 nm, whereas for even smaller diameters (∼0.5 nm) the most stable SiNWs have a simple hexagonal structure.21 All these results clearly indicate that the relatively large contribution of surface energy plays an important role in the stabilization of smalldiameter SiNWs. As compared to SiNWs, SiNTs have larger surface to bulk ratios, and thus probably more diverse stable configurations. Classical molecular dynamics simulations using Tersoff potential showed that multiwalled SiCNTs built analogously as CNTs are quite unstable, undergoing considerable structural transformation toward amorphous-like SiNTs by the formation of a large number of sp3 bonds when heated at high temperature.13 However, an extensive study of multiwalled SiNTs to determine the stable structures at room temperature by considering different geometries is currently lacking. In this work, a theoretical study is performed for doublewalled silicon nanotubes (DWSiNTs) by using first-principles calculations combined with molecular dynamics simulations. We focus on two types of DWSiNTs with hexagonal and tetrahedral structures because hexagonal and tetrahedral structures have been revealed as stable forms of very thin SiNWs.20 These faceted DWSiNTs have fourfold coordinated cores and threefold coordinated (exterior and interior) surfaces, in good contrast to the cylindrical SWSiNTs with purely threefold coordinated surfaces. Moreover, this faceted model can be easily
10.1021/jp066177i CCC: $37.00 © 2007 American Chemical Society Published on Web 12/14/2006
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implemented to describe multiwalled SiNTs with different diameters and tube wall thicknesses. The different electronic structures and hydrogenation effects in these DWSiNTs are also discussed. Method and Computational Details The calculations were performed with an efficient code known as SIESTA,22-24 adopting norm-conserving pseudopotentials,25,26 and the generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof (PBE) for the exchangecorrelation functional.27 The valence electron wave functions were expanded by using a double-ζ basis set plus polarization functions (DZP). The numerical integrals were performed on a real space grid with an equivalent cutoff of 100 Ry. Periodic boundary condition was implemented along the tube axis (taken as z-axis) and sufficient vacuum space (up to 10 Å) was kept along the radial direction (x- and y-directions) to create an infinite one-dimensional system. The Brillouin zone integrations were carried out by using a 1 × 1 × 8 k-mesh according to the Monkhorst-Pack scheme.28 All the atomic positions and the lattice vectors were fully optimized using a conjugate gradient (CG) algorithm, until each component of the stress tensor was reduced to below 0.02 GPa and the maximum atomic forces
