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Despite the increasing volume of researches on SiNWs, to the best of our knowledge, only limited information is currently available (theoretical or experimental) on their electromechanical properties [11]. In the absence of definitive experimental data, first-principles calculations can provide robust predictions of the mechanical properties of the silicon nanowires. In this Letter, we investigate energetic, relative stability, and mechanical properties of the hydrogen- passivated SiNWs with various diameters and growth directions using first-principles methods. To compare the physical properties and to understand the possible reason for a preferential growth direction, nanowires grown along the [100], [110], [111], and [112] crystallographic orientations have been studied. The starting configurations of the nanowires were cut from a bulk silicon crystal and were bounded by the low-index lateral surfaces. Fig. 1 shows the representative cross-sections of the SiNWs with different growth directions. The geometry of the first plot in Fig. 1 is bounded by four (110) planes in all lateral directions and is oriented along [100] direction. The geometry of the second SiNWs (Fig. 1) is the same as those of the larger diameter nanowires inferred from experiments [7]. It is oriented along [110] direction and has a hexagonal crosssection with four (111) and two (10 0) lateral surfaces.The third one (Fig. 1) is oriented along [11 1] direction and all of its lateral directions are bounded by (110) planes. Finally, the geometry of the last one (Fig. 1) is similar to the thinnest SiNWs observed experimentally [7]. It is oriented along [112] direction and bounded by two (110) and two (111) surfaces in the lateral directions. In all the SiNWs considered, the dangling bonds on the surface are fully terminated with H atoms so that each Si atom lying on the nanowire surface is tetrahedrally coordinated. Each wire was placed in a tetragonal supercell so that the nanowire was infinitely extended along axial direction and each nanowire is separated far enough from its periodic images in the lateral directions (at least 10A ˚ ). The number of atoms in the unit cell and the mean diameter of the SiNWs growth in different directions are summarized in Table 1. The mean diameter d of a wire is derived from S ¼ pðd=2Þ2, S is the cross-section area of the wire (excluding the H atoms). Geometry optimizations were performed using density functional theory (DFT) implemented in the DMOL package [12]. All-electron treatment and double numerical basis including p-polarization function (DNP) [13] were chosen. The exchange¨Ccorrelation interaction was treated within the generalized gradient approximation (GGA) with the functional parameterized by Perdew, Burke and Enzerhof (PBE) [13]. Self-consistent field calculations were done with a convergence criterion of 106 Hartree on the total energy. All the structures were fully optimized without any symmetry constraint with a convergence criterion of 0.002 Hartree/ A˚ for the forces and 0.005 A ˚ for the atomic displacements. The one-dimensional (1D) Brillouin zone along the wire axis was sampled by 10 k points. |
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