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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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