silicon, there may be structural transition from amorphous to ordered tetrahedral
structure. The structural transition to bulk diamond structure in nanosized silicon
clusters has been studied by the tight-binding molecular dynamics method combined with a simulated annealing technique [85]. For intermediate-sized clusters
(<200 atoms), the energetically favorable structures obtained consist of small
subunits like Si 10 and Si 12 (Figure 10.44), qualitatively consistent with the experimental fragmentation behavior of these clusters. For spherical silicon nanocrystals,
the surface atoms reconstruct to minimize the number of dangling bonds, forming
a continuum surface (Figure 10.45). The large curvature of the continuum surface
causes lattice contraction in the nanocrystals. Present calculations predict the
lattice contraction versus the particle radius as Da ¼ 0:38=R, with Da and R in A ˚ .
By comparing the cohesive energies of the two sorts of structures with the same
number of atoms, the structural transition is estimated to occur at about 400
atoms, or 2.5 nm in diameter.
10.8.2.2 Thinnest Stable Short Silicon Nanowires
Using a full-potential linear-muffin-tin-orbital molecular-dynamics method, we
have studied the geometric and electronic structures of thin short silicon nanowires consisting of tri-capped trigonal prism Si 9 sub-units and uncapped trigonal
prisms, respectively [86]. Comparing to other possible structures, these structures
are found to be the thinnest stable silicon nanowires, being in particular much
more stable than the silicon nanotubes built analogously to small carbon nanotubes (Figure 10.46). As for their electronic structures, these silicon wires show
very small gaps of only a few tenths of an eV between the lowest unoccupied energy level and the highest occupied energy level, and the gaps decrease as the
stacked layers increase. The results provide guidance to experimental efforts for
assembling and growing silicon nanowires.
10.8.2.3 Silicon Nanotubes
In contrast to the synthesis of large quantity of SiNWs, no Si nanotube has ever
been observed experimentally, indicating that silicon is an element very different
from carbon in forming nanotubular structures although they are in the same
group of the Periodic Table. The difficulty in the synthesis of silicon nanotubes is
widely attributed to the property of sp
3 hybridization in silicon. How and to what
extent such hybridization affects the tubular structural formation still needs further clarification. To understand the reason(s) for the hitherto unsuccessful synthesis of silicon nanotubes we have studied [87] the differences in the structures
and bonding between cubic (diamond-like) and tubular nanostructures of carbon
and silicon, and their relative stabilities in terms of their characteristic electronic
structures. Our calculated results indicate that when the dangling bonds at the
open ends of the tubular structure are properly terminated, Si nanotubes with a
severely puckered structure can, in principle, be formed. Such computationally
stable, energetically minimized, and geometrically optimized Si nanotube structures may serve as models for the design and synthesis of silicon nanotubes.
10.8 Modeling 361
structure. The structural transition to bulk diamond structure in nanosized silicon
clusters has been studied by the tight-binding molecular dynamics method combined with a simulated annealing technique [85]. For intermediate-sized clusters
(<200 atoms), the energetically favorable structures obtained consist of small
subunits like Si 10 and Si 12 (Figure 10.44), qualitatively consistent with the experimental fragmentation behavior of these clusters. For spherical silicon nanocrystals,
the surface atoms reconstruct to minimize the number of dangling bonds, forming
a continuum surface (Figure 10.45). The large curvature of the continuum surface
causes lattice contraction in the nanocrystals. Present calculations predict the
lattice contraction versus the particle radius as Da ¼ 0:38=R, with Da and R in A ˚ .
By comparing the cohesive energies of the two sorts of structures with the same
number of atoms, the structural transition is estimated to occur at about 400
atoms, or 2.5 nm in diameter.
10.8.2.2 Thinnest Stable Short Silicon Nanowires
Using a full-potential linear-muffin-tin-orbital molecular-dynamics method, we
have studied the geometric and electronic structures of thin short silicon nanowires consisting of tri-capped trigonal prism Si 9 sub-units and uncapped trigonal
prisms, respectively [86]. Comparing to other possible structures, these structures
are found to be the thinnest stable silicon nanowires, being in particular much
more stable than the silicon nanotubes built analogously to small carbon nanotubes (Figure 10.46). As for their electronic structures, these silicon wires show
very small gaps of only a few tenths of an eV between the lowest unoccupied energy level and the highest occupied energy level, and the gaps decrease as the
stacked layers increase. The results provide guidance to experimental efforts for
assembling and growing silicon nanowires.
10.8.2.3 Silicon Nanotubes
In contrast to the synthesis of large quantity of SiNWs, no Si nanotube has ever
been observed experimentally, indicating that silicon is an element very different
from carbon in forming nanotubular structures although they are in the same
group of the Periodic Table. The difficulty in the synthesis of silicon nanotubes is
widely attributed to the property of sp
3 hybridization in silicon. How and to what
extent such hybridization affects the tubular structural formation still needs further clarification. To understand the reason(s) for the hitherto unsuccessful synthesis of silicon nanotubes we have studied [87] the differences in the structures
and bonding between cubic (diamond-like) and tubular nanostructures of carbon
and silicon, and their relative stabilities in terms of their characteristic electronic
structures. Our calculated results indicate that when the dangling bonds at the
open ends of the tubular structure are properly terminated, Si nanotubes with a
severely puckered structure can, in principle, be formed. Such computationally
stable, energetically minimized, and geometrically optimized Si nanotube structures may serve as models for the design and synthesis of silicon nanotubes.
10.8 Modeling 361