Journal of Modern Physics, 2013, 4, 501-504 Published Online April 2013 (
Starting Point of Cluster-Derived Silicon Nanowires
Aijiang Lu
Science College, Donghua University, Shanghai, China
Received January 13, 2013; revised February 12, 2013; accepted February 21, 2013
Copyright © 2013 Aijiang Lu. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The assembly of medium-sized silicon nanoclusters was simulated to study the starting point of the formation of clu ster-
derived silicon nanowires (CDSiNWs). Hydrogen-terminated clusters were found repulsing each other and inter-con-
necting through the hydrogen bon ds, thus could not form a stable silicon nanowire (SiNW). Between the pristine silicon
clusters without hydrogen saturation, the assembly takes place automatically. An orientation priority in cluster assembly
is obtained, as silicon clusters Si29 are more possibly adh ered along <111> direction than the other direction s. Such an
assembly may be the starting po int of the SiNW growth along <111> direction . Moreover, it indicates the possibility o f
silicon tetrapods or zigzag wires formation, besides straight SiNWs.
Keywords: Cluster; Nanowire; First Principle Calculation
1. Introduction
Silicon nanowire (SiNW) is not a new topic as it has
been studied for decades due to the potential applications
in electric, electronic, optoelectronic and sensing fields
[1-6]. But the most basic problem, the wire growth has
not been demonstrated clearly. Much effort has been tak-
en as a number of reports on synthesis or characteristic of
SiNWs are available [7,8]. As reported, SiNWs along
<110>, <111> and <112> directions were successfully
synthesized in experiments and the diameters of them
range between 1.3 to 7 nm. The quasi-1D material was
regarded as a good candidate to show the quantum con-
finement in real systems [9,10]. However, the growth
direction of the SiNWs exhibits complexity, according to
the different methods and conditions in the synthesis [11,
12]. For example, in Vapor-Liquid-Solid (VLS) method
the small sized SiNWs (diameter less than 10 nm) prefer
<110> [13] direction, and the NWs with diameter larger
than 20 nm prefer the growth direction of <111> [14]. In
the etching process of (110) silicon substrate the crystal-
lographically of vertical wires prefers <100> direction
[15]. By thermal evaporation, non-unique crystallogra-
phic is found by Ma et al. [16]. The bond orientational
order was reported to influence the physical properties of
SiNWs heavily [17,18], so the direction of SiNWs need
to be determined first before they were u sed in real app li-
Thus, the motivation and procedure of the SiNWs
growth has been interested in widely. Although the oxy-
gen assisting, etching procedure and metallic catalyst
were suggested to explain the growth dynamics, there has
not a satisfactory answer been reached yet. Characteriza-
tion of SiNWs indicates the relation of NWs with the
bulk crystal. Consequently the model of SiNWs has been
suggested as the cylinder structure cut from bulk silicon
crystal. On the other hand, as the diameter of small sized
SiNW is close to that of the medium-sized silicon cluster,
cluster-derived SiNW (CDSiNW) is also concerned of as
a possible structural model to study the SiNW in theory.
The latter has been supported as the assembly of silicon
clusters on silicon surfaces confirmed with Scanning
Tunneling Microscopy (STM) in experiments [19,20].
The possibility of silicon clusters congregating and
forming a wire-like structure was focused in this work.
Si29 cluster with crystal structure was selected as the
building block. Different connections between several
Si29 clusters were studied. The energy analysis showed
that the assembly between silicon clusters with hydrogen
termination would not take place automatically. However,
between the pristine silicon clusters, the connection be-
tween them results in the decrease of total energy and the
bonding along <111> orientation showed the lowest for-
mation energy. The bonded structure could be the start-
ing point of SiNWs along <111> direction, instead of the
model cut from bulk crystal. Moreover, our work indi-
cated the formation of a tetrapod silicon structure or zig-
zag wire, besides straight SiNWs in the product of as-
opyright © 2013 SciRes. JMP
A. J. LU
2. Method
Our calculation was performed in density functional the-
ory, based on the iterative diagonalization and plane wave
basis sets. The GGA-LYP and GGA-PW91 exchange-
correlation functionals were adopted and the double nu-
merical basis with polarization (DNP) was selected to
describe the silicon atom. Norm-conserving poten tial was
used to describe the interaction between atoms. Spin of
electron was not included in this work as it was not of
importance to the cluster assembly. All of the atomic
structures had been full-relaxed and the interforce was
less than 0.04 eV/A in the geometry optimization.
Distance between silicon clusters and the arrang ed ori-
entation were controlled manually in the simulation, and
no constraint was applied. Si-Si bond length in the final
structure was larger than that in bulk crystal (2.3 A),
which agreed with the results in some other works on
silicon surface reconstruction [21].
3. Results and Discussion
Si29 clusters were selected as the building block with a
sphere-like profile, which was built based on silicon bu lk
crystal. The cluster was full-relaxed and the total energy
was used to calculate the formation energy of CDSiNW
in this work. Hydrogen atoms were bonded on the sur-
face to saturate the dangling bonds and the Si29H24 was
used to study the H-terminated cluster.
The assembly of H-terminated silicon clusters were
calculated first, and the initial distance between two clu-
sters ranged from 3.0 to 0.5 A. The approaching of the
clusters along different directions has been considered,
and the shortest distance between two atoms in neighbor-
ing clusters was found 1.5 A or so based on the energy
analysis. Such a distance was much larger than the bond
length of any chemical bonds formed by hydrogen. Thus
the interaction between H-terminated silicon clusters
could be explained as van de Waals interaction. This weak
connection between clusters ruled out the possibility of
CDSiNWs formation with H-terminated clusters.
The silicon clusters without hydrogen saturation were
studied next. The surface reconstruction was remarkable
in the optimized stru cture of Si29, as indicated in Figure
1. The profile of the opti mized cluster was close to a tet-
rahedron, as the (111) facets were flatter than that before
the relaxation. Si-Si bond length was increased and the
silicon atoms were 3-fold or 4-fold in the cluster.
The assembly of silicon clusters was concerned of be-
tween two clusters. The distance between them and the
orientation of the arrangement were modified manually.
The full relaxation was applied and no constraints were
added in the systems. Two silicon clusters were arranged
along different orientations and the binding energy Etot-
2*Esi29 were calculated and compared in Figure 2. In this
figure, the atomic structure of the connected clusters was
shown as inset just above or under the data points, and
the labels (a) to (e) corresponded with the different con-
necting directions. Namely, they were (a) (100)-(100)
dimer, (b) (100)-(110) dimer, (c) (100)-(111) dimer, (d)
(110)-(110) dimer and (e) (111)-(111) d imer respectively.
Here the Miller index showed the crystal surface the lat-
eral facet lied in. This series of models were prepared
through rotating one cluster around the other and laying
them together. The chemical bonds between them were
formed after a geometry optimization so that the cluster
dimer was obtained with an inter distance in the cluster
Due to the definition of binding energy in this work,
negative binding energy indicated exothermal procedure
and the process often took place automatically. As dis-
played in Figure 2, all of the Si29-Si29 systems concern-
ed showed negative binding energies. It was evidence
that the Si29 cluster would assemble to form a larger
Figure 1. Atomic structure of relaxed Si29 cluster.
Figure 2. Binding energy of Si29-Si29 dimer. Atomic struc-
ture is shown as inset, namely (a) (100)-(100) dimer; (b)
(100)-(110) dimer; (c) (100)-(111) dimer; (d) (110)-(110)
dimer and (e) (111)-(111) dimer.
Copyright © 2013 SciRes. JMP
A. J. LU 503
cluster automatically, no matter in which direction.
However, among the cluster dimers, (111)-(111) dimer
showed the lowest binding energy, which indicated that
the connection of Si29 clusters in <111> direction would
lead to the largest decrease of the total energy. Such a re-
sult also showed that the CDSiNW would be obtained in
<111> direction more possibly than in other orientations,
when the a ssembl y could take place in a steady stream or
a template. It was reported that the small-sized SiNWs
with crystalline structure prefer <110> direction in VLS
method. Only when the size of the SiNW increased the
SiNWs prefer to grow along <111> direction [14]. The
small sized<111> SiNWs were difficult to obtain in the
VLS process. But in our result, it was shown that the
small-sized <111> SiNWs could be obtained from cluster
assembly possibly.
Moreover, model (a) showed the largest binding ener-
gy among the five candidates. It was evidence that the
cluster assembly in <100> direction was not energy fa-
vored. So the SiNW in <100> direction reported would
be formed by cluster assembly less possibly. But etching
was an available method to manufacture the <100>
SiNWs from Si substrate [15]. Binding energies of model
(b), (c) and (d) are less than that of model (a) but larger
than that of model (e). It means that the cluster assembly
in these models led to meta-stable configurations and
also could be obtained in experiments with a less distri-
In further analysis it was noticed that Si29 cluster
showed the symmetry close to Td space group. The clus-
ter assembly in <111> direction could take place in 4
equivalent orientations. Consequ ently we built two struc-
tures with 3 Si29 clusters, displayed as Figure 3(a) a
corner-like structure and Figure 3(b) a chain-like one.
When the bonding happened on neighboring laterals of
the central cluster, a corner-like structure would be ob-
tained. On the contrary, a chain-like structure would be
observed when the assembly took place on both sides of
the central cluster. It was worth noting that the bonding
was assumed to take place on the <111> facets due to
above results.
The binding energy was defined as Etot-3*Esi29. Inter-
estingly, from the comparison we found that the binding
energy of corner-like structure was larger than that of the
chain-like model by 0.72 eV. The formation of chain-like
structure was energy favored, compared with the corner-
like one. When the chain-like assembly took place sev-
eral times a CDSiNWs should be formed. However, the
cluster assembly in <111> direction would not result in
straight wires merely. Tetrapod structure or larger con-
gregated cluster would be obtained in the assembly, ei-
ther. Consequently the assembly of clusters may be a rea-
son of the cluster growth.
Above results were interesting as the cluster assembly
Figure 3. Assembly result of three Si29 clusters, (a) is a
corner-like structure and (b) is a chain-like one.
showed the CDSiNW the possible growth process of the
small-sized <111> SiNW. The corner-like boding be-
tween the silicon clusters was not the most energy favor-
ed, but was the evidence of the cluster assembly in two
or three dimensions.
4. Conclusion
As a conclusion, the assembly of the medium-sized clus-
ters was important to the SiNW growth. The pristine
clusters assemble automatically and a direction prefer-
ence was revealed. The assembly of Si29 clusters would
form a CDSiNW in <111> direction more possibly, and
the direction preference would result in a tetrapod struc-
ture or zigzag structure besides of a CDSiNW. Moreover,
the cluster growth as well as the SiNW growth was
shown as a result of cluster assembly. It means that when
the template or environment is suitable, the CDSiNW or
some other cluster-derived materials could be obtained in
5. Acknowledgements
This work is supported by Natural Science Fund of
Shanghai (10ZR1400200), and the author thanks the
beneficial discussion with Dr. Lijuan Zhao and Prof.
Huaizhong Xing.
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