Starting Point of Cluster-Derived Silicon Nanowires

doi:10.4236/jmp.2013.44071

Paper Menu >>

Journal Menu >>

Journal of Modern Physics, 2013, 4, 501-504

http://dx.doi.org/10.4236/jmp.2013.44071 Published Online April 2013 (http://www.scirp.org/journal/jmp)

Starting Point of Cluster-Derived Silicon Nanowires

Aijiang Lu

Science College, Donghua University, Shanghai, China

Email: [email protected]

Received January 13, 2013; revised February 12, 2013; accepted February 21, 2013

permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

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-

cations.

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-

A. J. LU

502

sembly.

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

dimer.

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.

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-

bution.

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

(a)

(b)

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

experiments.

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.

REFERENCES

[1] Y. Cui, Z. Zhong, D. Wang, W. U. Wang and C. M. Lie-

A. J. LU

504

ber, “High Performance Silicon Nanowire Field Effect

Transistors,” Nano Letters, Vol. 3, No. 2, 2003, pp. 149-

152. doi:10.1021/nl025875l

[2] Y. Cui and C. M. Lieber, “Functional Nanoscale Electro-

nic Devices Assembled Using Silicon Nanowire Building

Blocks,” Science, Vol. 291, No. 5505, 2001, pp. 851-853.

doi:10.1126/science.291.5505.851

[3] X. H. Sun, N. B. Wong, C. P. Li, S. T. Lee and T. K.

Sham, “Chainlike Silicon Nanowires: Morphology, Elec-

tronic Structure and Luminescence Studies,” Journal of

Applied Physics, Vol. 96, No. 6, 2004, pp. 3447-3451.

doi:10.1063/1.1782958

[4] F. Sacconi, M. P. Persson, M. povolotskyi, L. Latessa, A.

Pecchia, A. Gagliardi, A. Balint, T. Fraunheim and A. D.

Carlo, “Electronic and Transport Properties of Silicon Na-

nowires,” Journal of Computational Electronics, Vol. 6,

No. 1-3, 2007, pp. 329-333.

doi:10.1007/s10825-006-0138-y

[5] H. Scheel, S. Reich and C. Thomsen, “Electronic Band

Structure of High-Index Silicon Nanowires,” Physica Sta-

tus Solid (b), Vol. 242, No. 12, 2005, pp. 1-6.

[6] X. T. Zhou, J. Q. Hu, C. P. Li, D. D. D. Ma, C. S. Lee and

S. T. Lee, “Silicon Nanowires a s Chemical Sensors,” Che-

mical Physics Letters, Vol. 369, No. 1-2, 2003, pp. 220-

224. doi:10.1016/S0009-2614(02)02008-0

[7] D. D. D. Ma, C. S. Lee, F. C. K. Au, S. Y. Tong and S. T.

Lee, “Small-Diameter Silicon Nanowire Surfaces,” Sci-

ence, Vol. 299, No. 5614, 2003, pp. 1874-1877.

doi:10.1126/science.1080313

[8] W. Park, G. Zheng, X. Jiang, B. Tian and C. M. Lieber,

“Controlled Synthesis of Millimeter-Long Silicon Nano-

wires with Uniform Electronic Properties,” Nano Letters,

Vol. 8, No. 9, 2008, pp. 3004-3009.

doi:10.1021/nl802063q

[9] Y. Cui, L. J. Lauhon, M. S. Gudikesen, J. Wang and C. M.

Lieber, “Diameter-Controlled Synthesis of Single-Crystal

Silicon Nanowires,” Applied Physics Letters, Vol. 78, No.

15, 2001, pp. 2214-2216. doi:10.1063/1.1363692

[10] J. Yan, L. Yang and M. Y. Chou, “Size and Orientation

Dependence in the Electronic Properties of Silicon Nano-

wires,” Physical Review B, Vol. 76, No. 11, 2007, Article

ID: 115319. doi:10.1103/PhysRevB.76.115319

[11] I. Zardo, L. Yu, S. Conesa-Boj, S. Estrade, P. J. Alet, J.

Rossler, M. Frimmer, P. R. Cabarrocas, F. Peiro, J. Arbiol,

J. R. Moreante and A. F. Morral, “Gallium Assisted Pla-

sma Enhanced Chemical Vapor Deposition of Silicon

Nanowires,” Nanotechnology, Vol. 20, No. 15, 2009, pp.

155602-155610. doi:10.1088/0957-4484/20/15/155602

[12] S. A. Fortuna and X. Li, “Metal-Catalyzed Semiconduc-

tornanowires: A Review on the Control of Growth Direc-

tions,” Semiconductor Science and Technology, Vol. 25,

No. 2, 2010, pp. 024005-024020.

doi:10.1088/0268-1242/25/2/024005

[13] Y. Wu, Y. Cui, L. Huynh, C. J. Barrelet, D. C. Bell and C.

M. Lieber, “Controlled Growth and Structures of Mole-

cular-Scale Silicon Nanowires,” Nano Letters, Vol. 4, No.

3, 2004, pp. 433-436. doi:10.1021/nl035162i

[14] Y. Wu, H. Yan and P. Yang, “Semiconductor Nanowire

Array: Potential Substrates for Photocatalysis and Photo-

voltaics,” Topics in Catalysis, Vol. 19, No. 2, 2002, pp.

197-201. doi:10.1023/A:1015260008046

[15] Z. Huang, T. Shimizu, S. Senz, Z. Zhang, X. Zhang, W.

Lee, N. Geyer and U. Gosele, “Ordered Arrays of Verti-

cally Aligned [110] Silicon Nanowires by Suppressing

the Crystallograpgically Preferred <100> Etching Direc-

tions,” Nano Letters, Vol. 9, No. 7, 2009, pp. 2519-2525.

doi:10.1021/nl803558n

[16] X. L. Ma, Y. L. Zhu and Z. Zhang, “Growth Orientation

of One-Dimensional Silicon Nanowires Prepared by Ther-

mal Evaporation,” Philosophical Magazine Letters, Vol.

82, No. 8, 2002, pp. 461-468.

doi:10.1080/09500830210144391

[17] H. Yorikawa, H. Uchida and S. Muramatsu , “Energy Gap

of Nanoscale Si Rods,” Journal of Applied Physics, Vol.

79, No. 7, 1996, pp. 3619-3621. doi:10.1063/1.361416

[18] J. D. Holmes, K. P. Johnston, R. C. Doty and B. A. Kor-

gel, “Control of the Thickness and Orientation of Solu-

tion-Grown Silicon Nanowires,” Science, Vol. 287, No.

5457, 2000, pp. 1471-1473.

doi:10.1126/science.287.5457.1471

[19] W. Ong, E. S. Tok, H. Johll and H. C. Kang, “Self-As-

sembly, Dynamics and Structure of Si Magic Clusters,”

Physical Review B, Vol. 79, No. 23, 2009, Article ID:

235439. doi:10.1103/PhysRevB.79.235439

[20] T. Sekiguchi, S. Yoshida and K. M. Itoh, “Self-Assembly

of Parallel Atomic Wires and Periodic Clusters of Silicon

on a Vicinal Si(111) Surface,” Physical Review Letters,

Vol. 95, No. 10, 2005, Article ID: 106101.

doi:10.1103/PhysRevLett.95.106101

[21] Z. Jing and J. L. Whitten, “Ab Initio Studies of Si(100)

Surface Reconstruction,” Surface Science, Vol. 274, No.

1, 1992, pp. 106-112.

doi:10.1016/0039-6028(92)90104-E