Molecular dynamics simulations of the tensile and melting behaviours of silicon nanowires

Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học

Trang 1

Molecular dynamics simulations of the tensile and melting behaviours of

silicon nanowires

Department of Astronautical Science and Mechanics, Harbin Institute of Technology, No.92, West Da-Zhi Street, Harbin 150001, People’s Republic of China

a r t i c l e i n f o

Article history:

Received 29 September 2008

Received in revised form

7 November 2008

Accepted 13 November 2008

Available online 3 December 2008

PACS:

61.46.Km

62.25.g

65.80.+n

Keywords:

Si nanowires

Molecular dynamics

Tension

Melting behaviour

a b s t r a c t The tensile and melting behaviours of single crystalline silicon nanowires (SiNWs) are studied using molecular dynamics simulations The atomic interactions are described using the Stillinger–Weber potential The tensile test results show that the tensile behaviour of the SiNWs is strongly dependent on the simulation temperature, strain rate, and diameter of the nanowires The critical load clearly decreases with increasing temperature and with decreasing strain rate, and increases with increasing diameter Additionally, the melting test results demonstrate that the melting temperature of the SiNWs decreases with decreasing diameter, due to the increase in surface energy The structural transition of SiNWs with an increasing temperature is also studied

1 Introduction

One-dimensional semiconductor nanostructures are attracting

great interest for their tremendous technological potential in

nanoscale devices[1,2] Utilizing the structure at the nanometer

level is a key technology in the development of electronic devices

and elements of nanoelectromechanical systems (NEMS)

There-fore, it is important to understand the mechanical properties for

engineering usefulness such as design of reliability in service

Silicon nanowires (SiNWs) appear to be an especially appealing

choice due to their compatibility with conventional Si-based

electronic technology Recently, SiNWs have been synthesized by

solution techniques [3], an oxide-assisted catalyst-free method

[4,5], and a metal-catalytic vapour–liquid–solid method [6–8]

High-resolution electron microscopy experiments have shown

that the resulting SiNWs carry cores with monocrystalline bulk

structures[7,9]

From a theoretical viewpoint, many correlative theoretical

predictions have been performed in recent years[10–15] In most

of the work, the Quantum mechanics methods were used, and the

attentions were mainly paid on the microstructural and electronic

properties of the SiNWs The mechanical strength of the nanowires

plays an important role in maintaining the structural integrity of the structures, devices or systems However, such calculations are very expensive Sizedependent and thermodynamical properties of nanowires are still unattainable to such methods Molecular dynamics (MD) simulations are increasingly being used to study the mechanical behaviour and deformation mechanisms of nanostructures A number of studies have used the MD simula-tions to analyze the tensile failure modes in metal nanowires

[16–19] Metal nanowires have been found to exhibit unique physical behaviour under tensile loading However, the studies on the mechanical characters of SiNWs are little reported [20,21] Although empirical methods carry a considerable simpliﬁcation of the underlying atomistic processes, they still represent an alternative to access those important nanowire properties[20,22]

In this paper, we report the results of MD simulations on the tensile and melting behaviours of [11 0]-oriented SiNWs The effect of temperature, strain rate, and cross-sectional size on the mechanical properties is studied We also investigate the size effect on the melting temperature of SiNWs

2 Simulation method Because the exact atomic structure of the SiNWs is unknown in most cases, some theoretical calculations of nanowires with different shapes can be found in the literature Zhao and Yakobson

Contents lists available atScienceDirect

journal homepage:www.elsevier.com/locate/physe

Physica E

Corresponding author Tel.: +86 451 864 00158.

E-mail address: jingyuhang@gmail.com (Y Jing).

Trang 2

[23] proposed the pentagonal and hexagonal SiNWs along the

/110S direction Justo et al [24]reported classical molecular

dynamic simulations of silicon nanowires of various shapes and

orientations Menon[20]and Ponomareva et al.[22]investigated

the tetragonal and clathrate SiNWs Based on the reported

experimental observation [9], the triangular-shaped nanowires

have relatively large size (diameter of about 100 nm) As for the

triangular-shaped SiNWs, no theoretical study has been reported

in the literature A detailed study of such SiNWs is necessary to

understand the properties of SiNWs with different shapes In this

study, we construct [11 0]-oriented SiNWs with triangular cross

sections directly from the bulk silicon by removing the atoms

outside a triangle To save computational time, the NWs are

relatively thin with diameter Do10 nm, the top and side views of

the optimized structures of single crystalline SiNWs are shown in

Fig 1 The nanowires with triangular cross-sectional shape are

enclosed with two {111} side planes and one {1 0 0} side plane

The atomic interactions are described using the Stillinger–

Weber (SW) potential [25] The empirical SW interatomic

potential consists of two- and three-body interaction terms and

were originally ﬁtted to describe the crystalline and liquid silicon

phases This potential consists of sums of two- and three-body

interaction contributions The two-body potential describes the

formation of a chemical bond between two atoms The three-body

potential favors structures in which the angles between two

bonds made by the same atom are close to the tetrahedral angle

The SW potential has been used in the study of molten Si[25]as

well as surfaces of crystalline Si[26] The SW potential has also

been adopted for the study of SiNWs and found to give good

results for nanowire properties [20,22] Therefore, the SW

potential should be reliable to study the mechanical properties

of SiNWs

The loading state in the present tension simulations is as

follows: the relative positions of atoms within the ﬁve atomic

layers at the top and bottom of NWs are ﬁxed during simulations,

forming two rigid borders; the others are set as thermal controlled

layers, as illustrated inFig 1 The system temperature is controlled

by rescaling the atom velocities [27] The SiNWs are initially

annealed at 700 K over a period of 106time-steps, where each step

is separated by an interval of 0.5 fs, and then the structures of the

nanowires were dynamically relaxed at a given temperature for

50 ps with traction-free boundary conditions, which allows the

nanowires to have stable conﬁguration The strain was then

applied along the axial direction to study the mechanical

proper-ties of the SiNWs In order to investigate the relative inﬂuences of

temperature, strain rate and cross-sectional size on the mechan-ical properties of the current SiNWs under tension loading conditions, this study simulates testing under various tempera-tures in the range of 10–1200 K, with strain rates varying from

2 104 to 2 102/ps and wire diameter ranging from 4.27 to 6.15 nm In the melting simulations, the periodic boundary condition is applied in the axial direction The initial conﬁguration was relaxed for 50 ps at 300 K The heating process is simulated by

a temperature increment of T ¼ 100 K However, a temperature increment of T ¼ 50 K is applied near the melting region For each temperature interval, the MD cell was relaxed for 50 ps

3 Results and discussion The generated results of the MD simulation are presented The deformation characteristics of the nanowire in uniaxial tension are considered at the ﬁrst stage The effect of temperature, strain rate, and cross-sectional size on the mechanical properties of the nanowires such as the critical load is studied Afterwards, the melting properties of the SiNWs are investigated

3.1 The tensile properties of the SiNWs

Fig 2(a) shows the axial load–strain curve for the SiNW with diameter 4.27 nm, simulated at 300 K, with strain rate of 0.04%/ps From the ﬁgure, it is seen that the load increases up to a maximum value of 141 nN corresponding to strain of 0.124, then the load suddenly decreases to 32 nN where the plastic zone is developed For low strains (eo0.05), the load–strain relation

is essentially linear in the elastic regime, and Young’s modulus can

be directly evaluated in this elastic region Young’s modulus is

Fig 2 (a) Load–strain curves of the SiNW with diameter 4.27 nm, simulated at

300 K, with strain rate of 0.04%/ps (b) Snapshots of atomic conﬁgurations at

Trang 3

estimated as 118.4 GPa according to the present model, which is

consistent with the experimental result of 93–180 GPa of SiNWs

[28,29] The deformation process can be better understood by the

wire evolution presented inFig 2(b) For small strains, the bonds

of the nanowire are just stretched and preserve their fourfold

coordination in the nanowire, and no structural defects appear at

this stage For larger strains, bond breakage in the outmost layer is

observed and spreads toward the center as the strain increases

With the strain increasing further more, we ﬁnd that sliding along

the {111} plane happens, and many atoms rearrange in the neck

region When a single crystal is stretched, the fundamental

deformation mechanism is a shearing action based on the

resolved shear stress on an active slip system The silicon is a

diamond structure and its slip plane is {111} [30], and in the

present simulation the load is along the [11 0] orientation and the

resolved shear stress on the (111) plane causes the sliding After

the formation of the neck, the plastic deformations have been

carried mainly through the reconstruction and rearrangement of

the neck region, which was previously reported in other studies

[16] Beyond this region, the nanowire keeps ordered structure

and have no signiﬁcant change

Since buckling occurs as a result of dynamic processes, the

mechanisms of material deformation are inﬂuenced both by

temperature and by strain rate Therefore, if material

deforma-tions in SiNWs are to be fully understood, the inﬂuences of these

factors must be investigated Fig 3 shows the effects of

temperature and strain rate on the tension behaviour.Fig 3(a)

shows the axial load–strain curves of SiNWs with diameter

4.27 nm, which were simulated at 10–1200 K with a strain rate of

0.04%/ps The results clearly demonstrate that the critical buckling

load decreases at higher temperature At higher temperature, the

atomic structure has high entropy, and the atoms vibrate about

their equilibrium position at much larger amplitude A greater

number of molecules gain sufﬁcient energy to overcome the

activation energy barrier, as compared to low temperature, and

hence deformation occurs This result suggests that a thermally

activated process plays an activating role in the complete

elongation of SiNWs.Fig 3(b) shows the axial load–strain curves

of SiNWs with diameter 4.27 nm, which were simulated at 300 K

with strain rate varying from 0.02 to 2%/ps The strain rate

adopted here is very high compared to that in experiment,

because only very short period of time can be simulated due to the

time scale of molecular dynamics set by the atomic motion One

consequence of the short time scale is that very high strain rates

are required to get any reasonable deformation within the

available time[31] For all strain rates, the load increases linearly

with strain up to 0.11 Below this value, the load–strain curves are

almost completely overlapped for all of strain rates applied,

indicating that in the linear elastic region no plastic deformation

occurs and the elastic properties of a nanowire is insensitive to

strain rate However, a slower strain rate results in a lower critical

buckling load Regarding the strain rate inﬂuence, the strain or

deformation tends not to be uniformly distributed within the

material, particularly when a large strain is applied Hence, some

regions of the nanowire are subjected to larger stresses or strains

than others, and it is within these regions that defects will ﬁrst

become evident When a lower strain rate is applied, the SiNWs

have more time to induce adequate local deformation, and hence

the onset of plastic deformation is accelerated Therefore, a slower

strain rate results in a lower critical load The present results

clearly demonstrate that the mechanical properties of SiNWs are

sensitive to the strain rate and temperature conditions

An important factor in evaluating the mechanical properties of

nanowire is the size effect Physical and chemical properties of

materials are expected to exhibit some dependencies on

dimen-sionality and cross-sectional size We describe the scaling

proper-ties of nanowires as a function of their diameters (as shown in

Fig 1) As for the triangular-shaped SiNWs in the present study, the method to estimate an effective wire size is similar to Ref

[24], where the perimeter of SiNWs were used to estimate an effective wire size To investigate the effect of the SW potential on the scaling properties of SiNWs, the critical loads are also computed using the Tersoff potential [32] and EDIP model

[33,34] The simulation results show that the SW potential seems

to be more reasonable to describe silicon nanowires Fig 4(a) shows the axial load–strain curves for nanowires with diameter 4.27 nm, which were simulated at 300 K with a strain rate of 0.04%/ps From the picture, it can be seen that the Tersoff potential shows the highest critical load and critical strain The SW potential shows somewhat higher critical load than the EDIP model, however, the EDIP model shows somewhat higher critical strain than the SW potential The critical strain (0.124) computed using the SW potential is in good agreement with experiment result (0.104) [35] The critical loads computed using the three different interatomic potentials are higher than the experimental estimates [35] It should be noted, however, that experimental samples almost always contain defects and impurities that can reduce the critical strength.Fig 4(b) shows the variation in critical load with diameter of SiNWs The result clearly demonstrates that Fig 3 Load–strain curves for the SiNWs under tensile loading Effects of (a) temperature and (b) strain rate on the tension behaviour of the SiNWs.

Trang 4

the critical load decreases with decreasing the diameter of the

nanowires Speciﬁcally, as the diameters increase from 4.27 to

6.15 nm, decreases of about 50% in the critical load computed

using the three different interatomic potentials The reason for

this behaviour may be the small atomic-coordination number and

weak cohesion of the atoms near the surface, as compared with

those in the bulk, and the increasing dominance of the surface

would decrease the strength of the structure

3.2 The melting properties of the SiNWs

The variation of potential energies as a function of temperature

is shown inFig 5 As can be seen from the results in the picture,

the energy generally increases with decreasing diameter of SiNWs

at a given temperature, which indicates that surface energy

increases with decreasing diameter The potential energies also

increase linearly with increasing temperature and change

abruptly near the melting region The melting temperature Tmis

deﬁned as the point of an abrupt change in the potential energies

for the heating process FromFig 5, it is found that the melting

temperature of SiNWs increases with increasing diameter, which

is consistent with the fact that the melting behaviour of

nanostructure materials is strongly dependent on size In general, the thermodynamic property of nanostructures is different from bulk materials[36] The change of the melting temperature of nanostructures depends on their surface This indicates that the unstable surface of free-standing nanowires leads to a decrease in the melting temperature

To understand the melting behaviour of SiNWs, the structural evolution of the nanowire with the diameter of 3.32 nm at different temperatures in the heating process is shown inFig 6 Before the melting behaviour starts, the atoms of the SiNW oscillate at their equilibrium position As the melting behaviour starts, the unstable atoms on the edge move to the facet of the SiNW It should be also noted that at 1450 K, which is 150 K below the melting point, several atoms in the central region of the nanowires are still in the crystalline conﬁgurations However, when the temperature is increased to 1600 K, none of the atoms are in their lattice conﬁgurations, and the atomic positions are

Fig 4 (a) Load–strain curves for SiNWs with diameter 4.27 nm, which were

simulated at 300 K with strain rate of 0.04%/ps (b) The variation in critical load

with the diameter of SiNWs.

Fig 5 Potential energy as a function of temperature for SiNWs.

Fig 6 Structural transition of the SiNW with a diameter of 3.32 nm at different temperatures.

Trang 5

disordered The nanowire ﬁnally collapses, which indicates the

melting of the nanowire

4 Conclusions

In this paper, molecular dynamics simulations with

Stillin-ger–Weber potentials are used to simulate the tensile and melting

behaviours of the SiNWs It is found that the tensile behaviour of

the SiNWs is strongly dependent on the simulation temperature,

strain rate, and diameter of the SiNWs The critical load clearly

decreases with increasing temperature and with decreasing strain

rate, and increases with increasing diameter Additionally, it is

observed that the melting temperature of the SiNWs increases

with increasing diameter, due to the surface energy increased

This indicates that the unstable surface of free-standing

nano-wires leads to a decrease in the melting temperature

Acknowledgement

This work was supported by the NSF of China under Grant no

10772062

References

[1] A.M Morales, C.M Lieber, Science 279 (1998) 208.

[2] C.M Lieber, Nano Lett 2 (2002) 81.

[3] J.D Holmes, K.P Johnston, R.C Doty, et al., Science 287 (2000) 1471.

[4] Y.F Zhang, Y.H Tang, N Wang, et al., Appl Phys Lett 72 (1998) 1835 [5] N Wang, Y.F Zhang, Y.H Tang, et al., Appl Phys Lett 73 (1998) 3902 [6] Y Cui, L.J Lauhon, M.S Gudiksen, et al., Appl Phys Lett 78 (2001) 2214 [7] Y Wu, Y Cui, L Huynh, et al., Nano Lett 4 (2004) 433.

[8] J Kikkawa, Y Ohno, S Takeda, Appl Phys Lett 86 (2005) 123109 [9] Chi-Pui Li, Chum-Sing Lee, Xiu-Liang Ma, et al., Adv Mater 15 (2003) 607 [10] R Kagimura, R.W Nunes, H Chacham, Phys Rev Lett 95 (2005) 115502 [11] R Rurali, N Lorente, Nanotechnology 16 (2005) S250.

[12] R Rurali, A Poissier, N Lorente, Phys Rev B 74 (2006) 165324.

[13] T Vo, A.J Williamson, G Galli, Phys Rev B 74 (2006) 045116.

[14] Alexei Svizhenko, Paul W Leu, Kyeongjae Cho, Phys Rev B 75 (2007) 125417 [15] Pavel B Sorokin, Pavel V Avramov, Alexander G Kvashnin, et al., Phys Rev B

77 (2008) 235417.

[16] S.J.A Koh, H.P Lee, C Lu, et al., Phys Rev B 72 (2005) 085414.

[17] E.Z da Silva, A.J.R da Silva, A Fazzio, Phys Rev Lett 87 (2001) 256102 [18] Xiaofan Li, Wangyu Hu, Shifang Xiao, et al., Physica E 40 (2008) 3030 [19] S.J.A Koh, H.P Lee, Nanotechnology 17 (2006) 3451.

[20] M Menon, D Srivastava, I Ponomareva, et al., Phys Rev B 70 (2004) 125313 [21] Paul W Leu, Alexei Svizhenko, Kyeongjae Cho, Phys Rev B 77 (2008) 235305 [22] I Ponomareva, M Menon, D Srivastava, et al., Phys Rev Lett 95 (2005) 265502.

[23] Y Zhao, B Yakobson, Phys Rev Lett 91 (2003) 035501.

[24] J.F Justo, R.D Menezes, L.V.C Assali, Phys Rev B 75 (2007) 045303 [25] F Stillinger, T Weber, Phys Rev B 31 (1985) 5262.

[26] F.F Abraham, I.P Batra, Surf Sci 163 (1985) L752.

[27] H Andersen, J Chem Phys 72 (1980) 2384.

[28] T Yi, L Li, C.J Kim, Sensor Actuator A 83 (2000) 172.

[29] M Tabib-Azar, M Nassirou, R Wang, et al., Appl Phys Lett 87 (2005) 113102 [30] J Godet, L Pizzagalli, S Brochard, Phys Rev B 70 (2004) 054109.

[31] Yu-Hua Wen, Zi-Zhong Zhu, Ru-Zeng Zhu, Comput Mater Sci 41 (2008) 553 [32] J Tersoff, Phys Rev B 38 (1988) 9902.

[33] M.Z Bazant, E Kaxiras, J.F Justo, Phys Rev B 56 (1997) 8542.

[34] J.F Justo, M.Z Bazant, E Kaxiras, et al., Phys Rev B 58 (1998) 2539 [35] T Kizuka, Y Takatani, K Asaka, et al., Phys Rev B 72 (2005) 035333 [36] W.H Qi, Physica B 368 (2005) 46.

Định dạng
Số trang	5
Dung lượng	711,88 KB