Mechanical Properties of Silicon Nanowires.

Abstract

Nanowires have been taken much attention as a nanoscale building block, which can perform the excellent mechanical function as an electromechanical device. Here, we have performed atomic force microscope (AFM)-based nanoindentation experiments of silicon nanowires in order to investigate the mechanical properties of silicon nanowires. It is shown that stiffness of nanowires is well described by Hertz theory and that elastic modulus of silicon nanowires with various diameters from ~100 to ~600 nm is close to that of bulk silicon. This implies that the elastic modulus of silicon nanowires is independent of their diameters if the diameter is larger than 100 nm. This supports that finite size effect (due to surface effect) does not play a role on elastic behavior of silicon nanowires with diameter of >100 nm.

Full text

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NANO EXPRESS
Mechanical Properties of Silicon Nanowires
Young-Soo Sohn•Jinsung Park•Gwonchan Yoon•
Jiseok Song•Sang-Won Jee•Jung-Ho Lee•
Sungsoo Na•Taeyun Kwon•Kilho Eom
Received: 2 June 2009/Accepted: 7 October 2009/Published online: 27 October 2009
? to the authors 2009
Abstract
nanoscale building block, which can perform the excellent
mechanical function as an electromechanical device. Here,
we have performed atomic force microscope (AFM)-based
nanoindentation experiments of silicon nanowires in order
to investigate the mechanical properties of silicon nano-
wires. It is shown that stiffness of nanowires is well
described by Hertz theory and that elastic modulus of sil-
icon nanowires with various diameters from *100 to
*600 nm is close to that of bulk silicon. This implies that
the elastic modulus of silicon nanowires is independent of
their diameters if the diameter is larger than 100 nm. This
supports that finite size effect (due to surface effect) does
not play a role on elastic behavior of silicon nanowires with
diameter of[100 nm.
Nanowires have been taken much attention as a
Keywords
Nanoindentation ? Atomic force microscope
Silicon nanowire ? Elastic modulus ?
Mechanical properties of nanostructures such as nanowires
[1], carbon nanotubes (CNT) [2], and/or graphene [3] have
been taken a lot of interest because of unique mechanical
response of such structures as a building block. Some
nanostructures exhibit the superior mechanical properties
such as elastic modulus and/or fracture stress to those of
bulk materials [4, 5]. The origin of such remarkable
properties of some nanostructures is still unclear. Because
of such anomalous mechanical properties, nanoscale
structures have been considered for developing the
mechanical devices such as nanoscale resonators. For
instance, various nanowires [6, 7], CNT [8], and/or
graphene [9] have been employed as a nanoscale resonant
device, which can bear the ultrahigh resonant frequency in
the range of 100 MHz to 1 GHz due to excellent elastic
properties. Moreover, nanoscale resonant device has
allowed the ultrasensitive detection of molecules even at
atomic resolution [10–13]. It is implied that mechanical
characterization of nanostructures is a priori requisite for
the development of electromechanical device based on
nanostructures such as nanowires and/or graphene.
Silicon nanowire has been regarded as one of popular
nanoscale materials because of its exceptional electrome-
chanical properties. A recent study [14] has reported that
silicon nanowires possess the piezoresistive properties,
indicating their potential in NEMS applications. Moreover,
Roukes and coworkers [7] have employed the piezoresis-
tive properties for actuation of silicon nanowires as a
nanomechanical resonator. These examples imply that
mechanical characterization of silicon nanowires is quite
essential for further applications of silicon nanowires to
electromechanical devices as a sensor and/or an actuator.
Mechanical properties of nanowires have been well
characterized by using atomic force microscope (AFM)
experiments. Specifically, Boland and coworkers [5, 15,
Young-Soo Sohn and Jinsung Park equally contributed to this work.
Y.-S. Sohn
Department of Biomedical Engineering, Catholic University of
Daegu, Gyeongbuk 712-702, Republic of Korea
J. Park ? G. Yoon ? J. Song ? S. Na ? K. Eom (&)
Department of Mechanical Engineering, Korea University,
Seoul 136-701, Republic of Korea
e-mail: kilhoeom@korea.ac.kr; kilhoeom@gmail.com
S.-W. Jee ? J.-H. Lee
Department of Chemical Engineering, Hanyang University,
Gyeonggi-do 426-791, Republic of Korea
T. Kwon (&)
Department of Biomedical Engineering, Yonsei University,
Kangwon-do 220-740, Republic of Korea
e-mail: tkwon@yonsei.ac.kr
123
Nanoscale Res Lett (2010) 5:211–216
DOI 10.1007/s11671-009-9467-7

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16] have taken into account the bending experiment of a
suspended nanowire using AFM experiments. If the
transverse deflection of nanowire is estimated with respect
to the applied force by AFM, then elasticity theory (Euler–
Bernoulli beam theory) is used to extract the elastic mod-
ulus (Young’s modulus) and/or the yield strength of
nanowires. A recent study [17] has showed that simply
supported boundary condition for double-clamped nano-
wire may be inappropriate to extract the elastic modulus
based on Euler–Bernoulli beam model. In other words, the
elastic modulus of nanowires from AFM bending experi-
ment is very sensitive to boundary conditions [17]. Recent
studies [18] have suggested the tensile test of nanowires
using in situ transmission electron microscope (TEM) and/
or micro-electro-mechanical system (MEMS) device.
Although MEMS device and/or in situ TEM enable the
direct measurement of stress–strain relationship of nano-
wires, during the tensile test by in situ TEM and or MEMS
device, the light used in TEM or MEMS device (for
imaging of extended nanowire) may induce the artifact in
estimation of elastic modulus of nanowire. This is attrib-
uted to photoelastic properties of nanostructures such that
light with a wavelength comparable to energy band gap of
nanostructures could induce the mechanical strain of
nanostructure [19]. Moreover, extraction of elastic modulus
of nanowires using resonance method (based on in situ
TEM) [1] may be incorrect due to photoelastic effect of
nanowire. It is implied that mechanical characterization
based on AFM bending test, MEMS or in situ TEM tension
test, and/or resonance method may be insufficient to gain
insight into elastic properties of nanowires.
In this work, we have employed the AFM indentation
test of silicon nanowires for mechanical characterization of
silicon nanowires. Here, based on AFM indentation
experiment, the elastic modulus of silicon nanowires has
been extracted from classical elasticity theory (i.e. Hertz
theory). It is shown that mechanical response of silicon
nanowires by indentation is well fitted to theoretical
expectation from Hertz theory. Moreover, in order to
understand the finite size effect of silicon nanowires on
their elastic properties, we have measured the elastic
modulus of silicon nanowires with various diameters in a
range of *80 to *600 nm using AFM indentation. It is
suggested that elastic modulus of silicon nanowires
is independent of nanowire’s diameter (when diameter is
larger than *80 nm) and that elastic modulus of nanowires
with their diameters in the range of *80 to *600 nm is
close to that of bulk silicon. This indicates that size effect
does not play any role on mechanical properties of silicon
nanowire as long as its diameter is larger than 100 nm.
For chemical growth of silicon nanowires, a 5-nm thick
Ni film was thermally evaporated on a hydrogen-termi-
nated n-Si(111) substrate under a base pressure of
1 9 10-6Torr. After ultrasonic cleaning in acetone, sam-
ples (with dimension of 1 9 1 cm2) were placed into a
quartz tube reactor in which H2gas (Ar 10%) was flowed
over 30 min at 400 ?C in order to remove the oxygen
molecules remained inside the tube. During the ramp-up,
ultrathin Ni films were alloyed with Si to form nano-sized
NiSxagglomerates. These nano-sized alloys could act as
metallic catalyst for the vapor–liquid–solid nanowire
growth. Vertically grown silicon nanowires can be
obtained in the quartz tube furnace from chemical vapor
decomposition using SiCl4as a source gas at atmospheric
pressure. Here, SiCl4allows the superior epitaxial growth
of nanowires on the Si substrate compared to SiH4,
attributed to the fact that the byproduct of HCl from SiCl4
induces the etching effect of any oxides as well as the
noncatalytic sidewall deposition. Here, the decomposition
temperature of SiCl4is compatible with the Ni–Si eutectic
temperature (966 ?C). Silicon nanowires were in situ axi-
ally grown by introduction of SiCl4 (10 sccm) and H2
(200 sccm) under 950–1,000 ?C for catalyst liquefaction.
Figure 1 shows the TEM image of chemically grown sili-
con nanowire with a diameter of *200 nm. Energy dis-
persive spectrometer (EDS) analysis shows that our
nanowires are well chemically grown. Further, EDS anal-
ysis provides that the tip of nanowire consists of Ni and Si,
indicating that the catalysis Ni is solidified, so that NiSi2is
formed at the tip of silicon nanowire. As shown in Fig. 1,
TEM analysis confirms the chemical grown of silicon
nanowire in (111) direction. NiSi2formed at nanowire tip
is established in epitaxial growth in (111) direction (see
Fig. 1). For mechanical characterization of silicon nano-
wires, we have employed the silicon nanowires with length
of[1 lm in order to remove the effect of NiSi2at nano-
wire tip on the mechanical properties of silicon nanowires.
For mechanical characterization of nanowires using
AFM nanoindentation, we have utilized commercially
available AFM (Innova, Santa Barbara, CA, USA) with
Nanodrive controller (Veeco, Santa Barbara, CA, USA)
and closed-loop scanner. For both imaging and indentation,
we have used Al-coated silicon cantilevers (TESPA,
Veeco, Santa Barbara, CA, USA) with their nominal tip
radius of *10 nm. The force constant of AFM cantilever is
calibrated from Sader’s method [20] such that spring
constant is directly computed from the measured resonant
frequency of such a cantilever. In this study, we have
employed the silicon cantilever whose calibrated force
constant is 34.5 N/m, otherwise specified. AFM images of
silicon nanowire is obtained from AFM tapping mode with
a scanning rate of 0.6 Hz and scan size in the range of
20 lm 9 20 lm to 500 nm 9 500 nm. Figure 2 shows the
AFM images of silicon nanowire and its cross-sectional
view. For reliable indentation of nanowires using AFM, we
have to insure that the sample is not rolled during the
212 Nanoscale Res Lett (2010) 5:211–216
123

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indentation. For such a reliable indentation, we have used
‘‘oscillation off’’ mode in Innova in order to turn off the
cantilever’s oscillation in tapping state. Further, the precise
probe positioning of AFM cantilever is attributed to the
closed-loop system. The reliable manipulation of AFM
cantilever due to ‘‘oscillation off’’ mode and precise probe
positioning enable us to acquire the vivid image of silicon
nanowire as well as the robust indentation response
recorded in load–displacement curve. Here, we have
applied a mechanical force until 800 nN with a loading rate
of 35 nm/s in order to insure that the indentation response
of nanowire resides in the linear elastic regime, which can
be depicted by classical Hertz theory.
A typical force-piezo displacement curve (F-z curve)
obtained from AFM nanoindentation of silicon nanowire is
shown in Fig. 3. It should be noted that the F-z curve is
independent of the indentation location where AFM can-
tilever is under contact with a nanowire. Specifically, as
shown in Fig. 3, we have confirmed that F-z curves
obtained from indentation at five different indentation
locations are identical to each other. This indicates that
mechanical response of a nanowire by nanoindentation
does not depend on the indentation location on a nanowire.
It should be recognized that the F-z curve does not directly
provide the relation between mechanical force and inden-
tation displacement, since the piezo displacement includes
both AFM cantilever bending deflection and indentation
displacement for a nanowire. Thus, because piezo dis-
placement is equal to summation of AFM cantilever
bending deflection and nanowire indentation displacement,
we have a relation of [21, 22]
?
where kAFMand kNWrepresent the force constants for AFM
cantileverandsilicon nanowire
respectively. Here, the force constant of AFM is estimated
as kAFM= 34. 5 N/m computed from Sader’s method.
Figure 4 depicts the force constant of silicon nanowire with
diameter of 525 nm obtained from AFM nanoindentation. It
is shown that the force constant of nanowire depends on the
applied force during indentation. In order to understand the
relationship between force constant of nanowire, kNW, and
applied force, F, we have employed the classical elasticity
theory such as Hertz theory, which provides the relationship
between applied force, F, and indentation displacement, s,
such as [23]
oF z ð Þ
oz
¼
1
kAFMþ
1
kNW
??1
ð1Þ
(for indentation),
F ¼4
Here,RistheAFMtipradius,andE*istheeffectiveYoung’s
modulusdefinedas
E*= [(1 - m1)/E1? (1 - m2)/
E2]-1, where Eiand miindicate the Young’s modulus and
the Poisson’s ratio for AFM tip (i = 1) or nanowire (i = 2),
3E?R1=2s3=2
ð2Þ
Fig. 1 a Transmission electron
microscopy (TEM) image of
nanowire and its tip. Energy
dispersive spectrometer (EDS)
analysis shows that nanowire
consists of silicon and that the
tip of nanowire is mostly
composed of silicon and nickel
that was used as a catalyst
during the chemical growth.
b TEM image of silicon
nanowire and its tip. TEM
image shows that silicon
nanowire is chemically grown
in the (111) direction, and so
does the tip of nanowire
Nanoscale Res Lett (2010) 5:211–216213
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respectively. As a consequence, the force constant for
nanowire as a function of mechanical force during an
indentation is given by
?
This indicates that the relationship between force constant
of nanowire during an indentation and applied force is well
described by scaling law such as kNW= aF1/3. It should be
noted that the scaling law for relationship between force
constant of nanowire for nanoindentation and applied force
is valid regardless of contact geometry (except the different
coefficient a) [21]. As shown in Fig. 4, the experimental
result showing the relation between nanowire’s stiffness
and force is well dictated by Eq. (3). This implies that our
nanoindentation experiments reside in the elastic regime as
long as applied force is in the range of 0\F\1 lN.
We have considered the mechanical properties of silicon
nanowires with various diameters in the range of *80 to
*600 nm in order to understand the any role of finite size
effect on the mechanical properties. From Hertz theory
described in Eq. 3, we have extracted the Young’s modulus
of silicon nanowires from the curves that show the rela-
tionship between force constant of nanowire and applied
force(e.g.,seeFig. 4).Figure 5showstheYoung’smodulus
of various nanowires with respect to their diameters. It is
kNW¼dF
ds¼ 6E?2RF
?1=3
ð3Þ
foundthatthediameterofnanowiredoesnotplayanyroleon
themechanicalpropertiesofnanowireifitsdiameterislarger
than *100 nm. This indicates that, for nanowires with their
diameter in the range of *80 to *600 nm, the Young’s
modulus of nanowires is close to that of bulk silicon in the
(111) direction. This is consistent with a recent study by Li
and coworker [24], who showed that elastic modulus of
Fig. 2 a Schematic illustration
of atomic force microscopy
(AFM) nanoindentation of
silicon nanowires. Laser beam
was used to measure the
cantilever bending deflection
(that can be converted to
mechanical force exerted by
AFM cantilever) during the
nanoindentation. b Typical
force-piezo displacement (F-z)
curve for AFM indentation of
nanowires. c The image of
silicon nanowire is obtained
from tapping-mode AFM. The
inset shows the scanning
electron microscopy (SEM)
image of silicon nanowires
chemically grown. d
Topological profile for cross
section of nanowire along the
line shown in (c)
Fig. 3 Force-piezo displacement (F-z) curves for five points in a
silicon nanowire. It is shown that F-z curves are identical to each
other, indicating that F-z curve is independent of position where AFM
tip contacts during the indentation
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123

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amorphous silicon nanowire is independent of its diameter
(intherangeof*80to*500 nm).Moreover,arecentstudy
by Boland and coworkers [5, 16] provides that the finite size
effect may not play a significant role on the mechanical
properties (e.g., elastic modulus) of nanowires. This is con-
sistentwithourfindingthatelasticmodulusofournanowires
is unaffected by their sizes and that Young’s modulus of
nanowires is close to that of bulk material. This implies that
the elastic modulus of bulk material can be employed for
design of nanomechanical devices using nanowires. How-
ever, it has to be reminded that the finite size effect does not
appearsince ournanowire hasthe diameterof[*80 nm.In
a recentstudyby Li and coworkers [25], the finite size effect
due to surface effect (e.g., surface stress effect) has played a
vital role on elastic modulus of nanowire (e.g., ZnO nano-
wire) with its diameter of *30 nm (?100 nm). Specifi-
cally,fordiameterlessthan*30 nm,thesurfaceeffectsuch
as surface stress reduces the elastic modulus of ZnO nano-
wire as its diameter is decreased [25]. In our case, the elastic
modulusof silicon nanowire with its diameter of *80 nm is
smaller than that of bulk silicon. This may imply that elastic
modulus of silicon nanowire may be reduced as its diameter
isdecreased[26].Itshould berecognizedthat the dimension
of our silicon nanowires is much larger than the critical
dimensionatwhichthesurfaceeffectdoesplayanimportant
role on elastic properties of nanowires. The role of surface
effect on the elastic properties of nanowires with a diameter
of *20 nm will be considered for our future study.
In conclusion, we have demonstrated the AFM nanoin-
dentation of nanowires for extracting their elastic modulus.
Specifically, we have employed the classical elasticity
theory (Hertz theory), which dictates the elastic response of
silicon nanowires to AFM indentation. It is shown that
Young’s modulus of silicon nanowires with their diameter
of *80 nm to *600 nm is independent of their diameters,
indicating that finite size effect due to surface effect does
not play any role on elastic properties of nanowires.
Moreover, the Young’s modulus of our nanowires with a
diameter in the range of[*100 nm is close to that of bulk
silicon. Therefore, the elastic modulus of bulk silicon can
be assumed for design of nanomechanical devices using
silicon nanowires with their diameters of[*100 nm.
Acknowledgments
and Engineering Foundation (KOSEF) under Grant No. 2009-0071246
(to K.E.), Korea Research Foundation (KRF) under Grant No. KRF-
2008-313-D00031(toT.K.),PioneerResearchCenterProgramthrough
NationalResearchFoundationofKoreaunderGrantNo.2009-0082820
(to Y.-S.S., and J.-H.L.), and KOSEF under Grant No. R11-2007-028-
03002 and Grant No. R01-2007-000-10497-0 (to S.N.).
This work supported in part by Korea Science
References
1. C.Q. Chen, Y. Shi, Y.S. Zhang, J. Zhu, Y.J. Yan, Phys. Rev. Lett.
96, 075505 (2006)
2. R.H. Baughman, C. Cui, A.A. Zakhidov, Z. Iqbal, J.N. Barisci,
G.M. Spinks, G.G. Wallace, A. Mazzoldi, D. De Rossi, A.G.
Rinzler, O. Jaschinski, S. Roth, M. Kertesz, Science 284, 1340
(1999)
3. C. Lee, X. Wei, J.W. Kysar, J. Hone, Science 321, 385 (2008)
4. L.T. Ngo, D. Almecija, J.E. Sader, B. Daly, N. Petkov, J.D.
Holmes, D. Erts, J.J. Boland, Nano Lett. 6, 2964 (2006)
5. B. Wu, A. Heidelberg, J.J. Boland, Nat. Mater. 4, 525 (2005)
6. A. Husain, J. Hone, H.W.C. Postma, X.M.H. Huang, T. Drake,
M. Barbic, A. Scherer, M.L. Roukes, Appl. Phys. Lett. 83, 1240
(2003)
7. X.L. Feng, R. He, P. Yang, M.L. Roukes, Nano Lett. 7, 1953
(2007)
Fig. 4 Stiffness of silicon nanowire, kNW, with its diameter of
525 nm as a function of indentation force, F. It is shown that the
relationship between kNWand F is well described by a scaling of
kNW= aF1/3, where a is a constant parameter depending on nanowire
geometry. It implies that nanoindentation of silicon nanowire is well
described by classical elasticity theory such as Hertz theory
Fig. 5 Young’s modulus of various silicon nanowires with their
diameters in the range of *100 to *600 nm extracted from AFM
indentation
Nanoscale Res Lett (2010) 5:211–216215
123

Page 6

8. K. Jensen, C. Girit, W. Mickelson, A. Zettl, Phys. Rev. Lett. 96,
215503 (2006)
9. J.S. Bunch, A.M. van der Zande, S.S. Verbridge, I.W. Frank,
D.M. Tanenbaum, J.M. Parpia, H.G. Craighead, P.L. McEuen,
Science 315, 490 (2007)
10. Y.T. Yang, C. Callegari, X.L. Feng, K.L. Ekinci, M.L. Roukes,
Nano Lett. 6, 583 (2006)
11. K. Eom, T.Y. Kwon, D.S. Yoon, H.L. Lee, T.S. Kim, Phys. Rev.
B 76, 113408 (2007)
12. K. Jensen, K. Kim, A. Zettl, Nat. Nanotechnol. 3, 533 (2008)
13. M. Zheng, K. Eom, C. Ke, J. Phys. D Appl. Phys. 42, 145408
(2009)
14. R. He, P. Yang, Nat. Nanotechnol. 1, 42 (2006)
15. A. Heidelberg, L.T. Ngo, B. Wu, M.A. Phillips, S. Sharma, T.I.
Kamins, J.E. Sader, J.J. Boland, Nano. Lett. 6, 1101 (2006)
16. B. Wen, J.E. Sader, J.J. Boland, Phys. Rev. Lett. 101, 175502
(2008)
17. J. He, C.M. Lilley, Nano Lett. 8, 1798 (2008)
18. B. Peng, M. Locascio, P. Zapol, S. Li, S.L. Mielke, G.C. Schatz,
H.D. Espinosa, Nat. Nanotechnol. 3, 626 (2008)
19. M.H. Zhao, Z.-Z. Ye, S.X. Mao, Phys. Rev. Lett. 102, 045502
(2009)
20. J.E. Sader, J.W.M. Chon, P. Mulvaney, Rev. Sci. Instrum. 70,
3967 (1999)
21. I. Palaci, S. Fedrigo, H. Brune, C. Klinke, M. Chen, E. Riedo,
Phys. Rev. Lett. 94, 175502 (2005)
22. M. Lucas, W. Mai, R. Yang, Z.L. Wang, E. Riedo, Nano Lett. 7,
1314 (2007)
23. K.L. Johnson, Contact Mechanics (Cambridge University Press,
Cambridge, 1987)
24. H. Ni, X. Li, H. Gao, Appl. Phys. Lett. 88, 043108 (2006)
25. G. Wang, X. Li, Appl. Phys. Lett. 91, 231912 (2007)
26. Y. Zhu, F. Xu, Q. Qin, W. Y. Fung, W. Lu, Nano Lett. (2009).
doi:10.1021/nl902132w (in press)
216Nanoscale Res Lett (2010) 5:211–216
123