# Mechanical Properties of Silicon Nanowires

- Young-Soo Sohn
^{1}, - Jinsung Park
^{2}, - Gwonchan Yoon
^{2}, - Jiseok Song
^{2}, - Sang-Won Jee
^{3}, - Jung-Ho Lee
^{3}, - Sungsoo Na
^{2}, - Taeyun Kwon
^{4}Email author and - Kilho Eom
^{2}Email author

**5**:211

**DOI: **10.1007/s11671-009-9467-7

© to the authors 2009

**Received: **2 June 2009

**Accepted: **7 October 2009

**Published: **27 October 2009

## 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.

### Keywords

Silicon nanowire Elastic modulus Nanoindentation Atomic force microscopeMechanical 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 electromechanical 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 piezoresistive 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, 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 modulus (Young’s modulus) and/or the yield strength of nanowires. A recent study [17] has showed that simply supported boundary condition for double-clamped nanowire 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 experiment 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 nanowires, 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 attributed 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.

^{−6}Torr. After ultrasonic cleaning in acetone, samples (with dimension of 1 × 1 cm

^{2}) were placed into a quartz tube reactor in which H

_{2}gas (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 NiS

_{ x }agglomerates. 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 SiCl

_{4}as a source gas at atmospheric pressure. Here, SiCl

_{4}allows the superior epitaxial growth of nanowires on the Si substrate compared to SiH

_{4}, attributed to the fact that the byproduct of HCl from SiCl

_{4}induces the etching effect of any oxides as well as the noncatalytic sidewall deposition. Here, the decomposition temperature of SiCl

_{4}is compatible with the Ni–Si eutectic temperature (966 °C). Silicon nanowires were in situ axially grown by introduction of SiCl

_{4}(10 sccm) and H

_{2}(200 sccm) under 950–1,000 °C for catalyst liquefaction. Figure 1 shows the TEM image of chemically grown silicon nanowire with a diameter of ~200 nm. Energy dispersive spectrometer (EDS) analysis shows that our nanowires are well chemically grown. Further, EDS analysis provides that the tip of nanowire consists of Ni and Si, indicating that the catalysis Ni is solidified, so that NiSi

_{2}is formed at the tip of silicon nanowire. As shown in Fig. 1, TEM analysis confirms the chemical grown of silicon nanowire in (111) direction. NiSi

_{2}formed at nanowire tip is established in epitaxial growth in (111) direction (see Fig. 1). For mechanical characterization of silicon nanowires, we have employed the silicon nanowires with length of >1 μm in order to remove the effect of NiSi

_{2}at nanowire tip on the mechanical properties of silicon nanowires.

*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 cantilever 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 indentation displacement, since the piezo displacement includes both AFM cantilever bending deflection and indentation displacement for a nanowire. Thus, because piezo displacement is equal to summation of AFM cantilever bending deflection and nanowire indentation displacement, we have a relation of [21, 22]

*k*

_{AFM}and

*k*

_{NW}represent the force constants for AFM cantilever and silicon nanowire (for indentation), respectively. Here, the force constant of AFM is estimated as

*k*

_{AFM}= 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,

*k*

_{NW}, 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]

*R*is the AFM tip radius, and

*E*

^{*}is the effective Young’s modulus defined as

*E*

^{*}= [(1 −

*ν*

_{1})/

*E*

_{1}+ (1 − ν

_{2})/

*E*

_{2}]

^{−1}, where

*E*

_{ i }and

*ν*

_{ i }indicate the Young’s modulus and the Poisson’s ratio for AFM tip (

*i*= 1) or nanowire (

*i*= 2), respectively. As a consequence, the force constant for nanowire as a function of mechanical force during an indentation is given by

*k*

_{NW}= α

*F*

^{1/3}. 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 α) [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 μN.

In conclusion, we have demonstrated the AFM nanoindentation 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.

## Misc

Young-Soo Sohn and Jinsung Park equally contributed to this work.

## Declarations

### Acknowledgments

This work supported in part by Korea Science and Engineering Foundation (KOSEF) under Grant No. 2009-0071246 (to K.E.), Korea Research Foundation (KRF) under Grant No. KRF-2008-313-D00031 (to T.K.), Pioneer Research Center Program through National Research Foundation of Korea under Grant No. 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.).

## Authors’ Affiliations

## References

- Chen CQ, Shi Y, Zhang YS, Zhu J, Yan YJ:
*Phys. Rev. Lett.*. 2006,**96:**075505. COI number [1:STN:280:DC%2BD283gtFCqsg%3D%3D]; Bibcode number [2006PhRvL..96g5505C] 10.1103/PhysRevLett.96.075505View ArticleGoogle Scholar - Baughman RH, Cui C, Zakhidov AA, Iqbal Z, Barisci JN, Spinks GM, Wallace GG, Mazzoldi A, De Rossi D, Rinzler AG, Jaschinski O, Roth S, Kertesz M:
*Science*. 1999,**284:**1340. COI number [1:CAS:528:DyaK1MXjs1Wjtb4%3D]; Bibcode number [1999Sci...284.1340B] 10.1126/science.284.5418.1340View ArticleGoogle Scholar - Lee C, Wei X, Kysar JW, Hone J:
*Science*. 2008,**321:**385. COI number [1:CAS:528:DC%2BD1cXosVOrs7k%3D]; Bibcode number [2008Sci...321..385L] 10.1126/science.1157996View ArticleGoogle Scholar - Ngo LT, Almecija D, Sader JE, Daly B, Petkov N, Holmes JD, Erts D, Boland JJ:
*Nano Lett.*. 2006,**6:**2964. COI number [1:CAS:528:DC%2BD28Xht1Slsr3F]; Bibcode number [2006NanoL...6.2964N] 10.1021/nl0619397View ArticleGoogle Scholar - Wu B, Heidelberg A, Boland JJ:
*Nat. Mater.*. 2005,**4:**525. COI number [1:CAS:528:DC%2BD2MXlvFOjurk%3D]; Bibcode number [2005NatMa...4..525W] 10.1038/nmat1403View ArticleGoogle Scholar - Husain A, Hone J, Postma HWC, Huang XMH, Drake T, Barbic M, Scherer A, Roukes ML:
*Appl. Phys. Lett.*. 2003,**83:**1240. COI number [1:CAS:528:DC%2BD3sXmtFOksbw%3D]; Bibcode number [2003ApPhL..83.1240H] 10.1063/1.1601311View ArticleGoogle Scholar - Feng XL, He R, Yang P, Roukes ML:
*Nano Lett.*. 2007,**7:**1953. COI number [1:CAS:528:DC%2BD2sXmslGjtb0%3D]; Bibcode number [2007NanoL...7.1953F] 10.1021/nl0706695View ArticleGoogle Scholar - Jensen K, Girit C, Mickelson W, Zettl A:
*Phys. Rev. Lett.*. 2006,**96:**215503. COI number [1:STN:280:DC%2BD28zptVyisw%3D%3D]; Bibcode number [2006PhRvL..96u5503J] 10.1103/PhysRevLett.96.215503View ArticleGoogle Scholar - Bunch JS, van der Zande AM, Verbridge SS, Frank IW, Tanenbaum DM, Parpia JM, Craighead HG, McEuen PL:
*Science*. 2007,**315:**490. COI number [1:CAS:528:DC%2BD2sXotFCjtw%3D%3D]; Bibcode number [2007Sci...315..490B] 10.1126/science.1136836View ArticleGoogle Scholar - Yang YT, Callegari C, Feng XL, Ekinci KL, Roukes ML:
*Nano Lett.*. 2006,**6:**583. COI number [1:CAS:528:DC%2BD28Xit1OrsLg%3D]; Bibcode number [2006NanoL...6..583Y] 10.1021/nl052134mView ArticleGoogle Scholar - Eom K, Kwon TY, Yoon DS, Lee HL, Kim TS:
*Phys. Rev. B*. 2007,**76:**113408. Bibcode number [2007PhRvB..76k3408E] Bibcode number [2007PhRvB..76k3408E] 10.1103/PhysRevB.76.113408View ArticleGoogle Scholar - Jensen K, Kim K, Zettl A:
*Nat. Nanotechnol.*. 2008,**3:**533. COI number [1:CAS:528:DC%2BD1cXhtVOqsLrL] 10.1038/nnano.2008.200View ArticleGoogle Scholar - Zheng M, Eom K, Ke C:
*J. Phys. D Appl. Phys.*. 2009,**42:**145408. Bibcode number [2009JPhD...42n5408Z] Bibcode number [2009JPhD...42n5408Z] 10.1088/0022-3727/42/14/145408View ArticleGoogle Scholar - He R, Yang P:
*Nat. Nanotechnol.*. 2006,**1:**42. COI number [1:CAS:528:DC%2BD28XhtFCisrrJ]; Bibcode number [2006NatNa...1...42H] 10.1038/nnano.2006.53View ArticleGoogle Scholar - Heidelberg A, Ngo LT, Wu B, Phillips MA, Sharma S, Kamins TI, Sader JE, Boland JJ:
*Nano. Lett.*. 2006,**6:**1101. COI number [1:CAS:528:DC%2BD28XksFWiu70%3D]; Bibcode number [2006NanoL...6.1101H] 10.1021/nl060028uView ArticleGoogle Scholar - Wen B, Sader JE, Boland JJ:
*Phys. Rev. Lett.*. 2008,**101:**175502. Bibcode number [2008PhRvL.101q5502W] Bibcode number [2008PhRvL.101q5502W] 10.1103/PhysRevLett.101.175502View ArticleGoogle Scholar - He J, Lilley CM:
*Nano Lett.*. 2008,**8:**1798. COI number [1:CAS:528:DC%2BD1cXmsVKhur4%3D]; Bibcode number [2008NanoL...8.1798H] COI number [1:CAS:528:DC%2BD1cXmsVKhur4%3D]; Bibcode number [2008NanoL...8.1798H] 10.1021/nl0733233View ArticleGoogle Scholar - Peng B, Locascio M, Zapol P, Li S, Mielke SL, Schatz GC, Espinosa HD:
*Nat. Nanotechnol.*. 2008,**3:**626. COI number [1:CAS:528:DC%2BD1cXht1SlurjO] 10.1038/nnano.2008.211View ArticleGoogle Scholar - Zhao MH, Ye Z-Z, Mao SX:
*Phys. Rev. Lett.*. 2009,**102:**045502. COI number [1:STN:280:DC%2BD1M7ot12qsA%3D%3D]; Bibcode number [2009PhRvL.102d5502Z] 10.1103/PhysRevLett.102.045502View ArticleGoogle Scholar - Sader JE, Chon JWM, Mulvaney P:
*Rev. Sci. Instrum.*. 1999,**70:**3967. COI number [1:CAS:528:DyaK1MXmt1yhtr4%3D]; Bibcode number [1999RScI...70.3967S] 10.1063/1.1150021View ArticleGoogle Scholar - Palaci I, Fedrigo S, Brune H, Klinke C, Chen M, Riedo E:
*Phys. Rev. Lett.*. 2005,**94:**175502. COI number [1:STN:280:DC%2BD2MzgsV2rtQ%3D%3D]; Bibcode number [2005PhRvL..94q5502P] 10.1103/PhysRevLett.94.175502View ArticleGoogle Scholar - Lucas M, Mai W, Yang R, Wang ZL, Riedo E:
*Nano Lett.*. 2007,**7:**1314. COI number [1:CAS:528:DC%2BD2sXktlChsLc%3D]; Bibcode number [2007NanoL...7.1314L] 10.1021/nl070310gView ArticleGoogle Scholar - Johnson KL:
*Contact Mechanics*. Cambridge University Press, Cambridge; 1987.Google Scholar - Ni H, Li X, Gao H:
*Appl. Phys. Lett.*. 2006,**88:**043108. Bibcode number [2006ApPhL..88d3108N] Bibcode number [2006ApPhL..88d3108N] 10.1063/1.2165275View ArticleGoogle Scholar - Wang G, Li X:
*Appl. Phys. Lett.*. 2007,**91:**231912. Bibcode number [2007ApPhL..91w1912W] Bibcode number [2007ApPhL..91w1912W] 10.1063/1.2821118View ArticleGoogle Scholar - Zhu Y, Xu F, Qin Q, Fung WY, Lu W:
*Nano Lett.*. 2009. 10.1063/1.2821118Google Scholar