Mechanical Properties of Silicon Nanowires
© to the authors 2009
Received: 2 June 2009
Accepted: 7 October 2009
Published: 27 October 2009
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.
KeywordsSilicon nanowire Elastic modulus Nanoindentation Atomic force microscope
Mechanical properties of nanostructures such as nanowires , carbon nanotubes (CNT) , and/or graphene  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 , and/or graphene  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  has reported that silicon nanowires possess the piezoresistive properties, indicating their potential in NEMS applications. Moreover, Roukes and coworkers  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  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 . Recent studies  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 . Moreover, extraction of elastic modulus of nanowires using resonance method (based on in situ TEM)  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.
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.
Young-Soo Sohn and Jinsung Park equally contributed to this work.
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.).
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- Jensen K, Kim K, Zettl A: Nat. Nanotechnol.. 2008, 3: 533. COI number [1:CAS:528:DC%2BD1cXhtVOqsLrL] 10.1038/nnano.2008.200View Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- 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 Article
- Johnson KL: Contact Mechanics. Cambridge University Press, Cambridge; 1987.
- Ni H, Li X, Gao H: Appl. Phys. Lett.. 2006, 88: 043108. Bibcode number [2006ApPhL..88d3108N] Bibcode number [2006ApPhL..88d3108N] 10.1063/1.2165275View Article
- Wang G, Li X: Appl. Phys. Lett.. 2007, 91: 231912. Bibcode number [2007ApPhL..91w1912W] Bibcode number [2007ApPhL..91w1912W] 10.1063/1.2821118View Article
- Zhu Y, Xu F, Qin Q, Fung WY, Lu W: Nano Lett.. 2009. 10.1063/1.2821118