- Email: [email protected]
Deep-cryogenic treatment of ZnO nanowires
Materials Letters 100 (2013) 145–147
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Deep-cryogenic treatment of ZnO nanowires Marcello Cabibbo n Dipartimento di Ingegneria Meccanica e Scienze Matematiche (DIISM), Università Politecnica delle Marche, Via Brecce Bianche, 60131 - Ancona, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2013 Accepted 5 March 2013 Available online 15 March 2013
Deep-cryogenic treatment was performed on vertically aligned ZnO nanowires produced by metal organic chemical vapour deposition. The mechanical response of the nanowires was detected by nanoindentation tests. It was found that Young's modulus, the critical buckling stress and strain of individual nanowires is not significantly influenced by cryogenic exposure. Yet, Young's modulus of the bulk base ZnO, from which the nanowires are grown, halved after a deep-cryogenic treatment. & 2013 Elsevier B.V. All rights reserved.
Keywords: Deep-cryogenic treatment ZnO nanowires Young's modulus Hardness Nanoindentation
1. Introduction Zinc oxide (ZnO) has drawn considerable interest because of its semiconducting and piezoelectric properties [1–3]. In particular, a lot of attention has been paid to ZnO which has a self-organized one-dimensional structure: the so-called nanowires or nanowhiskers. Nanowires (NWs) actually constitute important semiconducting and piezoelectric materials that have various applications in the field of microelectronics [3–5]. Due to the reported high elastic modulus and high aspect ratio [6], a further potential application of ZnO NWs is that as tips for atomic force microscopy. On this ground, it is important to understand the mechanical characteristics of ZnO NWs [3]. Recently, many studies reported on the mechanical properties of ZnO NWs [7,8]. For most electronic applications, axial buckling of the NWs is a major concern. For this reason, the mechanical properties of ZnO and similar NWs have been extensively studied by tensile loading, bending, and buckling, using different techniques including nanoindentation [9,10]. In this research work, ZnO NWs were grown by MOCVD [10] in a Si-(100) substrate, and the influence of a deep-cryogenic treatment on the MOCVD ZnO NWs mechanical properties, such Young's modulus and hardness, were studied.
2. Experimental details A vertical chamber MOCVD system was employed for the catalyst-free synthesis of a highly (00.2)-oriented ZnO NWs and beneath ZnO film (20 μm-thick) system. High-purity diethyl zinc n
Tel. þ39 0712204728; fax: þ 39 0712204801. E-mail addresses: [email protected], [email protected]
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.03.010
(purity 4 99.99%) and N2O (purity 4 99.99%) were used as zinc and oxygen sources, respectively; nitrogen was used as the carrier gas. The ZnO NWs were grown via a two-step process. First, a thin nucleation layer of ZnO was grown at a temperature of 400 1C. Thence, ZnO NWs were grown on the annealed nucleation layer at a temperature of 650 1C and for a total duration of 30 min. The elastic properties and hardness of the vertical aligned ZnO NWs were measured by an indentation method [11,12] and a calibrated trapezoid load function [12]. The tip was pushed downward against the aligned NWs so that typically 70–80 individual NWs would be in contact with the tip. By measuring the force– displacement curve and the average number of NWs in contact with the tip, an average elastic modulus and hardness of the NWs was determined. A Hysitron©Inc. triboscope nanoindenter Ubi®-1, with a 3-sided pyramidal Berkovich tip, was used. The Si/ZnO NWs samples were subjected to a cryogenic treatment consisting of a cooling from room temperature to −196 1C at a rate of 1 1C/min, holding at −196 1C for 120 min, and a slow recovery-back to room temperature at the same rate used for the cooling process. Microscopy inspections were carried out using a Zeiss© Supra®-40 field emission scanning electron microscope (FESEM), operated at 5 KeV.
3. Results and discussion Fig. 1 shows a cross-section FESEM image recorded at a 301 tilt angle of the as-grown ZnO NWs. ZnO NWs are densely well-aligned with uniform diameter. Mean diameter, length and density of these hexagonal NWs were 80±5 nm, 1000±180 nm, and 7.15 109 cm−2, respectively (see Fig. 1 inset). Fig. 2 reports a top-view FESEM micrograph of the deep-cryogenic treated NWs after the nanoindentation test. NWs were severely
146
M. Cabibbo / Materials Letters 100 (2013) 145–147
distorted and collapsed to the base ZnO coating from which NWs were grown. Since these tests were destructive, several measurements were carried out at different loads and in different ZnO NWs regions to ascertain the reproducibility of the method. Results yield a full and reliable reproducibility of the method. Typical continuous load–unload force–displacement curves for as-grown and cryogenic treated NWs are shown in Fig. 3, where the pop-in event is highlighted. Results showed that the critical load for the first pop-in, which is the elastic-plastic threshold value, essentially varies in a 300–480 μN range, with a average value of 390±20 μN, in the as-grown ZnO NWs, and 360–480 μN range, with a average value of 410±8 μN, after deep-cryogenic treatment. Thence, the mean critical load did not change significantly after cryogenic treatment. As such, it resulted that the range of variability of the buckling critical load after cryogenic treatment is far more narrow and limited to the upper value range than that showed in the as-grown condition. The ranging values of the ZnO NWs critical load depend on the maximum applied load, and in most cases it rises with applied load, which ranged 1.0–3.5 mN. Fig. 3 also shows large displacement versus load in the load range Po Pcr, which denotes a large flexibility of the ZnO NWs. This behaviour was observed not only in the as-grown condition, but also, and surprisingly, after deep-cryogenic treatment. It is well known that the high flexibility of the ZnO NWs is attributed to the low dimension of the structure [5]. A further reason may be
due to the movement of the NWs at the free ends, as a perfect rigid support is impossible, which is therefore not influenced by the cryogenic treatment. The FESEM top-view, reported in Fig. 2, easily allows to estimate the average critical buckling load of an individual ZnO NW. Thus, the critical buckling load of a single ZnO NW is about 4.9±0.1 and 5.10±0.05 μN, in the as-grown and cryogenic treated conditions, respectively. The unchanged buckling load of ZnO NWs after deepcryogenic treatment is surely an unexpected and remarkable result. This means that no change in the elastic-plastic properties of the ZnO NWs is induced by a cryogenic treatment. The present findings, in the case of the as-grown ZnO NWs, are in good agreement with other previously reported data [7,13]. Following the classical theory of elasticity of solids [14], the critical buckling load for an ideal elastic column can be expressed as (Euler load): Pcr ¼π2EI/L2eff, where E is Young's modulus of an individual ZnO NW, I¼πD4/32 is the momentum of inertia, D is the mean NW diameter (this is taken as the outer circumference of the NW hexagonal section), Leff is the effective NW length, which, for a fixed-pinned “cylindrical” NW, is 0.7L, L being the mean NW length. The critical buckling strain is given by εcr ¼ scr/E, where the critical buckling stress scr ¼Pcr/A, A being the mean section area of the hexagonal NWs (A¼(3√3/8)D2). Table 1 compiles the single ZnO NW obtained values of Young's modulus, E, the critical buckling stress, scr, and strain, εcr, in the as-grown and deep-cryogenic treated conditions. The quite close Young's modulus values (86 GPa in the as-grown, and 90 GPa in the deep-cryogenic treated single ZnO NW) clearly indicate an almost irrelevant influence of the cryogenic treatment on the elastic modulus of the ZnO NWs. The values obtained here are reasonably close to the reported elastic modulus of single-crystal ZnO bulk coating, E ¼111 GPa [13]. Previously reported data [5,15] showed Young's modulus of ZnO NWs to decrease dramatically with increasing diameter,
Fig. 1. Cross-section FESEM of the as-grown hexagonal (inset) ZnO NWs.
Fig. 3. Representative load–displacement nanoindentation curves showing the pop-in event upon loading of the ZnO NWs in the as-grown condition, and after deep-cryogenic treatment.
Table 1 Single ZnO NW critical buckling load, Pcr; Young's modulus, E; stress, scr; and strain, εcr. Pcr, μN
Fig. 2. FESEM top-view of the deep-cryogenic treated ZnO NWs after a nanoindentation test (applied load of 7 mN).
As-grown Deep-cryogenic treated
E, GPa scr, MPa
4.90±0.10 86±2 5.10±0.05 90±1
εcr
Variation, %
1190±20 0.014±10−3 – 1240±10 0.014±10−3 4
M. Cabibbo / Materials Letters 100 (2013) 145–147
reaching the ZnO bulk value for diameters typically larger than 120 nm. This behaviour was attributed to a surface stiffening effect dominating at large surface-to-volume ratios [5]. Therefore, the lower mean E value of the NWs with respect to the bulk ZnO value, can be attributed to the present NWs mean diameter. The similar critical buckling stress in both conditions also means that hardness of individual ZnO NWs is not significantly influenced by the cryogenic treatment. Due to the fact that the Oliver and Pharr analysis determination of the coating Young's modulus and hardness are determined by the tangent at the starting point of the unloading curve, the obtained value results from both ZnO base and NWs. This holds unless the substrate of Si-(100) starts to contribute to the measurements, which is likely to occur for penetration depths approaching 20%–25% of the total coating thickness. In the present case, even the maximum applied load of 3.5 mN did not reach this limit (the penetration depth being of 3500 nm, under a ZnO base thickness of 20 μm and NWs ∼1 μm-long). The curve analysis showed that Young's modulus of as-grown NWs Eas-grown ¼ 115±25 GPa, which more than doubled after deepcryogenic treatment (Epost-cryo ¼320±10 GPa). On the other hand, hardness increased slightly in the deep-cryogenic treated condition, being Has-grown ¼ 4.4±0.4 GPa, and Has-grown ¼ 5.3±0.3 GPa. Base bulk ZnO coating E and H well agreed with literature data (see for instance [15]). Thence, the hardness-to-elastic modulus ratio, H/E, of the ZnO coating, constituted by the base and NWs coating, almost halved after cryogenic treatment. As reported above, since the ZnO individual stress and Young's modulus did increase by only 4% after deep-cryogenic treatment, the most part of reduction of Young's modulus is to be attributed to the bulk base ZnO coating. H/E∝sy/E, where sy is the yield stress of the ZnO coating, and it measures the maximum energy stored per unit volume by the coating. Thence, the bulk ZnO sy/E is induced to more than halved by the deep-cryogenic treatment, while, scr/E does not change for the ZnO NWs. According to Gurtin et al. [16], surface effect on nanoscale elements, such as the ZnO NWs, is believed to be the key feature at the basis of the H/E non-variation upon deep-cryogenic treatment. On the contrary, the maximum stored energy of the ZnO bulk coating halved after the deep-cryogenic treatment chiefly because of the crystallographic stiffness dramatic increment (doubled E). This effect evidently did not occur in any of the thin 1-D NWs.
147
4. Conclusions Deep-cryogenic treatment of MOCVD ZnO NWs did not impair the large flexibility of the as-grown NWs. It did not influence Young's modulus nor the critical buckling load, stress, and strain to a significant extent, while Young's modulus of the bulk ZnO base, from which the NWs were grown, halved after the deep-cryogenic treatment.
Acknowledgements The author is grateful to Prof. Brian Johnson (Fitzwilliam College, Dept. of Chemistry, University of Cambridge) for having delivered the material. Mr. D. Ciccarelli is acknowledged for his assistance in performing the cryogenic treatment. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Wang ZL. J Phys Condens Matter 2004;16:R829–58. Zhao M-H, Wang ZL, Mao SX. Nano Lett 2004;4:587–90. Wang ZL, Song JH. Science 2006;312:242–6. Al-Hilli S, Öst A, Strålfors P, Willander M. J Appl Phys 2007;102:084304. Chen CQ, Shi Y, Zhang YS, Zhu J, Yan YJ. Phys Rev Lett 2006;96:075505. Lee W, Jeong MC, Myoung JM. Acta Mater 2004;52:3949–57. Young SJ, Ji LW, Chang SJ, Fang TH, Hsueh TJ, Meen TH, et al. Nanotechnology 2007;18:225603. Riaz M, Nur O, Willander M, Klason P. Appl Phys Lett 2008;92:103118. Qi HJ, Teo KBK, Lau KKS, Boyce MC, Milne WI, Robertson J, et al. J Mech Phys Solids 2003;51:2213–37. Yu MF, Lourie O, Dyer MJ, Moloni K, Kelly TF, Ruoff RS. Science 2000;287:637–40. Oliver WC, Pharr GM. J Mater Res 1992;7:1564–83. Cabibbo M, Ricci P, Cecchini R, Rymuza Z, Sullivan J, Dub S, et al. Micron 2012;43:215–22. Mai WJ, Wang ZL. Appl Phys Lett 2006;89:073112. Timoshenko SP, Gere JM. Theory of elastic stability. New York: McGraw-Hill; 1961 p. 46. Coleman VA, Bradby JE, Jagadish C, Munroe P, Heo YW, Pearton SJ, et al. Appl Phys Lett 2005;86:203105. Gurtin ME, Weissműller J, Larché F. Phil Mag A 1998;78:1093–109.
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Deep-cryogenic treatment of ZnO nanowires Marcello Cabibbo n Dipartimento di Ingegneria Meccanica e Scienze Matematiche (DIISM), Università Politecnica delle Marche, Via Brecce Bianche, 60131 - Ancona, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2013 Accepted 5 March 2013 Available online 15 March 2013
Deep-cryogenic treatment was performed on vertically aligned ZnO nanowires produced by metal organic chemical vapour deposition. The mechanical response of the nanowires was detected by nanoindentation tests. It was found that Young's modulus, the critical buckling stress and strain of individual nanowires is not significantly influenced by cryogenic exposure. Yet, Young's modulus of the bulk base ZnO, from which the nanowires are grown, halved after a deep-cryogenic treatment. & 2013 Elsevier B.V. All rights reserved.
Keywords: Deep-cryogenic treatment ZnO nanowires Young's modulus Hardness Nanoindentation
1. Introduction Zinc oxide (ZnO) has drawn considerable interest because of its semiconducting and piezoelectric properties [1–3]. In particular, a lot of attention has been paid to ZnO which has a self-organized one-dimensional structure: the so-called nanowires or nanowhiskers. Nanowires (NWs) actually constitute important semiconducting and piezoelectric materials that have various applications in the field of microelectronics [3–5]. Due to the reported high elastic modulus and high aspect ratio [6], a further potential application of ZnO NWs is that as tips for atomic force microscopy. On this ground, it is important to understand the mechanical characteristics of ZnO NWs [3]. Recently, many studies reported on the mechanical properties of ZnO NWs [7,8]. For most electronic applications, axial buckling of the NWs is a major concern. For this reason, the mechanical properties of ZnO and similar NWs have been extensively studied by tensile loading, bending, and buckling, using different techniques including nanoindentation [9,10]. In this research work, ZnO NWs were grown by MOCVD [10] in a Si-(100) substrate, and the influence of a deep-cryogenic treatment on the MOCVD ZnO NWs mechanical properties, such Young's modulus and hardness, were studied.
2. Experimental details A vertical chamber MOCVD system was employed for the catalyst-free synthesis of a highly (00.2)-oriented ZnO NWs and beneath ZnO film (20 μm-thick) system. High-purity diethyl zinc n
Tel. þ39 0712204728; fax: þ 39 0712204801. E-mail addresses: [email protected], [email protected]
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.03.010
(purity 4 99.99%) and N2O (purity 4 99.99%) were used as zinc and oxygen sources, respectively; nitrogen was used as the carrier gas. The ZnO NWs were grown via a two-step process. First, a thin nucleation layer of ZnO was grown at a temperature of 400 1C. Thence, ZnO NWs were grown on the annealed nucleation layer at a temperature of 650 1C and for a total duration of 30 min. The elastic properties and hardness of the vertical aligned ZnO NWs were measured by an indentation method [11,12] and a calibrated trapezoid load function [12]. The tip was pushed downward against the aligned NWs so that typically 70–80 individual NWs would be in contact with the tip. By measuring the force– displacement curve and the average number of NWs in contact with the tip, an average elastic modulus and hardness of the NWs was determined. A Hysitron©Inc. triboscope nanoindenter Ubi®-1, with a 3-sided pyramidal Berkovich tip, was used. The Si/ZnO NWs samples were subjected to a cryogenic treatment consisting of a cooling from room temperature to −196 1C at a rate of 1 1C/min, holding at −196 1C for 120 min, and a slow recovery-back to room temperature at the same rate used for the cooling process. Microscopy inspections were carried out using a Zeiss© Supra®-40 field emission scanning electron microscope (FESEM), operated at 5 KeV.
3. Results and discussion Fig. 1 shows a cross-section FESEM image recorded at a 301 tilt angle of the as-grown ZnO NWs. ZnO NWs are densely well-aligned with uniform diameter. Mean diameter, length and density of these hexagonal NWs were 80±5 nm, 1000±180 nm, and 7.15 109 cm−2, respectively (see Fig. 1 inset). Fig. 2 reports a top-view FESEM micrograph of the deep-cryogenic treated NWs after the nanoindentation test. NWs were severely
146
M. Cabibbo / Materials Letters 100 (2013) 145–147
distorted and collapsed to the base ZnO coating from which NWs were grown. Since these tests were destructive, several measurements were carried out at different loads and in different ZnO NWs regions to ascertain the reproducibility of the method. Results yield a full and reliable reproducibility of the method. Typical continuous load–unload force–displacement curves for as-grown and cryogenic treated NWs are shown in Fig. 3, where the pop-in event is highlighted. Results showed that the critical load for the first pop-in, which is the elastic-plastic threshold value, essentially varies in a 300–480 μN range, with a average value of 390±20 μN, in the as-grown ZnO NWs, and 360–480 μN range, with a average value of 410±8 μN, after deep-cryogenic treatment. Thence, the mean critical load did not change significantly after cryogenic treatment. As such, it resulted that the range of variability of the buckling critical load after cryogenic treatment is far more narrow and limited to the upper value range than that showed in the as-grown condition. The ranging values of the ZnO NWs critical load depend on the maximum applied load, and in most cases it rises with applied load, which ranged 1.0–3.5 mN. Fig. 3 also shows large displacement versus load in the load range Po Pcr, which denotes a large flexibility of the ZnO NWs. This behaviour was observed not only in the as-grown condition, but also, and surprisingly, after deep-cryogenic treatment. It is well known that the high flexibility of the ZnO NWs is attributed to the low dimension of the structure [5]. A further reason may be
due to the movement of the NWs at the free ends, as a perfect rigid support is impossible, which is therefore not influenced by the cryogenic treatment. The FESEM top-view, reported in Fig. 2, easily allows to estimate the average critical buckling load of an individual ZnO NW. Thus, the critical buckling load of a single ZnO NW is about 4.9±0.1 and 5.10±0.05 μN, in the as-grown and cryogenic treated conditions, respectively. The unchanged buckling load of ZnO NWs after deepcryogenic treatment is surely an unexpected and remarkable result. This means that no change in the elastic-plastic properties of the ZnO NWs is induced by a cryogenic treatment. The present findings, in the case of the as-grown ZnO NWs, are in good agreement with other previously reported data [7,13]. Following the classical theory of elasticity of solids [14], the critical buckling load for an ideal elastic column can be expressed as (Euler load): Pcr ¼π2EI/L2eff, where E is Young's modulus of an individual ZnO NW, I¼πD4/32 is the momentum of inertia, D is the mean NW diameter (this is taken as the outer circumference of the NW hexagonal section), Leff is the effective NW length, which, for a fixed-pinned “cylindrical” NW, is 0.7L, L being the mean NW length. The critical buckling strain is given by εcr ¼ scr/E, where the critical buckling stress scr ¼Pcr/A, A being the mean section area of the hexagonal NWs (A¼(3√3/8)D2). Table 1 compiles the single ZnO NW obtained values of Young's modulus, E, the critical buckling stress, scr, and strain, εcr, in the as-grown and deep-cryogenic treated conditions. The quite close Young's modulus values (86 GPa in the as-grown, and 90 GPa in the deep-cryogenic treated single ZnO NW) clearly indicate an almost irrelevant influence of the cryogenic treatment on the elastic modulus of the ZnO NWs. The values obtained here are reasonably close to the reported elastic modulus of single-crystal ZnO bulk coating, E ¼111 GPa [13]. Previously reported data [5,15] showed Young's modulus of ZnO NWs to decrease dramatically with increasing diameter,
Fig. 1. Cross-section FESEM of the as-grown hexagonal (inset) ZnO NWs.
Fig. 3. Representative load–displacement nanoindentation curves showing the pop-in event upon loading of the ZnO NWs in the as-grown condition, and after deep-cryogenic treatment.
Table 1 Single ZnO NW critical buckling load, Pcr; Young's modulus, E; stress, scr; and strain, εcr. Pcr, μN
Fig. 2. FESEM top-view of the deep-cryogenic treated ZnO NWs after a nanoindentation test (applied load of 7 mN).
As-grown Deep-cryogenic treated
E, GPa scr, MPa
4.90±0.10 86±2 5.10±0.05 90±1
εcr
Variation, %
1190±20 0.014±10−3 – 1240±10 0.014±10−3 4
M. Cabibbo / Materials Letters 100 (2013) 145–147
reaching the ZnO bulk value for diameters typically larger than 120 nm. This behaviour was attributed to a surface stiffening effect dominating at large surface-to-volume ratios [5]. Therefore, the lower mean E value of the NWs with respect to the bulk ZnO value, can be attributed to the present NWs mean diameter. The similar critical buckling stress in both conditions also means that hardness of individual ZnO NWs is not significantly influenced by the cryogenic treatment. Due to the fact that the Oliver and Pharr analysis determination of the coating Young's modulus and hardness are determined by the tangent at the starting point of the unloading curve, the obtained value results from both ZnO base and NWs. This holds unless the substrate of Si-(100) starts to contribute to the measurements, which is likely to occur for penetration depths approaching 20%–25% of the total coating thickness. In the present case, even the maximum applied load of 3.5 mN did not reach this limit (the penetration depth being of 3500 nm, under a ZnO base thickness of 20 μm and NWs ∼1 μm-long). The curve analysis showed that Young's modulus of as-grown NWs Eas-grown ¼ 115±25 GPa, which more than doubled after deepcryogenic treatment (Epost-cryo ¼320±10 GPa). On the other hand, hardness increased slightly in the deep-cryogenic treated condition, being Has-grown ¼ 4.4±0.4 GPa, and Has-grown ¼ 5.3±0.3 GPa. Base bulk ZnO coating E and H well agreed with literature data (see for instance [15]). Thence, the hardness-to-elastic modulus ratio, H/E, of the ZnO coating, constituted by the base and NWs coating, almost halved after cryogenic treatment. As reported above, since the ZnO individual stress and Young's modulus did increase by only 4% after deep-cryogenic treatment, the most part of reduction of Young's modulus is to be attributed to the bulk base ZnO coating. H/E∝sy/E, where sy is the yield stress of the ZnO coating, and it measures the maximum energy stored per unit volume by the coating. Thence, the bulk ZnO sy/E is induced to more than halved by the deep-cryogenic treatment, while, scr/E does not change for the ZnO NWs. According to Gurtin et al. [16], surface effect on nanoscale elements, such as the ZnO NWs, is believed to be the key feature at the basis of the H/E non-variation upon deep-cryogenic treatment. On the contrary, the maximum stored energy of the ZnO bulk coating halved after the deep-cryogenic treatment chiefly because of the crystallographic stiffness dramatic increment (doubled E). This effect evidently did not occur in any of the thin 1-D NWs.
147
4. Conclusions Deep-cryogenic treatment of MOCVD ZnO NWs did not impair the large flexibility of the as-grown NWs. It did not influence Young's modulus nor the critical buckling load, stress, and strain to a significant extent, while Young's modulus of the bulk ZnO base, from which the NWs were grown, halved after the deep-cryogenic treatment.
Acknowledgements The author is grateful to Prof. Brian Johnson (Fitzwilliam College, Dept. of Chemistry, University of Cambridge) for having delivered the material. Mr. D. Ciccarelli is acknowledged for his assistance in performing the cryogenic treatment. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Wang ZL. J Phys Condens Matter 2004;16:R829–58. Zhao M-H, Wang ZL, Mao SX. Nano Lett 2004;4:587–90. Wang ZL, Song JH. Science 2006;312:242–6. Al-Hilli S, Öst A, Strålfors P, Willander M. J Appl Phys 2007;102:084304. Chen CQ, Shi Y, Zhang YS, Zhu J, Yan YJ. Phys Rev Lett 2006;96:075505. Lee W, Jeong MC, Myoung JM. Acta Mater 2004;52:3949–57. Young SJ, Ji LW, Chang SJ, Fang TH, Hsueh TJ, Meen TH, et al. Nanotechnology 2007;18:225603. Riaz M, Nur O, Willander M, Klason P. Appl Phys Lett 2008;92:103118. Qi HJ, Teo KBK, Lau KKS, Boyce MC, Milne WI, Robertson J, et al. J Mech Phys Solids 2003;51:2213–37. Yu MF, Lourie O, Dyer MJ, Moloni K, Kelly TF, Ruoff RS. Science 2000;287:637–40. Oliver WC, Pharr GM. J Mater Res 1992;7:1564–83. Cabibbo M, Ricci P, Cecchini R, Rymuza Z, Sullivan J, Dub S, et al. Micron 2012;43:215–22. Mai WJ, Wang ZL. Appl Phys Lett 2006;89:073112. Timoshenko SP, Gere JM. Theory of elastic stability. New York: McGraw-Hill; 1961 p. 46. Coleman VA, Bradby JE, Jagadish C, Munroe P, Heo YW, Pearton SJ, et al. Appl Phys Lett 2005;86:203105. Gurtin ME, Weissműller J, Larché F. Phil Mag A 1998;78:1093–109.