Finite element analysis of nanowire indentation on a flat substrate
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Nanowires have attracted tremendous research interests due to their potential applications. Their mechanical properties are critical for the reliability and durability of the nanowire-based devices. Compared to many other characterization techniques, the lateral probing of a nanowire using nanoindentation has the advantage of relatively simple sample preparation. However, the data analysis is difficult due to the complex contact mechanics. In all previous studies, some questionable approximations have been made to proceed with data analysis. In this study, a quantitative physical picture of nanowire lateral probing is proposed, which we believe is the first time in the literature. Three-dimensional finite element analysis (FEA) is performed and compared to a double-contact analytical model in which the two contacts, namely contact 1 (indenter/nanowire) and contact 2 (nanowire/substrate), are considered. Both the FEA and analytical models are for a specific case: an elastic spherical indention of a GaN nanowire on a Si substrate. We find that contact 1 cannot be well approximated by a Hertzian elliptical contact as assumed in many studies. We also find a large contact deformation at contact 2, which has been ignored in almost all previous studies. Finally, the adhesion condition and nanowirereceding at contact 2 are found to have insignificant effects on the data analysis.
I. INTRODUCTION
Nanowires and nanotubes have wide range of potential applications, such as chemical and optical sensors,1,2 resonators and force sensors,3,4 high-resolution scanning probe microscope (SPM) tips,5 and reinforcements for nanocomposites.6,7 To design the devices composed of these nanomaterials, it is essential to know their behavior and properties, e.g., mechanical properties for the applications of force sensors, SPM tips, and nanocomposites. Mechanical characterization at such small scales is very challenging. Nanoindenter and atomic force microscope have been successfully used to laterally indent nanowires and nanotubes,8–18 whereas the associated rigorous analytical solution is not available due to the complex contact mechanics.9 Consequently, approximations were made in these previous studies8–18 to proceed with indentation data analysis. However, some of the approximations may be problematic: (i) treating the nanomaterial as half-space (using the Oliver–Pharr method19 for data analysis),10,14,15 (ii) neglecting the contact deformation between the nanomaterial and substrate,11,16 and (iii) neglecting the possibility of receding (the ends of the nanomaterial being
a)
Present address: Department of Engineering, The University of Texas at Brownsville and Texas Southmost College, 80 Fort Brown, Brownsville, Texas 78520 b) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.420 586
J. Mater. Res., Vol. 27, No. 3, Feb 14, 2012
separated from the substrate).8,10–18 To take account of the aforementioned effects, Feng et al. have proposed a double-contact (two contacts in series) model9: contact 1
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