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Simultaneous determination of the Young's modulus and Poisson's ratio in micro/nano materials

Li, L. and Polido Gomes, J.F. and Brown, J.G. and Uttamchandani, D.G. and Pan, W. and Weiland, D. and Begbie, M. and Lowrie, C. and Desmulliez, M.P.Y. (2009) Simultaneous determination of the Young's modulus and Poisson's ratio in micro/nano materials. Journal of Micromechanics and Microengineering, 19 (12). ISSN 0960-1317

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Abstract

Among the various mechanical properties of materials used in the manufacturing of micro/nano devices, the Young's modulus and Poisson's ratio are very important. These parameters determine the static and dynamic characteristics of micro/nano devices such as the force-deflection relationship and resonant frequencies. In the past, the Young's modulus of materials has been measured by the force-deflection method [1-4]. The Poisson's ratio was separately determined using the deflection method [5], nano-indentation method [6] or by using atomic force microscopy [7]. The resonant method permits the simultaneous extraction of the Young's modulus and Poisson's ratio [8, 9]; however, this method requires prior knowledge of the density of the material to determine the equivalent mass of the test structure, and this value may vary greatly if different processes are used for forming the material. A method that integrates atomic force microscopy (AFM) with digital image correlation (DIC) has also been reported to simultaneously extract the Young's modulus and Poisson's ratio [10], and more thorough and expanded work related to [10] was reported in [11-14]. The Young's modulus of thin film materials has been measured using the force-deflection method where the deflection was measured using an optical interferometer [15]. Determination of material properties of microcantilevers has also been reported by integrating interferometrically measured deflection data from electrostatically actuated microcantilevers with a numerical finite difference model [16]. The Young's modulus of silicon material has also been extracted using a purely optical method [17, 18]. Sharpe [19] summarized some of the progress in the area of experimental determination of mechanical properties of micrometer size sensors and actuators over the past 15 years. In this paper, a new cross-shaped structure is designed for extracting both the Poisson's ratio and Young's modulus simultaneously, based on the force-deflection approach, without the need for a priori density information of the test material. A KLA-Tencor Alpha-Step IQ Surface Profiler is used both for exerting forces on the test structure and measuring the resultant deflections. A series of analytical equations are derived for extracting the Young's modulus and Poisson's ratio based on beam mechanics. There are two main steps in the analysis. First, the Young's modulus is extracted from a clamped-clamped beam with a vertical load in the centre. In the second step, the Poisson's ratio is measured by exerting a vertical force on the tip of the 'cross' beam. The second step uses the value of the Young's modulus extracted from the first step. Accordingly this paper is organized as follows: the design of the cross-shaped structure and derivation of the analytical formulae for extracting the Young's modulus and Poisson's ratio are described in section 2. Fabrication and experimental results are presented in section 3. An established method for measuring the Young's modulus to validate the new approach is described in section 4. Section 5 concludes with the main findings of this paper.