Measurement of nanodisplacements and elastic properties of MEMS via the microscopic hole method

The objective of this paper is to demonstrate the application of the microscopic hole method as an alternative approach to assess the elastic properties of polycrystalline silicon freestanding thin films employed in microelectromechanical system (MEMS) devices. This method relies on the inverse solution of the problem of a hole in a plate. When accurate and repeatable full-field nanometric displacements are acquired in the vicinity of circular, micron-sized perforations, the elastic modulus and Poisson's ratio computed via this method agree well with those obtained from uniform tension experiments. In this work, the nanoscale displacements were obtained through a digital image correlation (DIC) analysis of atomic force microscopy (AFM) images acquired at various applied loads. The accuracy in determining both elastic constants hinges upon the selection of the optimum location at the hole perimeter for the acquisition of local displacements. Using a numerical analysis, the area of maximum compression was determined to provide the most accurate determination of Young's modulus (E = 155 ± 6.6 GPa) and Poisson's ratio (ν = 0.20 ± 0.04) which agreed very well with measurements obtained from uniform tension tests. The advantage of this hole method, an inverse problem approach, is that both isotropic elastic constants can be recovered from very small material domains (10 μm × 10 μm or smaller) with knowledge of the displacement field in only one direction.