Determination of elastic properties of MEMS materials using inverse solutions

The inverse solution of the problem of a hole in a plate was employed together with nanoscale deformation measurements on perforated freestanding MEMS-scale specimens to obtain the isotropic elastic constants of polycrystalline silicon. This method relied on full-field nanometric displacements acquired in the vicinity of circular, micron-sized perforations. The results for the elastic modulus and Poisson's ratio obtained this way agreed well with those from uniform tension experiments. The nanoscale displacements were obtained through Digital Image Correlation (DIG) analysis of Atomic Force Microscopy (AFM) images acquired at various applied loads. The accuracy in determining the elastic constants depended on the selection of the location for the acquisition of local displacements at the hole perimeter. Using numerical analysis the area of maximum compression provided the most accurate results for both Young's modulus (E= 155±6.6 GPa) and Poisson's ratio (v= 0.20±0.04) that agreed very well with measurements obtained from uniform tension tests. The advantage of this inverse problem approach is that both isotropic elastic constants were recovered from a very small material domain (10×10 um ²) with knowledge of the displacement field in only one direction.