Two-scale asymptotic homogenization in a MEMS auxetic structure for over etch identification

The development and optimization of Micro electro-mechanical systems (MEMS) devices, due to their small size scale, require testing and precise characterization. As an example, over etch, which is the deviation between the designed masks and the effective dimensions of the suspended parts, strongly influences the performances of MEMS; therefore, to predict the correct functioning of the device its actual value must be carefully identified. In this work, we propose an efficient, time-saving tool to identify fabrication imperfections in MEMS devices. In particular, we replace the complex geometry of a MEMS mechanical filter with an equivalent homogeneous medium, whose linear-elastic effective properties are evaluated employing twoscale asymptotic homogenization and we identify the over etch by minimizing the relative error between experimental data and corresponding predictions obtained for different combinations of over etch.