Modeling of gold microbeams for characterizing MEMS packages

Modeling of gold microbeams for characterizing MEMS packaging solutions in terms of strains induced to the MEMS devices as well as hermetic sealing capability is presented. The proposed test structures are meant to be manufactured by the surface micromachining front-end technology available at FBK. They are based on arrays of rectangular-shaped cantilever beams as well as clamped-clamped bridges, with a width of 20 μm and a length ranging from 100 to 400 μm, to be realized by a 2 μm thick film of electroplated gold. The resonant frequency of the microbeams is modeled by FEM simulations as a function of substrate deformations, which could be induced by the package. Clamped-clamped bridges show a linear change with respect to the square of the resonant frequency up to 1800 ppm/μstrain in case of in-plane deformations. The impact of temperature excursions is also simulated, in order to use these structures for assessing thermally induced deformations. Cantilever beams are modeled as variable capacitors to detect out-of-plane deformations. Finally, both an analytical model and FEM simulations are used to study cantilever beams as resonators for detecting pressure changes, showing an impact on the quality factor in a range from 1-2 bar down to 10^-3-10^-2 mbar