Modeling of gold microbeams as strain and pressure sensors for characterizing MEMS packages

This work presents the modeling of gold microbeams for characterizing Micro-electro-mechanical systems (MEMS) packages in terms of both strains induced to the MEMS devices and hermetic sealing capability. The proposed test structures are based on arrays of rectangular-shaped clamped-free and clamped–clamped beams, to be realized with a film of electroplated gold by surface micromachining technology. 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 of the square of the resonant frequency in case of in-plane deformations, in fairly good agreement with an approximate analytical model. Cantilever beams are modeled as variable capacitors to detect out-of-plane deformations. Finally, an analytical model to study cantilever beams as resonators for detecting pressure changes is discussed and compared with preliminary experimental results, showing an impact on the quality factor in a range from 10⁻² mbar to 1 bar.