A Poisson-Voronoi-based finite element stress analysis of resonating polysilicon micromachines

The development of reliable miniaturized devices capable of performing sensing, actuation, and computing functions in a robust manner strongly depends on the mechanical performance of arrays of micromachines subjected to alternating stresses during operation. Consequently, to enhance the functionality and longevity of these micromachines, it is essential to accurately determine the structural behavior under both static and dynamic loadings. However, this requires knowledge of the stress distribution and variation due to texture anisotropy effects in critical micromachine regions and insight into the material behavior at micrometer length scales. Accordingly, the objective of this study was to develop an effective computational mechanics framework for performing stress analysis of micromachines at resonance. Dynamic finite element analysis of resonating micromachines was performed to elucidate the effect of material damping on the dynamic response. A Poisson-Voronoi diagram was incorporated in the critical region of finite element models of polysilicon micromachines to mimic the local inhomogeneity and anisotropy of the polycrystalline microstructure. A computationally effective static finite element analysis of the steady-state resonant response, validated by the results of the dynamic analysis, was used to obtain the steady-state stress distribution in the critical region of polysilicon micromachines with different textures. Moreover, a probabilistic stress analysis of hundreds of simulations was carried out to examine the stochastic nature of the grain geometry, size, and orientation and the beam width on the maximum equivalent von Mises stress in the critical micromachine region. The present study provides an efficient computational methodology, which integrates local texture into continuum mechanics modeling, for performing stress analysis of dynamic microdevices exhibiting different polycrystalline microstructures.