Fatigue crack growth in polysilicon microstructures subjected to multi-axial loading: A Poisson–Voronoi-based finite element analysis

Abstract

Polycrystalline silicon (polysilicon) is the most commonly used structural material of microscopic electromechanical devices, such as sensors and actuators. Almost all of these miniaturized devices contain mechanical elements experiencing high-frequency loading cycles. Due to the rapidly accumulating loading cycles and very small thicknesses of these microstructures, basic understanding of fatigue crack growth in polysilicon at the microscale is critical to the design of durable microdevices that satisfy application requirements. In this investigation, fatigue crack growth in a typical polysilicon microstructure subjected to multi-axial loading was analyzed with the finite element method. To account for the inherent heterogeneity and anisotropy of polysilicon at the microscale, a Poisson-Voronoi tessellation was incorporated in the highly stressed region of the resonating microdevice to model a polycrystalline microstructure. Simulation results illuminated the effect of local texture on the direction and rate of crack growth. Transgranular or intergranular crack growth were predicted, depending on the angle between the crack-path direction and the grain boundary and the fracture resistance of the grain and the grain boundary. From a fundamental fracture mechanics perspective, the computational approach developed in this study provides a capability for examining the effect of local texture anisotropy on cracking in polycrystalline microstructures.