Multi-scale simulation of shock-induced failure of polysilicon MEMS

MEMS are often exposed to accidental shocks during service, specially when mounted on portable devices. The effects of shocks on polysilicon MEMS are here investigated within the framework of a multi-scale finite element approach. To accurately model MEMS failure, at least three length-scales need in fact to be explored: a macro-scale (package length-scale), characterized by stress waves propagating inside the package and impinging upon sensor anchors; a meso-scale (sensor length-scale), characterized by forced vibrations of the MEMS sensor as a whole; a micro-scale (polycrystal length-scale), characterized by nonlinear, dissipative processes like the nucleation and propagation of trans- and inter-granular cracks in the polysilicon film constituting critical regions of the sensor. Within such multi-scale problem, length-scale interactions can be disregarded because of the small ratio between sensor and package masses, and because of the brittleness of polysilicon at room temperature. At the bottom level, to understand whether crystal morphology affects MEMS failure, a stochastic (like e.g. a Monte Carlo) methodology is mandatory to appropriately handle: the orientation of the axes of elastic symmetry of each silicon grain; the topology of the the network of grain boundaries in the region surrounding the failing detail; the possible presence of defective grain boundaries. Micro-scale analyses thus turn out to be time consuming. We therefore compare the results obtained by three-scale simulations, wherein micro-scale features are fully accounted for, to results of two-scale simulations (with micro-scale analyses dropped), wherein homogenized (micro-mechanically informed) strength and toughness properties of the polysilicon are adopted. We show that, when the sensor layout causes localized failures, micro-scale simulations do not add significant information; from an industrial point of view it thus proves sufficient to span only the macro-scopic and meso-scopic length-scales to capture the effect of shock loadings on the MEMS.