A multiscale-stochastic finite element approach to shock-induced polysilicon MEMS failure

The effects of mechanical shocks on polysilicon MEMS accelerometers are here investigated within the frame of a multi-scale finite element approach. To accurately model MEMS dynamics and possible failure events, three length-scales are explored: macroscale, characterized by stress waves propagating inside the package and eventually impinging upon sensor anchors; mesoscale, characterized by forced vibrations of the whole sensor; microscale, characterized by possible nucleation and propagation up to percolation of trans- and/or inter-granular cracks in highly stressed regions of the sensor. Focusing on microstructural features, we show that the morphology of the polysilicon film constituting the movable parts of the sensor does affect MEMS failure. Account taken of brittleness of polysilicon at room temperature, a Monte Carlo methodology is employed to assess the links between failure mode and: the orientation of the axes of elastic symmetry of each FCC silicon grain; the trans-granular strength and toughness anisotropy; the network of grain boundaries (GBs); the mechanical properties of GBs.