Two-scale vs three-scale FE analyses of shock-induced failure in polysilicon MEMS

Shock-induced failure of polysilicon MEMS is investigated by adopting a multi-scale approach. To understand the capability of this approach and to assess its accuracy, we compare the failure forecasted through two-scale and three-scale simulations. In the first case we model the response of the device to the shocks at the package level (macroscopic scale) and at the sensor level (mesoscopic scale). In the latter case we also allow for micro-structural features of the polysilicon film constituting the movable parts of the MEMS, so as to track the failure mode. Focusing on a commercial off-the-shelf uniaxial accelerometer subject to drops, results of the three-scale approach show that the micro-cracking leading to failure is confined inside a rather narrow region close to the anchor points. Outcomes of the two-scale approach correctly match this evidence, provided an appropriately defined failure criterion for the anisotropic polysilicon film is adopted. Moreover, the time to failure predicted by the two approaches well agree. Therefore, while the three-scale approach furnishes much insights on the failure mode, the overall response of the sensor appears to be correctly (from an industrial perspective) estimated by the far simpler and more economic two-scale simulations.