Roberto Martini

Two-Scale Simulation of Drop-Induced Failure of Polysilicon MEMS Sensors

In this paper, an industrially-oriented two-scale approach is provided to model the drop-induced brittle failure of polysilicon MEMS sensors. The two length-scales here investigated are the package (macroscopic) and the sensor (mesoscopic) ones. Issues related to the polysilicon morphology at the micro-scale are disregarded; an upscaled homogenized constitutive law, able to describe the brittle cracking of silicon, is instead adopted at the meso-scale. The two-scale approach is validated against full three-scale Monte-Carlo simulations, which allow for stochastic effects linked to the microstructural properties of polysilicon. Focusing on inertial MEMS sensors exposed to drops, it is shown that the offered approach matches well the experimentally observed failure mechanisms.

A Finite Element Flux-Corrected Transport Method for Wave Propagation in Heterogeneous Solids

When moving discontinuities in solids need to be simulated, standard finite element (FE) procedures usually attain low accuracy because of spurious oscillations appearing behind the discontinuity fronts. To assure an accurate tracking of traveling stress waves in heterogeneous media, we propose here a flux-corrected transport (FCT) technique for structured as well as unstructured space discretizations. The FCT technique consists of post-processing the FE velocity field via diffusive/antidiffusive fluxes, which rely upon an algorithmic length-scale parameter. To study the behavior of heterogeneous bodies featuring compliant interphases of any shape, a general scheme for computing diffusive/antidiffusive fluxes close to phase boundaries is proposed too. The performance of the new FE-FCT method is assessed through one-dimensional and two-dimensional simulations of dilatational stress waves propagating along homogeneous and composite rods.

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.

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.