MEMS Reliability: On-Chip Testing for the Characterization of the Out-of-Plane Polysilicon Strength.

Polycrystalline silicon is a brittle material, and its strength results are stochastically linked to microscale (or even nanoscale) defects, possibly dependent on the grain size and morphology. In this paper, we focus on the out-of-plane tensile strength of columnar polysilicon. The investigation has been carried out through a combination of a newly proposed setup for on-chip testing and finite element analyses to properly interpret the collected data. The experiments have aimed to provide a static loading to a stopper, exploiting electrostatic actuation to move a massive shuttle against it, up to failure. The failure mechanism observed in the tested devices has been captured by the numerical simulations. The data have been then interpreted by the Weibull theory for three different stopper sizes, leading to an estimation of the reference out-of-plane strength of polysilicon on the order of 2.8-3.0 GPa, in line with other results available in the literature.

An Experimental and Numerical Study on Glass Frit Wafer-to-Wafer Bonding.

A thermo-mechanical wafer-to-wafer bonding process is studied through experiments on the glass frit material and thermo-mechanical numerical simulations to evaluate the effect of the residual stresses on the wafer warpage. To experimentally characterize the material, confocal laser profilometry and scanning electron microscopy for surface observation, energy dispersive X-ray spectroscopy for microstructural investigation, and nanoindentation and die shear tests for the evaluation of mechanical properties are used. An average effective Young's modulus of 86.5 ± 9.5 GPa, a Poisson's ratio of 0.19 ± 0.02, and a hardness of 5.26 ± 0.8 GPa were measured through nanoindentation for the glass frit material. The lowest nominal shear strength ranged 1.13 ÷ 1.58 MPa in the strain rate interval to 0.33 ÷ 4.99 × 10-3 s-1. To validate the thermo-mechanical model, numerical results are compared with experimental measurements of the out-of-plane displacements at the wafer surface (i.e., warpage), showing acceptable agreement.

A New Approach for the Control and Reduction of Warpage and Residual Stresses in Bonded Wafer.

A geometrical modification on silicon wafers before the bonding process, aimed to decrease (1) the residual stress caused by glass frit bonding, is proposed. Finite element modeling showed that (2) by introducing this modification, the wafer out-of-plane deflection was decreased by 34%. Moreover, (3) fabricated wafers with the proposed geometrical feature demonstrated an improvement for the (4) warpage with respect to the plain wafers. A benefit for curvature variation and overall shape of the (5) bonded wafers was also observed.

Effect of Imperfections Due to Material Heterogeneity on the Offset of Polysilicon MEMS Structures.

Monte Carlo analyses on statistical volume elements allow quantifying the effect of polycrystalline morphology, in terms of grain topology and orientation, on the scattering of the elastic properties of polysilicon springs. The results are synthesized through statistical (lognormal) distributions depending on grain size and morphology: such statistical distributions are an accurate and manageable alternative to numerically-burdensome analyses. Together with this quantification of material property uncertainties, the effect of the scattering of the over-etch on the stiffness of the supporting springs can also be accounted for, by subdividing them into domains wherein statistical fluctuations are assumed not to exist. The effectiveness of the proposed stochastic approach is checked with the problem of the quantification of the offset from the designed configuration, due to the residual stresses, for a statically-indeterminate MEMS structure made of heterogeneous (polycrystalline) material.

Statistical Investigation of the Mechanical and Geometrical Properties of Polysilicon Films through On-Chip Tests.

In this work, we provide a numerical/experimental investigation of the micromechanics-induced scattered response of a polysilicon on-chip MEMS testing device, whose moving structure is constituted by a slender cantilever supporting a massive perforated plate. The geometry of the cantilever was specifically designed to emphasize the micromechanical effects, in compliance with the process constraints. To assess the effects of the variability of polysilicon morphology and of geometrical imperfections on the experimentally observed nonlinear sensor response, we adopt statistical Monte Carlo analyses resting on a coupled electromechanical finite element model of the device. For each analysis, the polysilicon morphology was digitally built through a Voronoi tessellation of the moving structure, whose geometry was in turn varied by sampling out of a uniform probability density function the value of the over-etch, considered as the main source of geometrical imperfections. The comparison between the statistics of numerical and experimental results is adopted to assess the relative significance of the uncertainties linked to variations in the micro-fabrication process, and the mechanical film properties due to the polysilicon morphology.

Physically-based reduced order modelling of a uni-axial polysilicon MEMS accelerometer.

In this paper, the mechanical response of a commercial off-the-shelf, uni-axial polysilicon MEMS accelerometer subject to drops is numerically investigated. To speed up the calculations, a simplified physically-based (beams and plate), two degrees of freedom model of the movable parts of the sensor is adopted. The capability and the accuracy of the model are assessed against three-dimensional finite element simulations, and against outcomes of experiments on instrumented samples. It is shown that the reduced order model provides accurate outcomes as for the system dynamics. To also get rather accurate results in terms of stress fields within regions that are prone to fail upon high-g shocks, a correction factor is proposed by accounting for the local stress amplification induced by re-entrant corners.

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.

Modeling Impact-induced Failure of Polysilicon MEMS: A Multi-scale Approach.

Failure of packaged polysilicon micro-electro-mechanical systems (MEMS) subjected to impacts involves phenomena occurring at several length-scales. In this paper we present a multi-scale finite element approach to properly allow for: (i) the propagation of stress waves inside the package; (ii) the dynamics of the whole MEMS; (iii) the spreading of micro-cracking in the failing part(s) of the sensor. Through Monte Carlo simulations, some effects of polysilicon micro-structure on the failure mode are elucidated.

Multi-scale Analysis of MEMS Sensors Subject to Drop Impacts.

The effect of accidental drops on MEMS sensors are examined within the frame-work of a multi-scale finite element approach. With specific reference to a polysilicon MEMSaccelerometer supported by a naked die, the analysis is decoupled into macro-scale (at dielength-scale) and meso-scale (at MEMS length-scale) simulations, accounting for the verysmall inertial contribution of the sensor to the overall dynamics of the device. Macro-scaleanalyses are adopted to get insights into the link between shock waves caused by the impactagainst a target surface and propagating inside the die, and the displacement/acceleration his-tories at the MEMS anchor points. Meso-scale analyses are adopted to detect the most stresseddetails of the sensor and to assess whether the impact can lead to possible localized failures.Numerical results show that the acceleration at sensor anchors cannot be considered an ob-jective indicator for drop severity. Instead, accurate analyses at sensor level are necessary toestablish how MEMS can fail because of drops.