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

Abstract

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.

Mechanical Characterization of Polysilicon MEMS: A Hybrid TMCMC/POD-Kriging Approach

“…Such a statistically determinate mechanical scheme of the movable structure was devised to reduce to a minimum the effects of residual stresses on the measured response to the actuation. Although a slight in-plane offset of the rotor can be induced by gradients of the residual stress field inside the polysilicon film, such effect can be considered negligible (see [ 24 , 25 ]). The target geometrical characteristics of the tested devices are summarized in Table 1 .…”

“…In this work, only the aforementioned purely bending one is investigated, to focus on the statistics and dispersion of the results induced by micromechanical features and by the measurement noise. Additional details on this device and on its response to the actuation can be found in [ 23 , 24 , 25 , 30 , 31 , 32 ].…”

“…In this paper, following our former works [ 23 , 24 , 25 ], a methodology is proposed to deal with the response of an on-chip testing device. The method is based upon standard electrical probing, and aims to stochastically characterize geometrical and material properties of polysilicon films through a flexible and powerful data reduction technique.…”

“…Within a stochastic framework, the experimental results are interpreted by means of a transitional Markov chain Monte Carlo (TMCMC) analysis, to also account for the effects of measurement errors on the estimation of the unknown parameters ruling geometrical and material uncertainties. A high fidelity, finite element (FE) model of the testing device was adopted to properly represent the complexity of the system, potentially in terms of the polysilicon morphology too [ 25 ]. Since the handling of FE simulations is prohibitive in a TMCMC analysis, a parametric model order reduction method was proposed to reduce the computational effort, preserving the required accuracy of the solution.…”

Polysilicon MEMS Sensors: Sensitivity to Sub-Micron Imperfections

“…The drive towards miniaturization in the MEMS industry leads unavoidably to questions of homogeneity, which is commonly accepted from the continuum mechanics perspective. For polysilicon films, grain morphology and orientation eventually influence the mechanical response of MEMS devices when critical structural components (such as the suspension springs) are downsized [1][2][3][4][5][6]. Moreover, the deep reactive-ion etching process, leading to so-called over-etch [7] whose relevance gets increased when referred to dimensions comparable with the grain size, affects the accuracy of the geometrical layout [8].…”