Abstract
Microscale uncertainties related to the geometry and morphology of polycrystalline silicon films, constituting the movable structures of micro electro-mechanical systems (MEMS), were investigated through a joint numerical/experimental approach. An on-chip testing device was designed and fabricated to deform a compliant polysilicon beam. In previous studies, we showed that the scattering in the input–output characteristics of the device can be properly described only if statistical features related to the morphology of the columnar polysilicon film and to the etching process adopted to release the movable structure are taken into account. In this work, a high fidelity finite element model of the device was used to feed a transitional Markov chain Monte Carlo (TMCMC) algorithm for the estimation of the unknown parameters governing the aforementioned statistical features. To reduce the computational cost of the stochastic analysis, a synergy of proper orthogonal decomposition (POD) and kriging interpolation was adopted. Results are reported for a batch of nominally identical tested devices, in terms of measurement error-affected probability distributions of the overall Young’s modulus of the polysilicon film and of the overetch depth.
Highlights
By combining electronic and structural components, micro electro-mechanical systems (MEMS)have been a successful example of micro-technology surpassing conventional ones for a variety of devices like e.g., accelerometers, magnetometers, scanners, pressure sensors and gyroscopes [1].the development of these devices involves relatively complicated steps, due to their small size scale
For ten devices randomly chosen from the same wafer, the proposed approach has been used to quantitatively assess the effective stiffness of the micro-cantilever and the overetch depth, the latter being defined as a defect in the in-plane geometry of the movable structure caused by fluctuations of temperature and etchant concentration [28] that lead to a real geometry of the device different from the target one
The movable structure was modeled with quadratic triangular elements with displacement degrees of freedom only, whereas the gaps at capacitors were discretized with linear elements featuring both displacement and voltage degrees of freedom
Summary
By combining electronic and structural components, micro electro-mechanical systems (MEMS). Common approaches to characterize process variations at the microscale are instead based on surface inspections through optical or scanning electron microscopy [19,20], or laser interferometry [21] These methods, even if characterized by a rather easy data reduction, are generally expensive and need the devices to be on open wafers, so that they are limited to pre-packaged testing. For ten devices randomly chosen from the same wafer, the proposed approach has been used to quantitatively assess the effective stiffness of the micro-cantilever and the overetch depth, the latter being defined as a defect in the in-plane geometry of the movable structure caused by fluctuations of temperature and etchant concentration [28] that lead to a real geometry of the device different from the target one Both polysilicon elastic properties and overetch depth were assumed isotropic in the plane of motion, in terms of their most probable values and through their scattering around the mean.
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