Uncertainty Quantification of Microstructure—Governed Properties of Polysilicon MEMS

Abstract

In this paper, we investigate the stochastic effects of the microstructure of polysilicon films on the overall response of microelectromechanical systems (MEMS). A device for on-chip testing has been purposely designed so as to maximize, in compliance with the production process, its sensitivity to fluctuations of the microstructural properties; as a side effect, its sensitivity to geometrical imperfections linked to the etching process has also been enhanced. A reduced-order, coupled electromechanical model of the device is developed and an identification procedure, based on a genetic algorithm, is finally adopted to tune the parameters ruling microstructural and geometrical uncertainties. Besides an initial geometrical imperfection that can be considered specimen-dependent due to its scattering, the proposed procedure has allowed identifying an average value of the effective polysilicon Young’s modulus amounting to 140 GPa, and of the over-etch depth with respect to the target geometry layout amounting to O=−0.09 μm. The procedure has been therefore shown to be able to assess how the studied stochastic effects are linked to the scattering of the measured input–output transfer function of the device under standard working conditions. With a continuous trend in miniaturization induced by the mass production of MEMS, this study can provide information on how to handle the foreseen growth of such scattering.

Estimation of Air Damping in Out-of-Plane Comb-Drive Actuators

“…In the proposed analysis, the geometry of the fluid domain has been considered deterministically known. Stochastic effects induced by micro-fabrication, see, e.g., [27,28,29,30,31], have been therefore disregarded, though they may modify the solution by affecting the gap between rotor and stator. Within the current analytical frame, by partially allowing for the finite geometry of comb-drives, stochastic effects induced by microfabrication can be accounted for rather easily, to provide confidence intervals for the damping coefficient.…”

Stochastic Effects on the Dynamics of the Resonant Structure of a Lorentz Force MEMS Magnetometer

“…As the width h of the film depends on the over-etch depth induced by the micro-fabrication process (see [15][16][17]) a discussion pertinent to this effect is provided in Section 4.…”

“…As far as is concerned, for each value of ℎ the lognormal distribution best fitting the results of the numerical homogenization of Section 3 has been adopted; we recall that, depending on the type of BCs, relevant values of mean and standard deviation are reported in Table 1. As for the over-etch, in accordance with former studies [15,16] its distribution has been assumed to be Gaussian, centered around the reference condition = 0; the corresponding standard deviation has been set to = 0.05 μm, so that the range −0.15 μm ≤ ≤ 0.15 μm inspected in the previous parametric analysis represents the 99.7% confidence interval. The output of the stochastic analysis is shown in Figures 7 and 8 for ℎ = 2 μm and ℎ = 3 μm, respectively, in terms of the nondimensional values of .…”

“…Focusing on the operational conditions of micro-devices, an on-chip test procedure was proposed in [15,16]. To avoid accounting for the additional effects of residual stresses possibly induced by micro-fabrication, the movable structure was purposely designed as statically determinate.…”

Polysilicon MEMS Sensors: Sensitivity to Sub-Micron Imperfections

“…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]. Under these conditions, the expected spread in the operational behavior of the devices is a matter of concern both for MEMS design and reliability [9,10].…”