Uncertainty quantification of microstructure-governed properties of polysilicon MEMS

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.