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

Abstract

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.

Stochastic Mechanical Characterization of Polysilicon MEMS: A Deep Learning Approach

“…The mean value and standard deviation for the obtained effective Young's modulus are: Under the Voigt assumption, = 150.0 GPa, = 5.5 GPa; under the Reuss assumption, = 148.1 GPa, = 5.4 GPa. An interesting feature of these results is that the mean values are very close to the average between the asymptotic Reuss and Voigt bounds; in [27], it was shown that the scattering in the solution around the mean is instead greatly affected by ℎ ⁄ . Similar results can also be attained for the other elastic moduli of the film, assumed to be in-plane isotropic (namely, transversely isotropic with the mentioned texture aligned with the out-of-plane direction) at varying ℎ ⁄ ratios.…”

A Stochastic Model to Describe the Scattering in the Response of Polysilicon MEMS

“…As far as the elasticity of the polysilicon film is concerned, a model was proposed in [18]. Since the morphology varies along the beam axis in an unpredictable way, a Monte Carlo analysis was resorted to define the effective value of 𝐸 to be adopted in Equation (1).…”

“…To speed-up the computation of the pdf of 𝐸, in [18] the pdfs for the elastic moduli given by the computational homogenization on the SVEs were fitted with lognormal distributions. In our analysis, we still allow for such pdfs even if they can introduce an approximation in the model.…”

“…In this work, we aim to extend and improve the former studies by accounting for some recent results described in [18], to feed a methodology able to account for local fluctuations of the imperfections in a more accurate and robust way. The improvement consists in subdividing the structural components subjected to the major deformation field into smaller blocks, locally upscaling the elastic properties and then assembling everything to stochastically describe the overall device response.…”

The Study of Reactive Ion Etching of Heavily Doped Polysilicon Based on HBr/O2/He Plasmas for Thermopile Devices

“…Polysilicon, including both undoped and heavily doped polysilicon, has many important applications in complementary metal oxide semiconductor (CMOS) and micro electro mechanical systems (MEMS) technologies [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. Compared to undoped polysilicon, heavily doped polysilicon has higher Seebeck coefficient, lower electrical resistivity and thermal conductivity.…”