A Study On Uncertainty Quantification Of Process Deviation Based On MEMS Multilayered Thin Films

With the increasing complexity of Micro Electro-Mechanical System(MEMS)design,it is more and more difficult to control the process accurately.The uncertainty of the geometric size and mechanical parameters of MEMS devices caused by the process deviation may lead to the deviation of the operating state and performance parameters from the design target.In order to achieve MEMS robust engineering design and optimal decision,it is necessary to quantify the impact of uncertainty on the performance of complex systems with efficient stochastic solvers.Therefore,in order to realize accurate prediction of MEMS structural performance parameters and yield,the possible process deviation is taken into account in the initial stage of device design,and the optimal design is proposed to shorten the development cycle and reduce the production cost,aiming to develop the devices and systems with low sensitivity to process deviation and high yield.In this dissertation,the uncertainty quantification of MEMS multilayered thin films with process deviation is mainly studied.The three-layer cantilever beam and two-layer doublyclamped beam based on Pizeo MUMPS process are taken as the research objects,and the uncertainty quantification algorithm of the resonance frequency of multilayered thin films with random process deviation is proposed.At the same time,the uncertainty quantification algorithm is applied to the in-situ testing of mechanical parameters,that provides suggestion for the optimization design of MEMS multilayered film structure.The main work and innovations of this dissertation are described as following:Firstly,based on the elastic theory of multilayered thin films and the boundary conditions of different multilayered thin films,the resonant model of three-layer cantilever beam and twolayer doubly-clamped beam is established,and then the rationality and accuracy of the model are proved by using the finite element simulation tool COMSOL.At the same time,the error accuracy between the exact solution and the approximate solution of the resonance model is compared,and it is found that the approximation of the model has a slight impact on the resonance characteristics of the large-size beam.In order to balance the time and accuracy of the numerical calculation,the approximate model is used for the large-size beam,while the accurate model is still used for the small-size beam,which provides a theoretical basis for quantifying the uncertainty of the resonance frequency on the multilayered thin films.Secondly,the uncertainty quantification of the resonance frequency on multilayered thin films with the random process deviation is studied on three-layer cantilever beam as the research object.Due to the different accuracy of the approximate analytical formula,the research is divided into two aspects.The large-size beam chooses the explicit and analytic approximate expression,while the small-size beam uses the partial differential equation which can not be solved directly.The multi-dimensional Polynomial Interpolation Fitting algorithm(PIF)and the Stochastic Barycenter Interpolation Collocation method(SBICM)are used for the uncertainty analysis of the resonance frequency respectively.The results are compared with Monte Carlo Simulation(MCS),and the probability density distribution of resonance frequency and yield are predicted efficiently and accurately.Meanwhile,in order to improve the yield of the small size beam,a design optimization for the size parameters is proposed,which effectively improves the yield of the structures based on the process line.Finally,a novel in-situ extracting method for Young’s modulus and residual stresses of multilayered thin films by measuring the resonant frequencies of two-layer doubly-clamped beam is developed.Without considering the process deviation of the multilayered thin films thickness,the Optimized Newton Downhill method(OND)solves the problem of memory overflow during the iteration process,accelerates the convergence speed,and improves the efficiency and accuracy of the iteration.Considering the process deviation of the multilayered thin films thickness,the OND algorithm and the PIF algorithm are combined to successfully predict the random distribution of Young’s modulus and residual stresses of each layer.At last,the in-situ extracting algorithm and multilayered thin films test structure are optimized to get more accurate extraction results and more stable test structure.