The Study On MEMS Microphone Model Based On Artificial Neural Network

Micro-electro-mechanical system(MEMS)is the micro-system based on microelectronic technology and modern information technology,which integrates micromachining and precise machining.MEMS microphone is the sensor that converts audio signal into electrical signal.Compared with traditional microphone,MEMS microphone has some advantages of thermal stability,excellent frequency response,small size and low power comsumption.MEMS microphone modeling involves multiple disciplines,and the complex mechanical sturcture and multi-physical field coupling lead to a large amount of consumption of computing resources for accurate simulation.Therefore,the improvement of simulation efficiency is the hotspots of MEMS microphone modeling.Recent,there are some types of MEMS microphone model,including lumped parameter model(LPM),finite element model(FEM)and macro-model.The physical meanings are clear and the equations are simple in the lumped parameter model with high simulation efficiency.However,when the diaphragm deflection is in the nonlinear range,the simulation errors become larger.Finite element model can simualte the performance of diaphragm in any shape,and the simulation accuracy is high.But,the sensitivity simulation of finely meshed diaphragm consumes a lot of computing resources,the simulation efficiency is very low.If the diaphragm structure changes obviously,the simulation should be done again.Micro-model extracts the key physical properties of MEMS microphone,which is suitable for system simulation.However,it belongs to reduced order model,the simulation accuracy of which is low.In order to solve these problems of recent models,this paper represents the MEMS microphone model based on artificial neural network(ANN).The contributions include:(1)MEMS microphone model based on artificial neural networkANN is adopted to establish model of MEMS microphone.The inputs of model include the geometry and material parameters of diaphragm,and the output is the sensitivity.In this study,eight different types of microphones are designed,including square and circular clamped diaphragm made from three materials,slotted and notched polysilicon diaphragm.Three kinds of materials include polysilicon,Si C and Si O₂.The samples simulated by Ansys software that employs the finite element method are used to train the ANNs.The single calculation time of the trained ANN model is 0.6 seconds,and the root mean square error(RMSE)is found to be less than 1%.Compared with the finite element model of MEMS microphone,the simulation efficiency increases by more than 500 times.Take polysilicon clamped diaphragm microphone for example,the influences of training data quantity and network architecture on simulation accuracy are studied in this paper.The ANN with single hidden layer and 5 hidden neurons,which is trained by 30 data,is the optimal model of clamped diaphragm microphone.(2)Uncertainty analysis of sensitivity of MEMS microphone based on ANN modelDue to the defects from manufacturing processes,MEMS microphone may exhibit significant variations in structure and material compared to the nominal design,which always lead to the sensitivity uncertainty.In this study,the Monte Carlo simulation(MCS)based on ANN model is presented to analyze the sensitivity uncertainty of polysilicon circular clamped diaphragm microphone.The research objectives includ qualified rate,sensitivity probability density and the sensitivities of diaphragm parameters.Using the probabilistic design system(PDS)and MC simulation to predict the qualified rate of microphone,the simulated results are 91.2%and 91.4%respectively.The qualified rate of manufactured microphones is 91.5%.In addition,two different methods are used to simulate sensitivity probability density.The relative error of mean value is 0.4%,and the relative error of standard error is 3.6%.the time-consuming of these two methods are about 12minutes and 3000 minutes,the simulation efficiency increases by 300 times.This paper also studies the change of sensitivity probability densities with the varieties of nominal parameters of diaphragm.As the radius increases,the means and deviations keep a increasing tendency.Differently,the means and deviations decrease with the increase of thickness.The change of young modulus only affects the mean values of sensitivity probability density,but has no influence on the deviations.Using the linear regression of MC samples,the sensitivities of diaphragm parameters are analyzed in thia paper.The results show that the design values influence the sensitivities of diaphragm parameters significantly.When the diaphragm parameters are constant,three main factors affecting the distribution of microphone sensitivity in order from strength to weakness are radius,thickness,and young modulus.This dissertation designs and manufactures the polysilicon circular clamped diaphragm microphones,and measures the sensitivity probability density of microphones.The radius and thickness of diaphragm are 1mm and 10?m respectively.The cavity height is 1mm,and air-gap distance is 30?m.The materials of diaphragm,substrate and insulation are polysilicon,Si and Si O₂ respectively.10000 microphones are fabricated and the sensitivity probability density of these microphones is measured.The error between test and simulation results is less than 2%.Therefore,the presented MCS with accuracy and high efficiency is an alternative to the traditional methods.In order to further improve simulation efficiency,Latin hypercube Monte Carlo Simulation(LHMCS)is proposed to analyze sensitivity uncertainty.Results show that the amount of samples of LHMCS is only 11%of traditional MCS at the same accuracy.The time-consuming of these two methods are about 10 seconds and 12 minutes respecvively,the simulation efficiency increases by 12 times.(3)A new multi-objective optimization algorithm for sensitivity probability densityIn order to improve both mean value and standard error of sensitivity probability density,this paper presents a new Monte Carlo simulation-non-dominated sorting genetic algorithm(MCS-NSGA)hybrid algorithm based on artificial neural network.ANN model calculates the sensitivity,and MCS subprogram simulates the parameters of sensitivity probability density,including the mean value and standard deviation.NSGA is the core program of multi-objective optimization,which finds the Pareto optimal solution set iteratively.When radius,thickness and young modulus take 0.85 mm,8.01?m and 171 GPa,the sensitivity probability density reach the optimal value.The mean value,standard deviation and qualified rate are 1.026,0.0527 and 94.3%,respectively.Compared with the initial design,for the optimal point,sensitivity increases 8.8%,standard deviation decreases 7.5%and qualified rate improves 3.1%.Therefore,the multi-objective optimization algorithm for sensitivity probability density is accurate and efficient.In brief,MEMS microphone model based on ANN is built in this study,which combined with Monte Carlo simulation is adopted to analyze the sensitivity uncertainty of microphone.This paper designs and produces the polysilicon circular clamped diaphragm microphone,and measures the sensitivity probability density.The comparison between simulation and testing results show that the MCS based on ANN model is accuracy and efficient to analyze sensitivity uncertainty.In order to further improve simulation efficiency,LHMCS is proposed to analyze sensitivity uncertainty.This paper also presents a new multi-objective optimization algorithm for sensitivity probability density of MEMS microphone.The improvements of sensitivity and qualified rate shows that the new algorithm is effective.