A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling

This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural frequency, proof mass displacement, pull-in voltage, capacitance change, and Brownian noise equivalent acceleration (BNEA) are optimized simultaneously with respect to the geometric design parameters, environmental conditions, and microfabrication process constraints. The sampling design space is created using DACE based Latin hypercube sampling (LHS) technique and corresponding output responses are obtained using multiphysics coupled field electro–thermal–structural interaction based finite element method (FEM) simulations. The metamodels for the individual output responses are obtained using statistical GP analysis. The developed metamodels not only allowed to analyze the effect of individual design parameters on an output response, but to also study the interaction of the design parameters. An objective function, considering the performance requirements of the MEMS accelerometer, is defined and simultaneous multi-objective optimization of the output responses, with respect to the design parameters, is carried out by using a combined gradient descent algorithm and desirability function approach. The accuracy of the optimization prediction is validated using FEM simulations. The behavioral model of the final optimized MEMS accelerometer design is integrated with the readout electronics in the simulation environment and voltage sensitivity is obtained. The results show that the combined DACE and GP based design methodology can be an efficient technique for the design space exploration and optimization of multiphysics MEMS devices at the design phase of their development cycle.

[1]  J. Ramakrishnan,et al.  Structural design, analysis and DOE of MEMS-based capacitive accelerometer for automotive airbag application , 2020, Microsystem Technologies.

[2]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[3]  Meng Wang,et al.  Micro-Inertial-Aided High-Precision Positioning Method for Small-Diameter PIG Navigation , 2019, Advances in Human and Machine Navigation Systems.

[4]  H. Kahveci,et al.  An optimization study for rotorcraft avionics bay cooling , 2019, Aerospace Science and Technology.

[5]  Eung-Sug Lee,et al.  Application of Design of Experiment Method for Thrust Force Minimization in Step-feed Micro Drilling , 2008, Sensors.

[6]  Bruce E. Ankenman,et al.  Comparison of Gaussian process modeling software , 2016, 2016 Winter Simulation Conference (WSC).

[7]  Christophe Loussert,et al.  Optimization of Capacitive Acoustic Resonant Sensor Using Numerical Simulation and Design of Experiment , 2015, Sensors.

[8]  Rachel T. Johnson,et al.  Design and analysis for the Gaussian process model , 2009, Qual. Reliab. Eng. Int..

[9]  H. Toshiyoshi,et al.  A dual-axis MEMS capacitive inertial sensor with high-density proof mass , 2016 .

[10]  M. M. Saleem,et al.  Effect of environmental conditions and geometric parameters on the squeeze film damping in RF-MEMS switches , 2018, Analog Integrated Circuits and Signal Processing.

[11]  Tamal Mukherjee,et al.  Optimization-based synthesis of microresonators , 1998 .

[12]  Hong Yun Yang,et al.  Genetic Algorithm Based Multidisciplinary Design Optimization of MEMS Accelerometer , 2011 .

[13]  Soumen Mandal,et al.  MEMS accelerometer: From engineering to medicine , 2016, IEEE Potentials.

[14]  E. Sánchez-Sinencio,et al.  Gaussian-Process-Based Surrogate for Optimization-Aided and Process-Variations-Aware Analog Circuit Design , 2020, Electronics.

[15]  Pingfeng Wang,et al.  Reliability-based design optimization of crane bridges using Kriging-based surrogate models , 2019, Structural and Multidisciplinary Optimization.

[16]  Perpetual Hope Akwensi,et al.  Forecasting of Horizontal Gas Well Production Decline in Unconventional Reservoirs using Productivity, Soft Computing and Swarm Intelligence Models , 2018, Natural Resources Research.

[17]  Yunbo Shi,et al.  Design, fabrication and calibration of a high-G MEMS accelerometer , 2018, Sensors and Actuators A: Physical.

[18]  N. Mathivanan,et al.  Design of MEMS accelerometer based acceleration measurement system for automobiles , 2012 .

[19]  Chih-Yung Huang,et al.  Development of Dual-Axis MEMS Accelerometers for Machine Tools Vibration Monitoring , 2016 .

[20]  Javaid Iqbal,et al.  Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope , 2020, Micromachines.

[21]  L McKay,et al.  Engineering in Medicine , 1975, Springer Berlin Heidelberg.

[22]  Douglas C. Montgomery,et al.  Modified Desirability Functions for Multiple Response Optimization , 1996 .

[23]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[24]  Tayfun Akin,et al.  A Bulk-Micromachined Three-Axis Capacitive MEMS Accelerometer on a Single Die , 2015, Journal of Microelectromechanical Systems.

[25]  A. Khuri,et al.  Simultaneous Optimization of Multiple Responses Represented by Polynomial Regression Functions , 1981 .

[26]  Francesco Braghin,et al.  Topology optimization of 2D in-plane single mass MEMS gyroscopes , 2020, Structural and Multidisciplinary Optimization.

[27]  Mourad Benmessaoud,et al.  Optimization of MEMS capacitive accelerometer , 2013 .

[28]  Tayfun Akin,et al.  A new design and a fabrication approach to realize a high performance three axes capacitive MEMS accelerometer , 2016 .

[29]  Muhammad Zubair,et al.  Multiphysics design optimization of RF-MEMS switch using response surface methodology , 2018, Microelectron. J..

[30]  Timothy W. Simpson,et al.  On the Use of Statistics in Design and the Implications for Deterministic Computer Experiments , 1997 .

[31]  G. Andersson,et al.  A monolithic three-axial SOI-accelerometer with uniform sensitivity , 2005 .

[32]  Wei Cai,et al.  Efficient Yield Optimization for Analog and SRAM Circuits via Gaussian Process Regression and Adaptive Yield Estimation , 2018, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[33]  P. Naveena,et al.  Design, Modeling and Analysis of Perforated RF MEMS Capacitive Shunt Switch , 2019, IEEE Access.

[34]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[35]  M. M. Saleem,et al.  Design of experiments based factorial design and response surface methodology for MEMS optimization , 2015 .

[36]  Ronald N. Miles,et al.  Dynamic response of a tunable MEMS accelerometer based on repulsive force , 2019, Sensors and Actuators A: Physical.

[37]  Robson Pederiva,et al.  MEMS accelerometers for mechanical vibrations analysis: a comprehensive review with applications , 2018, Journal of the Brazilian Society of Mechanical Sciences and Engineering.

[38]  N. Kacem,et al.  Design and modeling of a MEMS accelerometer based on coupled mode-localized nonlinear resonators under electrostatic actuation , 2021 .

[39]  George Xereas,et al.  Wafer level vacuum encapsulated tri-axial accelerometer with low cross-axis sensitivity in a commercial MEMS Process , 2015 .

[40]  Jerome Sacks,et al.  Computer Experiments for Quality Control by Parameter Design , 1990 .

[41]  Felipe A. C. Viana,et al.  A Tutorial on Latin Hypercube Design of Experiments , 2016, Qual. Reliab. Eng. Int..

[42]  T. Gabrielson.  Mechanical-thermal noise in micromachined acoustic and vibration sensors , 1993 .

[43]  Javad Yavand Hasani,et al.  Design and optimization of fully differential capacitive MEMS accelerometer based on surface micromachining , 2018, Microsystem Technologies.

[44]  Sergiusz Łuczak.  Effects of Misalignments of MEMS Accelerometers in Tilt Measurements , 2014 .

[45]  Young-Hyun Ko,et al.  A New Loss Function-Based Method for Multiresponse Optimization , 2005 .

[46]  Pijush Samui,et al.  Utilization of Gaussian Process Regression for Determination of Soil Electrical Resistivity , 2014, Geotechnical and Geological Engineering.

[47]  M. Rasras,et al.  Design, modelling and characterization of comb drive MEMS gap-changeable differential capacitive accelerometer , 2021 .

[48]  Design of Experiments for Agriculture and the Natural Sciences , 2007 .

[49]  Aveek N. Chatterjee,et al.  An optimization technique for performance improvement of gap-changeable MEMS accelerometers , 2017 .