微机电系统级建模与仿真研究
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摘要
微机电系统(MEMS)是目前迅速发展的多学科技术交叉领域,但存在 MEMS 产品开发周期长、成本高的问题,设计水平远滞后于制造水平,导致 MEMS 产品不能形成规模。因此当前 MEMS 设计方法和设计工具研究已成为国际上 MEMS 研究的重点, 而微机电系统的建模和仿真技术是实现 MEMS 计算机虚拟设计的关键。
本文采用集总参数建模思想,建立了 NODAS 单元模型库,用于 MEMS 的系统仿真和设计。NODAS 模型库包括系列模型单元(二维、三维线性梁、几何非线性梁、锚点、质量块、静电间隙、静电梳齿、复合热梁、电热梁等),其行为模型由MAST 硬件描述语言描述。本文给出了库中所有单元的物理建模和仿真验证,模型由 ANSYS 有限元模拟验证准确性,误差均在 5%以内。实现在 EDA 电路仿真器SABER 环境下,由原理图可视化构建 MEMS 系统,进行 MEMS 系统层次的建模和仿真,并提出基于 MAST 单元库的 MEMS 系统结构参数化设计流程和验证方法。
本文 NODAS MAST 库模型建模和系统仿真可支持结构、静电、热学等多物理场分析,能与电路兼容,满足复杂系统仿真的精度要求,为 MEMS 系统的快速设计提供了高效的验证方法,易于实现对设计结构的优化。
作者另一项工作为微机械薄膜在静电力和 Casimir 力作用下的稳定性研究,研究了 Casimir 效应对薄膜横向偏移影响。由数值方法计算得到了决定薄膜稳定性的参数 K 及 K 曲线临界值 KC,并提供了设计高长厚比(L/h)的静电薄膜结构的方法。
Microelectromechancial systems is a manufacturing technology of multi- discipline which develops rapidly. At present, the high cost and long design cycle of MEMS products restrict the growing due to the comparatively low design level. Thus, the design of methodology MEMS and CAD tools have been great significances in international MEMS researches with important theoretical and applied value. System-level modeling and simulations are the key issues to realize computer-aid virtual design of MEMS.
This thesis presents a NODAS (Nodal Design of Acutators and Sensors) library for simulation and design of suspended MEMS. NODAS is a library of a series of low-level elements (2D, 3D beams, nonlinear beams, anchors, plate masses, electrostatic gaps, combs, eletrothermal beams, et al). The lumped parameterized behavioral models are implemented in MAST, which is an analog hardware description language. All the detail model dervations and verification simulations are given. The NODAS simulation of element models showed more than 95% accuracy of ANSYS simulation. In an EDA simulator SABER, system-level simulations of MEMS devices are based on the schematics composed of the MAST elements. A structural parameterized design flow and verification methodology of MEMS based on the MAST elements library are presented. The key issues of this thesis include modeling physics, schematic representation, accuracy verification, application examples.
Modeling and system-level simulation based on the MEMS behavioral models enable the structural, electrostatic and thermal multi-field analysis and are compatible with circuit design. With high simulation accuracy and speed, the methodology supports iterative design and evaluation, provides an high-level efficient verification for MEMS design, and ease the optimization of large systems.
Study is also made on the the deflection and stability of membrane structures under electrostatic and Casimir forces in MEMS. The effect of the Casimir force on the deflection is analysized. The static stability of the membrane structure can be determined by a dimensionless parameter K related with the geometrical parameters of the membrane. The critical value K C is obtained through numerical calculations and a design method of elelctrostatically driven membrane with a high aspect ratio ( L / h )is presented avoiding the potential instability.
本文采用集总参数建模思想,建立了 NODAS 单元模型库,用于 MEMS 的系统仿真和设计。NODAS 模型库包括系列模型单元(二维、三维线性梁、几何非线性梁、锚点、质量块、静电间隙、静电梳齿、复合热梁、电热梁等),其行为模型由MAST 硬件描述语言描述。本文给出了库中所有单元的物理建模和仿真验证,模型由 ANSYS 有限元模拟验证准确性,误差均在 5%以内。实现在 EDA 电路仿真器SABER 环境下,由原理图可视化构建 MEMS 系统,进行 MEMS 系统层次的建模和仿真,并提出基于 MAST 单元库的 MEMS 系统结构参数化设计流程和验证方法。
本文 NODAS MAST 库模型建模和系统仿真可支持结构、静电、热学等多物理场分析,能与电路兼容,满足复杂系统仿真的精度要求,为 MEMS 系统的快速设计提供了高效的验证方法,易于实现对设计结构的优化。
作者另一项工作为微机械薄膜在静电力和 Casimir 力作用下的稳定性研究,研究了 Casimir 效应对薄膜横向偏移影响。由数值方法计算得到了决定薄膜稳定性的参数 K 及 K 曲线临界值 KC,并提供了设计高长厚比(L/h)的静电薄膜结构的方法。
Microelectromechancial systems is a manufacturing technology of multi- discipline which develops rapidly. At present, the high cost and long design cycle of MEMS products restrict the growing due to the comparatively low design level. Thus, the design of methodology MEMS and CAD tools have been great significances in international MEMS researches with important theoretical and applied value. System-level modeling and simulations are the key issues to realize computer-aid virtual design of MEMS.
This thesis presents a NODAS (Nodal Design of Acutators and Sensors) library for simulation and design of suspended MEMS. NODAS is a library of a series of low-level elements (2D, 3D beams, nonlinear beams, anchors, plate masses, electrostatic gaps, combs, eletrothermal beams, et al). The lumped parameterized behavioral models are implemented in MAST, which is an analog hardware description language. All the detail model dervations and verification simulations are given. The NODAS simulation of element models showed more than 95% accuracy of ANSYS simulation. In an EDA simulator SABER, system-level simulations of MEMS devices are based on the schematics composed of the MAST elements. A structural parameterized design flow and verification methodology of MEMS based on the MAST elements library are presented. The key issues of this thesis include modeling physics, schematic representation, accuracy verification, application examples.
Modeling and system-level simulation based on the MEMS behavioral models enable the structural, electrostatic and thermal multi-field analysis and are compatible with circuit design. With high simulation accuracy and speed, the methodology supports iterative design and evaluation, provides an high-level efficient verification for MEMS design, and ease the optimization of large systems.
Study is also made on the the deflection and stability of membrane structures under electrostatic and Casimir forces in MEMS. The effect of the Casimir force on the deflection is analysized. The static stability of the membrane structure can be determined by a dimensionless parameter K related with the geometrical parameters of the membrane. The critical value K C is obtained through numerical calculations and a design method of elelctrostatically driven membrane with a high aspect ratio ( L / h )is presented avoiding the potential instability.
引文
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[11] J. E. Vandemeer,M. S. Kranz and G. Fedder,Hierarchical Representation and Simulation of Micromachined Inertial Sensors,in Technical Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM '98),Santa Clara, CA, USA,1998:540～545.
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[31] Eihab M Abdel-Rahman,Mohamed I Younis,Ali H Nayfeh,Characterization of the mechanical behavior of an electrically actuated microbeam , Journal of Micromechanical and Microengineering,2002,12:759~766.
[32] Mohammad I Younis,Eihab M. Abdel-Rahman,Ali Nayfeh,A Reduced-Order Model for Electrocally Actuated Microbeam-Based MEMS,Journal of Microelectromechanical Systems,2003,12 (5):672~680.
[33] Ofir Bochobza-Degani,Yael Nemirovsky.Modeling the Pull-in Parameters of Electrostatic Actuators with a Novel Lumped two Degrees of Freedom Pull-in Model.Sensors and Actuators A,2002,(97-98):569~578.
[34] S.P Timoshenko,J. N. Goodier,Theory of Elasticity,McGraw-Hill,New York,1970.
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[36] W. A. Johnson,L. K. Warne,Electrophysics of Micromechanical Comb Actuators,Jounal of Microelectromechanical Systems,1995,vol 4 (1):49~59.
[37] Nilesh D Mankame,G K Ananthasuresh,Comprehensive thermal modelling and characterization of an electro-thermal-compliant microactuator , Journal of Micromechanics and Microengineering,2001,11:452~462.
[38] Chi Shiang Pan,Wensyang Hsu,An electro-thermally and laterally driven polysilicon microactuator,Journal of Micromechanics and Microengineering,1997,7:7~13.
[39] Liwei Li n,Mu Chiao,Electrothermal responses of lineshape microstructures,Sensors and Actuators A,1996,55:35~41.
[40] Sitaraman Iyer,Hasnain Lakdawala,Gary K. Fedder,et al,Macromodeling Temperature- Dependent Curl in CMOS Micromachined Beams,in International Conference on Modeling and Simulation of Microsystems (MSM’ 01),U.S.A,2001:19~21.
[41] 苏翼林,材料力学,北京,高等教育出版社,1987。
[42] Iyer,Modeling and Simulation of Non-idealities in a Z-axis CMOS-MEMS Gyroscope,Ph.D thesis,Carnegie Mellon University,2003.
[43] 奥齐西克, 热传导, 北京, 高等教育出版社, 1983。
[44] 孔祥谦, 热应力有限单元法分析, 上海, 上海交通大学出版社, 1999。
[45] 俞昌铭, 热传导及其数值分析, 北京, 清华大学出版社, 1981。
[46] T. Mukherjee.,CAD for Integrated MEMS Design,Design, Test, Integration and Packaging of MEMS/MOEMS (DTIP '00),Paris,France,2000.
[47] B. Baidya,S. K. Gupta and T. Mukherjee,An extraction-based verification methodology for MEMS,in Journal of Microelectromechanical Systems,2002,11(1):2~11.
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[2] S. T. Picraux, P. J. McWhorter, The broad sweep of Integrated Microsystems, IEEE Spectrum,December 1998,24~33.
[3] 周兆英,王小浩,叶雄英,等,微机电系统,中国机械工程,2000,11(1~2):163~168。
[4] 李国平,陈子辰,微机电的研究内容与发展现状,微电子学,2001,31(6):389~391。
[5] 莫锦秋,梁庆华,汪国宝,等,微机电系统设计与制造,北京,化学工业出版社,2004。
[6] 孙道恒,MEMS 耦合场分析与系统级仿真,中国机械工程,2002,13(9):765~768。
[7] 季国顺,张永康,微机械系统建模与仿真技术研究,光学 精密工程,2002,10(6),626~630。
[8] Gabbay L D,Computer Aid Macromodeling of MEMS。PhD Thesis,MIT,1998.
[9] Jan E. Vandemeer,Nodal Design of Actuators and Sensors (NODAS),Technical Report,May 7,1998,Carnegie Mellon University.
[10] Q. Jing, T. Mukherjee and G. Fedder,Schematic-Based Lumped Parameterized Behavioral Modeling for Suspended MEMS,in Technical Digest of the ACM/IEEE International Conference on Computer Aided Design (ICCAD '02),San Jose, California,2002:367~373.
[11] J. E. Vandemeer,M. S. Kranz and G. Fedder,Hierarchical Representation and Simulation of Micromachined Inertial Sensors,in Technical Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM '98),Santa Clara, CA, USA,1998:540～545.
[12] Aluru N R, White J. Multi-level Newton method for static and fundamental frequency analysis of electromechanical systems. International Conference on Simulation of Semiconductor Processes and Devices,SISPAD,1997:125~128.
[13] Aluru N R , White J , Coupled numerical technique for self-consistent of micro-electro-mechanical-systems , American Society of Mechanical Engineers , Dynamic Systems and Control Division,1996(59):275~280.
[14] 高行山,林胜勇,加速松弛法及其在静电-力耦合问题仿真分析中的应用,机械强度,2001,23(4):500~502。
[15] ANSYS耦合场分析指南,2000,1。
[16] 谢寄石,机电系统动力学,北京,国防工业出版社,1989。
[17] Dennis Gibson, Carla Purdy, Extracting Behavioral Data from Physical Descriptions of MEMS for Simulation,Analog Integrated Circuits and Signal Processing,1999,20:227–238.
[18] 常洪龙,基于“Top-down”的 MEMS 集成设计方法及关键技术研究,硕士论文,西北工业大学,2002。
[19] C.M.克洛斯,D.K.弗雷德里克,动态系统模型的建立和分析,机械工业出版社,1981。
[20] Ningning Zhou,Simulation and Synthesis of Microelectromechanical Systems. PhD thesis,University of California, Berkeley,2002.
[21] Saber book,Synopsys, Inc. 2003.
[22] 赵超燮,结构矩阵分析原理,人民教育出版社,1982。
[23] 鲁斯(Ross,C.T.F.),结构力学的有限元法,人民交通出版社,1991.1。
[24] P.Y. Papalambros,D.J. Wilde,Principles of Optimization Design: Modeling and Computation. Cambridge University Press, Cambridge,U.K,1988.
[25] Q. Jing,Modeling and Simulation for Design of Suspended MEMS.PhD thesis,Dept. of Electrical and Computer Engineering,Carnegie Mellon University,May 2003.
[26] J.B.Starr,Squeeze Film Damping n Solid State Accelerometer,Tech. Digest,IEEE Solid State Sensors and Actuators Workshop,SC,USA,1990:44~47.
[27] S. Vemuri,G.K. Fedder,T.Mukherjee,Low-Order Squeeze Film Model for Simulation of MEMS Devices,in Technical Proceedings of the Third International Conference on Modeling and Simulation of Microsystems (MSM’00),San Diego, CA, USA,2000:205~208.
[28] X.Zhang,W.C.Tang,Viscous Air Damping in Laterally Driven Microresonators,Sensors and Matericals,1995,7 (6):415~430.
[29] Q. Jing,T. Mukherjee,G. Fedder,Large-Deflection Beam Model for Schematic-Based Behavioral Simulation in NODAS,in Technical Proceedings of the Fifth International Conference on Modeling and Simulation of Microsystems (MSM '02),San Juan,Puerto Rico ,2002:136-139.
[30] G. K. Fedder,Simulation of Microelectromechanical Systems,PhD thesis,Dept. of Electrical Engineering and Computer Sciences,University of California at Berkeley,September 1994.
[31] Eihab M Abdel-Rahman,Mohamed I Younis,Ali H Nayfeh,Characterization of the mechanical behavior of an electrically actuated microbeam , Journal of Micromechanical and Microengineering,2002,12:759~766.
[32] Mohammad I Younis,Eihab M. Abdel-Rahman,Ali Nayfeh,A Reduced-Order Model for Electrocally Actuated Microbeam-Based MEMS,Journal of Microelectromechanical Systems,2003,12 (5):672~680.
[33] Ofir Bochobza-Degani,Yael Nemirovsky.Modeling the Pull-in Parameters of Electrostatic Actuators with a Novel Lumped two Degrees of Freedom Pull-in Model.Sensors and Actuators A,2002,(97-98):569~578.
[34] S.P Timoshenko,J. N. Goodier,Theory of Elasticity,McGraw-Hill,New York,1970.
[35] S. Iyer,T. Muhkerjee,G. Fedder,Multi-mode Sensitive Layout Syntheses of Microresonators,Modeling and Simulation of Microsystems,Santa Clara,CA,1998:6-8.
[36] W. A. Johnson,L. K. Warne,Electrophysics of Micromechanical Comb Actuators,Jounal of Microelectromechanical Systems,1995,vol 4 (1):49~59.
[37] Nilesh D Mankame,G K Ananthasuresh,Comprehensive thermal modelling and characterization of an electro-thermal-compliant microactuator , Journal of Micromechanics and Microengineering,2001,11:452~462.
[38] Chi Shiang Pan,Wensyang Hsu,An electro-thermally and laterally driven polysilicon microactuator,Journal of Micromechanics and Microengineering,1997,7:7~13.
[39] Liwei Li n,Mu Chiao,Electrothermal responses of lineshape microstructures,Sensors and Actuators A,1996,55:35~41.
[40] Sitaraman Iyer,Hasnain Lakdawala,Gary K. Fedder,et al,Macromodeling Temperature- Dependent Curl in CMOS Micromachined Beams,in International Conference on Modeling and Simulation of Microsystems (MSM’ 01),U.S.A,2001:19~21.
[41] 苏翼林,材料力学,北京,高等教育出版社,1987。
[42] Iyer,Modeling and Simulation of Non-idealities in a Z-axis CMOS-MEMS Gyroscope,Ph.D thesis,Carnegie Mellon University,2003.
[43] 奥齐西克, 热传导, 北京, 高等教育出版社, 1983。
[44] 孔祥谦, 热应力有限单元法分析, 上海, 上海交通大学出版社, 1999。
[45] 俞昌铭, 热传导及其数值分析, 北京, 清华大学出版社, 1981。
[46] T. Mukherjee.,CAD for Integrated MEMS Design,Design, Test, Integration and Packaging of MEMS/MOEMS (DTIP '00),Paris,France,2000.
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