考虑漏电场的扭转式微执行器Pull-in机理分析
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摘要
微型化始终是当代科学技术发展的重要方向。随着微电子技术的发展,基于MEMS(微机械系统)技术的微传感器、微执行器得到了快速发展,在其各种驱动方式中,静电驱动占有重要地位,因此对静电微执行器的研究是非常必要的。在静电微执行器中,存在做快速吸合现象,也被称为pull-in失稳现象,它是静电微执行器的一个重要特征。现今国内外对于静电微执行器pull-in失稳问题的研究非常多,但考虑静电微执行器边缘效应的研究还是微乎其微。由于微型化器件灵敏度的增大,所以获得精确的pull-in点的相关参数都是非常必要的。
本文在分析了国内外相关研究工作的基础上,基于能量法进行分析扭转式静电微执行器的pull-in失稳现象,把扭转式静电微执行器的边缘漏电场考虑到模型中去,建立更符合实际的物理模型,通过与ANSYS软件实际仿真结果相比较,论证了建立模型的准确性。
本文首先通过求解忽略微执行器边缘电场效应的pull-in失稳参数,介绍了微执行器的pull-in机理,并重点分析了扭转式微执行器电极相对于极板的位置不同而对微执行器pull-in参数的影响和控制。然后介绍了漏电场对微执行器pull-in参数的影响,建立相关的漏电场的模型,在考虑漏电场的情况下,得出了pull-in现象的相关数据。通过实例分析,分别考察了扭转式微执行器的各项参数的变化对于pull-in电压和pull-in点的影响。最后通过ANSYS有限元分析软件建立出扭转式静电微执行器结构,考虑了上下极板之间的边缘效应进行求解,得出实际数据,通过与模型求解的数据相比较分析,说明了模型的精确性,并给出模型的适用范围。
Miniaturization has always been the important direction in the development of modern science and technology currently. With the development of microelectronics technology, micro-actuators are growing rapidly based on the micro-sensors of MEMS (micro-electromechanical system) technology. Among their various actuation methods, electrostatic actuation is the most important method and therefore it is necessary to study the electrostatic micro-actuators. In the process of studying electrostatic micro-actuators, there is a quick pull-in phenomenon, which is also known as pull-in instability phenomenon, and which is an important feature of the electrostatic micro-actuators. Presently, many people at home and abroad are studying the pull-in instability problem of electrostatic micro-actuators, but the study of taking into account the fringing field effect of electrostatic micro-actuators can be negligible. As the sensitivity of miniaturizational devices increases, it is very necessary to obtain accurate data of pull-in points.
Based on the analysis of the research work at home and abroad, this paper presents the analysis of the pull-in instability phenomena of electrostatic micro-actuator in the use of energy method. The fringing field effect is taken into account in the model of electrostatic torsion micro-actuator in order to establish more realistic physical model. By comparing with the results of the ANSYS software, the accuracy of model can be demonstrated.
Firstly, the pull-in mechanism of electrostatic micro-actuator is introduced by solving the pull-in parameters without considering the fringing field effect in this paper. It focuses on analyzing the control and influence of the different electrode positions relative to the plate of electrostatic torsion micro-actuator on pull-in parameters.Then it presents the influence of ignoring the fringing field effect on the micro-actuator pull-in parameters. And the model of the fringing field capacitances are set up. The relevant data of pull-in phenomenon are obtained in the case of taking into account the fringing field effect. The impact of the change of the micro-actuator parameters on the pull-in voltage and pull-in point is investigated through analyzing the cases. Finally, electrostatic torsion micro-actuator structure is established by ANSYS finite element analysis software. The actual data are obtained by taking into account the fringing effect between the upper and lower plates. Comparing with the data from the solve of model, the accurate of model is showed and the scope of model is given.
本文在分析了国内外相关研究工作的基础上,基于能量法进行分析扭转式静电微执行器的pull-in失稳现象,把扭转式静电微执行器的边缘漏电场考虑到模型中去,建立更符合实际的物理模型,通过与ANSYS软件实际仿真结果相比较,论证了建立模型的准确性。
本文首先通过求解忽略微执行器边缘电场效应的pull-in失稳参数,介绍了微执行器的pull-in机理,并重点分析了扭转式微执行器电极相对于极板的位置不同而对微执行器pull-in参数的影响和控制。然后介绍了漏电场对微执行器pull-in参数的影响,建立相关的漏电场的模型,在考虑漏电场的情况下,得出了pull-in现象的相关数据。通过实例分析,分别考察了扭转式微执行器的各项参数的变化对于pull-in电压和pull-in点的影响。最后通过ANSYS有限元分析软件建立出扭转式静电微执行器结构,考虑了上下极板之间的边缘效应进行求解,得出实际数据,通过与模型求解的数据相比较分析,说明了模型的精确性,并给出模型的适用范围。
Miniaturization has always been the important direction in the development of modern science and technology currently. With the development of microelectronics technology, micro-actuators are growing rapidly based on the micro-sensors of MEMS (micro-electromechanical system) technology. Among their various actuation methods, electrostatic actuation is the most important method and therefore it is necessary to study the electrostatic micro-actuators. In the process of studying electrostatic micro-actuators, there is a quick pull-in phenomenon, which is also known as pull-in instability phenomenon, and which is an important feature of the electrostatic micro-actuators. Presently, many people at home and abroad are studying the pull-in instability problem of electrostatic micro-actuators, but the study of taking into account the fringing field effect of electrostatic micro-actuators can be negligible. As the sensitivity of miniaturizational devices increases, it is very necessary to obtain accurate data of pull-in points.
Based on the analysis of the research work at home and abroad, this paper presents the analysis of the pull-in instability phenomena of electrostatic micro-actuator in the use of energy method. The fringing field effect is taken into account in the model of electrostatic torsion micro-actuator in order to establish more realistic physical model. By comparing with the results of the ANSYS software, the accuracy of model can be demonstrated.
Firstly, the pull-in mechanism of electrostatic micro-actuator is introduced by solving the pull-in parameters without considering the fringing field effect in this paper. It focuses on analyzing the control and influence of the different electrode positions relative to the plate of electrostatic torsion micro-actuator on pull-in parameters.Then it presents the influence of ignoring the fringing field effect on the micro-actuator pull-in parameters. And the model of the fringing field capacitances are set up. The relevant data of pull-in phenomenon are obtained in the case of taking into account the fringing field effect. The impact of the change of the micro-actuator parameters on the pull-in voltage and pull-in point is investigated through analyzing the cases. Finally, electrostatic torsion micro-actuator structure is established by ANSYS finite element analysis software. The actual data are obtained by taking into account the fringing effect between the upper and lower plates. Comparing with the data from the solve of model, the accurate of model is showed and the scope of model is given.
引文
[1]刘成刚.MEMS技术的发展与应用[J].济南职业学院学报,2007,(1):5-77.
[2]张威,张大成等.MEMS概况及其发展趋势[J].微纳电子技术,2002,(1):22-28.
[3]赵醇生,陈启东.微型机械的特点、研究现状与应用[J].震动、测试与诊断,1988,18(1):61-70.
[4]张英,戚红向,李德强等.MEMS航天惯导产品及技术发展简介[J].航天标准化,2010,3:40-43.
[5] Weissler.Microsystems[J].Sensors and actuators,1944,40:2
[6]牛君,刘云桥.MEMS技术的发展与应用[J].高新技术,2007,11:1-2
[7]张琛.微执行器[M].上海交通大学出版社.2005.12(5):1-10.
[8]王喆垚.微系统设计与制造.清华大学出版社.2008.2(1):1-10,264-301.
[9] MEMS.百度百科http://baike.baidu.com/view/37086.html?wtp=tt.
[10] Stephen D. Senturia. Microsystem Design. Second Printing. United States of American: Boston/London/Dordrecht: Kluwer Academic Publishers. 2000
[11]黄庆安译.微机电系统基础[M].北京机械工业出版社,2007:1-10.
[12] Petersen K E. Silicon as a mechanical materal[A]. Proc. IEEE[C]. 1982,70:420
[13]孙立宁,周兆英,龚振邦.MEMS国内外发展状况及我国MEMS发展战略的思考[J].机器人技术与应用,2002,1:2-4.
[14]王亚珍,朱文坚.微机电系统(MEMS)技术及发展趋势[期刊论文]-机械设计与研究2004(02).
[15]马强. MEMS的研究现状及其进展[期刊论文]-中国集成电路2004(10).
[16] S M Speakking. Materials issues in microelectromechanical systems[J]. Acta materials, 2000,48:179-196.
[17]匡一宁,黄庆安,“基于热膨胀效应的微执行进展”,电子器件,22(1999) 3, pp.162-170.
[18]“走进MEMS世界”,电子产品世界,2000.9/2000.10
[19] S.D.Senturia,”CAD challenges for microsensors,microactuators,and microsystems”Proc.IEEE,vol.86,no.8,1998,pp.1611.
[20]方玉明,黄庆安,李伟华.一种磁微执行器PULL-IN模型[J].半导体学报,2007,28(10).
[21]孙东明,董玮等.扭臂式静电微驱动器的pull-in现象分析.MEMS器件与技术,2006,5(251-253).
[22] S Chowdhury,M Ahmadi and W C Miller,“A closed-form model for the pull-in voltage of electrostaticcally actuated cantilever beams”, Journal of micromechanics mircoengineering.15(2005) 756-763.
[23] Mehran Hosseini,Guchuan Zhu,Yves-Alain Peter,“A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic mirco-actuators”,Analog Inter Circ Sig Process(2007)53:119-128.
[24] Lee S S,Huang L S,Kim C J,et al.Free-space fiber-optic switches based on MEMS vertical torsion mirrors[J].J Lightwave Technol,1999,17(1):7-13.
[25] K.Gabbriel, J.Jarvis, W.Trimmer,“Small machines, large opportunities,”Proc. NTS Workshop onMicro-Electro-Mechanical System,USA,1987,pp.1-31.
[26] Yael Nemirovsky and Ofir Bochobza-Degani,“A methodology and model for the pull-in parameters of electrostatic actuators”, Journal of microelectromechanical systems,VOL.10,NO.4,December 2001,10(4):601-605.
[27] R. Puers and D. Lapadatu,“Electrostatic forces and their effects on capacitive mechanical sensors,”Sens. Actuators A, vol. 56, pp. 203–210,1996.
[28] P. M. Osterberg, Electrostatically actuated microelectromechanical teststructures for material property measurements,Ph.D. dissertation, MIT,Cambridge, MA, Sept. 1995.
[29] Meijs N V D and Fokkema J T 1984 VLSI circuit reconstruction from mask topology Integr. VLSI J. 285–119.
[30] Xiao Z X,Wu X T,Peng W Y,et al.An angle-based design approach for rectangular electrostatic torsion actuators[J].J Microelectromech Syst,2001,10(4):561-568.
[31] ZHANG X M,CHAU F S,QUAN C,et al.Astudy of the static characteristics of a torsional micromirror[J].Sens Actuators A,2001,90:73-81.
[32] Lee S S,Huang L S,Kim C J,et al.Free-space fiber-optic switches based on MEMS vertical torsion mirrors[J].J Lightwave Technol,1999,17(1):7-13.
[33] Degani O, Nemirosky Y. Design Considerations of Rectangular Electrostatic Torsion Actuators Based on New Analytical Pull-in Expressions. Journal of Microelectromechanical Systems, 2002, 11(1): 20 -26.
[34] Y. Nemirovsky and O. Bochobza-Degani,“A Methodology and Model for the Pull-In Parameters of Magnetostatic Actuators,”JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14, NO. 6, DECEMBER 2005.
[35] H. Toshiyoshi and H. Fujita,“Electrostatic micro torsion mirrors for an optical switch matrix,”IEEE J. Microelectromech. Syst., vol. 5, no. 4,pp. 231–237, 1996.
[36] Degani O, Socher E, Lipson A, et al. Pull-In Study of an Electrostatic Torsion Microactuator . Journal of Microelectromechanical Systems, 1998, 7(4): 373 -379.
[37] Fang Yuming, Huang Qingan, Li Weihua. A mechanical-magnetic coupling macromodel for a magnetic microbeam actuator. Chinese Journal of Semiconductors, 2005,26(8):1599-1603.
[38]闻国椿.共形映射与边值问题[M],高等教育出版社,1985.
[39]闻国椿,戴中维,田茂英.自由边界问题的函数论方法及去在力学中的应用[M],高等教育出版社,1996.
[40]朱满座.数值保角变换及其在电磁理论中的应用.西安电子科技大学博士论文,2008.
[41]秦德培.非平行板电容器电场和电容的简化计算.大学物理,1995,14(1):13-14.
[42]王磊.非理想电容器电容计算的探讨,海南师范大学学报(自然科学板)2008,6(158-160).
[43]解锦秋,朱益清.非平行板电容器电容的探讨.物理与工程,1999,9(1):2-3.
[44]郑民伟.非平行板电容器的电容和电场的一种计算.大学物理,2001,20(2):17-18.
[45]葛松华.关于非平行板电容器的电容计算的讨论.物理与工程,2004,23(11):40-41.
[46]朱益清,徐坚宏.计及边缘效应的平行板电容器的电容计算.工科物理,1998,8(1):6-9.
[47]梁昆淼.数学物理方法.北京:人民教育出版社,1987.
[48] C. P. Yuan and T. N. Trick,“Calculation of capacitance inVLSI circuits,”in Proc. IEEE Conf. Comput.-Aided Design, 1984, pp. 263–265.
[49] Sazzadur Chowdhury,Member,IEEE,Majid Ahmadi,Fellow,IEEE,and William C.Miller,LifeFellow,IEEE.Pull-in Voltage Study of Electrostatically Actuated Fixed-Fixed Beams using a VLSL On-Chip Interconnect Capacitance Model.Journal of microelectromechanical systems,vol.15,NO.3,june 2006.
[50]曾余庚,徐国华,宋国乡.电磁场有限单元法.科学出版社,1982.
[51]阎照文等.ANSYS 10.0工程电磁分析技术与实例详解.中国水利水电出版社,2006.
[52]党沙沙,许洋,张红松等.ANSYS 12.0多物理耦合场有限元分析入门到精通,机械工业出版社2010.
[2]张威,张大成等.MEMS概况及其发展趋势[J].微纳电子技术,2002,(1):22-28.
[3]赵醇生,陈启东.微型机械的特点、研究现状与应用[J].震动、测试与诊断,1988,18(1):61-70.
[4]张英,戚红向,李德强等.MEMS航天惯导产品及技术发展简介[J].航天标准化,2010,3:40-43.
[5] Weissler.Microsystems[J].Sensors and actuators,1944,40:2
[6]牛君,刘云桥.MEMS技术的发展与应用[J].高新技术,2007,11:1-2
[7]张琛.微执行器[M].上海交通大学出版社.2005.12(5):1-10.
[8]王喆垚.微系统设计与制造.清华大学出版社.2008.2(1):1-10,264-301.
[9] MEMS.百度百科http://baike.baidu.com/view/37086.html?wtp=tt.
[10] Stephen D. Senturia. Microsystem Design. Second Printing. United States of American: Boston/London/Dordrecht: Kluwer Academic Publishers. 2000
[11]黄庆安译.微机电系统基础[M].北京机械工业出版社,2007:1-10.
[12] Petersen K E. Silicon as a mechanical materal[A]. Proc. IEEE[C]. 1982,70:420
[13]孙立宁,周兆英,龚振邦.MEMS国内外发展状况及我国MEMS发展战略的思考[J].机器人技术与应用,2002,1:2-4.
[14]王亚珍,朱文坚.微机电系统(MEMS)技术及发展趋势[期刊论文]-机械设计与研究2004(02).
[15]马强. MEMS的研究现状及其进展[期刊论文]-中国集成电路2004(10).
[16] S M Speakking. Materials issues in microelectromechanical systems[J]. Acta materials, 2000,48:179-196.
[17]匡一宁,黄庆安,“基于热膨胀效应的微执行进展”,电子器件,22(1999) 3, pp.162-170.
[18]“走进MEMS世界”,电子产品世界,2000.9/2000.10
[19] S.D.Senturia,”CAD challenges for microsensors,microactuators,and microsystems”Proc.IEEE,vol.86,no.8,1998,pp.1611.
[20]方玉明,黄庆安,李伟华.一种磁微执行器PULL-IN模型[J].半导体学报,2007,28(10).
[21]孙东明,董玮等.扭臂式静电微驱动器的pull-in现象分析.MEMS器件与技术,2006,5(251-253).
[22] S Chowdhury,M Ahmadi and W C Miller,“A closed-form model for the pull-in voltage of electrostaticcally actuated cantilever beams”, Journal of micromechanics mircoengineering.15(2005) 756-763.
[23] Mehran Hosseini,Guchuan Zhu,Yves-Alain Peter,“A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic mirco-actuators”,Analog Inter Circ Sig Process(2007)53:119-128.
[24] Lee S S,Huang L S,Kim C J,et al.Free-space fiber-optic switches based on MEMS vertical torsion mirrors[J].J Lightwave Technol,1999,17(1):7-13.
[25] K.Gabbriel, J.Jarvis, W.Trimmer,“Small machines, large opportunities,”Proc. NTS Workshop onMicro-Electro-Mechanical System,USA,1987,pp.1-31.
[26] Yael Nemirovsky and Ofir Bochobza-Degani,“A methodology and model for the pull-in parameters of electrostatic actuators”, Journal of microelectromechanical systems,VOL.10,NO.4,December 2001,10(4):601-605.
[27] R. Puers and D. Lapadatu,“Electrostatic forces and their effects on capacitive mechanical sensors,”Sens. Actuators A, vol. 56, pp. 203–210,1996.
[28] P. M. Osterberg, Electrostatically actuated microelectromechanical teststructures for material property measurements,Ph.D. dissertation, MIT,Cambridge, MA, Sept. 1995.
[29] Meijs N V D and Fokkema J T 1984 VLSI circuit reconstruction from mask topology Integr. VLSI J. 285–119.
[30] Xiao Z X,Wu X T,Peng W Y,et al.An angle-based design approach for rectangular electrostatic torsion actuators[J].J Microelectromech Syst,2001,10(4):561-568.
[31] ZHANG X M,CHAU F S,QUAN C,et al.Astudy of the static characteristics of a torsional micromirror[J].Sens Actuators A,2001,90:73-81.
[32] Lee S S,Huang L S,Kim C J,et al.Free-space fiber-optic switches based on MEMS vertical torsion mirrors[J].J Lightwave Technol,1999,17(1):7-13.
[33] Degani O, Nemirosky Y. Design Considerations of Rectangular Electrostatic Torsion Actuators Based on New Analytical Pull-in Expressions. Journal of Microelectromechanical Systems, 2002, 11(1): 20 -26.
[34] Y. Nemirovsky and O. Bochobza-Degani,“A Methodology and Model for the Pull-In Parameters of Magnetostatic Actuators,”JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14, NO. 6, DECEMBER 2005.
[35] H. Toshiyoshi and H. Fujita,“Electrostatic micro torsion mirrors for an optical switch matrix,”IEEE J. Microelectromech. Syst., vol. 5, no. 4,pp. 231–237, 1996.
[36] Degani O, Socher E, Lipson A, et al. Pull-In Study of an Electrostatic Torsion Microactuator . Journal of Microelectromechanical Systems, 1998, 7(4): 373 -379.
[37] Fang Yuming, Huang Qingan, Li Weihua. A mechanical-magnetic coupling macromodel for a magnetic microbeam actuator. Chinese Journal of Semiconductors, 2005,26(8):1599-1603.
[38]闻国椿.共形映射与边值问题[M],高等教育出版社,1985.
[39]闻国椿,戴中维,田茂英.自由边界问题的函数论方法及去在力学中的应用[M],高等教育出版社,1996.
[40]朱满座.数值保角变换及其在电磁理论中的应用.西安电子科技大学博士论文,2008.
[41]秦德培.非平行板电容器电场和电容的简化计算.大学物理,1995,14(1):13-14.
[42]王磊.非理想电容器电容计算的探讨,海南师范大学学报(自然科学板)2008,6(158-160).
[43]解锦秋,朱益清.非平行板电容器电容的探讨.物理与工程,1999,9(1):2-3.
[44]郑民伟.非平行板电容器的电容和电场的一种计算.大学物理,2001,20(2):17-18.
[45]葛松华.关于非平行板电容器的电容计算的讨论.物理与工程,2004,23(11):40-41.
[46]朱益清,徐坚宏.计及边缘效应的平行板电容器的电容计算.工科物理,1998,8(1):6-9.
[47]梁昆淼.数学物理方法.北京:人民教育出版社,1987.
[48] C. P. Yuan and T. N. Trick,“Calculation of capacitance inVLSI circuits,”in Proc. IEEE Conf. Comput.-Aided Design, 1984, pp. 263–265.
[49] Sazzadur Chowdhury,Member,IEEE,Majid Ahmadi,Fellow,IEEE,and William C.Miller,LifeFellow,IEEE.Pull-in Voltage Study of Electrostatically Actuated Fixed-Fixed Beams using a VLSL On-Chip Interconnect Capacitance Model.Journal of microelectromechanical systems,vol.15,NO.3,june 2006.
[50]曾余庚,徐国华,宋国乡.电磁场有限单元法.科学出版社,1982.
[51]阎照文等.ANSYS 10.0工程电磁分析技术与实例详解.中国水利水电出版社,2006.
[52]党沙沙,许洋,张红松等.ANSYS 12.0多物理耦合场有限元分析入门到精通,机械工业出版社2010.