微加速度计的机电耦合特性及关键技术研究
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摘要
静电驱动与检测技术被大规模地应用于MEMS(Micro-Electro-Mechanical Systems,微电子机械系统)转换器与传感器中,具有灵敏度高、响应速度快、精度高、容易制造与加工以及易于与CMOS(Complementary Metal Oxide Semiconductor,互补金属氧化物半导体)技术相集成等优点。本论文以微电子机械系统中的直线轮廓平行板电容结构为研究对象,结合其在电容式微加速度计和谐振式微加速度计的应用特点,总结得出“弹簧—质量—电容”结构的三种宏模型形式：单弹簧单电容模型、双弹簧单电容模型和单弹簧双电容模型,课题研究了三类模型的结构组成、误差模型、机电耦合特性及其在微加速度计中的应用技术,主要研究内容包括以下几个方面：
1.根据MEMS平行板电容器的应用特点提取出了“弹簧—质量—电容器”宏模型,并分析了弹簧、质量与电容器在微电子机械系统中的表现形式。重点研究了两类折叠梁形式的“微弹簧”结构的刚度误差依赖性,指出了“内折叠分散桁架”的折叠梁结构在正偏差影响下刚度误差灵敏度较小；结合微工艺深刻蚀特点得出：选用内折叠分散桁架结构来支撑微器件中的可动质量块具有工艺简单、误差灵敏度较小、易于扩展等优点。
2.分析了宏模型的静电刚度效应与“吸附”效应等机电耦合特性。研究了开、闭环刚度的形成条件及解析表达式,以及双弹性支撑下结构位移刚度的耦合特性；运用能量法研究了阶跃电压下的宏模型响应,得出了结构发生“吸附”现象的刚度比为1/4;分析了双电容结构“吸附”电压的间隙误差依赖性,其理论结果与仿真分析结果的相对误差小于5%.
3.结合双电容宏模型的闭环刚度特性研究了力平衡式微加速度计在线性反馈电压下的机电耦合特性及位移刚度“刚化”与“软化”效应；结合微加工工艺特点,重点研究了间隙非对称误差与电路零偏情况下的机电耦合特性及其对加速度计输出零偏的影响。指出了在深度反馈条件下,间隙非对称误差对零偏输出的影响远大于电路零偏的影响,并在此结论的基础上提出了结合解析法与逆标度法的微加速度计表芯加工工艺线非对称误差预测技术,得出的预测结果与经验值相吻合。此预测技术合理地运用了成熟器件与加工工艺的特点,将机电耦合的理论结果应用到工程实践中来满足工程实际需求,为MEMS结构研究开辟了新的方法。
4.基于机械刚度与静电刚度耦合原理,提出静电刚度与谐振原理相结合的理论分析方法,设计出了基于静电刚度变化的谐振式微加速度计表芯结构。整个结构设计过程包括了谐振原理与静电刚度结合理论、静电刚度谐振器设计及频率鲁棒性设计与输入输出关系推导以及性能参数设计与版图尺寸确立。在运用静电刚度与谐振原理相结合的理论结果设计表芯结构及尺寸时,考虑到了频率的鲁棒性条件,使加工完成的样机灵敏度与设计值十分接近,整个结构仅经历两次制版与加工就达到了预期设计指标。这不仅说明理论结果的正确性,还说明了理论设计的有效性,降低了性能参数的工艺依赖性,提高了结构设计效率。
5.运用微工艺的深反应离子刻蚀技术(DRIE, Deep Reaction Ion Etching)与硅微键合技术制造出了加速度计的表芯结构,并通过原理样机的离心机测试验证了理论的正确性与有效性。
本论文运用宏模型原理分析MEMS平行板电容器的机电耦合特性,简化了复杂系统的分析过程,使理论推导过程更明确更直观。提出了运用机械场与静电场的耦合效应来开辟MEMS设计分析新方法,包括基于电路参数补偿的鲁棒性设计方法、基于系统测试的工艺误差预测方法以及基于静电刚度的微谐振器研制等。
Electrostatic driving and sensing technology is broadly applied in MEMS (Micro-Electro-Mechanical Systems) transducers and sensors, due to its advantages of high sensitivity, high speed of response, high precise, easy fabrication and easy integration with CMOS (Complementary Metal Oxide Semiconductor) technology. The parallel plates capacitors with straight line outline in micro-electro-mechanical-systems and its characteristics of application in capacitive micro accelerometer and resonant micro accelerometer are studied, and three types of macro-model are extracted in common spring-mass-capacitor structure:one with single spring and single capacitor, one with double springs and single capacitor, and one with single spring and double capacitor. The structure form, error model, electromechanical coupling characteristics and apllication technology in micro acceleroemter of those models are studed in paper, which contain subsequent aspects:
1. The macro models of spring-mass-capacitor are extracted according to the application traits of MEMS parallel plate capacitors, and the concrete forms of spring, mass and capacitor in MEMS are analyzed. The concentration of research is on the error dependence of stiffness of two typical micro-spring structure builded as folded beams. It is concluded that the one with inner fold and discontinuous truss has smaller sensitivity under positive error, and also has the advantages of simple process and easily expanding under considering the characteristics of deep etching when used as a supporting structure of movable sensing mass block.
2. The electromechanical coupling characteristics including effects of electrostatic stiffness and pull-in of macro model are analyzed. The generation condition and analytical expressions of electrostatic stiffness under open loop and closed loop, and the coupling characteristics of displacement stiffness in double elastic supporting structure are studied, respectively. It is concluded that the pull-in phenomenon of macro model occurs under step voltage when the ratio of stiffness is less than 1/4, and finally, the dependence of pull-in voltage on gap error in double capacitor model is analyzed, the theoretical results have the relative error less than 5% compared with simulating results.
3. The electromechanical coupling characteristics and 'stiffen' effects and 'soften' effects of displacement stiffness in balanced-force micro accelerometer under linear feedback voltage is studied by combining with the closed loop stiffness of double capacitor model. The studies focus on the influence of the gap asymmetric error and circuit zero bias on the electromechanical coupling characteristics and zero bias of accelerometer output, which indicate that the influence of the former part is much lager than later, based on this conclusion, a prediction theory of average gap asymmetric error from process line is established by combining analytical method and reverse calibration, and the results are coincident with the experience value. The prediction technology can meet the requirements in practical engineering by apply the theoretical results of electromechanical coupling into engineering based on the application of the characteristics of mature device and processing.
4. The theoretical analyzing method of combining electrostatic stiffness and resonant theory is proposed and a resonant accelerometer structure based on the change of electrostatic stiffness is designed according to the coupling theory between mechanical stiffness and electrostatic stiffness. The whole structure design process consist of theory of combining resonant principle and electrostatic stiffness, design of resonator with electrostatic stiffness and its frequency robustness, the analytic relation between input and output, design of performance parameters and determination of layout dimension. The condition of robustness of frequency is considered in determining the parameters of sensing structure by the combination theory of electrostatic stiffness and resonant theory, which makes the sensitivity of fabricating prototype close to the design value. The design performance is realized only by twice plate-making and processing, which not only proves the rightness of theory results, also clarifies the validity of theoretical design, reducing the dependence of performance on process and promoting the efficiency of structural design.
5. The structure of sensor is fabricated by DRIE (Deep Reaction Ion Etching) technology and silicon bonding technology, and finally, the experiment on centrifuge is carried to verify the feasibility and validity of theories.
The macro model method is selected in this paper to analyze the electromechanical coupling characteristics of MEMS parallel plate capacitor, which simplified the analyzing process of complicated systems, made the whole process of derivation more definitude and explicit, it is concluded that the coupling effects of mechanical field and electrostatic field can be used to cultivate new methods of MEMS design and analysis, such as ruboust design based on compensation of quantity in circuit, method of error prediction based on results of system tests and micro resonator based on electrostatic stiffness.
1.根据MEMS平行板电容器的应用特点提取出了“弹簧—质量—电容器”宏模型,并分析了弹簧、质量与电容器在微电子机械系统中的表现形式。重点研究了两类折叠梁形式的“微弹簧”结构的刚度误差依赖性,指出了“内折叠分散桁架”的折叠梁结构在正偏差影响下刚度误差灵敏度较小；结合微工艺深刻蚀特点得出：选用内折叠分散桁架结构来支撑微器件中的可动质量块具有工艺简单、误差灵敏度较小、易于扩展等优点。
2.分析了宏模型的静电刚度效应与“吸附”效应等机电耦合特性。研究了开、闭环刚度的形成条件及解析表达式,以及双弹性支撑下结构位移刚度的耦合特性；运用能量法研究了阶跃电压下的宏模型响应,得出了结构发生“吸附”现象的刚度比为1/4;分析了双电容结构“吸附”电压的间隙误差依赖性,其理论结果与仿真分析结果的相对误差小于5%.
3.结合双电容宏模型的闭环刚度特性研究了力平衡式微加速度计在线性反馈电压下的机电耦合特性及位移刚度“刚化”与“软化”效应；结合微加工工艺特点,重点研究了间隙非对称误差与电路零偏情况下的机电耦合特性及其对加速度计输出零偏的影响。指出了在深度反馈条件下,间隙非对称误差对零偏输出的影响远大于电路零偏的影响,并在此结论的基础上提出了结合解析法与逆标度法的微加速度计表芯加工工艺线非对称误差预测技术,得出的预测结果与经验值相吻合。此预测技术合理地运用了成熟器件与加工工艺的特点,将机电耦合的理论结果应用到工程实践中来满足工程实际需求,为MEMS结构研究开辟了新的方法。
4.基于机械刚度与静电刚度耦合原理,提出静电刚度与谐振原理相结合的理论分析方法,设计出了基于静电刚度变化的谐振式微加速度计表芯结构。整个结构设计过程包括了谐振原理与静电刚度结合理论、静电刚度谐振器设计及频率鲁棒性设计与输入输出关系推导以及性能参数设计与版图尺寸确立。在运用静电刚度与谐振原理相结合的理论结果设计表芯结构及尺寸时,考虑到了频率的鲁棒性条件,使加工完成的样机灵敏度与设计值十分接近,整个结构仅经历两次制版与加工就达到了预期设计指标。这不仅说明理论结果的正确性,还说明了理论设计的有效性,降低了性能参数的工艺依赖性,提高了结构设计效率。
5.运用微工艺的深反应离子刻蚀技术(DRIE, Deep Reaction Ion Etching)与硅微键合技术制造出了加速度计的表芯结构,并通过原理样机的离心机测试验证了理论的正确性与有效性。
本论文运用宏模型原理分析MEMS平行板电容器的机电耦合特性,简化了复杂系统的分析过程,使理论推导过程更明确更直观。提出了运用机械场与静电场的耦合效应来开辟MEMS设计分析新方法,包括基于电路参数补偿的鲁棒性设计方法、基于系统测试的工艺误差预测方法以及基于静电刚度的微谐振器研制等。
Electrostatic driving and sensing technology is broadly applied in MEMS (Micro-Electro-Mechanical Systems) transducers and sensors, due to its advantages of high sensitivity, high speed of response, high precise, easy fabrication and easy integration with CMOS (Complementary Metal Oxide Semiconductor) technology. The parallel plates capacitors with straight line outline in micro-electro-mechanical-systems and its characteristics of application in capacitive micro accelerometer and resonant micro accelerometer are studied, and three types of macro-model are extracted in common spring-mass-capacitor structure:one with single spring and single capacitor, one with double springs and single capacitor, and one with single spring and double capacitor. The structure form, error model, electromechanical coupling characteristics and apllication technology in micro acceleroemter of those models are studed in paper, which contain subsequent aspects:
1. The macro models of spring-mass-capacitor are extracted according to the application traits of MEMS parallel plate capacitors, and the concrete forms of spring, mass and capacitor in MEMS are analyzed. The concentration of research is on the error dependence of stiffness of two typical micro-spring structure builded as folded beams. It is concluded that the one with inner fold and discontinuous truss has smaller sensitivity under positive error, and also has the advantages of simple process and easily expanding under considering the characteristics of deep etching when used as a supporting structure of movable sensing mass block.
2. The electromechanical coupling characteristics including effects of electrostatic stiffness and pull-in of macro model are analyzed. The generation condition and analytical expressions of electrostatic stiffness under open loop and closed loop, and the coupling characteristics of displacement stiffness in double elastic supporting structure are studied, respectively. It is concluded that the pull-in phenomenon of macro model occurs under step voltage when the ratio of stiffness is less than 1/4, and finally, the dependence of pull-in voltage on gap error in double capacitor model is analyzed, the theoretical results have the relative error less than 5% compared with simulating results.
3. The electromechanical coupling characteristics and 'stiffen' effects and 'soften' effects of displacement stiffness in balanced-force micro accelerometer under linear feedback voltage is studied by combining with the closed loop stiffness of double capacitor model. The studies focus on the influence of the gap asymmetric error and circuit zero bias on the electromechanical coupling characteristics and zero bias of accelerometer output, which indicate that the influence of the former part is much lager than later, based on this conclusion, a prediction theory of average gap asymmetric error from process line is established by combining analytical method and reverse calibration, and the results are coincident with the experience value. The prediction technology can meet the requirements in practical engineering by apply the theoretical results of electromechanical coupling into engineering based on the application of the characteristics of mature device and processing.
4. The theoretical analyzing method of combining electrostatic stiffness and resonant theory is proposed and a resonant accelerometer structure based on the change of electrostatic stiffness is designed according to the coupling theory between mechanical stiffness and electrostatic stiffness. The whole structure design process consist of theory of combining resonant principle and electrostatic stiffness, design of resonator with electrostatic stiffness and its frequency robustness, the analytic relation between input and output, design of performance parameters and determination of layout dimension. The condition of robustness of frequency is considered in determining the parameters of sensing structure by the combination theory of electrostatic stiffness and resonant theory, which makes the sensitivity of fabricating prototype close to the design value. The design performance is realized only by twice plate-making and processing, which not only proves the rightness of theory results, also clarifies the validity of theoretical design, reducing the dependence of performance on process and promoting the efficiency of structural design.
5. The structure of sensor is fabricated by DRIE (Deep Reaction Ion Etching) technology and silicon bonding technology, and finally, the experiment on centrifuge is carried to verify the feasibility and validity of theories.
The macro model method is selected in this paper to analyze the electromechanical coupling characteristics of MEMS parallel plate capacitor, which simplified the analyzing process of complicated systems, made the whole process of derivation more definitude and explicit, it is concluded that the coupling effects of mechanical field and electrostatic field can be used to cultivate new methods of MEMS design and analysis, such as ruboust design based on compensation of quantity in circuit, method of error prediction based on results of system tests and micro resonator based on electrostatic stiffness.
引文
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