基于宏模型技术的MEMS系统级仿真研究
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摘要
随着微纳加工技术与集成电路制造工艺的不断发展与兼容,出现了CMOS-MEMS等多种新型集成制造工艺,使得MEMS产业从早期生产单个的MEMS器件发展到目前以片上系统(System on Chip, SOC)或者片内封装系统(System in Package, SiP)为代表性的,能实现MEMS功能结构器件与集成电路混合信号处理单元集成的复杂系统。MEMS中元器件的高集成度与系统功能的多样化要求面向MEMS的计算机辅助设计工具能够对MEMS整体行为进行快速建模和仿真分析。结构化设计思想的形成则使面向MEMS的系统级设计技术得到了长足的发展,目前应用基于MEMS宏模型技术的系统级设计工具来获得整个系统的行为特性已成为研究热点。本文结合目前MEMS系统中结构与电路单元的高度集成化与功能日趋复杂化的发展现状,重点针对MEMS多能量域耦合等非线性特点,主要做了以下研究工作：
基于结构力学等基本理论,利用解析法建立了线性梁、非线性梁、刚性平板、弹性平板、静电间隙、静电梳齿、“V”形驱动器等常用MEMS规则结构的解析宏模型。将自建宏模型利用MAST硬件语言描述,可放入到CoventorWare软件ARCHITECT模块中的模型元件库。利用自建的模型元件与商业软件元件库中提供的结构和电路元件,设计并优化了一种片内集成拉伸测试结构,系统级仿真结果与有限元模型相比较表明建立的解析模型精度较高。
提出了一种利用精化Arnoldi算法生成Krylov子空间,基于传递函数矩匹配原理在Krylov子空间上进行投影从而生成MEMS数值宏模型的方法。与传统Arnoldi方法相比精化投影方法能够提高对系统相关矩阵特征值的求解精度,相当于能更加准确的逼近系统传递函数的极点,得到的降阶模型精度更高,同时此方法还可以提高Krylov子空间降阶模型的有效阶数范围。利用Krylov子空间法建立了电热驱动微夹钳的电热结构耦合宏模型,仿真和实验结果表明了宏模型的有效性。
提出了一种新的求解MEMS非线性动力问题的MOR-PIM方法。将基于Krylov子空间投影等模型降阶方法(Model Order Reduction, MOR)应用于精细积分法(Precise Integration Method, PIM)中,通过对指数矩阵的降阶处理,提高精细积分法的计算与存储效率,使精细积分算法更适用于多自由度变系数强非线性、非保守MEMS动力学系统,为MEMS系统级仿真方法提供新思路。
根据MEMS CAD结构化的思想,结合精化Arnoldi算法和MOR-PIM方法,提出并开发了MEMS_DUT系统级仿真平台。整个过程以VC++6.0编译器为平台,通过对有限元软件ANSYS的二次开发建立器件有限元模型,利用封装MATLAB语言降阶算法得到的动态链接库对MEMS器件进行降阶以获取器件宏模型。将器件宏模型嵌入到系统级仿真平台仿真器Simulink中进行系统级仿真,来实现模拟分析整个系统的动态特性。
利用MEMS_DUT仿真平台,对电热驱动的片内集成微拉伸测试结构,电热驱动和静电驱动的片内集成疲劳弯曲测试结构等进行了系统级仿真,验证了本平台系统级仿真分析的整个流程以及在效率和准确性等方面的性能。最后对精化Arnoldi降阶算法以及系统级仿真平台MEMS DUT需要进一步完善和改进的内容提出了若干建议。
With the appearance of CMOS-MEMS and other various new integrated manufacturing process for the continuous development and compatibility between the micro-nanofabrication technology and integrated circuit manufacturing process, the focus of MEMS production has changed from the early research of individual MEMS device to the current complex system integrated with functional structure of MEMS devices and circuits for mixed-signal processing unit, such as System on Chip (SOC) and System in Package (SIP) representatively. Rapid modeling and simulation on the overall behavior of MEMS devices by computer-aided design tools for MEMS are required for high integration and system functional diversification of MEMS components, and MEMS-design technology inspired by idea of structural designing achieves a significant development. System-level simulation methods based on macromodel which can get behavior characteristic of MEMS have become a famous research field specific to the across multiple coupled energy domains. Aiming at the requirements of fast system-level modeling and simulation as well as the characteristics of multiple energy domains interaction, research works in this paper are presented as follows:
Analytical macromodels for linear beam, nonlinear beam, rigid plate, flexible plate, electrostatic gap, electrostatic comb, "V" shaped drive and other common regular structure for MEMS are established using the analytical method based on the basic theory of structural mechanics. Macromodels are described by MAST hardware language and put into the model library of ARCHITECT module in the CoventorWare software. An on-chip tensile testing structure is designed and optimized by the combined use of the self-built component models and the library structure and circuit elements in commercial software, achieving a high model accuracy according to system-level simulation results.
A refined approach producing MEMS numerical macromodels is proposed by generating the iterative Krylov subspace using a refined Arnoldi algorithm, and project polycondensing the degree of freedom (DOF) of the original system equations described by the state space method in the Krylov subspace based on the transfer function moment matching principle. Compared with traditional methods, the refined approach improves approximation accuracy of the system matrix eigenvalues equivalent to a more accurate approximation to the poles of the system transfer function, obtaining a reduced-order model accuracy. Finite element reduced-order macromodel for V-shaped driven electrothermal microgripper is achieved using this method, and simulation results show that accuracy meets with general requirement. A new Model Order Reduction- Precise Integration Method (MOR-PIM) method for the solution of nonlinear dynamic problems in MEMS area is provided. Model Order Reduction method based on Krylov subspace projection is applied to the precise integration method to enhance its computing and storage efficiency by reduced-order processing the index matrix, therefore precise integration algorithm is more suitable for the nonlinear and non-conservative dynamical systems with multi-degree of freedom and variable coefficients, offering new ideas to system-level simulation.
MEMS_DUT platform for system-level simulation is developed according to MEMS CAD structural idea. Finite element model (FEM) of the device developed secondary by ANSYS software is transformed to macromodel after reduced-order processing by the dynamic link library with MATLAB language of reduced-order algorithm encapsulated on the platform of VC++6.0 compiler throughout the whole flow, and dynamic characteristic of MEMS system is performed by the system-level simulation of macromodel built by embedding in Simulink which is the system-level simulation platform emulator.
Finally, the on-chip tensile testing structures actuated by electrothermal V-shape beam and fatigue testing structures actuated by electrothermal and electrostatic methods respectively are system-level simulated on the MEMS_DUT simulation platform to verify the whole flow and the performance for accuracy and efficiency of the MEMS_DUT platform. And several advices about improving model order reduction algorithm and optimizing the system-level simulation tool has been proposed.
基于结构力学等基本理论,利用解析法建立了线性梁、非线性梁、刚性平板、弹性平板、静电间隙、静电梳齿、“V”形驱动器等常用MEMS规则结构的解析宏模型。将自建宏模型利用MAST硬件语言描述,可放入到CoventorWare软件ARCHITECT模块中的模型元件库。利用自建的模型元件与商业软件元件库中提供的结构和电路元件,设计并优化了一种片内集成拉伸测试结构,系统级仿真结果与有限元模型相比较表明建立的解析模型精度较高。
提出了一种利用精化Arnoldi算法生成Krylov子空间,基于传递函数矩匹配原理在Krylov子空间上进行投影从而生成MEMS数值宏模型的方法。与传统Arnoldi方法相比精化投影方法能够提高对系统相关矩阵特征值的求解精度,相当于能更加准确的逼近系统传递函数的极点,得到的降阶模型精度更高,同时此方法还可以提高Krylov子空间降阶模型的有效阶数范围。利用Krylov子空间法建立了电热驱动微夹钳的电热结构耦合宏模型,仿真和实验结果表明了宏模型的有效性。
提出了一种新的求解MEMS非线性动力问题的MOR-PIM方法。将基于Krylov子空间投影等模型降阶方法(Model Order Reduction, MOR)应用于精细积分法(Precise Integration Method, PIM)中,通过对指数矩阵的降阶处理,提高精细积分法的计算与存储效率,使精细积分算法更适用于多自由度变系数强非线性、非保守MEMS动力学系统,为MEMS系统级仿真方法提供新思路。
根据MEMS CAD结构化的思想,结合精化Arnoldi算法和MOR-PIM方法,提出并开发了MEMS_DUT系统级仿真平台。整个过程以VC++6.0编译器为平台,通过对有限元软件ANSYS的二次开发建立器件有限元模型,利用封装MATLAB语言降阶算法得到的动态链接库对MEMS器件进行降阶以获取器件宏模型。将器件宏模型嵌入到系统级仿真平台仿真器Simulink中进行系统级仿真,来实现模拟分析整个系统的动态特性。
利用MEMS_DUT仿真平台,对电热驱动的片内集成微拉伸测试结构,电热驱动和静电驱动的片内集成疲劳弯曲测试结构等进行了系统级仿真,验证了本平台系统级仿真分析的整个流程以及在效率和准确性等方面的性能。最后对精化Arnoldi降阶算法以及系统级仿真平台MEMS DUT需要进一步完善和改进的内容提出了若干建议。
With the appearance of CMOS-MEMS and other various new integrated manufacturing process for the continuous development and compatibility between the micro-nanofabrication technology and integrated circuit manufacturing process, the focus of MEMS production has changed from the early research of individual MEMS device to the current complex system integrated with functional structure of MEMS devices and circuits for mixed-signal processing unit, such as System on Chip (SOC) and System in Package (SIP) representatively. Rapid modeling and simulation on the overall behavior of MEMS devices by computer-aided design tools for MEMS are required for high integration and system functional diversification of MEMS components, and MEMS-design technology inspired by idea of structural designing achieves a significant development. System-level simulation methods based on macromodel which can get behavior characteristic of MEMS have become a famous research field specific to the across multiple coupled energy domains. Aiming at the requirements of fast system-level modeling and simulation as well as the characteristics of multiple energy domains interaction, research works in this paper are presented as follows:
Analytical macromodels for linear beam, nonlinear beam, rigid plate, flexible plate, electrostatic gap, electrostatic comb, "V" shaped drive and other common regular structure for MEMS are established using the analytical method based on the basic theory of structural mechanics. Macromodels are described by MAST hardware language and put into the model library of ARCHITECT module in the CoventorWare software. An on-chip tensile testing structure is designed and optimized by the combined use of the self-built component models and the library structure and circuit elements in commercial software, achieving a high model accuracy according to system-level simulation results.
A refined approach producing MEMS numerical macromodels is proposed by generating the iterative Krylov subspace using a refined Arnoldi algorithm, and project polycondensing the degree of freedom (DOF) of the original system equations described by the state space method in the Krylov subspace based on the transfer function moment matching principle. Compared with traditional methods, the refined approach improves approximation accuracy of the system matrix eigenvalues equivalent to a more accurate approximation to the poles of the system transfer function, obtaining a reduced-order model accuracy. Finite element reduced-order macromodel for V-shaped driven electrothermal microgripper is achieved using this method, and simulation results show that accuracy meets with general requirement. A new Model Order Reduction- Precise Integration Method (MOR-PIM) method for the solution of nonlinear dynamic problems in MEMS area is provided. Model Order Reduction method based on Krylov subspace projection is applied to the precise integration method to enhance its computing and storage efficiency by reduced-order processing the index matrix, therefore precise integration algorithm is more suitable for the nonlinear and non-conservative dynamical systems with multi-degree of freedom and variable coefficients, offering new ideas to system-level simulation.
MEMS_DUT platform for system-level simulation is developed according to MEMS CAD structural idea. Finite element model (FEM) of the device developed secondary by ANSYS software is transformed to macromodel after reduced-order processing by the dynamic link library with MATLAB language of reduced-order algorithm encapsulated on the platform of VC++6.0 compiler throughout the whole flow, and dynamic characteristic of MEMS system is performed by the system-level simulation of macromodel built by embedding in Simulink which is the system-level simulation platform emulator.
Finally, the on-chip tensile testing structures actuated by electrothermal V-shape beam and fatigue testing structures actuated by electrothermal and electrostatic methods respectively are system-level simulated on the MEMS_DUT simulation platform to verify the whole flow and the performance for accuracy and efficiency of the MEMS_DUT platform. And several advices about improving model order reduction algorithm and optimizing the system-level simulation tool has been proposed.
引文
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