基于小波多尺度的无网格RF微器件建模研究
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摘要
RF微器件的制造融合了微加工、集成电路SI工艺等各种技术,其在工作中又受到多种物理因素(如初始应力、机械接触、温度、热弹性、电磁效应、高度)的耦合影响,因此其计算模型的建立和求解面临很大挑战。为了准确预测耦合效应下RF微器件的动作特性,近年来研究人员采用多种方法研究不同物理场之间的耦合机理,探寻快速分析与模拟RF微器件动作的方法,相继建立了能较全面描述多物理场耦合效应下RF微器件动作特性的有限元模型,但这种模型涉及大量自由度。
本文以两种典型的RF微器件——静电驱动电容式开关和扭转微镜为研究对象,对其在多物理场耦合效应下的求解模型,算法理论和求解过程等方面进行了研究。本文给出了新的以较少自由度全面描述RF微器件动作特性的,基于无网格法的数值模拟计算格式和算法设计,实现了对RF微器件机械和电学性能的数值模拟,并与实际试验模型结果进行比较,优化了器件设计。同时,从另一个角度对RF微器件的仿真方法进行了补充、完善和提高。
本文针对RF微器件多物理场耦合效应下的求解模型这一问题进行了一系列研究,主要的研究内容和创新成果如下：
1、针对静电驱动电容式开关多尺度结构,提出了以小波尺度函数为形函数的一维无网格伽辽金法(Wavelet-EFG)求解模型；以无网格法的点适应性代替网格自适应性离散模型的控制方程,进行插值运算；解决了在一维结构分析中施加边界条件问题。实验证明该方法离散控制方程的过程直接,实现离散方程的算法简洁,提高了获取开关Pull-in电压的准确性。
2、在考虑电容边缘场影响的情况下,针对光通信转换器件-扭转微镜多尺度结构,提出了以小波多尺度函数为形函数的无网格再生质点法(Wavelet-RKPM)求解模型；采用机械场-电场分步耦合的方法进行插值运算,求解控制方程；通过多尺度RKPM自适应算法来得到更精确的局部解。实验证明该方法简洁,易于算法实现。
3、进行了微结构层面上基于小波多尺度函数的耦合域多尺度分析研究。根据需要改变分析尺度,实现局部化分析。该方法可以对开关和扭转微镜的临界电压、临界转角场函数梯度变化大的区域采用小的分析尺度,获得这两个参数更多的信息。该算法数值稳定性好,运算速度快,求解精度高。
It is a great challenge to build RF Micro Device's(RF MD) model because they are manufactured by micro-process, SI process etc. and be subject to multiple coupled physical phenomena at process level, such as initial stress, temperature, thermoelastic and electromagnetic effects. In order to accurately predict the characteristics of RF MD under the coupled effect, researchers study mechanism in the physical fields based on a variety of methods and have established more comprehensive multi-physics coupled finite element models which involve a large number of degrees of freedom(DF).
The multi-physics coupled solution model, algorithm theory and the solution process on two typical RF MD-capacitive switch&torsional mirror in this paper. Propose the new numerical scheme and algorithm design method with less DF based on meshless.The mechanical and electrical properties of RF MD are studied in the numerical simulation that used to guide the design with comparison the theoretical model. Meanwhile RF MD simulation methods are supplement and improved.
Coupled model of RF MD under the effect of multi-physics are studied and the main research content and innovations are as follows:
1, Propose solving model of electrostatic droved capacitive switch based on Wavelet-EFG; Model equations are discreted with the non-adaptive grid instead of net grid adaptive. So do interpolation operations; One method is proposed to impose boundary conditions in one-dimensional structural analysis. Experiments confirmed that equations are discreted directly and discrete equations are achieved simply.
2Considering the edge field, propose solving model of torsional mirror based on Wavelet-RKPM; Interpolate, solve equations at Mechanical field-electric field coupling step; More precise local solution is achieved through multi-scale RKPM adaptive algorithm. Experiments confirmed that the method is simple and easy.
3, Coupled multi-scale analysis based on wavelet functions in the micro-structure level. The scales of analysis can be changed to achieve partial analysis to obtain more information of Pull-in and turn angle in capacitive switch&torsional mirror models.
本文以两种典型的RF微器件——静电驱动电容式开关和扭转微镜为研究对象,对其在多物理场耦合效应下的求解模型,算法理论和求解过程等方面进行了研究。本文给出了新的以较少自由度全面描述RF微器件动作特性的,基于无网格法的数值模拟计算格式和算法设计,实现了对RF微器件机械和电学性能的数值模拟,并与实际试验模型结果进行比较,优化了器件设计。同时,从另一个角度对RF微器件的仿真方法进行了补充、完善和提高。
本文针对RF微器件多物理场耦合效应下的求解模型这一问题进行了一系列研究,主要的研究内容和创新成果如下：
1、针对静电驱动电容式开关多尺度结构,提出了以小波尺度函数为形函数的一维无网格伽辽金法(Wavelet-EFG)求解模型；以无网格法的点适应性代替网格自适应性离散模型的控制方程,进行插值运算；解决了在一维结构分析中施加边界条件问题。实验证明该方法离散控制方程的过程直接,实现离散方程的算法简洁,提高了获取开关Pull-in电压的准确性。
2、在考虑电容边缘场影响的情况下,针对光通信转换器件-扭转微镜多尺度结构,提出了以小波多尺度函数为形函数的无网格再生质点法(Wavelet-RKPM)求解模型；采用机械场-电场分步耦合的方法进行插值运算,求解控制方程；通过多尺度RKPM自适应算法来得到更精确的局部解。实验证明该方法简洁,易于算法实现。
3、进行了微结构层面上基于小波多尺度函数的耦合域多尺度分析研究。根据需要改变分析尺度,实现局部化分析。该方法可以对开关和扭转微镜的临界电压、临界转角场函数梯度变化大的区域采用小的分析尺度,获得这两个参数更多的信息。该算法数值稳定性好,运算速度快,求解精度高。
It is a great challenge to build RF Micro Device's(RF MD) model because they are manufactured by micro-process, SI process etc. and be subject to multiple coupled physical phenomena at process level, such as initial stress, temperature, thermoelastic and electromagnetic effects. In order to accurately predict the characteristics of RF MD under the coupled effect, researchers study mechanism in the physical fields based on a variety of methods and have established more comprehensive multi-physics coupled finite element models which involve a large number of degrees of freedom(DF).
The multi-physics coupled solution model, algorithm theory and the solution process on two typical RF MD-capacitive switch&torsional mirror in this paper. Propose the new numerical scheme and algorithm design method with less DF based on meshless.The mechanical and electrical properties of RF MD are studied in the numerical simulation that used to guide the design with comparison the theoretical model. Meanwhile RF MD simulation methods are supplement and improved.
Coupled model of RF MD under the effect of multi-physics are studied and the main research content and innovations are as follows:
1, Propose solving model of electrostatic droved capacitive switch based on Wavelet-EFG; Model equations are discreted with the non-adaptive grid instead of net grid adaptive. So do interpolation operations; One method is proposed to impose boundary conditions in one-dimensional structural analysis. Experiments confirmed that equations are discreted directly and discrete equations are achieved simply.
2Considering the edge field, propose solving model of torsional mirror based on Wavelet-RKPM; Interpolate, solve equations at Mechanical field-electric field coupling step; More precise local solution is achieved through multi-scale RKPM adaptive algorithm. Experiments confirmed that the method is simple and easy.
3, Coupled multi-scale analysis based on wavelet functions in the micro-structure level. The scales of analysis can be changed to achieve partial analysis to obtain more information of Pull-in and turn angle in capacitive switch&torsional mirror models.
引文
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