WO2020048106A1 - 一种基于柔性基板弯曲条件下的rf mems静电驱动开关微波特性分析方法 - Google Patents

一种基于柔性基板弯曲条件下的rf mems静电驱动开关微波特性分析方法 Download PDF

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WO2020048106A1
WO2020048106A1 PCT/CN2019/078320 CN2019078320W WO2020048106A1 WO 2020048106 A1 WO2020048106 A1 WO 2020048106A1 CN 2019078320 W CN2019078320 W CN 2019078320W WO 2020048106 A1 WO2020048106 A1 WO 2020048106A1
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flexible substrate
mems
electrostatically driven
switch
double
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PCT/CN2019/078320
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French (fr)
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韩磊
于洋
吝晓楠
吴虹剑
田蕾
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东南大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/327—Testing of circuit interrupters, switches or circuit-breakers

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  • the invention relates to a method for mechanical analysis, in particular to a method for analyzing microwave characteristics of an RF MEMS electrostatically driven switch based on a flexible substrate bending condition.
  • flexible electronic devices In the current wave of informatization development, flexible electronic devices have very broad application prospects in the fields of national defense, information, medical, energy and other fields due to their unique bendable ductility and their efficient and low-cost manufacturing processes.
  • Flexible electronic devices as a popular development direction of next-generation semiconductor devices, are emerging electronic technologies based on flexible / stretchable substrates. They make active / passive organic / inorganic electronic devices on flexible substrates, which have both traditional rigid electronic systems. The performance also has the unique characteristics of stretching, twisting and folding, so it has unparalleled importance and advantages in conformity, miniaturization, light weight, and intelligence for complex environmental space applications.
  • MEMS microelectromechanical systems
  • RFMEMS radio frequency fingerprinting
  • RF MEMS flexible electrowetting-semiconductor
  • Flexible devices due to their wide application prospects in airborne / spaceborne radar and IoT communication systems, have made various RF MEMS flexible actuators / sensors a hot topic in recent years.
  • RF MEMS flexible device As an RF MEMS flexible device, its primary characteristic is nothing more than its unique bendability, which is also the application basis and research motivation for the development of related flexible devices. Therefore, the bending characteristics of RF MEMS flexible devices is the scientific problem that needs to be studied most.
  • the present invention provides an RF MEMS electrostatically driven switch microwave based on complex environmental space, including a double deformation model of RF MEMS electrostatically driven switches and flexible substrates. Characteristic analysis methods.
  • the present invention provides a method for analyzing microwave characteristics of an RF MEMS electrostatically driven switch based on a flexible substrate bending condition, which is characterized by including the following steps:
  • Step 1 Establish a deformation coupling model based on the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate.
  • the beam length of the double-ended fixed beam is L
  • the beam thickness is t
  • the Young's modulus of the beam is E
  • the Poisson's ratio is n.
  • Step 2 After the flexible substrate is bent, the coplanar waveguide signal line and the ground line will not be on the same plane, and their impedance will change. Assume that the width of the coplanar waveguide signal line is S, the distance between the signal line and the ground is W, and the bending curvature radius of the flexible substrate is R. At this time, the characteristic impedance of the coplanar waveguide is:
  • Step 3 Based on the deformation coupling model of the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate, obtain the deformation amount of the double deformation of the RF MEMS electrostatically driven switch / substrate. Based on the above parameters, the microwave characteristic model of RF MEMS electrostatically driven switch was reconstructed, and the influence of bending deformation on the microwave characteristics of RF MEMS electrostatically driven switch was analyzed. For RF MEMS electrostatically driven parallel switches, the impact of the switch on-state capacitance on the return loss (S 11 parameter) is:
  • ⁇ is the operating frequency of the RF MEMS electrostatically driven switch
  • Cu is the parallel capacitance between the switch and the signal line of the coplanar waveguide
  • Z 0 is the characteristic impedance of the coplanar waveguide.
  • Step 4 The deformation of the RF electrostatic MEMS electrostatically driven switch caused by the bending of the flexible substrate will affect the pull-in voltage in two ways. One is that the bending of the flexible substrate will cause the initial distance between the upper and lower plates of the electrostatically driven switch to change and change the on-state capacitance of the switch. Second, the bending of the flexible substrate will cause the characteristic impedance of the coplanar waveguide to change. For RF MEMS double-ended fixed-beam switches, the flexible substrate is not bent.
  • the double-ended fixed-beam structure will be upward ( Or downward) buckling occurs, and the open-state return loss of the RF MEMS double-ended clamped beam switch is:
  • u (x) is the shape of the buckling mode of the double-end clamped beam
  • w is the width of the double-end clamped beam
  • g is the distance between the switch plates of the double-end clamped beam
  • Z 0 is the total of the flexible substrate under bending conditions.
  • the open-state return loss of the RF MEMS double-ended fixed-beam switch is:
  • u (x) is the shape of the buckling mode of the double-ended fixed beam
  • w is the width of the double-ended fixed beam
  • g is the initial distance between the switch plates of the double-ended fixed beam
  • Z 0 is the bending condition of the flexible substrate
  • y (x) is the distance between the upper and lower plates of the double-end fixed beam under the flexible substrate bending condition:
  • the open-state return loss of the RF MEMS double-ended clamped beam switch is:
  • u (x) is the shape of the buckling mode of the double-ended fixed beam
  • w is the width of the double-ended fixed beam
  • g is the initial distance between the switch plates of the double-ended fixed beam
  • Z 0 is the bending condition of the flexible substrate
  • y (x) is the distance between the upper and lower plates of the double-end fixed beam under the bending condition of the flexible substrate.
  • Step 1 Establish a deformation coupling model based on the double deformation of the RF MEMS electrostatic drive switch and the flexible substrate.
  • the stress gradient of the cantilever beam in the length direction will produce an equivalent bending moment effect on the beam, and the shape of the beam will act on the bending moment. Curls will occur underneath.
  • the direction of curl and the degree of deviation are related to the nature, magnitude of the residual stress and the direction of the stress gradient.
  • the equivalent bending moment caused by the stress gradient on the cantilever beam is:
  • t is the thickness of the beam
  • w is the width of the beam
  • z is the position in the thickness direction of the cantilever beam
  • ⁇ (z) is a function of the residual stress in the longitudinal direction of the cantilever beam as a function of thickness.
  • a negative residual stress indicates the internal stress is Compressive stress and positive residual stress mean the internal stress is tensile stress.
  • the bending moment acting on the end of the cantilever beam makes the deflection at the end of the beam:
  • Step 2 After the flexible substrate is bent, the coplanar waveguide signal line and the ground line will not be on the same plane, and their impedance will change. Assume that the width of the coplanar waveguide signal line is S, the distance between the signal line and the ground is W, and the bending curvature radius of the flexible substrate is R. At this time, the characteristic impedance of the coplanar waveguide is:
  • Step 3 Based on the deformation coupling model of the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate, obtain the deformation amount of the double deformation of the RF MEMS electrostatically driven switch / substrate. Based on the above parameters, the microwave characteristic model of RF MEMS electrostatically driven switch was reconstructed, and the influence of bending deformation on the microwave characteristics of RF MEMS electrostatically driven switch was analyzed. For RF MEMS electrostatically driven parallel switches, the impact of the switch on-state capacitance on the return loss (S 11 parameter) is:
  • ⁇ is the operating frequency of the RF MEMS electrostatically driven switch
  • Cu is the parallel capacitance between the switch and the signal line of the coplanar waveguide
  • Z 0 is the characteristic impedance of the coplanar waveguide.
  • Step 4 The deformation of the RF electrostatic MEMS electrostatically driven switch caused by the bending of the flexible substrate will affect the pull-in voltage in two ways. One is that the bending of the flexible substrate will cause the initial distance between the upper and lower plates of the electrostatically driven switch to change and change the on-state capacitance of the switch. Second, the bending of the flexible substrate will cause the characteristic impedance of the coplanar waveguide to change. For RF MEMS cantilever switches, the flexible substrate is not bent and deformed. If there is a residual stress gradient in the length direction of the cantilever beam, the cantilever structure will bend upward (or downward). The open-state return loss of the RF MEMS cantilever switch is:
  • w is the width of the cantilever beam
  • g is the initial distance between the switch plates of the cantilever beam
  • Z 0 is the characteristic impedance of the coplanar waveguide when the flexible substrate is bent.
  • the flexible substrate is bent and deformed, the radius of curvature is R, the cantilever beam structure is buckled, and the open-state return loss of the RF MEMS cantilever switch is:
  • w is the width of the cantilever beam
  • g is the initial distance between the cantilever switch plates
  • Z 0 is the characteristic impedance of the coplanar waveguide under flexible substrate bending conditions
  • y (x) is the flexible substrate bending The distance between the upper and lower plates of the cantilever under the conditions.
  • the present invention provides an estimation method based on the variation law of microwave characteristic parameters of RF MEMS electrostatic drive switch under flexible substrate bending conditions.
  • the present invention mainly adopts two steps to process the microwave characteristic modeling of the RF MEMS electrostatically driven switch under the bending deformation condition of the flexible substrate, so as to obtain an analytical model of the influence of the RF MEMS electrostatically driven switch on the microwave characteristics of the device after deformation.
  • the first is to establish a deformation coupling model based on the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate to realize the extraction of key structural parameter changes between the RF MEMS electrostatically driven switch and the flexible substrate.
  • the second is based on the RF MEMS electrostatically driven switch bending characteristic model to obtain the deformation of the RF MEMS electrostatically driven switch / substrate double deformation. Based on the above parameters, the microwave characteristic model of the RF MEMS electrostatically driven switch was reconstructed, and the influence of bending deformation on the microwave characteristics of the RF MEMS electrostatically driven switch was analyzed.
  • the present invention establishes for the first time a deformation coupling model based on the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate, and realizes the extraction of key structural parameter changes between the RF MEMS electrostatically driven switch and the flexible substrate.
  • the microwave characteristic model of RF MEMS electrostatically driven switches after bending deformation is further established, and a method for analyzing the microwave characteristics of RF MEMS electrostatically driven switches based on complex environmental space, including a dual deformation model of RF MEMS electrostatically driven switches and flexible substrates, is provided to fill domestic and foreign countries.
  • the research on the microwave characteristic model of RF MEMS electrostatic drive switch is blank.
  • FIG. 1 is a flowchart of the present invention
  • FIG. 2 is a comparison diagram of the analysis method, simulation, and test results of the electrostatically driven switch of the double-end fixed beam provided by the present invention.
  • FIG. 3 is a comparison diagram of the analysis method, simulation and test results of the cantilever beam electrostatically driven switch provided by the present invention.
  • the present invention takes an RF MEMS double-ended fixed beam as an example.
  • the material of the RF MEMS double-ended fixed beam for electrostatically driving the switch beam is gold and a flexible substrate material. It is a liquid crystal polymer (LCP).
  • LCP liquid crystal polymer
  • the ratio n 0.42.
  • Step 1 Establish a deformation coupling model based on the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate.
  • the beam length of the double-ended fixed beam is L
  • the beam thickness is t
  • the Young's modulus of the beam is E
  • the Poisson's ratio is n.
  • Step 2 After the flexible substrate is bent, the coplanar waveguide signal line and the ground line will not be on the same plane, and their impedance will change. Assume that the width of the coplanar waveguide signal line is S, the distance between the signal line and the ground is W, and the bending curvature radius of the flexible substrate is R. At this time, the characteristic impedance of the coplanar waveguide is:
  • Step 3 Based on the deformation coupling model of the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate, obtain the deformation amount of the double deformation of the RF MEMS electrostatically driven switch / substrate. Based on the above parameters, the microwave characteristic model of RF MEMS electrostatically driven switch was reconstructed, and the influence of bending deformation on the microwave characteristics of RF MEMS electrostatically driven switch was analyzed. For RF MEMS electrostatically driven parallel switches, the impact of the switch on-state capacitance on the return loss (S 11 parameter) is:
  • ⁇ is the operating frequency of the RF MEMS electrostatically driven switch
  • Cu is the parallel capacitance between the switch and the signal line of the coplanar waveguide
  • Z 0 is the characteristic impedance of the coplanar waveguide.
  • Step 4 The deformation of the RF electrostatic MEMS electrostatically driven switch caused by the bending of the flexible substrate will affect the pull-in voltage in two ways. One is that the bending of the flexible substrate will cause the initial distance between the upper and lower plates of the electrostatically driven switch to change and change the on-state capacitance of the switch. Second, the bending of the flexible substrate will cause the characteristic impedance of the coplanar waveguide to change. For RF MEMS double-ended fixed-beam switches, the flexible substrate is not bent.
  • the double-ended fixed-beam structure will be upward ( Or downward) buckling occurs, and the open-state return loss of the RF MEMS double-ended clamped beam switch is:
  • u (x) is the shape of the buckling mode of the double-end clamped beam
  • w is the width of the double-end clamped beam
  • g is the distance between the switch plates of the double-end clamped beam
  • Z 0 is the total of the flexible substrate under bending conditions.
  • the open-state return loss of the RF MEMS double-ended fixed-beam switch is:
  • u (x) is the shape of the buckling mode of the double-ended fixed beam
  • w is the width of the double-ended fixed beam
  • g is the initial distance between the switch plates of the double-ended fixed beam
  • Z 0 is the bending condition of the flexible substrate
  • y (x) is the distance between the upper and lower plates of the double-end fixed beam under the flexible substrate bending condition:
  • the open-state return loss of the RF MEMS double-ended clamped beam switch is:
  • u (x) is the shape of the buckling mode of the double-ended fixed beam
  • w is the width of the double-ended fixed beam
  • g is the initial distance between the switch plates of the double-ended fixed beam
  • Z 0 is the bending condition of the flexible substrate
  • y (x) is the distance between the upper and lower plates of the double-end fixed beam under the bending condition of the flexible substrate.
  • the present invention takes an RF MEMS cantilever as an example.
  • parameters are set.
  • the material of the RF MEMS cantilever electrostatically driven switch beam is gold, and the flexible substrate material is a liquid crystal polymer (LCP). ),
  • the width w ′ 150 ⁇ m.
  • the above-mentioned cantilever structure electrostatic actuator initially has a biaxial residual compressive stress of 2.5 MPa.
  • the curvature of the substrate gradually increases from 0 to 33.3 m -1 .
  • Step 1 Establish a deformation coupling model based on the double deformation of the RF MEMS electrostatic drive switch and the flexible substrate.
  • the stress gradient of the cantilever beam in the length direction will produce an equivalent bending moment effect on the beam, and the shape of the beam will act on the bending moment. Curls will occur underneath.
  • the direction of curl and the degree of deviation are related to the nature, magnitude of the residual stress and the direction of the stress gradient.
  • the equivalent bending moment caused by the stress gradient on the cantilever beam is:
  • t is the thickness of the beam
  • w is the width of the beam
  • z is the position in the thickness direction of the cantilever beam
  • ⁇ (z) is a function of the residual stress of the cantilever beam in the length direction as a function of the thickness.
  • Compressive stress and positive residual stress mean the internal stress is tensile stress.
  • the bending moment acting on the end of the cantilever beam makes the deflection at the end of the beam:
  • Step 2 After the flexible substrate is bent, the coplanar waveguide signal line and the ground line will not be on the same plane, and their impedance will change. Assume that the width of the coplanar waveguide signal line is S, the distance between the signal line and the ground is W, and the bending curvature radius of the flexible substrate is R. At this time, the characteristic impedance of the coplanar waveguide is:
  • Step 3 Based on the deformation coupling model of the double deformation of the RF MEMS electrostatically driven switch and the flexible substrate, obtain the deformation amount of the double deformation of the RF MEMS electrostatically driven switch / substrate. Based on the above parameters, the microwave characteristic model of RF MEMS electrostatically driven switch was reconstructed, and the influence of bending deformation on the microwave characteristics of RF MEMS electrostatically driven switch was analyzed. For RF MEMS electrostatically driven parallel switches, the impact of the switch on-state capacitance on the return loss (S 11 parameter) is:
  • ⁇ is the operating frequency of the RF MEMS electrostatically driven switch
  • Cu is the parallel capacitance between the switch and the signal line of the coplanar waveguide
  • Z 0 is the characteristic impedance of the coplanar waveguide.
  • Step 4 The deformation of the RF electrostatic MEMS electrostatically driven switch caused by the bending of the flexible substrate will affect the pull-in voltage in two ways. One is that the bending of the flexible substrate will cause the initial distance between the upper and lower plates of the electrostatically driven switch to change and change the on-state capacitance of the switch. Second, the bending of the flexible substrate will cause the characteristic impedance of the coplanar waveguide to change. For RF MEMS cantilever switches, the flexible substrate is not bent and deformed. If there is a residual stress gradient in the length direction of the cantilever beam, the cantilever structure will bend upward (or downward). The open-state return loss of the RF MEMS cantilever switch is:
  • w is the width of the cantilever beam
  • g is the initial distance between the switch plates of the cantilever beam
  • Z 0 is the characteristic impedance of the coplanar waveguide when the flexible substrate is bent.
  • the flexible substrate is bent and deformed, the radius of curvature is R, the cantilever beam structure is buckled, and the open-state return loss of the RF MEMS cantilever switch is:
  • w is the width of the cantilever beam
  • g is the initial distance between the cantilever switch plates
  • Z 0 is the characteristic impedance of the coplanar waveguide under flexible substrate bending conditions
  • y (x) is the flexible substrate bending The distance between the upper and lower plates of the cantilever under the conditions.
  • the present invention takes an RF MEMS double-ended fixed beam as an example.
  • the material of the RF MEMS double-ended fixed beam for electrostatically driving the switch beam is gold and a flexible substrate material. It is a liquid crystal polymer (LCP).
  • LCP liquid crystal polymer
  • the ratio n 0.42.
  • the curvature of the substrate gradually increases from 0 to 33.3 m -1 .
  • the method provided by the present invention can be applied to a complex environmental space, and includes a dual deformation model of an RF MEMS electrostatically driven switch and a flexible substrate, which fills a gap in the research on the microwave characteristic model of the RF MEMS electrostatically driven switch at home and abroad.
  • the present invention takes an RF MEMS cantilever as an example.
  • parameters are set.
  • the material of the RF MEMS cantilever electrostatically driven switch beam is gold, and the flexible substrate material is a liquid crystal polymer (LCP). ),
  • the width w ′ 150 ⁇ m
  • the thickness is determined by the thickness of the CPW transmission line.
  • the above-mentioned cantilever structure electrostatic actuator initially has a biaxial residual compressive stress of 2.5 MPa.
  • the curvature of the substrate gradually increases from 0 to 33.3 m -1 .
  • the method provided by the present invention can be applied to complex environmental spaces, including a dual deformation model of a MEMS cantilever structure and a flexible substrate. At the same time, considering the influence of the residual stress gradient of the MEMS cantilever structure, it fills the gaps in the research of MEMS cantilever structure flexible device models at home and abroad .

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Abstract

本发明公开了一种基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法。旨在提供一种柔性基板弯曲变形条件下RF MEMS静电驱动开关微波特性变化规律的估计方法。本发明主要采取两个步骤来处理柔性基板弯曲变形条件下RF MEMS静电驱动开关微波特性建模，从而得到RF MEMS静电驱动开关变形后对器件微波特性影响的解析模型。其一是建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，实现RF MEMS静电驱动开关与柔性基板之间关键结构参数变化量的提取。其二是基于RF MEMS静电驱动开关弯曲特性模型，获得RF MEMS静电驱动开关/基板双变形的形变量。通过以上参数为基础，重建RF MEMS静电驱动开关微波特性模型，分析弯曲变形对RF MEMS静电驱动开关微波特性的影响。为了填补国内外对RF MEMS静电驱动开关微波特性模型的研究空白，本发明提供了一种基于复杂环境空间，包含RF MEMS静电驱动开关与柔性基板双变形模型的RF MEMS静电驱动开关微波特性分析方法。

Description

一种基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法 技术领域
本发明涉及一种力学分析方法，特别涉及一种基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法。
背景技术
在当今信息化发展的浪潮中，柔性电子器件以其独特的可弯曲延展性及其高效、低成本的制造工艺，在国防、信息、医疗、能源等领域具有非常广阔的应用前景。柔性电子器件作为新一代半导体器件的热门发展方向，是建立在可弯曲/延展基板上的新兴电子技术，其将主动/被动的有机/无机电子器件制作在柔性基板上，既具有传统刚性电子系统的性能，也具有拉伸、扭曲、折叠这种独特的特性，因此在对复杂环境空间应用的保形、小型化、轻量化、智能化等方面具有无可比拟的重要性和优势。MEMS(微机电系统)柔性器件作为柔性电子器件的重要分支，其保形、高性能、小体积、智能化的传感器/执行器成为当今柔性电子系统中必不可少的组成部分，特别是RF MEMS(射频微机电系统)柔性器件，由于其在机载/星载雷达和物联网通信系统中的广泛应用前景，使得各种RF MEMS柔性执行器/传感器成为了近年来的研究热点。作为RF MEMS柔性器件，其首要特性无非是具备独特的可弯曲性，这也是相关柔性器件发展的应用基础和研究动力，因此RF MEMS柔性器件弯曲特性是最需要研究的科学问题。目前无论是基于硅基的还是基于各类柔性基板的RF MEMS柔性器件，其主要的研究内容和目的还都处于器件设计、制备和非弯曲条件下的性能测试阶段，RF MEMS柔性器件的弯曲特性建模和实验表征验证的研究目前还处于空白。然而，不管从科学研究角度还是工程应用层面，都迫切需要建立起基于柔性基板的RF MEMS器件的弯曲特性模型，以推动RF MEMS柔性器件的深入研究和开发应用。
发明内容
发明目的：为了填补国内外对RF MEMS静电驱动开关弯曲特性模型的研究空白，本发明提供了一种基于复杂环境空间，包含RF MEMS静电驱动开关与柔性基板双变形模型的RF MEMS静电驱动开关微波特性分析方法。
技术方案：本发明提供了一种基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：包括以下步骤：
其一，对于RF MEMS静电驱动双端固支梁开关：
步骤1：建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，假设双端固支梁梁长为L，梁厚为t，梁的杨氏模量为E，泊松比为n，当双端固支梁结构存在较大 的残余压应力P，残余压应力大于发生屈曲的临界应力
Figure PCTCN2019078320-appb-000001
时，双端固支梁结构会向上(或者向下)发生屈曲，屈曲模态的形状为：
Figure PCTCN2019078320-appb-000002
其中双端固支梁中心点的最大位移大小为h：
Figure PCTCN2019078320-appb-000003
进一步，假设双端固支梁膜桥到基板初始间距为g，柔性基板弯曲曲率半径为R，柔性基板弯曲后对应的圆心角为α，可得：
Figure PCTCN2019078320-appb-000004
进一步，柔性基板弯曲后膜桥到基板间距变化量为：
Figure PCTCN2019078320-appb-000005
步骤2：柔性基板弯曲后，共面波导信号线和地线将不在一个平面，其阻抗将发生变化。假设共面波导信号线宽度为S，信号线到地线之间距离为W，柔性基板弯曲曲率半径为R，此时共面波导特性阻抗为：
Figure PCTCN2019078320-appb-000006
其中：
Figure PCTCN2019078320-appb-000007
Figure PCTCN2019078320-appb-000008
Figure PCTCN2019078320-appb-000009
Figure PCTCN2019078320-appb-000010
Figure PCTCN2019078320-appb-000011
步骤3：基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，获得RF MEMS 静电驱动开关/基板双变形的形变量。通过以上参数为基础，重建RF MEMS静电驱动开关微波特性模型，分析弯曲变形对RF MEMS静电驱动开关微波特性的影响。对于RF MEMS静电驱动并联开关，开关开态电容对回波损耗(S 11参数)的影响为：
Figure PCTCN2019078320-appb-000012
进一步，如果S 11≤-10dB或ωC uZ 0＜＜2，可得：
Figure PCTCN2019078320-appb-000013
其中ω为RF MEMS静电驱动开关的工作频率，C u为开关到共面波导信号线间的并联电容，Z 0为共面波导的特性阻抗。
步骤4：柔性基板弯曲引起的RF MEMS静电驱动开关变形会从两方面影响吸合电压，其一是柔性基板弯曲后会导致静电驱动开关上下极板的初始间距变化而引入开关开态电容的变化，其二是柔性基板弯曲后会导致共面波导弯曲后特性阻抗发生变化。对于RF MEMS双端固支梁开关，柔性基板未弯曲变形，如果双端固支梁存在较大的残余压应力，残余压应力大于发生屈曲的临界应力时，双端固支梁结构会向上(或者向下)发生屈曲，RF MEMS双端固支梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000014
(向上屈曲)
Figure PCTCN2019078320-appb-000015
(向下屈曲)
其中，u(x)为双端固支梁屈曲模态的形状，w为双端固支梁的宽度，g为双端固支梁开关极板间距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗。
进一步，柔性基板弯曲变形，曲率半径为R，双端固支梁结构发生屈曲，RF MEMS双端固支梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000016
(向上屈曲)
Figure PCTCN2019078320-appb-000017
(向下屈曲)
其中，u(x)为双端固支梁屈曲模态的形状，w为双端固支梁的宽度，g为双端固支梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条件下双端固支梁上下极板间的距离：
Figure PCTCN2019078320-appb-000018
进一步，柔性基板弯曲变形，曲率半径为R，双端固支梁结构未发生屈曲，RF MEMS双端固支梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000019
其中，u(x)为双端固支梁屈曲模态的形状，w为双端固支梁的宽度，g为双端固支梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条件下双端固支梁上下极板间的距离。
其二，对于RF MEMS静电驱动悬臂梁开关：
步骤1：建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，悬臂梁在长度方向上的应力梯度将在梁上产生一个等效的弯矩作用，梁的形态在弯矩的作用下将会发生卷曲。卷曲的方向和偏离的程度与残余应力的性质、大小和应力梯度的方向有关。由悬臂梁上的应力梯度引起的等效弯矩大小为：
Figure PCTCN2019078320-appb-000020
其中，t为梁厚，w为梁宽，z为悬臂梁厚度方向上的位置，σ(z)为悬臂梁在长度方向上的残余应力关于厚度的函数，残余应力为负值表示内应力为压应力，残余应力为正值表示内应力为张应力。可得作用在悬臂梁末端的弯矩使得梁末端产生的挠度大小为：
Figure PCTCN2019078320-appb-000021
进一步，假设悬臂梁膜桥到基板初始间距为g，柔性基板弯曲曲率半径为R，柔性基板弯曲后对应的圆心角为α，可得：
Figure PCTCN2019078320-appb-000022
进一步，柔性基板弯曲后膜桥到基板间距变化量为：
Figure PCTCN2019078320-appb-000023
步骤2：柔性基板弯曲后，共面波导信号线和地线将不在一个平面，其阻抗将发生变化。假设共面波导信号线宽度为S，信号线到地线之间距离为W，柔性基板弯曲曲率半径为R，此时共面波导特性阻抗为：
Figure PCTCN2019078320-appb-000024
其中：
Figure PCTCN2019078320-appb-000025
Figure PCTCN2019078320-appb-000026
Figure PCTCN2019078320-appb-000027
Figure PCTCN2019078320-appb-000028
Figure PCTCN2019078320-appb-000029
步骤3：基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，获得RF MEMS静电驱动开关/基板双变形的形变量。通过以上参数为基础，重建RF MEMS静电驱动开关微波特性模型，分析弯曲变形对RF MEMS静电驱动开关微波特性的影响。对于RF MEMS静电驱动并联开关，开关开态电容对回波损耗(S 11参数)的影响为：
Figure PCTCN2019078320-appb-000030
进一步，如果S 11≤-10dB或ωC uZ 0＜＜2，可得：
Figure PCTCN2019078320-appb-000031
其中ω为RF MEMS静电驱动开关的工作频率，C u为开关到共面波导信号线间的并联电 容，Z 0为共面波导的特性阻抗。
步骤4：柔性基板弯曲引起的RF MEMS静电驱动开关变形会从两方面影响吸合电压，其一是柔性基板弯曲后会导致静电驱动开关上下极板的初始间距变化而引入开关开态电容的变化，其二是柔性基板弯曲后会导致共面波导弯曲后特性阻抗发生变化。对于RF MEMS悬臂梁开关，柔性基板未弯曲变形，如果悬臂梁在长度方向上存在残余应力梯度，悬臂梁结构会向上(或者向下)发生弯曲，RF MEMS悬臂梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000032
(向上屈曲)
Figure PCTCN2019078320-appb-000033
(向下屈曲)
其中，
Figure PCTCN2019078320-appb-000034
为悬臂梁屈曲模态的形状，w为悬臂梁的宽度，g为悬臂梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗。
进一步，柔性基板弯曲变形，曲率半径为R，悬臂梁结构发生屈曲，RF MEMS悬臂梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000035
(向上屈曲)
Figure PCTCN2019078320-appb-000036
(向下屈曲)
其中，
Figure PCTCN2019078320-appb-000037
为悬臂梁屈曲模态的形状，w为悬臂梁的宽度，g为悬臂梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条件下悬臂梁上下极板间的距离。
工作原理：本发明为了填补国内外对RF MEMS静电驱动开关弯曲特性模型的研究空白，提供一种基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性参数变化规律的估计方法。本发明主要采取两个步骤来处理柔性基板弯曲变形条件下RF MEMS静电驱动开关微波特性建模，从而得到RF MEMS静电驱动开关变形后对器件微波特性影响的解析模型。其一是建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，实现RF MEMS静电 驱动开关与柔性基板之间关键结构参数变化量的提取。其二是基于RF MEMS静电驱动开关弯曲特性模型，获得RF MEMS静电驱动开关/基板双变形的形变量。通过以上参数为基础，重建RF MEMS静电驱动开关微波特性模型，分析弯曲变形对RF MEMS静电驱动开关微波特性的影响。
有益效果：与现有技术相比，本发明首次建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，实现RF MEMS静电驱动开关与柔性基板之间关键结构参数变化量的提取。进一步建立弯曲变形后RF MEMS静电驱动开关的微波特性模型，提供了一种基于复杂环境空间，包含RF MEMS静电驱动开关与柔性基板双变形模型的RF MEMS静电驱动开关微波特性分析方法，填补国内外对RF MEMS静电驱动开关微波特性模型的研究空白。
附图说明
图1是本发明的流程图；
图2是本发明提供的双端固支梁静电驱动开关分析方法与模拟、测试结果对比图。
图3是本发明提供的悬臂梁静电驱动开关分析方法与模拟、测试结果对比图。
具体实施方式
下面结合附图对本发明做更进一步的解释。
其一，对于双端固支梁静电驱动开关：
如图1所示，本发明以RF MEMS双端固支梁为例，在本实施例中对各参数取值，RF MEMS双端固支梁静电驱动开关梁的材料为金，柔性衬底材料为液晶聚合物(LCP)，梁的长度L＝600μm，梁的宽度w＝100μm，梁的厚度t＝2μm，上下极板初始间距g＝2μm，梁的杨氏模量E＝78Gpa，泊松比n＝0.42。假设上述RF MEMS双端固支梁静电驱动开关初始存在双轴残余压应力，梁向上屈曲，最大屈曲距离h＝0.5μm，随着柔性基板逐渐弯曲，基板的曲率由0逐渐增大至33.3m -1。
具体步骤如下所示：
步骤1：建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，假设双端固支梁梁长为L，梁厚为t，梁的杨氏模量为E，泊松比为n，当双端固支梁结构存在较大的残余压应力P，残余压应力大于发生屈曲的临界应力
Figure PCTCN2019078320-appb-000038
时，双端固支梁结构会向上(或者向下)发生屈曲，屈曲模态的形状为：
Figure PCTCN2019078320-appb-000039
其中双端固支梁中心点的最大位移大小为h：
Figure PCTCN2019078320-appb-000040
其中，
Figure PCTCN2019078320-appb-000041
为转动惯量。
进一步，假设双端固支梁膜桥到基板初始间距为g，柔性基板弯曲曲率半径为R，柔性基板弯曲后对应的圆心角为α，可得：
Figure PCTCN2019078320-appb-000042
进一步，柔性基板弯曲后膜桥到基板间距变化量为：
Figure PCTCN2019078320-appb-000043
步骤2：柔性基板弯曲后，共面波导信号线和地线将不在一个平面，其阻抗将发生变化。假设共面波导信号线宽度为S，信号线到地线之间距离为W，柔性基板弯曲曲率半径为R，此时共面波导特性阻抗为：
Figure PCTCN2019078320-appb-000044
其中：
Figure PCTCN2019078320-appb-000045
Figure PCTCN2019078320-appb-000046
Figure PCTCN2019078320-appb-000047
Figure PCTCN2019078320-appb-000048
Figure PCTCN2019078320-appb-000049
步骤3：基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，获得RF MEMS静电驱动开关/基板双变形的形变量。通过以上参数为基础，重建RF MEMS静电驱动开关微波特性模型，分析弯曲变形对RF MEMS静电驱动开关微波特性的影响。对于RF MEMS静电驱动并联开关，开关开态电容对回波损耗(S 11参数)的影响为：
Figure PCTCN2019078320-appb-000050
进一步，如果S 11≤-10dB或ωC uZ 0＜＜2，可得：
Figure PCTCN2019078320-appb-000051
其中ω为RF MEMS静电驱动开关的工作频率，C u为开关到共面波导信号线间的并联电容，Z 0为共面波导的特性阻抗。
步骤4：柔性基板弯曲引起的RF MEMS静电驱动开关变形会从两方面影响吸合电压，其一是柔性基板弯曲后会导致静电驱动开关上下极板的初始间距变化而引入开关开态电容的变化，其二是柔性基板弯曲后会导致共面波导弯曲后特性阻抗发生变化。对于RF MEMS双端固支梁开关，柔性基板未弯曲变形，如果双端固支梁存在较大的残余压应力，残余压应力大于发生屈曲的临界应力时，双端固支梁结构会向上(或者向下)发生屈曲，RF MEMS双端固支梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000052
(向上屈曲)
Figure PCTCN2019078320-appb-000053
(向下屈曲)
其中，u(x)为双端固支梁屈曲模态的形状，w为双端固支梁的宽度，g为双端固支梁开关极板间距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗。
进一步，柔性基板弯曲变形，曲率半径为R，双端固支梁结构发生屈曲，RF MEMS双端固支梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000054
(向上屈曲)
Figure PCTCN2019078320-appb-000055
(向下屈曲)
其中，u(x)为双端固支梁屈曲模态的形状，w为双端固支梁的宽度，g为双端固支梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条 件下双端固支梁上下极板间的距离：
Figure PCTCN2019078320-appb-000056
进一步，柔性基板弯曲变形，曲率半径为R，双端固支梁结构未发生屈曲，RF MEMS双端固支梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000057
其中，u(x)为双端固支梁屈曲模态的形状，w为双端固支梁的宽度，g为双端固支梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条件下双端固支梁上下极板间的距离。
其二，对于悬臂梁静电驱动开关：
如图1所示，本发明以RF MEMS悬臂梁为例，在本实施例中对各参数取值，RF MEMS悬臂梁静电驱动开关梁的材料为金，柔性衬底材料为液晶聚合物(LCP)，梁的长度L＝150μm，梁的宽度w＝100μm，梁的厚度t＝2μm，下极板的尺寸为长L′＝60μm；宽w′＝150μm，厚度由CPW传输线厚度决定。假设上述悬臂梁结构静电驱动器初始存在大小为2.5MPa的双轴残余压应力，随着柔性基板逐渐弯曲，基板的曲率由0逐渐增大至33.3m -1。
具体步骤如下所示：
步骤1：建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，悬臂梁在长度方向上的应力梯度将在梁上产生一个等效的弯矩作用，梁的形态在弯矩的作用下将会发生卷曲。卷曲的方向和偏离的程度与残余应力的性质、大小和应力梯度的方向有关。由悬臂梁上的应力梯度引起的等效弯矩大小为：
Figure PCTCN2019078320-appb-000058
其中，t为梁厚，w为梁宽，z为悬臂梁厚度方向上的位置，σ(z)为悬臂梁在长度方向上的残余应力关于厚度的函数，残余应力为负值表示内应力为压应力，残余应力为正值表示内应力为张应力。可得作用在悬臂梁末端的弯矩使得梁末端产生的挠度大小为：
Figure PCTCN2019078320-appb-000059
其中，
Figure PCTCN2019078320-appb-000060
为转动惯量。
进一步，假设悬臂梁膜桥到基板初始间距为g，柔性基板弯曲曲率半径为R，柔性基板弯曲后对应的圆心角为α，可得：
Figure PCTCN2019078320-appb-000061
进一步，柔性基板弯曲后膜桥到基板间距变化量为：
Figure PCTCN2019078320-appb-000062
步骤2：柔性基板弯曲后，共面波导信号线和地线将不在一个平面，其阻抗将发生变化。假设共面波导信号线宽度为S，信号线到地线之间距离为W，柔性基板弯曲曲率半径为R，此时共面波导特性阻抗为：
Figure PCTCN2019078320-appb-000063
其中：
Figure PCTCN2019078320-appb-000064
Figure PCTCN2019078320-appb-000065
Figure PCTCN2019078320-appb-000066
Figure PCTCN2019078320-appb-000067
Figure PCTCN2019078320-appb-000068
步骤3：基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，获得RF MEMS静电驱动开关/基板双变形的形变量。通过以上参数为基础，重建RF MEMS静电驱动开关微波特性模型，分析弯曲变形对RF MEMS静电驱动开关微波特性的影响。对于RF MEMS静电驱动并联开关，开关开态电容对回波损耗(S 11参数)的影响为：
Figure PCTCN2019078320-appb-000069
进一步，如果S 11≤-10dB或ωC uZ 0＜＜2，可得：
Figure PCTCN2019078320-appb-000070
其中ω为RF MEMS静电驱动开关的工作频率，C u为开关到共面波导信号线间的并联电容，Z 0为共面波导的特性阻抗。
步骤4：柔性基板弯曲引起的RF MEMS静电驱动开关变形会从两方面影响吸合电压，其一是柔性基板弯曲后会导致静电驱动开关上下极板的初始间距变化而引入开关开态电容的变化，其二是柔性基板弯曲后会导致共面波导弯曲后特性阻抗发生变化。对于RF MEMS悬臂梁开关，柔性基板未弯曲变形，如果悬臂梁在长度方向上存在残余应力梯度，悬臂梁结构会向上(或者向下)发生弯曲，RF MEMS悬臂梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000071
(向上屈曲)
Figure PCTCN2019078320-appb-000072
(向下屈曲)
其中，
Figure PCTCN2019078320-appb-000073
为悬臂梁屈曲模态的形状，w为悬臂梁的宽度，g为悬臂梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗。
进一步，柔性基板弯曲变形，曲率半径为R，悬臂梁结构发生屈曲，RF MEMS悬臂梁开关开态回波损耗为：
Figure PCTCN2019078320-appb-000074
(向上屈曲)
Figure PCTCN2019078320-appb-000075
(向下屈曲)
其中，
Figure PCTCN2019078320-appb-000076
为悬臂梁屈曲模态的形状，w为悬臂梁的宽度，g为悬臂梁开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条件下悬臂梁上下极板间的距离。
如图2所示，本发明以RF MEMS双端固支梁为例，在本实施例中对各参数取值，RF MEMS双端固支梁静电驱动开关梁的材料为金，柔性衬底材料为液晶聚合物(LCP)，梁的长 度L＝600μm，梁的宽度w＝100μm，梁的厚度t＝2μm，上下极板初始间距g＝2μm，梁的杨氏模量E＝78Gpa，泊松比n＝0.42。假设上述RF MEMS双端固支梁静电驱动开关初始存在双轴残余压应力，梁向上屈曲，最大屈曲距离h＝0.5μm，随着柔性基板逐渐弯曲，基板的曲率由0逐渐增大至33.3m -1。采用本发明提供的方法分析获得的基于柔性基板弯曲条件下RF MEMS双端固支梁静电驱动开关回波损耗与模拟的结果几乎完全相似，并且与测试结果几乎完全吻合。本发明提供的方法可以应用于复杂环境空间，包含RF MEMS静电驱动开关与柔性基板双变形模型，填补国内外对RF MEMS静电驱动开关微波特性模型的研究空白。
如图3所示，本发明以RF MEMS悬臂梁为例，在本实施例中对各参数取值，RF MEMS悬臂梁静电驱动开关梁的材料为金，柔性衬底材料为液晶聚合物(LCP)，梁的长度L＝150μm，梁的宽度w＝100μm，梁的厚度t＝2μm，下极板的尺寸为长L′＝60μm；宽w′＝150μm，厚度由CPW传输线厚度决定。假设上述悬臂梁结构静电驱动器初始存在大小为2.5MPa的双轴残余压应力，随着柔性基板逐渐弯曲，基板的曲率由0逐渐增大至33.3m -1。采用本发明提供的方法分析获得的基于柔性基板弯曲条件下悬臂梁静电驱动开关回波损耗与模拟的结果几乎完全相似，并且与测试结果几乎完全吻合。本发明提供的方法可以应用于复杂环境空间，包含MEMS悬臂梁结构与柔性基板双变形模型，同时考虑MEMS悬臂梁结构残余应力梯度的影响，填补国内外对MEMS悬臂梁结构柔性器件模型的研究空白。
以上所述仅为本发明的较佳实施方式，本发明的保护范围并不以上述实施方式为限，但凡本领域普通技术人员根据本发明所揭示内容所作的等效修饰或变化，皆应纳入权利要求书中记载的保护范围内。

Claims (6)

  1. 一种基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：包括以下步骤：
    建立基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，所述RF MEMS静电驱动开关为双端固支梁结构或者悬臂梁，所述双端固支梁结构或者悬臂梁通过锚区与所述柔性基板相连接；
    基于所述形变耦合模型：所述柔性基板变形后，获取所述RF MEMS静电驱动开关膜桥至所述柔性基板的间距；
    基于所述柔性基板变形后的参数值，重建RF MEMS静电驱动开关的微波特性模型；
    基于所述重建的RF MEMS静电驱动开关的微波特性模型，获取柔性基板弯曲对RF MEMS静电驱动开关微波特性的影响；
  2. 根据权利要求1所述的基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：基于RF MEMS静电驱动开关与柔性基板双变形的形变耦合模型，所述柔性基板弯曲后双端固支梁或者悬臂梁膜桥到基板间距变化量为：
    Figure PCTCN2019078320-appb-100001
    其中，L为双端固支梁或悬臂梁梁长，R为柔性基板弯曲曲率半径。
  3. 根据权利要求2所述的基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：所述柔性基板弯曲后，共面波导信号线和地线将不在一个平面，其阻抗将发生变化，由柔性基板弯曲曲率半径可得柔性基板弯曲后共面波导的特性阻抗。
  4. 根据权利要求3所述的基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：所述共面波导的特性阻抗为：
    Figure PCTCN2019078320-appb-100002
    其中：
    Figure PCTCN2019078320-appb-100003
    Figure PCTCN2019078320-appb-100004
    Figure PCTCN2019078320-appb-100005
    Figure PCTCN2019078320-appb-100006
    Figure PCTCN2019078320-appb-100007
  5. 根据权利要求4所述的基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：分析弯曲变形对RF MEMS静电驱动开关微波特性的影响，对于RF MEMS静电驱动并联开关，开关开态电容对回波损耗(S 11参数)的影响为：
    Figure PCTCN2019078320-appb-100008
    进一步，如果S 11≤-10dB或ωC uZ 0＜＜2，可得：
    Figure PCTCN2019078320-appb-100009
    其中ω为RF MEMS静电驱动开关的工作频率，C u为开关到共面波导信号线间的并联电容，Z 0为共面波导的特性阻抗。
  6. 根据权利要求1所述的基于柔性基板弯曲条件下的RF MEMS静电驱动开关微波特性分析方法，其特征在于：RF MEMS静电驱动开关开态回波损耗为：
    Figure PCTCN2019078320-appb-100010
    或
    Figure PCTCN2019078320-appb-100011
    其中，式(1)向上屈曲、式(2)向下屈曲；w为梁的宽度，g为开关极板间初始距离，Z 0为柔性基板弯曲条件下共面波导的特性阻抗，y(x)为柔性基板弯曲条件下静电驱动开关上下极板间的距离。
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