CN109375096A - A kind of RF MEMS electrostatic drive under the bending condition based on flexible base board switchs microwave property analysis method - Google Patents
A kind of RF MEMS electrostatic drive under the bending condition based on flexible base board switchs microwave property analysis method Download PDFInfo
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Abstract
The invention discloses the RF MEMS electrostatic drives under a kind of bending condition based on flexible base board to switch microwave property analysis method, mainly include two steps: one is establishing the deformation coupling model based on RF MEMS electrostatic drive switch Yu flexible base board co-deflection, realizing the extraction of key structural parameters variable quantity between RF MEMS electrostatic drive switch and flexible base board.The second is switching flexural property model based on RF MEMS electrostatic drive, the deformation quantity of RF MEMS electrostatic drive switch/substrate co-deflection is obtained.Based on the above parameter, rebuilds RF MEMS electrostatic drive and switch microwave property model, influence of the analysis bending deformation to RF MEMS electrostatic drive switch microwave property.The present invention provides one kind to be based on complex environment space, and the RF MEMS electrostatic drive comprising RF MEMS electrostatic drive switch and flexible base board co-deflection model switchs microwave property analysis method.
Description
Technical Field
The invention relates to a mechanical analysis method, in particular to a method for analyzing microwave characteristics of an RFMEMS (radio frequency micro-electromechanical system) electrostatic driving switch based on a flexible substrate bending condition.
Background
In the wave of information development at present, the flexible electronic device has very wide application prospect in the fields of national defense, information, medical treatment, energy and the like due to the unique flexible ductility and the efficient and low-cost manufacturing process. Flexible electronic devices, as a popular development direction of a new generation of semiconductor devices, are a new electronic technology built on a bendable/extensible substrate, and active/passive organic/inorganic electronic devices are manufactured on the flexible substrate, so that the flexible electronic devices have the performance of a traditional rigid electronic system, and also have the unique characteristics of stretching, twisting and folding, and therefore have incomparable importance and advantages in the aspects of shape preservation, miniaturization, light weight, intellectualization and the like applied to a complex environment space. As an important branch of flexible electronic devices, MEMS (micro electro mechanical system) flexible devices, which are conformal, high performance, small volume, and intelligent sensors/actuators, become essential components in the present flexible electronic systems, especially RF MEMS (radio frequency micro electro mechanical system) flexible devices, and due to their wide application prospects in airborne/satellite-borne radar and internet-of-things communication systems, various RF MEMS flexible actuators/sensors become research hotspots in recent years. As the RF MEMS flexible device has no primary characteristic but unique flexibility, which is the application basis and research power of the development of the related flexible device, the bending characteristic of the RF MEMS flexible device is the most scientific problem to be researched. At present, the main research content and purpose of the RF MEMS flexible device based on silicon-based or various flexible substrates are in the performance test stage under the conditions of device design, preparation and non-bending, and the research of the bending characteristic modeling and experimental characterization verification of the RF MEMS flexible device is blank at present. However, from the aspect of scientific research and engineering application, it is urgently needed to establish a bending characteristic model of the RF MEMS device based on the flexible substrate so as to promote the deep research and development application of the RF MEMS flexible device.
Disclosure of Invention
The purpose of the invention is as follows: in order to fill the blank of the research on the bending characteristic model of the RF MEMS electrostatic driving switch at home and abroad, the invention provides a microwave characteristic analysis method of the RF MEMS electrostatic driving switch, which is based on a complex environment space and comprises an RF MEMS electrostatic driving switch and a flexible substrate double-deformation model.
The technical scheme is as follows: the invention provides a method for analyzing microwave characteristics of an RF MEMS electrostatic driving switch based on a flexible substrate bending condition, which is characterized by comprising the following steps of: the method comprises the following steps:
for the first, for the RF MEMS electrostatically driven double clamped beam switch:
step 1: establishing a deformation coupling model based on double deformation of the RF MEMS electrostatic drive switch and the flexible substrate, assuming that the length of a double-end clamped beam is L, the thickness of the beam is t, the Young modulus of the beam is E, the Poisson ratio is n, and when a double-end clamped beam structure has larger residual compressive stress P which is larger than the critical stress of buckling, the residual compressive stress is larger than the critical stress of bucklingDuring the process, the double-end clamped beam structure can be bent upwards (or downwards), and the shape of the bending mode is as follows:
wherein the maximum displacement of the central point of the double-end clamped beam is h:
further, assuming that the initial distance between the double-end clamped beam film bridge and the substrate is g, the bending curvature radius of the flexible substrate is R, and the corresponding central angle after the flexible substrate is bent is α, it can be obtained:
further, the variable quantity of the distance between the flexible substrate and the film bridge after bending is as follows:
step 2: after the flexible substrate is bent, the coplanar waveguide signal line and the ground line are not in the same plane, and the impedance of the coplanar waveguide signal line and the ground line changes. Assuming that the width of a signal line of the coplanar waveguide is S, the distance between the signal line and a ground line is W, and the bending curvature radius of the flexible substrate is R, the characteristic impedance of the coplanar waveguide is as follows:
wherein:
and step 3: and obtaining the deformation quantity of the RFMEMS electrostatic driving switch/substrate double deformation based on the deformation coupling model of the RF MEMS electrostatic driving switch and the flexible substrate double deformation. And reconstructing a microwave characteristic model of the RF MEMS electrostatic driving switch based on the parameters, and analyzing the influence of the bending deformation on the microwave characteristic of the RF MEMS electrostatic driving switch. For RF MEMS electrostatically driven parallel switches, the switch on capacitance versus return loss (S)11Parameters) are:
further, if S11Less than or equal to-10 dB or omega CuZ0＜＜2，The following can be obtained:
where ω is the operating frequency of the RF MEMS electrostatically actuated switch, CuFor parallel capacitance between switch and coplanar waveguide signal lines, Z0Is the characteristic impedance of the coplanar waveguide.
And 4, step 4: the RF MEMS electrostatic driving switch deformation caused by the bending of the flexible substrate can affect the pull-in voltage from two aspects, one is that the initial distance between an upper polar plate and a lower polar plate of the electrostatic driving switch is changed after the flexible substrate is bent to introduce the change of the on-state capacitance of the switch, and the other is that the characteristic impedance of the coplanar waveguide is changed after the flexible substrate is bent. For the RF MEMS double-end clamped beam switch, the flexible substrate is not bent and deformed, if the double-end clamped beam has larger residual compressive stress, and the residual compressive stress is larger than the critical stress of buckling, the double-end clamped beam structure can buckle upwards (or downwards), and the on-state return loss of the RF MEMS double-end clamped beam switch is as follows:
wherein 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, and Z0Is the characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate.
Further, the flexible substrate is bent and deformed, the curvature radius is R, the double-end clamped beam structure is bent, and the on-state return loss of the RF MEMS double-end clamped beam switch is as follows:
wherein 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 initial distance between the switch plates of the double-end clamped beam, and Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower polar plates of the double-end clamped beam under the bending condition of the flexible substrate:
further, the flexible substrate is bent and deformed, the curvature radius is R, the double-end clamped beam structure is not bent, and the on-state return loss of the RF MEMS double-end clamped beam switch is as follows:
wherein 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 initial distance between the switch plates of the double-end clamped beam, and Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower electrode plates of the double-end clamped beam under the bending condition of the flexible substrate.
Secondly, for the RF MEMS electrostatically driven cantilever switch:
step 1: a deformation coupling model based on double deformation of the RF MEMS electrostatic driving switch and the flexible substrate is established, the stress gradient of the cantilever beam in the length direction generates an equivalent bending moment effect on the beam, and the shape of the beam is curled under the action of the bending moment. The direction of the curl and the degree of deviation are related to the nature, magnitude of the residual stress and the direction of the stress gradient. The magnitude of the equivalent bending moment caused by the stress gradient on the cantilever beam is as follows:
wherein t is the beam thickness, w is the beam width, z is the position of the cantilever beam in the thickness direction, σ (z) is a function of the residual stress of the cantilever beam in the length direction with respect to the thickness, the negative value of the residual stress indicates that the internal stress is compressive stress, and the positive value of the residual stress indicates that the internal stress is tensile stress. The bending moment acting on the tail end of the cantilever beam can be obtained, so that the deflection generated by the tail end of the beam is as follows:
further, assuming that the initial distance between the cantilever beam film bridge and the substrate is g, the bending curvature radius of the flexible substrate is R, and the corresponding central angle after the flexible substrate is bent is α, we can obtain:
further, the variable quantity of the distance between the flexible substrate and the film bridge after bending is as follows:
step 2: after the flexible substrate is bent, the coplanar waveguide signal line and the ground line are not in the same plane, and the impedance of the coplanar waveguide signal line and the ground line changes. Assuming that the width of a signal line of the coplanar waveguide is S, the distance between the signal line and a ground line is W, and the bending curvature radius of the flexible substrate is R, the characteristic impedance of the coplanar waveguide is as follows:
wherein:
and step 3: and obtaining the deformation quantity of the RFMEMS electrostatic driving switch/substrate double deformation based on the deformation coupling model of the RF MEMS electrostatic driving switch and the flexible substrate double deformation. And reconstructing a microwave characteristic model of the RF MEMS electrostatic driving switch based on the parameters, and analyzing the influence of the bending deformation on the microwave characteristic of the RF MEMS electrostatic driving switch. For RF MEMS electrostatically driven parallel switches, the switch on capacitance versus return loss (S)11Parameters) are:
further, if S11Less than or equal to-10 dB or omega CuZ0< 2, can obtain:
where ω is the operating frequency of the RF MEMS electrostatically actuated switch, CuFor parallel capacitance between switch and coplanar waveguide signal lines, Z0Is the characteristic impedance of the coplanar waveguide.
And 4, step 4: the RF MEMS electrostatic driving switch deformation caused by the bending of the flexible substrate can affect the pull-in voltage from two aspects, one is that the initial distance between an upper polar plate and a lower polar plate of the electrostatic driving switch is changed after the flexible substrate is bent to introduce the change of the on-state capacitance of the switch, and the other is that the characteristic impedance of the coplanar waveguide is changed after the flexible substrate is bent. For the RF MEMS cantilever switch, the flexible substrate is not bent, if there is a residual stress gradient in the length direction of the cantilever, the cantilever structure will be bent upward (or downward), and the on-state return loss of the RF MEMS cantilever switch is:
wherein,is the shape of the bending mode of the cantilever beam, w is the width of the cantilever beam, g is the initial distance between the switch electrode plates of the cantilever beam, and Z0Is the characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate.
Further, the flexible substrate is bent and deformed, the curvature radius is R, the cantilever beam structure is bent, and the on-state return loss of the RF MEMS cantilever beam switch is as follows:
wherein,is the shape of the bending mode of the cantilever beam, w is the width of the cantilever beam, g is the initial distance between the switch electrode plates of the cantilever beam, and Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower electrode plates of the cantilever beam under the bending condition of the flexible substrate.
The working principle is as follows: the invention provides an estimation method of microwave characteristic parameter change rule of an RF MEMS electrostatic driving switch based on flexible substrate bending condition, aiming at filling the blank of research on RF MEMS electrostatic driving switch bending characteristic models at home and abroad. The method mainly adopts two steps to process the RF MEMS electrostatic driving switch microwave characteristic modeling under the condition of flexible substrate bending deformation, thereby obtaining an analytic model of the influence of the deformed RF MEMS electrostatic driving switch on the device microwave characteristic. One method is to establish a deformation coupling model based on the double deformation of the RF MEMS electrostatic driving switch and the flexible substrate to extract the variation of the key structure parameter between the RF MEMS electrostatic driving switch and the flexible substrate. And the other one is to obtain the deformation quantity of the RF MEMS electrostatic driving switch/substrate double deformation based on the RF MEMS electrostatic driving switch bending characteristic model. And reconstructing a microwave characteristic model of the RF MEMS electrostatic driving switch based on the parameters, and analyzing the influence of the bending deformation on the microwave characteristic of the RF MEMS electrostatic driving switch.
Has the advantages that: compared with the prior art, the method has the advantages that the deformation coupling model based on the double deformation of the RF MEMS electrostatic driving switch and the flexible substrate is established for the first time, and the extraction of the key structure parameter variation between the RF MEMS electrostatic driving switch and the flexible substrate is realized. The microwave characteristic model of the RF MEMS electrostatic driving switch after bending deformation is further established, the method for analyzing the microwave characteristic of the RF MEMS electrostatic driving switch based on the complex environment space and comprising the RF MEMS electrostatic driving switch and the flexible substrate double-deformation model is provided, and the blank of the research on the RF MEMS electrostatic driving switch microwave characteristic model at home and abroad is filled.
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FIG. 1 is a flow chart of the present invention;
fig. 2 is a comparison diagram of the analysis method and simulation and test results of the electrostatic driving switch with the double-end clamped beam provided by the invention.
FIG. 3 is a comparison graph of the analysis method and simulation and test results of the cantilever beam electrostatic driving switch provided by the present invention.
Detailed Description
The invention is further explained below with reference to the drawings.
Firstly, for a double-end clamped beam electrostatic drive switch:
as shown in fig. 1, the RF MEMS double-end clamped beam is taken as an example, in this embodiment, the RF MEMS double-end clamped beam electrostatically drives the switch beam to be made of gold, the flexible substrate is made of Liquid Crystal Polymer (LCP), the length L of the beam is 600 μm, the width w of the beam is 100 μm, the thickness t of the beam is 2 μm, the initial distance g between the upper and lower plates is 2 μm, the young modulus E of the beam is 78Gpa, and the poisson ratio n is 0.42. Assuming that biaxial residual compressive stress initially exists in the RF MEMS double-ended clamped beam electrostatic actuation switch, the beam bends upward, the maximum bending distance h is 0.5 μm, and the curvature of the substrate gradually increases from 0 to 33.3m as the flexible substrate is gradually bent-1。
The specific steps are as follows:
step 1: establishing a deformation coupling model based on double deformation of the RF MEMS electrostatic drive switch and the flexible substrate, assuming that the length of a double-end clamped beam is L, the thickness of the beam is t, the Young modulus of the beam is E, the Poisson ratio is n, and when a double-end clamped beam structure has larger residual compressive stress P which is larger than the critical stress of buckling, the residual compressive stress is larger than the critical stress of bucklingDuring the process, the double-end clamped beam structure can be bent upwards (or downwards), and the shape of the bending mode is as follows:
wherein the maximum displacement of the central point of the double-end clamped beam is h:
wherein,is the moment of inertia.
Further, assuming that the initial distance between the double-end clamped beam film bridge and the substrate is g, the bending curvature radius of the flexible substrate is R, and the corresponding central angle after the flexible substrate is bent is α, it can be obtained:
further, the variable quantity of the distance between the flexible substrate and the film bridge after bending is as follows:
step 2: after the flexible substrate is bent, the coplanar waveguide signal line and the ground line are not in the same plane, and the impedance of the coplanar waveguide signal line and the ground line changes. Assuming that the width of a signal line of the coplanar waveguide is S, the distance between the signal line and a ground line is W, and the bending curvature radius of the flexible substrate is R, the characteristic impedance of the coplanar waveguide is as follows:
wherein:
and step 3: and obtaining the deformation quantity of the RFMEMS electrostatic driving switch/substrate double deformation based on the deformation coupling model of the RF MEMS electrostatic driving switch and the flexible substrate double deformation. And reconstructing a microwave characteristic model of the RF MEMS electrostatic driving switch based on the parameters, and analyzing the influence of the bending deformation on the microwave characteristic of the RF MEMS electrostatic driving switch. For RF MEMS electrostatically driven parallel switches, the switch on capacitance versus return loss (S)11Parameters) are:
further, if S11Less than or equal to-10 dB or omega CuZ0< 2, can obtain:
where ω is the operating frequency of the RF MEMS electrostatically actuated switch, CuFor parallel capacitance between switch and coplanar waveguide signal lines, Z0Is the characteristic impedance of the coplanar waveguide.
And 4, step 4: the RF MEMS electrostatic driving switch deformation caused by the bending of the flexible substrate can affect the pull-in voltage from two aspects, one is that the initial distance between an upper polar plate and a lower polar plate of the electrostatic driving switch is changed after the flexible substrate is bent to introduce the change of the on-state capacitance of the switch, and the other is that the characteristic impedance of the coplanar waveguide is changed after the flexible substrate is bent. For the RF MEMS double-end clamped beam switch, the flexible substrate is not bent and deformed, if the double-end clamped beam has larger residual compressive stress, and the residual compressive stress is larger than the critical stress of buckling, the double-end clamped beam structure can buckle upwards (or downwards), and the on-state return loss of the RF MEMS double-end clamped beam switch is as follows:
wherein 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, and Z0Is the characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate.
Further, the flexible substrate is bent and deformed, the curvature radius is R, the double-end clamped beam structure is bent, and the on-state return loss of the RF MEMS double-end clamped beam switch is as follows:
wherein 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 initial distance between the switch plates of the double-end clamped beam, and Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower polar plates of the double-end clamped beam under the bending condition of the flexible substrate:
further, the flexible substrate is bent and deformed, the curvature radius is R, the double-end clamped beam structure is not bent, and the on-state return loss of the RF MEMS double-end clamped beam switch is as follows:
wherein 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 initial distance between the switch plates of the double-end clamped beam, and Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower electrode plates of the double-end clamped beam under the bending condition of the flexible substrate.
Secondly, for the cantilever beam electrostatic driving switch:
as shown in fig. 1, the present invention takes an RF MEMS cantilever as an example, in this embodiment, values are taken for each parameter, a material of the RF MEMS cantilever electrostatic driving switch beam is gold, a material of the flexible substrate is Liquid Crystal Polymer (LCP), a length L of the beam is 150 μm, a width w of the beam is 100 μm, a thickness t of the beam is 2 μm, and a size of the lower plate is a length L' of 60 μm; the width w' is 150 μm, and the thickness is determined by the thickness of the CPW transmission line. Assuming that the cantilever beam structure electrostatic actuator initially has a biaxial residual compressive stress of 2.5MPa, the curvature of the substrate gradually increases from 0 to 33.3m as the flexible substrate is gradually bent-1。
The specific steps are as follows:
step 1: a deformation coupling model based on double deformation of the RF MEMS electrostatic driving switch and the flexible substrate is established, the stress gradient of the cantilever beam in the length direction generates an equivalent bending moment effect on the beam, and the shape of the beam is curled under the action of the bending moment. The direction of the curl and the degree of deviation are related to the nature, magnitude of the residual stress and the direction of the stress gradient. The magnitude of the equivalent bending moment caused by the stress gradient on the cantilever beam is as follows:
wherein t is the beam thickness, w is the beam width, z is the position of the cantilever beam in the thickness direction, σ (z) is a function of the residual stress of the cantilever beam in the length direction with respect to the thickness, the negative value of the residual stress indicates that the internal stress is compressive stress, and the positive value of the residual stress indicates that the internal stress is tensile stress. The bending moment acting on the tail end of the cantilever beam can be obtained, so that the deflection generated by the tail end of the beam is as follows:
wherein,is the moment of inertia.
Further, assuming that the initial distance between the cantilever beam film bridge and the substrate is g, the bending curvature radius of the flexible substrate is R, and the corresponding central angle after the flexible substrate is bent is α, we can obtain:
further, the variable quantity of the distance between the flexible substrate and the film bridge after bending is as follows:
step 2: after the flexible substrate is bent, the coplanar waveguide signal line and the ground line are not in the same plane, and the impedance of the coplanar waveguide signal line and the ground line changes. Assuming that the width of a signal line of the coplanar waveguide is S, the distance between the signal line and a ground line is W, and the bending curvature radius of the flexible substrate is R, the characteristic impedance of the coplanar waveguide is as follows:
wherein:
and step 3: and obtaining the deformation quantity of the RFMEMS electrostatic driving switch/substrate double deformation based on the deformation coupling model of the RF MEMS electrostatic driving switch and the flexible substrate double deformation. Based on the parameters, a microwave characteristic model of the RF MEMS electrostatic driving switch is reconstructed, and the bending deformation is analyzed for the RF MEMS staticInfluence of the microwave characteristics of the electrically driven switch. For RF MEMS electrostatically driven parallel switches, the switch on capacitance versus return loss (S)11Parameters) are:
further, if S11Less than or equal to-10 dB or omega CuZ0< 2, can obtain:
where ω is the operating frequency of the RF MEMS electrostatically actuated switch, CuFor parallel capacitance between switch and coplanar waveguide signal lines, Z0Is the characteristic impedance of the coplanar waveguide.
And 4, step 4: the RF MEMS electrostatic driving switch deformation caused by the bending of the flexible substrate can affect the pull-in voltage from two aspects, one is that the initial distance between an upper polar plate and a lower polar plate of the electrostatic driving switch is changed after the flexible substrate is bent to introduce the change of the on-state capacitance of the switch, and the other is that the characteristic impedance of the coplanar waveguide is changed after the flexible substrate is bent. For the RF MEMS cantilever switch, the flexible substrate is not bent, if there is a residual stress gradient in the length direction of the cantilever, the cantilever structure will be bent upward (or downward), and the on-state return loss of the RF MEMS cantilever switch is:
wherein,is the shape of the bending mode of the cantilever beam, w is the width of the cantilever beam, g is the initial distance between the switch electrode plates of the cantilever beam, and Z0Is the characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate.
Further, the flexible substrate is bent and deformed, the curvature radius is R, the cantilever beam structure is bent, and the on-state return loss of the RF MEMS cantilever beam switch is as follows:
wherein,is the shape of the bending mode of the cantilever beam, w is the width of the cantilever beam, g is the initial distance between the switch electrode plates of the cantilever beam, and Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower electrode plates of the cantilever beam under the bending condition of the flexible substrate.
As shown in fig. 2, the RF MEMS double-end clamped beam is taken as an example, in this embodiment, the RF MEMS double-end clamped beam electrostatically drives the switch beam to be made of gold, the flexible substrate is made of Liquid Crystal Polymer (LCP), the length L of the beam is 600 μm, the width w of the beam is 100 μm, the thickness t of the beam is 2 μm, the initial distance g between the upper and lower plates is 2 μm, the young modulus E of the beam is 78Gpa, and the poisson ratio n is 0.42. Assuming that biaxial residual compressive stress initially exists in the RF MEMS double-ended clamped beam electrostatic actuation switch, the beam bends upward, the maximum bending distance h is 0.5 μm, and the curvature of the substrate gradually increases from 0 to 33.3m as the flexible substrate is gradually bent-1. The return loss of the RF MEMS double-end clamped beam electrostatic drive switch under the bending condition based on the flexible substrate obtained by analysis by adopting the method provided by the invention is almost completely similar to the simulation result and is several times of the test resultAlmost completely anastomotic. The method provided by the invention can be applied to a complex environment space, comprises an RF MEMS electrostatic driving switch and flexible substrate double-deformation model, and fills the blank of domestic and foreign research on the RF MEMS electrostatic driving switch microwave characteristic model.
As shown in fig. 3, the present invention takes an RF MEMS cantilever as an example, in this embodiment, values are taken for each parameter, a material of the RF MEMS cantilever electrostatic driving switch beam is gold, a material of the flexible substrate is Liquid Crystal Polymer (LCP), a length L of the beam is 150 μm, a width w of the beam is 100 μm, a thickness t of the beam is 2 μm, and a size of the lower plate is a length L' of 60 μm; the width w' is 150 μm, and the thickness is determined by the thickness of the CPW transmission line. Assuming that the cantilever beam structure electrostatic actuator initially has a biaxial residual compressive stress of 2.5MPa, the curvature of the substrate gradually increases from 0 to 33.3m as the flexible substrate is gradually bent-1. The return loss of the cantilever beam electrostatic drive switch under the bending condition based on the flexible substrate obtained by analysis by the method provided by the invention is almost completely similar to the simulation result and almost completely matched with the test result. The method provided by the invention can be applied to a complex environment space, comprises a MEMS cantilever beam structure and flexible substrate double-deformation model, and simultaneously takes the influence of the residual stress gradient of the MEMS cantilever beam structure into consideration, thereby filling the blank of the domestic and foreign research on the flexible device model of the MEMS cantilever beam structure.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.
Claims (6)
1. A microwave characteristic analysis method for an RF MEMS electrostatic driving switch based on a flexible substrate bending condition is characterized by comprising the following steps: the method comprises the following steps:
establishing a deformation coupling model based on double deformation of an RF MEMS electrostatic driving switch and a flexible substrate, wherein the RF MEMS electrostatic driving switch is a double-end clamped beam structure or a cantilever beam, and the double-end clamped beam structure or the cantilever beam is connected with the flexible substrate through an anchor area;
based on the deformation coupling model: after the flexible substrate is deformed, acquiring the distance from the RF MEMS electrostatic driving switch membrane bridge to the flexible substrate;
reconstructing a microwave characteristic model of the RF MEMS electrostatic driving switch based on the parameter value after the flexible substrate is deformed;
and acquiring the influence of the bending of the flexible substrate on the microwave characteristic of the RF MEMS electrostatic driving switch based on the reconstructed microwave characteristic model of the RF MEMS electrostatic driving switch.
2. The RF MEMS electrostatic drive switch microwave characteristic analysis method according to claim 1, wherein: based on the deformation coupling model of RF MEMS electrostatic drive switch and the two deformations of flexible substrate, the flexible substrate bending back bi-polar clamped beam or cantilever beam membrane bridge is to the base plate interval variation volume:
wherein, L is the length of the double-end clamped beam or the cantilever beam, and R is the bending curvature radius of the flexible substrate.
3. The RF MEMS electrostatic drive switch microwave characteristic analysis method according to claim 2, wherein: after the flexible substrate is bent, the coplanar waveguide signal line and the ground line are not in the same plane, the impedance of the coplanar waveguide signal line and the ground line is changed, and the characteristic impedance of the coplanar waveguide after the flexible substrate is bent can be obtained through the bending curvature radius of the flexible substrate.
4. The RF MEMS electrostatic drive switch microwave characteristic analysis method based on the flexible substrate bending condition as claimed in claim 3, wherein: the characteristic impedance of the coplanar waveguide is as follows:
wherein:
5. the RF MEMS electrostatic drive switch microwave characteristic analysis method based on the flexible substrate bending condition as claimed in claim 4, wherein: analyzing the influence of bending deformation on the microwave characteristics of the RF MEMS electrostatic drive switch, and for the RFMEMS electrostatic drive parallel switch, the switch on-state capacitance is opposite to the return loss (S)11Parameters) are:
further, if S11Less than or equal to-10 dB or omega CuZ0< 2, can obtain:
where ω is the operating frequency of the RF MEMS electrostatically actuated switch, CuFor parallel capacitance between switch and coplanar waveguide signal lines, Z0Is the characteristic impedance of the coplanar waveguide.
6. The RF MEMS electrostatic drive switch microwave characteristic analysis method according to claim 1, wherein: the return loss of the RF MEMS electrostatic driving switch in an open state is as follows:
or
Wherein the formula (1) is bent upwards, and the formula (2) is bent downwards; w is the width of the beam, g is the initial distance between the switch plates, Z0The characteristic impedance of the coplanar waveguide under the bending condition of the flexible substrate, and y (x) is the distance between the upper and lower electrode plates of the electrostatic drive switch under the bending condition of the flexible substrate.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2020048106A1 (en) * | 2018-09-04 | 2020-03-12 | 东南大学 | Rf mems electrostatic drive switch microwave characteristic analysis method based on flexible substrate bending condition |
| WO2023023976A1 (en) * | 2021-08-25 | 2023-03-02 | 京东方科技集团股份有限公司 | Radio frequency microelectronic mechanical switch and radio frequency device |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1910109A (en) * | 2003-09-09 | 2007-02-07 | 乔基姆·奥伯哈默 | Film actuator based mems device and method |
| CN106644205A (en) * | 2017-01-12 | 2017-05-10 | 东南大学 | Pressure sensor based on MEMS (Micro Electro Mechanical System) online microwave power sensor structure |
| CN106672894A (en) * | 2017-01-12 | 2017-05-17 | 东南大学 | Curvature sensor based on flexible substrate MEMS switch structure |
| US20170186578A1 (en) * | 2015-12-29 | 2017-06-29 | Synergy Microwave Corporation | High performance switch for microwave mems |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP5437921B2 (en) * | 2010-06-08 | 2014-03-12 | 日本電信電話株式会社 | Inspection system |
| CN104993192A (en) * | 2015-07-29 | 2015-10-21 | 东南大学 | Thermally-driven RF MEMS switch |
| CN106932263A (en) * | 2017-04-07 | 2017-07-07 | 东南大学 | Two-end fixed beam mechanics parameter measuring method and device based on resonant frequency |
| CN107395156A (en) * | 2017-07-10 | 2017-11-24 | 池州睿成微电子有限公司 | A kind of RF MEMS tunable filters based on co-planar waveguide |
| CN109375096B (en) * | 2018-09-04 | 2021-06-29 | 东南大学 | RF MEMS electrostatic drive switch microwave characteristic analysis method based on flexible substrate bending condition |
-
2018
- 2018-09-04 CN CN201811029817.6A patent/CN109375096B/en active Active
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1910109A (en) * | 2003-09-09 | 2007-02-07 | 乔基姆·奥伯哈默 | Film actuator based mems device and method |
| US20170186578A1 (en) * | 2015-12-29 | 2017-06-29 | Synergy Microwave Corporation | High performance switch for microwave mems |
| CN106644205A (en) * | 2017-01-12 | 2017-05-10 | 东南大学 | Pressure sensor based on MEMS (Micro Electro Mechanical System) online microwave power sensor structure |
| CN106672894A (en) * | 2017-01-12 | 2017-05-17 | 东南大学 | Curvature sensor based on flexible substrate MEMS switch structure |
Non-Patent Citations (2)
| Title |
|---|
| 苏锐: ""RF MEMS 开关的设计与优化"", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
| 高晓峰: ""基于LCP基板加工工艺的RF MEMS开关器件的研究"", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2020048106A1 (en) * | 2018-09-04 | 2020-03-12 | 东南大学 | Rf mems electrostatic drive switch microwave characteristic analysis method based on flexible substrate bending condition |
| WO2023023976A1 (en) * | 2021-08-25 | 2023-03-02 | 京东方科技集团股份有限公司 | Radio frequency microelectronic mechanical switch and radio frequency device |
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