CN109472113B - Dynamic model analysis method for flexible MEMS electrostatic drive switch mechanics - Google Patents
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Abstract
The patent proposes a dynamic model analysis method of flexible MEMS electrostatic drive switch mechanics, comprising the following steps: establishing an initial mechanical dynamic model of the MEMS electrostatic drive switch; establishing a deformation coupling model based on double deformation of the MEMS electrostatic drive switch and the flexible substrate; after the flexible substrate is buckled and deformed, the distance between the MEMS electrostatic driving switch membrane bridge and the flexible substrate is acquired; after the flexible substrate is subjected to buckling deformation, obtaining a parameter value of the flexible substrate after buckling deformation; reconstructing a mechanical dynamic model of the MEMS electrostatic drive switch according to the parameter value after the flexible substrate is buckled and deformed; based on the reconstructed model, the influence of flexible substrate buckling on the MEMS electrostatic drive switch mechanical dynamic model is obtained, and the gap of research on the RF MEMS electrostatic drive switch bending characteristic model at home and abroad is filled.
Description
Technical Field
The invention relates to a mechanical analysis method, in particular to an RF MEMS electrostatic drive switch mechanical dynamic model analysis method based on flexible substrate bending conditions.
Background
In the wave of the information development at present, the flexible electronic device has very wide application prospect in the fields of national defense, information, medical treatment, energy sources and the like by the unique flexible ductility and the high-efficiency and low-cost manufacturing process thereof. The flexible electronic device is a new generation of semiconductor device, and is an emerging electronic technology built on a flexible/extensible substrate, and active/passive organic/inorganic electronic devices are manufactured on the flexible substrate, so that the flexible electronic device has the characteristics of traditional rigid electronic systems, and unique characteristics of stretching, twisting and folding, and therefore, the flexible electronic device has incomparable importance and advantages in the aspects of shape preservation, miniaturization, light weight, intellectualization and the like applied to complex environmental space. MEMS (micro-electro-mechanical systems) flexible devices are an important branch of flexible electronic devices, and conformal, high-performance, small-volume and intelligent sensors/actuators become indispensable components in present flexible electronic systems, particularly RF MEMS (radio frequency micro-electro-mechanical systems) flexible devices, and due to their wide application prospects in airborne/satellite radar and internet of things communication systems, various RF MEMS flexible actuators/sensors become research hotspots in recent years. As RF MEMS flexible devices, the primary characteristics are not unique in flexibility, which is also the application basis and research power for the development of related flexible devices, so the bending characteristics of RF MEMS flexible devices are the scientific problems that need to be studied most. At present, the main research content and purposes of the RF MEMS flexible device based on silicon base and various flexible substrates are in the performance test stage under the device design, preparation and non-bending conditions, and the research of bending characteristic modeling and experimental characterization verification of the RF MEMS flexible device is still blank at present. However, from the aspect of scientific research and engineering application, it is highly desirable to build a bending property model of the RF MEMS device based on the flexible substrate, so as to promote the deep research and development of the RF MEMS flexible device.
Disclosure of Invention
The invention aims to: in order to fill the blank of research on the bending characteristic model of the RF MEMS electrostatic drive switch at home and abroad, the invention provides an analysis method of the dynamic model of the RF MEMS electrostatic drive switch based on a complex environment space and comprising the RF MEMS electrostatic drive switch and a flexible substrate dual-deformation model.
The technical scheme is as follows: the invention provides a dynamic model analysis method of flexible MEMS electrostatic drive switch mechanics, which mainly comprises the following steps:
establishing an initial mechanical dynamic model of the MEMS electrostatic drive switch;
establishing a deformation coupling model based on double deformation of the MEMS electrostatic drive switch and the flexible substrate;
after the flexible substrate is buckled and deformed, the distance between the MEMS electrostatic driving switch membrane bridge and the flexible substrate is acquired;
after the flexible substrate is subjected to buckling deformation, obtaining a parameter value of the flexible substrate after buckling deformation;
reconstructing a mechanical dynamic model of the MEMS electrostatic drive switch according to the parameter value after the flexible substrate is buckled and deformed;
based on the reconstructed model, the influence of flexible substrate buckling on the MEMS electrostatic drive switch mechanical dynamic model is obtained.
Further, the initial mechanical dynamic model of the MEMS electrostatic driving switch is:
wherein x is the pull-down distance of the membrane bridge, m is the mass of the electrostatic drive switch, f is the electrostatic force between the polar plates, and k is the equivalent spring coefficient of the middle beam structure of the electrostatic drive switch.
Further, the MEMS electrostatic driving switch is a double-end clamped beam RFMEMS electrostatic driving switch.
Further, the MEMS electrostatic driving switch is a cantilever RFMEMS electrostatic driving switch.
Further, the deformation coupling model is as follows:
wherein h is the maximum displacement of the center point of the double-end clamped beam:
wherein ,
for moment of inertia, L is the double-ended clamped beam length, t is Liang Hou, w is the beam width, E is the Young's modulus of the beam, n is the Poisson's ratio, and P is the residual compressive stress.
Further, after the flexible substrate is buckled and deformed, the distance variation from the MEMS electrostatic drive switch membrane bridge to the flexible substrate is as follows;
wherein L is a double-ended clamped beam or cantilever Liang Liangchang, and R is the buckling curvature radius of the flexible substrate.
Further, after the buckling deformation of the double-end clamped beam structure, the mechanical dynamic model of the reconstructed MEMS electrostatic driving switch is as follows:
Wherein X is the pull-down distance of the membrane bridge of the double-end clamped beam, t is Liang Hou, m is the mass of the double-end clamped beam switch, h is the buckling maximum displacement of the double-end clamped beam, k 'is the equivalent spring coefficient caused by the rigidity of the double-end clamped beam structure, k' is the equivalent spring coefficient caused by the biaxial residual stress of the double-end clamped beam structure, X is the change amount of the distance from the membrane bridge to the flexible substrate after buckling deformation of the flexible substrate, A is the overlapping area between polar plates, V is the bias voltage applied between the polar plates, g is the initial distance between the polar plates, epsilon r Dielectric constant epsilon of the medium between the polar plates 0 Is vacuum dielectric constant.
Further, the buckling maximum displacement h of the double-end clamped beam is as follows:
wherein ,
for moment of inertia, Δp is tensile stress induced in the double-ended clamped beam by buckling of the flexible substrate, P is residual compressive stress in the double-ended clamped beam when the flexible substrate is buckled and deformed, E is young modulus of the beam, t is Liang Hou, w is beam width, n is poisson's ratio, and L is the length of the double-ended clamped beam.
Further, the equivalent spring coefficient k″ caused by the biaxial residual stress of the double-ended clamped beam structure is:
where Δp is the tensile stress induced in the double clamped beam by flex substrate buckling and q (z) is the applied vertical load.
Further, the tensile stress Δp induced in the double clamped beam by the flexible substrate buckling is:
wherein E is Young's modulus of the beam, t is Liang Hou, w is beam width, n is Poisson's ratio, R is flexible substrate buckling curvature radius, L is double-end clamped beam length, and g is initial distance between upper and lower polar plates.
Working principle: the invention provides an estimation method of a dynamic model parameter change rule of an RF MEMS electrostatic drive switch based on a flexible substrate bending condition, which aims to fill the blank of research on the RF MEMS electrostatic drive switch bending characteristic model at home and abroad. The invention mainly adopts two steps to process the modeling of the dynamic model of the RF MEMS electrostatic drive switch under the bending deformation condition of the flexible substrate, thereby obtaining an analysis model of the influence on the dynamic model of the device after the RF MEMS electrostatic drive switch is deformed. Firstly, a deformation coupling model based on double deformation of the RF MEMS electrostatic drive switch and the flexible substrate is established, and the extraction of the change quantity of key structural parameters between the RF MEMS electrostatic drive switch and the flexible substrate is realized. And secondly, based on the bending characteristic model of the RF MEMS electrostatic drive switch, the deformation quantity of the RF MEMS electrostatic drive switch/substrate double deformation is obtained. Based on the parameters, reconstructing a dynamic model of the RF MEMS electrostatic drive switch, and analyzing the influence of bending deformation on the dynamic model of the RF MEMS electrostatic drive switch.
The beneficial effects are that: compared with the prior art, the method establishes the deformation coupling model based on the double deformation of the RF MEMS electrostatic driving switch and the flexible substrate for the first time, and realizes the extraction of the change quantity of key structural parameters between the RF MEMS electrostatic driving switch and the flexible substrate. The dynamic model of the RF MEMS electrostatic drive switch after bending deformation is further established, and a dynamic model analysis method of the RF MEMS electrostatic drive switch based on a complex environment space and comprising the RF MEMS electrostatic drive switch and a flexible substrate double-deformation model is provided, so that the gap of research on the dynamic model of the RF MEMS electrostatic drive switch at home and abroad is filled.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a graph comparing the analysis method and simulation and test results of the electrostatic driving switch of the double-ended clamped beam provided by the invention.
FIG. 3 is a graph comparing the analysis method and simulation and test results of the cantilever beam electrostatic drive switch provided by the invention.
Detailed Description
The invention is further explained below with reference to the drawings.
Example 1
The MEMS is a double-end clamped beam type RF MEMS, the electrostatic driving switch beam of the RF MEMS is made of gold, the flexible substrate material is made of Liquid Crystal Polymer (LCP), the length L=600 μm of the beam, the width w=100 μm of the beam, the thickness t=2 μm of the beam, the initial distance g=2 μm between the upper polar plate and the lower polar plate, the Young modulus E=78 Gpa of the beam, and the Poisson's ratio n=0.42. The RF MEMS double-end clamped beam static drive switch initially has double-shaft residual compressive stress, the beam bends upwards, the maximum bending distance h=0.5 mu m, and the curvature of the substrate gradually increases from 0 to 33.3m along with the gradual bending of the flexible substrate -1 A bias voltage of 1.4 times of threshold voltage is applied between the upper and lower plates of the switch.
The embodiment is described with reference to fig. 1, and specifically includes the following steps:
and step 1, establishing a mechanical dynamic model of the RF MEMS electrostatic drive switch. The dynamic equation of the RF MEMS electrostatic drive double-end clamped beam switch attraction process without considering damping effect is as follows:
wherein x is the pull-down distance of the membrane bridge of the double-end clamped beam, liang Hou is t, m is the mass of the double-end clamped beam switch, f is the electrostatic force between polar plates, and k is the equivalent spring coefficient of the double-end clamped beam structure.
And 2, establishing a deformation coupling model based on double deformation of the RF MEMS electrostatic drive switch and the flexible substrate.
The double-end clamped beam has the length L, liang Hou t, the width w, the Young modulus E and the Poisson ratio n, and when the double-end clamped beam structure has larger residual compressive stress P, the residual compressive stress is larger than the critical stress of buckling
When the double-end clamped beam structure is used, buckling can occur upwards (or downwards), and the buckling mode is as follows:
the maximum displacement of the center point of the double-end clamped beam is h:
wherein ,
is the moment of inertia.
And 3, after the flexible substrate is buckled and deformed, obtaining the distance between the RF MEMS electrostatic drive switch membrane bridge and the flexible substrate.
The initial distance from the membrane bridge of the two-end supporting beam to 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 alpha, so that the method can be obtained:
further, the change amount of the film bridge-to-substrate distance after bending the flexible substrate is as follows:
and 4, obtaining the parameter value of the deformed flexible substrate. The parameter values after the flexible substrate is deformed comprise tensile stress delta P introduced in the double-end clamped beam by bending the flexible substrate and an equivalent spring coefficient when the double-end clamped beam structure is subjected to axial force.
First, tensile stress Δp induced in the double clamped beam by bending the flexible substrate is obtained. Under the condition that the flexible substrate is bent, the upper polar plate of the double-end clamped beam has certain stretching, the stretching can introduce tensile stress into the upper polar plate, and the introduced tensile stress is as follows:
wherein Δp is tensile stress induced in the double-ended clamped beam by bending the flexible substrate, E is young's modulus of the beam, n is poisson's ratio, R is bending radius of curvature of the flexible substrate, L is length of the double-ended clamped beam, g is initial distance between upper and lower polar plates, liang Hou is t, and beam width is w.
And secondly, obtaining the equivalent spring coefficient of the double-end clamped beam structure when the double-end clamped beam structure is subjected to axial force. The spring rate of a double clamped beam can be described in two parts: one part is the equivalent spring coefficient k 'caused by the rigidity of the double-ended clamped beam structure, and the other part is the equivalent spring coefficient k' caused by the double-ended clamped beam structure double-shaft residual stress.
Wherein, the equivalent spring coefficient caused by the rigidity of the double-end clamped beam structure can be obtained by utilizing the superposition principle:
further, the k "of a double clamped beam structure with biaxial residual stress can be deduced by simplifying the beam into a tensile line model, and the residual stress causes the tensile force at both ends P:
P＝σ(1-n)tw
further, if the beam bending is small deformation, let the applied vertical load q (z) equal to the projection of Liang Nali in the vertical direction, the application of the superposition principle can calculate the equivalent spring coefficient caused by the non-uniform load distributed on the double clamped beam as:
wherein sigma is biaxial residual stress, t is double-end clamped beam thickness, w is double-end clamped beam width, n is poisson's ratio of material, and q (z) is vertical load applied to the beam at the z point.
Further, the equivalent spring coefficient of the double-end clamped beam structure when being subjected to axial tensile stress is as follows: k=k' +k ", and similarly, the equivalent spring rate of the double-ended clamped beam structure when subjected to axial compressive stress is: k=k' -k ".
And 5, reconstructing a mechanical dynamic model of the RF MEMS electrostatic drive switch.
Based on the deformation coupling model of the RF MEMS electrostatic drive switch and the flexible substrate double deformation, the deformation quantity of the RF MEMS electrostatic drive switch/substrate double deformation is obtained. Based on the parameters, reconstructing a dynamic model of the RF MEMS electrostatic drive switch, and analyzing the influence of bending deformation on the dynamic model of the RF MEMS electrostatic drive switch.
The MEMS double-end clamped beam deformation caused by the bending of the flexible substrate can influence the switch suction time from two aspects, namely the initial distance between the upper polar plate and the lower polar plate of the double-end clamped beam structure can be changed after the flexible substrate is bent, the double-end clamped beam is stretched to introduce internal attraction after the flexible substrate is bent, the flexible substrate is not bent and deformed, if the double-end clamped beam has larger residual compressive stress, the double-end clamped beam structure can be bent upwards (or downwards) when the residual compressive stress is larger than the critical stress for buckling, and the dynamic equation of the damping effect is not considered in the suction process of the RF MEMS electrostatic driving double-end clamped beam switch is as follows:
Wherein x is the pull-down distance of the membrane bridge of the double-end clamped beam, t is the thickness of the double-end clamped beam, m is the mass of the double-end clamped beam switch, h is the buckling maximum displacement of the double-end clamped beam, k 'is the equivalent spring coefficient caused by the rigidity of the double-end clamped beam structure, k' is the equivalent spring coefficient caused by the double-end clamped beam structure double-shaft residual stress, A is the overlapping area between polar plates, V is the bias voltage applied between polar plates, and g is the initial spacing between polar plates.
Further, the flexible substrate is bent and deformed, the residual compressive stress in the double-end clamped beam is P, the curvature radius is R, the double-end clamped beam structure is buckled, and a dynamic equation of the RF MEMS electrostatic driving double-end clamped beam switch in the suction process without considering damping action is that the reconstructed dynamic equation is:
Wherein X is the pull-down distance of the membrane bridge of the double-end clamped beam, t is the thickness of the double-end clamped beam, m is the mass of the double-end clamped beam switch, h is the buckling maximum displacement of the double-end clamped beam, k 'is the equivalent spring coefficient caused by the rigidity of the double-end clamped beam structure, k' is the equivalent spring coefficient caused by the double-end clamped beam structure double-shaft residual stress, X is the change amount of the distance between the membrane bridge and the substrate after the flexible substrate is bent, A is the overlapping area between the polar plates, V is the bias voltage applied between the polar plates, and g is the initial distance between the polar plates.
Wherein, the biggest displacement of bi-polar clamped beam buckling is:
wherein, the equivalent spring coefficient caused by the double-end clamped beam structure double-shaft residual stress is as follows:
wherein ,
for moment of inertia, Δp is the tensile stress induced in the double-ended clamped beam by buckling of the flexible substrate, P is the residual compressive stress in the double-ended clamped beam during buckling deformation of the flexible substrate, E is the young's modulus of the beam, t is Liang Hou, w is the beam width, n is poisson's ratio, L is the double-ended clamped beam length, and q (z) is the vertical load applied to the beam at the z point.
Further, the flexible substrate is bent and deformed, the curvature radius is R, the double-end clamped beam structure is not buckled, the internal stress after the beam is stretched is P, and a dynamic equation of the RF MEMS electrostatic drive double-end clamped beam switch in the suction process without considering damping action is that:
Wherein X is the pull-down distance of the membrane bridge of the double-end clamped beam, m is the mass of the double-end clamped beam switch, k 'is the equivalent spring coefficient caused by the rigidity of the double-end clamped beam structure, k' is the equivalent spring coefficient caused by the double-end clamped beam structure double-shaft residual stress, X is the change amount of the distance between the membrane bridge and the substrate after the flexible substrate is bent, A is the overlapping area between polar plates, V is the bias voltage applied between polar plates, and g is the initial distance between polar plates.
And 6, based on the reconstructed model, acquiring the influence of the bending of the flexible substrate on the dynamic model of the RF MEMS electrostatic drive switch.
And (3) solving the reconstructed dynamic equation in the step (5) to obtain the switching time of the RF MEMS electrostatic driving switch, and comparing the switching time with the switching time of the RF MEMS electrostatic driving switch in the traditional method (without considering the action condition of the flexible substrate), and obtaining the influence of the bending of the flexible substrate on the dynamic model of the RF MEMS electrostatic driving switch by comparing the difference of the switching times.
By the method provided by the embodiment, a working condition analysis model of the RF MEMS electrostatic drive switch is established under the condition that the influence of the flexible substrate on the RF MEMS is considered, and the control precision of the working process of the flexible RF MEMS electrostatic drive switch is improved.
As shown in fig. 2, the present invention takes an RF MEMS double-end clamped beam as an example, in this embodiment, the material of the RF MEMS double-end clamped beam electrostatic driving switch beam is gold, the flexible substrate material is Liquid Crystal Polymer (LCP), the length l=600 μm of the beam, the width w=100 μm of the beam, the thickness t=2 μm of the beam, the initial spacing g=2 μm between upper and lower polar plates, the young modulus e=78 Gpa of the beam, and the poisson ratio n=0.42. If the RF MEMS double-end fixed beam static drive switch initially has double-shaft residual compressive stress, the beam bends upwards, the maximum bending distance h=0.5 μm, and the curvature of the substrate gradually increases from 0 to 33.3m along with the gradual bending of the flexible substrate -1 A bias voltage of 1.4 times of threshold voltage is applied between the upper and lower plates of the switch. The method provided by the invention has the advantages that the switching time of the RF MEMS double-end supporting beam electrostatic driving switch based on the flexible substrate bending condition obtained by analysis is almost similar to the simulation result, and almost completely coincides with the test result, so that the switching time of the flexible MEMS double-end supporting beam electrostatic driving switch can be accurately calculated by the method provided by the invention, and a foundation is provided for accurately controlling the flexible MEMS switch in engineering use. The method provided by the invention can be applied to complex environment space, comprises a double-deformation model of the RF MEMS electrostatic drive switch and the flexible substrate, and fills the gap of research on a dynamic model of the RF MEMS electrostatic drive switch at home and abroad.
Example 2
The MEMS is a double-end cantilever type RF MEMS, the material of the RF MEMS cantilever beam electrostatic driving switch beam is gold, the flexible substrate material is Liquid Crystal Polymer (LCP), the length L=150 μm of the beam, the width w=100 μm of the beam, the thickness t=2 μm of the beam, and the size of the lower polar plate is long L' =60 μm; width w' =150 μm, thickness fromCPW transmission line thickness determination. If the cantilever 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 along with the gradual bending of the flexible substrate -1 A bias voltage of 1.4 times of threshold voltage is applied between the upper and lower plates of the switch.
The embodiment is described with reference to fig. 1, and specifically includes the following steps:
and step 1, establishing a mechanical dynamic model of the RF MEMS electrostatic drive switch. The dynamic equation of the RF MEMS electrostatic drive double-end clamped beam switch attraction process without considering damping effect is as follows:
wherein x is the pull-down distance of the cantilever beam film bridge, t is Liang Hou, m is the mass of the cantilever beam switch, f is the electrostatic force between polar plates, and k is the equivalent spring coefficient of the cantilever beam structure.
And 2, establishing a deformation coupling model based on double deformation of the RF MEMS electrostatic drive switch and the flexible substrate.
And (3) establishing a deformation coupling model based on the double deformation of the RF MEMS electrostatic drive switch and the flexible substrate, wherein the stress gradient of the cantilever beam in the length direction can generate an equivalent bending moment effect on the beam, and the shape of the beam can be curled under the bending moment effect. The direction of curl and the extent of deflection are related to the nature, magnitude, and direction of the stress residual gradient. The magnitude of the equivalent bending moment caused by the stress gradient on the cantilever beam is:
wherein t is Liang Hou, w is the beam width, z is the position of the cantilever beam in the thickness direction, sigma (z) is the function of the residual stress of the cantilever beam in the length direction relative to the thickness, the residual stress is negative, the internal stress is compressive, and the residual stress is positive, the internal stress is tensile. 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 ,
for moment of inertia, L is cantilever Liang Liangchang, t is Liang Hou, w is beam width, and E is Young's modulus of the beam.
And 3, after the flexible substrate is deformed, obtaining the distance between the RF MEMS electrostatic drive switch membrane bridge and the flexible substrate.
The initial distance between the cantilever Liang Moqiao 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 alpha, so that the following steps are obtained:
further, the film bridge-to-substrate spacing variation after bending of the flexible substrate is:
and 4, obtaining the parameter value of the deformed flexible substrate. The parameter value after the flexible substrate is deformed is the spring coefficient k of the cantilever beam.
The spring coefficient k of the cantilever beam is caused by the structural rigidity of the cantilever beam, and when external force is applied to the sections x to L, the equivalent spring coefficient of the cantilever beam can be obtained by utilizing the superposition principle:
and 5, reconstructing a mechanical dynamic model of the RF MEMS electrostatic drive switch.
Based on the deformation coupling model of the RF MEMS electrostatic drive switch and the flexible substrate double deformation, the deformation quantity of the RF MEMS electrostatic drive switch/substrate double deformation is obtained. Based on the parameters, reconstructing a dynamic model of the RF MEMS electrostatic drive switch, and analyzing the influence of bending deformation on the dynamic model of the RF MEMS electrostatic drive switch.
After the flexible substrate is bent, the MEMS cantilever beam deformation can cause the initial distance between the upper polar plate and the lower polar plate of the cantilever beam structure to change, thereby influencing the actuation voltage of the cantilever beam. The flexible substrate is not bent and deformed, if the cantilever beam has residual stress gradient in the length direction, the cantilever beam structure is bent upwards (or downwards), and a dynamic equation of the RF MEMS electrostatic drive cantilever beam switch actuation process without considering damping action is as follows:
Wherein x is the pull-down distance of the cantilever beam film bridge, m is the mass of the cantilever beam switch,
the bending distance of the tail end of the cantilever beam is k, the equivalent spring coefficient caused by the structural rigidity of the cantilever beam is k, A is the overlapping area between the polar plates, V is the bias voltage applied between the polar plates, and g is the initial spacing between the polar plates.
Further, the flexible substrate is bent and deformed, the residual compressive stress in the cantilever beam is P, the curvature radius is R, the cantilever beam structure is buckled, and a dynamic equation of the RF MEMS electrostatic drive cantilever beam switch actuation process without considering damping action is as follows:
Wherein X is the pull-down distance of the cantilever beam film bridge, m is the mass of the cantilever beam switch, deltaz is the bending distance of the tail end of the cantilever beam, k is the equivalent spring coefficient caused by the structural rigidity of the cantilever beam, X is the change amount of the distance between the film bridge and the substrate after the flexible substrate is bent, A is the overlapping area between polar plates, V is the bias voltage applied between polar plates, and g is the initial distance between polar plates.
And 6, based on the reconstructed model, acquiring the influence of the bending of the flexible substrate on the dynamic model of the RF MEMS electrostatic drive switch.
And (3) solving the reconstructed dynamic equation in the step (5) to obtain the switching time of the RF MEMS electrostatic driving switch, and comparing the switching time with the switching time of the RF MEMS electrostatic driving switch in the traditional method (without considering the action condition of the flexible substrate), and obtaining the influence of the bending of the flexible substrate on the dynamic model of the RF MEMS electrostatic driving switch by comparing the difference of the switching times.
By the method provided by the embodiment, a working condition analysis model of the RF MEMS electrostatic drive switch is established under the condition that the influence of the flexible substrate on the RF MEMS is considered, and the control precision of the working process of the flexible RF MEMS electrostatic drive switch is improved.
As shown in fig. 3, in the present embodiment, the RF MEMS cantilever electrostatic driving switch is exemplified by an RF MEMS cantilever electrostatic driving switch, in which the material of the RF MEMS cantilever electrostatic driving switch beam is gold, the flexible substrate material is a Liquid Crystal Polymer (LCP), the length l=150 μm of the beam, the width w=100 μm of the beam, the thickness t=2 μm of the beam, and the size of the lower plate is long L' =60 μm; the width w' =150 μm, and the thickness is determined by the CPW transmission line thickness. If the cantilever 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 along with the gradual bending of the flexible substrate -1 A bias voltage of 1.4 times of threshold voltage is applied between the upper and lower plates of the switch. The method provided by the invention has the advantages that the switching time of the cantilever beam electrostatic drive switch under the flexible substrate bending condition obtained by analysis is almost similar to the simulation result, and almost completely coincides with the test result, so that the switching time of the flexible MEMS double-end cantilever beam electrostatic drive switch can be accurately calculated by the method provided by the invention, and a foundation is provided for accurately controlling the flexible MEMS switch in engineering use. The method provided by the invention canThe method is applied to a complex environment space and comprises a MEMS cantilever structure and flexible substrate double-deformation model, and meanwhile, the influence of residual stress gradient of the MEMS cantilever structure is considered, so that the gap of research on the MEMS cantilever structure flexible device model at home and abroad is filled.
The above description is merely of preferred embodiments of the present invention, and the scope of the present invention is not limited to the above embodiments, but all equivalent modifications or variations according to the present disclosure will be within the scope of the claims.
Claims (4)
1. The dynamic model analysis method for the mechanics of the flexible MEMS electrostatic drive switch is characterized by comprising the following steps of:
establishing an initial mechanical dynamic model of the MEMS electrostatic driving switch, wherein the initial mechanical dynamic model of the MEMS electrostatic driving switch is as follows:
wherein x is the pull-down distance of the membrane bridge, m is the mass of the electrostatic drive switch, f is the electrostatic force between polar plates, and k is the equivalent spring coefficient of the middle beam structure of the electrostatic drive switch;
establishing a deformation coupling model based on double deformation of the MEMS electrostatic drive switch and the flexible substrate, wherein the deformation coupling model is as follows:
wherein h is the maximum displacement of the center point of the double-end clamped beam:
wherein ,
for moment of inertia, L is the beam length of the double-end clamped beam, t is Liang Hou, w is the beam width, E is the Young's modulus of the beam, n is the Poisson's ratio, and P is the residual compressive stress;
after the flexible substrate is buckled and deformed, the distance from the membrane bridge of the MEMS electrostatic drive switch to the flexible substrate is obtained, and after the flexible substrate is buckled and deformed, the distance change amount from the membrane bridge of the MEMS electrostatic drive switch to the flexible substrate is as follows:
wherein L is the beam length of the double-end clamped beam, and R is the buckling curvature radius of the flexible substrate;
after the flexible substrate is subjected to buckling deformation, obtaining a parameter value of the flexible substrate after buckling deformation;
reconstructing a mechanical dynamic model of the MEMS electrostatic driving switch according to the parameter value after the flexible substrate is buckled and deformed, wherein the reconstructed mechanical dynamic model of the MEMS electrostatic driving switch is as follows:
Wherein x is the pull-down distance of the membrane bridge of the double-end clamped beam, t is Liang Hou, m is the mass of the double-end clamped beam switch, h is the maximum displacement of the center point of the double-end clamped beam, k 'is the equivalent spring coefficient caused by the rigidity of the double-end clamped beam structure, k' is the equivalent spring coefficient caused by the double-end clamped beam structure double-shaft residual stress, A is the overlapping area between polar plates, V is the bias voltage applied between polar plates, g is the initial distance between polar plates, epsilon r Dielectric constant epsilon of the medium between the polar plates 0 Is vacuum dielectric constant;
based on the reconstructed model, the influence of flexible substrate buckling on the MEMS electrostatic drive switch mechanical dynamic model is obtained.
2. The method for analyzing a dynamic model of a flexible MEMS electrostatic drive switch according to claim 1, wherein after the flexible substrate is buckled, the maximum displacement h of the center point of the double-ended clamped beam is:
wherein ,
for moment of inertia, Δp is tensile stress induced in the double-ended clamped beam by buckling of the flexible substrate, P is residual compressive stress in the double-ended clamped beam when the flexible substrate is buckled and deformed, E is young modulus of the beam, t is Liang Hou, w is beam width, n is poisson's ratio, and L is the length of the double-ended clamped beam.
3. The method for analyzing a dynamic model of a flexible MEMS electrostatic driven switch according to claim 1, wherein the equivalent spring coefficient k″ caused by the biaxial residual stress of the double-ended clamped beam structure is:
where Δp is the tensile stress induced in the double clamped beam by buckling of the flexible substrate, q (z) is the vertical load applied to the beam at the z point, z being the position along the length of the double clamped beam.
4. A method of analyzing a dynamic model of a flexible MEMS electrostatic driven switch according to claim 2 or claim 3, wherein the tensile stress Δp induced in the double-ended clamped beam by the flexible substrate buckling is:
wherein E is Young's modulus of the beam, t is Liang Hou, w is beam width, n is Poisson's ratio, R is flexible substrate buckling curvature radius, L is double-end clamped beam length, and g is initial distance between upper and lower polar plates.
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