CN109635423B - Flexible MEMS device V-shaped beam structure mechanics dynamic model analysis method - Google Patents

Flexible MEMS device V-shaped beam structure mechanics dynamic model analysis method Download PDF

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CN109635423B
CN109635423B CN201811502748.6A CN201811502748A CN109635423B CN 109635423 B CN109635423 B CN 109635423B CN 201811502748 A CN201811502748 A CN 201811502748A CN 109635423 B CN109635423 B CN 109635423B
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韩磊
于洋
吴虹剑
田蕾
吝晓楠
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Southeast University
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Abstract

The invention discloses a mechanical dynamic model analysis method of a flexible MEMS device, which comprises the steps of establishing a double-deformation coupling model between a beam structure of the flexible MEMS device and a flexible substrate; establishing a relation between a driving parameter and a driving signal of a beam structure of the flexible MEMS device; detecting a deformation parameter value of a beam structure when the flexible substrate deforms; obtaining a driving parameter correction value of the beam structure according to the deformation parameter value of the beam structure detected in the S03 and the double-deformation coupling model in the S01; correcting the driving parameters of the beam structure by using the corrected values of the driving parameters of the beam structure to obtain accurate values of the driving parameters of the beam structure; and obtaining an accurate value of the driving signal according to the relationship established in the S02. And (4) according to the dynamic equation of the beam structure in the S07 without considering the damping effect, obtaining the switching time of the beam structure, and analyzing the influence of the bending deformation on the dynamic model of the beam structure mechanics. The patent provides an MEMS device mechanics dynamic model analysis method based on a complex environment space and comprising a beam structure and flexible substrate double-deformation model.

Description

Flexible MEMS device V-shaped beam structure mechanics dynamic model analysis method
Technical Field
The invention relates to a mechanical dynamic model analysis method for a V-shaped beam structure of a flexible MEMS device, in particular to a precision improvement method for the mechanical dynamic model analysis of the MEMS V-shaped beam structure based on the bending condition of a flexible substrate.
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. The MEMS (micro electro mechanical system) flexible device is taken as an important branch of a flexible electronic device, and a conformal, high-performance, small-volume and intelligent sensor/actuator of the MEMS flexible device becomes an indispensable component in the current flexible electronic system, particularly an RF MEMS (radio frequency micro electro mechanical system) flexible device, so that various RF MEMS flexible actuators/sensors become research hotspots in recent years due to the wide application prospect in airborne/satellite-borne radar and Internet of things communication systems. 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 still in the stage of device design, preparation and performance test under non-bending conditions, and the research on 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
Therefore, the patent provides a mechanical dynamic model analysis method for a flexible MEMS device. By combining the bending characteristic of the MEMS flexible device, the patent provides an MEMS device mechanical dynamic model analysis method based on a complex environment space and comprising a beam structure and flexible substrate double-deformation model.
A mechanical dynamic model analysis method for a V-shaped beam structure of a flexible MEMS device comprises the following steps:
s01: establishing a double-deformation coupling model between a V-shaped beam structure of a flexible MEMS device and a flexible substrate;
s02: establishing a relation between a driving parameter and a driving signal of a V-shaped beam structure of the flexible MEMS device;
s03: detecting a deformation parameter value of the V-shaped beam structure when the flexible substrate deforms;
s04: obtaining a driving parameter correction value of the beam structure according to the deformation parameter value of the V-shaped beam structure detected in the step S03 and the double-deformation coupling model in the step S01;
s05: correcting the driving parameters of the beam structure by using the corrected values of the driving parameters of the beam structure to obtain accurate values of the driving parameters of the beam structure;
s06: and obtaining an accurate value of the driving signal according to the relationship established in the S02.
Further, the beam structure is a V-shaped beam with a middle push rod.
Further, the double deformation coupling model in S01 is:
Figure GDA0003961570490000021
wherein L is the length of the V-shaped beam, X is the increment of the distance between the anchor areas at two ends of the V-shaped beam, g is the initial distance between the V-shaped beam film bridge and the substrate, R is the bending curvature radius of the flexible substrate,
Figure GDA0003961570490000022
is the included angle between the beam and the horizontal direction in the plane of the V-shaped beam.
Further, the flexible MEMS device is a thermal driving device, and the relationship between the driving parameter of the V-shaped beam structure and the driving signal in S02 is as follows:
Figure GDA0003961570490000023
wherein L is the length of the V-shaped beam, w is the width of the V-shaped beam, t is the thickness of the V-shaped beam,
Figure GDA0003961570490000024
is the included angle between the beam and the horizontal direction in the plane of the V-shaped beam, k is the thermal conductivity, C p The specific heat capacity of the material is rho, the material density is rho, the thermal expansion coefficient of the material is alpha, the delta Y is the displacement of the single V-shaped beam in the driving direction, namely the driving parameter of the beam structure, and the I is the driving current, namely the driving signal, for driving the V-shaped beam of the MEMS device.
Further, in S03, the deformation parameter value is a change value of an included angle between the beam and the horizontal direction in the plane where the V-shaped beam is located:
Figure GDA0003961570490000025
wherein L is the length of the V-shaped beam,
Figure GDA0003961570490000026
the bending curvature radius of the flexible substrate is R, wherein g is the included angle between the beam and the horizontal direction in the plane of the V-shaped beam, and g is the initial distance between the V-shaped beam film bridge and the substrate.
Further, in the step S04, the driving parameter correction value is the retreating distance of the middle push rod of the V-shaped beam:
Figure GDA0003961570490000031
wherein L is the length of the V-shaped beam, g is the initial distance between the V-shaped beam film bridge and the substrate, R is the bending curvature radius of the flexible substrate,
Figure GDA0003961570490000032
is the included angle between the beam and the horizontal direction in the plane of the V-shaped beam.
Further, the accurate value of the driving parameter in S05 is the accurate displacement of the V-shaped beam in the driving direction:
Figure GDA0003961570490000033
wherein L is the length of the V-shaped beam, w is the width of the V-shaped beam, t is the thickness of the V-shaped beam,
Figure GDA0003961570490000034
is the included angle between the beam and the horizontal direction in the plane of the V-shaped beam, k is the thermal conductivity, C p The specific heat capacity of the material is defined, rho is the density of the material, alpha is the coefficient of thermal expansion of the material, and I is the driving current for driving the MEMS V-shaped beam.
Further, a flexible substrateHas a curvature variation range of [0, 33.3 ]]m -1 。
Further, the method also comprises the following steps:
s07: establishing a dynamic equation of a V-shaped beam switch actuation process of the flexible MEMS device without considering damping action;
s08: establishing a distribution relation of temperature increment delta T on the V-shaped beam;
s09: the displacement relation of the V-shaped beam in the length direction;
s10: and solving to obtain the switching time of the V-shaped beam switch of the MEMS device according to a dynamic equation without considering the damping action in the closing process of the V-shaped beam switch in the S07, the distribution relation of the temperature increment delta T on the V-shaped beam in the S08 and the displacement relation of the V-shaped beam in the length direction in the S09.
Further, in the S07, a dynamic equation of the flexible MEMS device V-shaped beam switch closing process without considering the damping effect is:
Figure GDA0003961570490000035
wherein T is the temperature of the V-shaped beam,
Figure GDA0003961570490000036
is the amount of heat generated per unit volume of material at a given voltage, V is the applied voltage, R is the resistance, V is the electrical resistance R Volume of resistive material, k thermal conductivity, C p Is the specific heat capacity of the material, and rho is the density of the material;
the distribution relation of the temperature increment delta T on the V-shaped beam in the S08 is as follows:
Figure GDA0003961570490000037
wherein T is the temperature of the V-shaped beam, q is the heat generated in the unit volume of the material under a certain voltage, L is the length of the V-shaped beam, k is the thermal conductivity, and x represents the x-axis direction of a space rectangular coordinate system;
the displacement relation of the V-shaped beam in the length direction in the S09 is as follows:
Figure GDA0003961570490000041
wherein alpha is the thermal expansion coefficient of the material, T is the temperature of the V-shaped beam, q is the heat generated in the unit volume of the material under a certain voltage, L is the length of the V-shaped beam, k is the thermal conductivity, and x represents the x-axis direction of the rectangular space coordinate system.
Therefore, the patent provides a mechanical dynamic model analysis method for a flexible MEMS device. By combining the bending characteristic of the MEMS flexible device, the patent provides an MEMS device mechanical dynamic model analysis method based on a complex environment space and comprising a beam structure and flexible substrate double-deformation model.
Drawings
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a MEMS V-beam structure in an embodiment of the invention;
FIG. 3 is a comparison graph of the analysis method provided by the present invention with simulation and test results.
Detailed Description
A method for improving the precision of the flexible MEMS device proposed in this patent will be described in detail with reference to the accompanying drawings.
Example 1
The structure of the flexible MEMS device in this patent is described with reference to fig. 2, and it can be seen that the flexible MEMS device includes a V-shaped beam structure 1 and a flexible substrate 2, where the V-shaped beam structure 1 includes a single beam 11, an anchor region 12 and an intermediate push rod 13, and since the flexible MEMS device in fig. 2 is a top view of the flexible MEMS device, the V-shaped beam is connected to the flexible substrate through the anchor region 12, taking an RF MEMS V-shaped beam thermally-driven switch as an example, in this embodiment, the V-shaped beam expands due to heating and pushes the push rod 13 to move, so as to contact with the signal transmission line 3, and intercept the signal, thereby implementing a switching function.
In this embodiment, the MEMS device is an RF MEMS V-beam thermally-actuated switch, and in this embodiment, the RF MEMS V-beam thermally-actuated switch beam is made of gold, the flexible substrate is made of Liquid Crystal Polymer (LCP), and the MEMS V-beam structure beam takes values of various parametersThe length L =400 μm, the width w =7 μm, the thickness t =10 μm, and the included angle between the beam and the horizontal direction in the plane of the V-shaped beam
Figure GDA0003961570490000042
The size of the intermediate push rod is L' =355 μm; width w' =50 μm, and as the flexible substrate is gradually bent, the curvature of the substrate is gradually increased from 0 to 33.3m -1 。
A method for improving the precision of a flexible MEMS device proposed in this patent will be described in detail with reference to fig. 1
S01: and establishing a double-deformation coupling model between the beam structure of the flexible MEMS device and the flexible substrate. The length of the V-shaped beam is L, the initial distance from the V-shaped beam film bridge to the substrate is g, the bending curvature radius of the flexible substrate is R, and the increment of the distance between anchor areas at two ends of the V-shaped beam is as follows:
Figure GDA0003961570490000051
s02: and establishing a relation between the driving parameters and the driving signals of the beam structure of the flexible MEMS device. The length of a single beam in the basic unit of the V-shaped beam structure is L, the width is w, the thickness is t, and the included angle between the beam and the horizontal direction in the plane of the V-shaped beam structure is
Figure GDA0003961570490000052
The heat distribution of the V-shaped beam can be calculated by a heat conduction equation as follows:
Figure GDA0003961570490000053
wherein T is the temperature of the V-shaped beam,
Figure GDA0003961570490000054
is the amount of heat generated per unit volume of material at a given voltage, V is the applied voltage, R is the resistance, V is the electrical resistance R Volume of resistive material, k thermal conductivity, C p Is the specific heat capacity of the material, and ρ is the material density. Assume a V-shapeThe heat q that produces in the beam material unit volume is the constant, and the structure is in stable condition, then the above formula can simplify to:
Figure GDA0003961570490000055
further, the distribution of the temperature increment Δ T on the V-shaped beam obtained from the boundary conditions is as follows, wherein the boundary conditions are that the temperature of the anchor area of the V-shaped beam is not changed:
Figure GDA0003961570490000056
further, the displacement of the V-beam in the length direction can be obtained as follows:
Figure GDA0003961570490000057
where α is the coefficient of thermal expansion of the material.
Further, the displacement of the single V-shaped beam in the driving direction obtained by the parameters is:
Figure GDA0003961570490000061
wherein I is a driving current for driving the MEMS V-shaped beam. To this end, we have established a relationship between the drive signal (drive current) and the drive parameters of the beam structure (displacement of a single V-beam in the drive direction).
S03: and detecting the deformation parameter value of the beam structure when the flexible substrate deforms.
After the flexible substrate is bent, the deformation of the MEMS V-shaped beam can cause the distance change between anchor areas at two ends, so that the included angle between the inner beam at the plane where the V-shaped beam is located and the horizontal direction is changed, and the middle push rod of the V-shaped beam retreats to influence the driving distance of the V-shaped beam, thereby influencing the driving current of the V-shaped beam. According to the geometrical relationship, after the flexible substrate is bent, the change of the included angle between the beam and the horizontal direction in the plane where the V-shaped beam is located is as follows:
Figure GDA0003961570490000062
s04: and obtaining a driving parameter correction value of the beam structure according to the deformation parameter value phi' of the beam structure detected in the step S03 and the double-deformation coupling model in the step S01. The retreating distance of the middle push rod of the V-shaped beam after the flexible substrate is bent can be obtained according to the geometrical relationship:
Figure GDA0003961570490000063
s05: and correcting the driving parameters of the beam structure by using the corrected values of the driving parameters of the beam structure to obtain accurate values of the driving parameters of the beam structure.
The included angle obtained
Figure GDA0003961570490000064
And the intermediate push rod retreating distance Y' is brought into the driving distance formula in S02, and the intermediate push rod retreating of the V-shaped beam structure is considered at the same time, so that the driving distance of the MEMS V-shaped beam structure based on the bending condition of the flexible substrate is as follows:
Figure GDA0003961570490000065
so far, we obtain the accurate values of the driving parameters of the beam structure.
S06: the relation between the driving signal (driving current) and the driving parameter of the beam structure (the displacement of a single V-shaped beam in the driving direction) obtains the accurate value of the driving signal through the accurate value of the displacement of the corrected V-shaped beam in the driving direction, namely the accurate value of the driving parameter.
Example 2
On the basis of the embodiment 1, the method further comprises the following steps:
s07: and establishing a dynamic equation of the V-shaped beam switch closing process of the flexible MEMS device without considering the damping action.
The dynamic equation without considering the damping action in the actuation process of the RF MEMS V-shaped beam switch can be obtained by the heat conduction equation in S02 and is as follows:
Figure GDA0003961570490000071
wherein T is the temperature of the V-shaped beam,
Figure GDA0003961570490000072
is the amount of heat generated per unit volume of material at a given voltage, V is the applied voltage, R is the resistance, V is the electrical resistance R Volume of resistive material, k thermal conductivity, C p Is the specific heat capacity of the material, and rho is the density of the material;
s08: and establishing a distribution relation of temperature increment delta T on the V-shaped beam.
From the heat conduction equation in S02, it can be known that the distribution relationship of the temperature increment Δ T on the V-shaped beam is:
Figure GDA0003961570490000073
wherein T is the temperature of the V-shaped beam, q is the heat generated in the unit volume of the material under a certain voltage, L is the length of the V-shaped beam, k is the heat conductivity, and x represents the x-axis direction of a space rectangular coordinate system;
s09: the displacement relation of the V-shaped beam in the length direction.
From the heat conduction equation in S02, it can be known that the displacement relationship of the V-shaped beam in the length direction is:
Figure GDA0003961570490000074
wherein alpha is the thermal expansion coefficient of the material, T is the temperature of the V-shaped beam, q is the heat generated in the unit volume of the material under a certain voltage, L is the length of the V-shaped beam, k is the thermal conductivity, and x represents the x-axis direction of the rectangular space coordinate system.
S10: and (3) according to a dynamic equation without considering the damping effect in the actuation process of the V-shaped beam switch in the S07, the distribution relation of the temperature increment delta T on the V-shaped beam in the S08 and the displacement relation of the V-shaped beam in the length direction in the S09, combining the three equations, and solving to obtain the switching time of the V-shaped beam switch of the MEMS device.
As shown in fig. 3, the result of the switching time variation caused by the variation of the substrate curvature when the driving current of 0.6A is applied to the V-shaped beam structure under the bending condition of the flexible substrate, which is obtained by the analysis of the method provided by the present invention, is almost completely consistent with the result of the simulation and the actual test result. It can be seen that the actual measurement value of the switching time of the flexible MEMS device obtained by using the method provided by the invention is basically the same as the actual measurement value of the switching time of the flexible MEMS device, namely, the method provided by the invention can accurately measure the switching time of the flexible MEMS device in a complex space environment, and plays an important role in accurately mastering the switching time of the flexible MEMS device in engineering application.
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 disclosure of the present invention should be included in the scope of the present invention as set forth in the appended claims.

Claims (6)

1. A mechanical dynamic model analysis method for a V-shaped beam structure of a flexible MEMS device comprises the following steps:
s01: establishing a double-deformation coupling model between a V-shaped beam structure of the flexible MEMS device and a flexible substrate,
the double deformation coupling model is as follows:
Figure FDA0003961570480000011
wherein L is the length of the V-shaped beam, X is the increment of the distance between the anchor areas at two ends of the V-shaped beam, g is the initial distance between the V-shaped beam film bridge and the substrate, R is the bending curvature radius of the flexible substrate,
Figure FDA0003961570480000012
the included angle between the beam and the horizontal direction in the plane of the V-shaped beam;
s02: establishing a relation between a driving parameter and a driving signal of a V-shaped beam structure of the flexible MEMS device,
the flexible MEMS device is a thermal driving device, and the relation between the driving parameters of the V-shaped beam structure and the driving signals is as follows:
Figure FDA0003961570480000013
wherein L is the length of the V-shaped beam, w is the width of the V-shaped beam, t is the thickness of the V-shaped beam,
Figure FDA0003961570480000014
is the angle between the beam and the horizontal direction in the plane of the V-shaped beam, k is the thermal conductivity, C p Is the specific heat capacity of the material, rho is the density of the material, alpha is the coefficient of thermal expansion of the material,
Δ Y is the displacement of a single V-shaped beam in the driving direction, i.e., the driving parameter of the beam structure, and I is the driving current, i.e., the driving signal, for driving the V-shaped beam of the MEMS device;
s03: detecting a deformation parameter value of the V-shaped beam structure when the flexible substrate deforms;
s04: obtaining a driving parameter correction value of the beam structure according to the deformation parameter value of the V-shaped beam structure detected in the step S03 and the double-deformation coupling model in the step S01,
and in S04, the corrected value of the driving parameter is the retreating distance of the middle push rod of the V-shaped beam:
Figure FDA0003961570480000015
wherein L is the length of the V-shaped beam, g is the initial distance between the V-shaped beam film bridge and the substrate, R is the bending curvature radius of the flexible substrate,
Figure FDA0003961570480000016
is a flat place of the V-shaped beamThe included angle between the in-plane beam and the horizontal direction;
s05: correcting the driving parameters of the beam structure by using the corrected values of the driving parameters of the beam structure to obtain accurate values of the driving parameters of the beam structure,
in S05, the accurate value of the driving parameter is the accurate displacement of the V-shaped beam in the driving direction:
Figure FDA0003961570480000017
wherein L is the length of the V-shaped beam, w is the width of the V-shaped beam, t is the thickness of the V-shaped beam,
Figure FDA0003961570480000018
is the angle between the beam and the horizontal direction in the plane of the V-shaped beam, k is the thermal conductivity, C p The specific heat capacity of the material is adopted, rho is the density of the material, alpha is the thermal expansion coefficient of the material, and I is the driving current for driving the MEMS V-shaped beam;
s06: and obtaining an accurate value of the driving signal according to the relationship established in the S02.
2. The mechanical dynamic model analysis method for the V-shaped beam structure of the flexible MEMS device as claimed in claim 1, wherein the beam structure is a V-shaped beam with a middle push rod.
3. The mechanical dynamic model analysis method for the V-shaped beam structure of the flexible MEMS device as recited in claim 2, wherein the deformation parameter value in S03 is a change value of an included angle between a beam and a horizontal direction in a plane where the V-shaped beam is located:
Figure FDA0003961570480000021
wherein L is the length of the V-shaped beam,
Figure FDA0003961570480000022
the clamp is used for clamping the beam in the plane of the V-shaped beam and the horizontal directionAnd the angle g is the initial distance between the V-shaped beam film bridge and the substrate, and the bending curvature radius of the flexible substrate R.
4. The mechanical dynamic model analysis method for the V-shaped beam structure of the flexible MEMS device as claimed in claim 1, wherein the curvature variation range of the flexible substrate is [0, 33.3 ]]m -1 。
5. The mechanical dynamic model analysis method for the V-shaped beam structure of the flexible MEMS device as claimed in claim 2, further comprising the following steps:
s07: establishing a dynamic equation of the flexible MEMS device V-shaped beam switch actuation process without considering damping action;
s08: establishing a distribution relation of temperature increment delta T on the V-shaped beam;
s09: the displacement relation of the V-shaped beam in the length direction;
s10: and solving to obtain the switching time of the V-shaped beam switch of the MEMS device according to a dynamic equation without considering the damping action in the closing process of the V-shaped beam switch in the S07, the distribution relation of the temperature increment delta T on the V-shaped beam in the S08 and the displacement relation of the V-shaped beam in the length direction in the S09.
6. The mechanical dynamic model analysis method for the V-shaped beam structure of the flexible MEMS device as recited in claim 5, wherein the mechanical dynamic model analysis method comprises the following steps:
the dynamic equation of the flexible MEMS device V-shaped beam switch closing process without considering the damping action in the S07 is as follows:
Figure FDA0003961570480000023
wherein T is the temperature of the V-shaped beam,
Figure FDA0003961570480000024
is the amount of heat generated per unit volume of material at a given voltage, V is the applied voltage, R is the resistance, V R Volume of resistive material, k thermal conductivity, C p Is the specific heat capacity of the material, and rho is the density of the material;
the distribution relation of the temperature increment delta T on the V-shaped beam in the S08 is as follows:
Figure FDA0003961570480000031
wherein T is the temperature of the V-shaped beam, q is the heat generated in the unit volume of the material under a certain voltage, L is the length of the V-shaped beam, k is the thermal conductivity, and x represents the x-axis direction of a space rectangular coordinate system;
the displacement relation of the V-shaped beam in the length direction in the S09 is as follows:
Figure FDA0003961570480000032
wherein alpha is the thermal expansion coefficient of the material, T is the temperature of the V-shaped beam, q is the heat generated in the unit volume of the material under a certain voltage, L is the length of the V-shaped beam, k is the thermal conductivity, and x represents the x-axis direction of a space rectangular coordinate system.
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