WO2020048107A1

WO2020048107A1 - Mechanical analysis method for mems v-beam structure under bending condition of flexible substrate

Info

Publication number: WO2020048107A1
Application number: PCT/CN2019/078321
Authority: WO
Inventors: 韩磊; 于洋; 刘星; 陈柳宏; 吴虹剑; 徐粲然
Original assignee: 东南大学
Priority date: 2018-09-04
Filing date: 2019-03-15
Publication date: 2020-03-12
Also published as: CN109446544B; CN109446544A

Abstract

Disclosed in the present invention is a mechanical analysis method for a MEMS V-beam structure under a bending condition of a flexible substrate. The purpose is to provide a method for estimating a parameter variation law of mechanical properties of a V-beam structure under a bending deformation condition of a flexible substrate. The present invention mainly adopts two steps to deal with the modeling of bending characteristics of the MEMS V-beam structure under the bending condition of the flexible substrate, thereby obtaining an analytical model for the influence of the deformation of the V-beam structure on the mechanical properties of a device. One is establishing a deformation coupling model based on double deformation of the MEMS V-beam structure and the flexible substrate, and the other is obtaining a deformation amount of V-beam structure/substrate double deformation on the basis of the bending characteristic model of the MEMS V-beam structure. Based on the above parameters, the mechanical model of the MEMS V-beam structure is reconstructed, and the influence of the bending deformation on the mechanical properties of the V-beam structure is analyzed. In order to fill the gap in the research on flexible device models of MEMS V-beam structures at home and abroad, the present invention provides a mechanical analysis method for a MEMS V-beam structure comprising a double deformation model of the V-beam structure and a flexible substrate based on a complex environment space.

Description

Mechanical analysis method of MEMS V-beam structure based on flexible substrate bending conditions

Technical field

The invention relates to a mechanical analysis method, in particular to a MEMS V-beam structure mechanical analysis method based on a flexible substrate bending condition.

Background technique

In the current wave of informatization development, flexible electronic devices have very broad application prospects in the fields of national defense, information, medical, energy and other fields due to their unique bendable ductility and their efficient and low-cost manufacturing processes. Flexible electronic devices, as a popular development direction of next-generation semiconductor devices, are emerging electronic technologies based on flexible / stretchable substrates. They make active / passive organic / inorganic electronic devices on flexible substrates, which have both traditional rigid electronic systems. The performance also has the unique characteristics of stretching, twisting and folding, so it has unparalleled importance and advantages in conformity, miniaturization, light weight, and intelligence for complex environmental space applications. As an important branch of flexible electronic devices, MEMS (microelectromechanical systems) flexible devices, its conformal, high performance, small size, and intelligent sensors / actuators have become an indispensable part of today's flexible electronic systems, especially RFMEMS. (RF MEMS) Flexible devices, due to their wide application prospects in airborne / spaceborne radar and IoT communication systems, have made various RF MEMS flexible actuators / sensors a hot topic in recent years. As an RF MEMS flexible device, its primary characteristic is nothing more than its unique bendability, which is also the application basis and research motivation for the development of related flexible devices. Therefore, the bending characteristics of RF MEMS flexible devices is the scientific problem that needs to be studied most. At present, whether it is silicon-based or various types of flexible substrate-based RF MEMS flexible devices, its main research content and purpose are still in the stage of device design, preparation, and performance testing under non-bending conditions. The bending characteristics of RF MEMS flexible devices Research on modeling and experimental characterization verification is currently blank. However, no matter from the perspective of scientific research or engineering application, it is urgent to establish a bending characteristic model of RF MEMS devices based on flexible substrates in order to promote the in-depth research and development of RF MEMS flexible devices.

Summary of the Invention

Purpose of the invention: In order to fill the research gap of MEMS V-beam structure flexible device models at home and abroad, the present invention provides a MEMS V-beam structure mechanics based on complex environmental space, including a MEMS V-beam structure and a flexible substrate double deformation model. Analytical method.

Technical solution: The present invention provides a MEMS V-beam structure mechanical analysis method based on a flexible substrate bending condition, including the following steps:

Step 1: Establish a deformation coupling model based on the double deformation of the MEMS V-beam structure and the flexible substrate. Assume that the length of the V-beam beam is L, the initial distance between the membrane bridge and the substrate is g, and the bending radius of the flexible substrate is R. The increment of the distance between the anchor areas at both ends of the beam is:

Step 2: Assume that the length of a single beam in the basic unit of the V-beam structure is L, the width is w, and the thickness is t. The angle between the beam in the plane where the V-beam is located and the horizontal direction is

The heat distribution of the V-beam can be calculated from the heat conduction equation as:

Where T is the temperature of the V-beam,

Is the heat generated per unit volume of the material at a certain voltage, V is the applied voltage, R is the resistance, V _R is the volume of the resistive material, k is the thermal conductivity, C _p is the specific heat capacity of the material, and ρ is the material density. Assuming that the heat q generated in the unit volume of the V-beam material is constant and the structure is in a stable state, the above formula can be simplified as:

Further, the distribution of the temperature increase ΔT on the V-beam can be obtained from the boundary conditions as:

Further, it can be obtained that the displacement of the V-shaped beam in the length direction is:

Where α is the thermal expansion coefficient of the material.

Further, by taking in the parameters, the displacement of the single V-beam in the driving direction is:

Among them, I is the driving current to drive the MEMS V-beam.

Step 3: After the flexible substrate is bent, the deformation of the MEMS V-beam will cause the distance between the anchor areas at both ends to change, which in turn will cause the angle between the beam in the plane where the V-beam is located and the horizontal direction, and the middle pusher of the V-beam to recede. Affects the driving distance of the V-beam and thus the driving current of the V-beam. According to the geometric relationship, after the flexible substrate is bent, the angle between the beam in the plane where the V-beam is located and the horizontal direction changes is:

Further, from the geometric relationship, after the flexible substrate is bent, the retreat distance of the V-beam middle pusher is:

The included angle

And the intermediate pusher receding distance Y ′ are brought into the driving distance formula in step 2 above, and at the same time, considering the V-beam structure intermediate pusher receding, the driving distance formula based on the MEMS V-beam structure under flexible substrate bending conditions can be obtained as :

Further, the magnitude of the driving current I in the formula is obtained from this.

Working principle: In order to fill the research gaps of MEMS V-beam structure flexible device models at home and abroad, the present invention provides an estimation method for the variation law of mechanical performance parameters of MEMS V-beam structure under the condition of bending deformation of flexible substrate. The invention mainly takes two steps. The first step is to establish a deformation coupling model based on the double deformation of the MEMS V-beam structure and the flexible substrate. The second step is to obtain the V-beam structure / substrate based on the MEMS V-beam structure bending characteristic model. Deformation of double deformation. Based on the above parameters, the mechanical model of the MEMS V-beam structure was reconstructed, and the influence of bending deformation on the mechanical properties of the MEMS V-beam structure was analyzed.

Beneficial effect: Compared with the prior art, the present invention establishes for the first time a deformation coupling model based on double deformation of a MEMS V-beam structure and a flexible substrate. The pull-in voltage model of the MEMS V-beam structure after bending deformation is further established to realize the model characterization of the mechanical characteristics of the MEMS V-beam structure. A complex environmental space-based model including the double deformation model of the V-beam structure and the flexible substrate is provided. The mechanical analysis method of MEMS V-beam structure fills the gaps in domestic and foreign research on the flexible device model of MEMS V-beam structure.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a flowchart of the present invention;

2 is a structural schematic diagram of a MEMS V-beam in the present invention;

FIG. 3 is a comparison diagram of the analysis method, simulation and test results provided by the present invention.

detailed description

The invention is explained further below with reference to the drawings.

As shown in Figure 1-2, the present invention takes an RF MEMS V-beam as an example. Referring to FIG. 2, the RF MEMS V-beam is fixedly connected to the substrate through the anchor zone 1 and the V-beam is connected to the push rod 2, 3 A signal transmission line provided on the substrate, 4 is a single V-shaped beam, and its length is L. In this embodiment, the parameters are taken. The material of the RF MEMS V-beam thermally driven switch beam is gold, the flexible substrate material is liquid crystal polymer (LCP), the length of the MEMS V-beam structure beam is L = 400 μm, and the beam The width w = 7μm, the thickness of the beam t = 10μm, the angle between the beam in the plane where the V-beam is located and the horizontal direction

The size of the intermediate pusher is L ′ = 355 μm; width w ′ = 50 μm. As the flexible substrate is gradually bent, the curvature of the substrate is gradually increased from 0 to 33.3 m ^-1 .

In order to study the influence of the flexible substrate on the mechanical properties of the MEMS V-beam structure after bending, the present invention proposes the following technical solution.

The specific steps are as follows:

Step 1: Establish a deformation coupling model based on the double deformation of the MEMS V-beam structure and the flexible substrate. Assume that the length of the V-beam beam is L, the initial distance between the membrane bridge and the substrate is g, and the bending curvature radius of the flexible substrate is R. The increment of the distance between the anchor areas at both ends of the beam is:

among them,

The angle between the beam in the plane where the V-beam is located and the horizontal direction.

Step 2: Assume that the basic element of the V-beam structure includes multiple beams. The length of a single beam is the same as the length of the V-beam. The angle is

Where T is the temperature of the V-beam,

Is the heat generated in a unit volume of the material at a certain voltage, V is the applied voltage, R is the resistance, V _R is the volume of the resistive material, k is the thermal conductivity, C _p is the specific heat capacity of the material, and ρ is the material density. Assuming that the heat q generated in the unit volume of the V-beam material is constant and the structure is in a stable state, the above formula can be simplified as:

Where α is the thermal expansion coefficient of the material.

Among them, I is the driving current to drive the MEMS V-beam.

The included angle

As shown in FIG. 2, the present invention takes an RF MEMS V-beam as an example. In this embodiment, parameters are set. The material of the RF MEMS V-beam thermally driven switch beam is gold, and the flexible substrate material is liquid crystal polymer. (LCP), the length of the MEMS V-beam structure beam is L = 400μm, the width of the beam is w = 7μm, the thickness of the beam is t = 10μm, the angle between the beam in the plane where the V-beam is located and the horizontal direction

The size of the intermediate pusher is L ′ = 355 μm; width w ′ = 50 μm. As the flexible substrate is gradually bent, the curvature of the substrate is gradually increased from 0 to 33.3 m ^-1 . The driving distance for applying a current of 0.6A to the V-beam structure under the bending conditions of the flexible substrate obtained by the method provided by the present invention is almost completely similar to the simulation result, and is almost completely consistent with the test result. The method provided by the present invention can be applied to a complex environmental space, and includes a double deformation model of a V-beam structure and a flexible substrate, which fills a gap in the research of MEMS V-beam structure flexible device models at home and abroad.

The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. Any equivalent modification or change made by a person of ordinary skill in the art based on the disclosure of the present invention should be included Within the scope of protection described in the claims.

Claims

A mechanical analysis method of a MEMS V-beam structure based on a flexible substrate bending condition is characterized in that it includes the following steps:

Establishing a deformation coupling model based on the double deformation of the RF MEMS V-beam structure and the flexible substrate; the RF MEMS V-beam structure is connected to the flexible substrate through a fixed anchor area;

Based on the deformation coupling model: after the flexible substrate is bent and deformed, obtaining an angle change amount of the RF MEMS V-beam structure and a receding distance of the intermediate push rod;

Reconstructing a mechanical characteristic model of the RF MEMS V-beam structure based on the parameter values after the flexible substrate is deformed;

Based on the reconstructed mechanical characteristic model of the RF MEMS V-shaped beam structure, the influence of the flexible substrate bending on the mechanical characteristics of the RF MEMS V-shaped beam structure is obtained.
The mechanical analysis method of a MEMS V-beam structure under flexible substrate bending conditions according to claim 1, wherein:

Based on the deformation coupling model of the double deformation of the MEMS V-beam structure and the flexible substrate, the increment X of the distance between the anchor areas at both ends of the V-beam is:

Among them, L is the length of the V-beam beam, g is the initial distance from the V-beam membrane bridge to the substrate, and the radius of curvature of the flexible substrate bending curvature
The angle between the beam in the plane where the V-beam is located and the horizontal direction.
The mechanical analysis method of a MEMS V-beam structure under flexible substrate bending conditions according to claim 1 or 2, wherein:

After the MEMS V-shaped beam is thermally driven, the middle push rod is driven to move forward to realize the switch pull-in; and the displacement of the MEMS V-shaped beam structure in the driving direction is obtained.
The mechanical analysis method for a MEMS V-beam structure under flexible substrate bending conditions according to claim 3, wherein the displacement of the MEMS V-beam structure in the driving direction is:

Among them, I is the driving current driving the MEMS V-beam, α is the thermal expansion coefficient of the material, ρ is the material density, k is the thermal conductivity, L is the length of a single beam in the basic unit of the V-beam structure, w is the width, t is the thickness.
The method for mechanically analyzing a MEMS V-beam structure under flexible substrate bending conditions according to claim 1 or 2, characterized in that after the flexible substrate is bent and deformed, the distance between the anchor regions at both ends of the MEMS V-beam is changed, In addition, the angle between the beam in the plane where the V-beam is located and the horizontal direction changes, and the middle pusher of the V-beam recedes, which affects the driving distance of the V-beam and thus the driving current of the V-beam.
The method for mechanically analyzing a MEMS V-beam structure under a flexible substrate bending condition according to claim 5, characterized in that: acquiring the included angle of the MEMS V-beam structure after the flexible substrate is bent and deformed, and the intermediate pusher receding distance, and According to the driving distance formula, obtaining the mechanical characteristics of the MEMS V-beam structure based on the flexure of the flexible substrate includes testing the driving distance of the V-beam.
The mechanical analysis method of a MEMS V-beam structure under flexible substrate bending conditions according to claim 6, wherein the driving distance formula is:

Among them, ⊿Y is the displacement of the MEMS V-beam structure in the driving direction, I is the driving current driving the MEMS V-beam, α is the thermal expansion coefficient of the material, ρ is the material density, k is the thermal conductivity, and L is the V-shape. The length, w is the width and t is the thickness of a single beam in the basic unit of a beam structure.