CN110661505A - Low-extrusion-film damping micromechanical resonator with large length-width ratio structure - Google Patents

Low-extrusion-film damping micromechanical resonator with large length-width ratio structure Download PDF

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CN110661505A
CN110661505A CN201910831468.8A CN201910831468A CN110661505A CN 110661505 A CN110661505 A CN 110661505A CN 201910831468 A CN201910831468 A CN 201910831468A CN 110661505 A CN110661505 A CN 110661505A
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rectangular
vibrator
damping
low
substrate
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李普
方玉明
王金湘
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Southeast University
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Southeast University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/02—Details
    • H03H9/02244—Details of microelectro-mechanical resonators
    • H03H9/02338—Suspension means
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B81—MICROSTRUCTURAL TECHNOLOGY
    • B81B—MICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B3/00—Devices comprising flexible or deformable elements, e.g. comprising elastic tongues or membranes
    • B81B3/0018—Structures acting upon the moving or flexible element for transforming energy into mechanical movement or vice versa, i.e. actuators, sensors, generators
    • B81B3/0021—Transducers for transforming electrical into mechanical energy or vice versa
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B81—MICROSTRUCTURAL TECHNOLOGY
    • B81B—MICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B3/00—Devices comprising flexible or deformable elements, e.g. comprising elastic tongues or membranes
    • B81B3/0064—Constitution or structural means for improving or controlling the physical properties of a device
    • B81B3/0067—Mechanical properties
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/02—Details
    • H03H9/02244—Details of microelectro-mechanical resonators
    • H03H9/02433—Means for compensation or elimination of undesired effects
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/24—Constructional features of resonators of material which is not piezoelectric, electrostrictive, or magnetostrictive
    • H03H9/2405—Constructional features of resonators of material which is not piezoelectric, electrostrictive, or magnetostrictive of microelectro-mechanical resonators

Abstract

The invention discloses a low-squeeze-film damping micromechanical resonator with a large length-width ratio structure, which comprises a rigid rectangular oscillator with a large length-width ratio, an elastic supporting beam, a fixed support and a substrate. The rectangular vibrator is supported by an elastic beam and vibrates perpendicularly to the substrate. Previous transducer structures have generally been rectangular, or square, with an aspect ratio close to 1. The squeeze film of the vibrator has large damping, so that the quality factor of the device is not high, and the mechanical energy loss is high. When the device is used as an actuator, the response of the device is slow, and the application value is low. According to the low-extrusion-film-damping micro-resonance device, the vibrator is of a rectangular structure with a large length-width ratio, so that the pressure difference inside and outside the extrusion film gap is remarkably reduced, and the low-extrusion-film-damping micro-resonance device has small extrusion film damping. The device has low mechanical energy loss, high quality factor, fast response and high application value.

Description

Low-extrusion-film damping micromechanical resonator with large length-width ratio structure
Technical Field
The invention belongs to the field of Micro Electro Mechanical Systems (MEMS), and particularly relates to a low-extrusion-film damping micro-resonance device with a large length-width ratio structure.
Background
The micromechanical resonance device is composed of a vibrator, an elastic supporting beam and a substrate. The vibrator is equivalent to a rigid mass block and generally adopts a rectangular structure. The resilient supporting beam corresponds to a spring element. Fig. 1 is a schematic diagram of such a device. In the figure, x and y directions are the length and width directions of the rectangular vibrator, respectively, and an alternating current driving voltage is applied between the rectangular vibrator and the substrate. The vibrator vibrates at a natural frequency to make a parallel plate vibration with respect to the substrate. The "parallel plate vibration" is: the lower surface of the rectangular vibrator is always parallel to the upper surface of the substrate during vibration.
The micro-resonant device is generally made of silicon material, and is required to have a high quality factor, i.e. a small damping. In order to be able to generate a large driving force with a small driving voltage, the resonator and the substrate of the resonator device must be very close, forming a gap of very small size, i.e.: the dimension g0 of the gap between the lower surface of the transducer and the substrate should be much smaller than the side length of the transducer. At the moment, when the vibrator moves downwards, the gas in the gap is compressed and extruded; when the vibrator moves upward, the gas around the gap is sucked into the gap. This effect creates a pressure differential between the inside and outside of the gap. This pressure difference has a damping effect. This damping effect is squeeze film damping [1 ]. When g0 is much smaller than the rectangular transducer size, squeeze film damping is very significant [1 ]. This is the main reason why the quality factor of such devices is not high. To reduce squeeze film damping, two approaches may be employed:
in the first method, the gap g0 is enlarged. However, the electrostatic driving force is inversely proportional to the square of g0 [2 ]. I.e., g0, is doubled and the electrostatic driving force is quadrupled. The driving voltage must be increased by four times to generate the same driving force as the original magnitude. Large driving voltages are very disadvantageous for the circuitry.
In the second method, the current vibrators are all rectangular, and the damping size of the extrusion film is a function of the length, the width and the area of the vibrator. The planar structure of the vibrator can be improved and the squeeze film damping can be reduced. At present, no effective technical scheme for improving the device structure by utilizing the functional relation exists.
Document 1: darling RB, Hivick C, Xu J (1998) Compact analytical model of size file sampling with indexing calibration using a Green's function of the Sens analyzers A70: 32-41;
document 2: sentura, Microsystem design, Kluwer academic publishers, 2001;
document 3: fangyuming, Lepu, parallel plate electrostatic microactuator Pull-in model considering edge effect, journal of sensing technology 2011, vol.24, No.6, page 848-.
Disclosure of Invention
The prior vibrator is generally designed into a square shape or a rectangle with a small length-width ratio when being designed. The pressure difference between the inside and the outside of the extrusion film gap of the vibrator is large, so that the extrusion film has large damping, high energy loss and low quality factor. The device has low application value. When the device is used as a micro actuator, the damping force is large, and the response of the oscillator is slow.
Therefore, the invention provides a low-extrusion-film damping micro-resonance device with a large length-width ratio structure, and the resonance device has small energy loss and high quality factor.
The invention relates to a low-extrusion film damping micro-resonance device with a large length-width ratio structure, which comprises a rectangular oscillator with a large length-width ratio, an elastic supporting beam, a fixed support and a substrate; one end of the elastic support beam is connected with the fixed support, and the other end of the elastic support beam is vertically connected with the rectangular vibrator; the rectangular array is supported and fixed by the elastic supporting beam; the fixed support is fixedly arranged on the upper surface of the substrate; a driving voltage is applied between the rectangular vibrator and the substrate; the width of the rectangular oscillator is as follows: ly＝20·g0；g0Is the size of the gap between the rectangular vibrator and the substrate; the length of the rectangular oscillator is as follows:
Figure BDA0002190844100000031
where a is the area of the rectangular vibrator.
Further, the aspect ratio of the rectangular vibrator (4) is:
furthermore, the number of the elastic supporting beams supporting the rectangular oscillator is more than or equal to 1; one end of each elastic supporting beam is fixedly connected with the fixed support.
First, the operation and principle of the present invention when used as a resonator device will be explained as follows:
in order to be able to generate a large driving force with a small driving voltage, the vibrator and the substrate of the resonator device must be very close together. At the moment, when the vibrator moves downwards, the gas in the gap is compressed and extruded; when the vibrator moves upwards, the gas in the gap is stretched, and the gas around the gap is sucked into the gap. This effect creates a pressure differential between the inside and outside of the gap. The damping effect of this pressure differential is known as squeeze film damping. This damping results in the conversion of the mechanical kinetic energy of the vibrator into gas potential energy and kinetic energy which is lost. The lost energy needs to be supplemented by electrostatic force work. Obviously, the smaller this energy loss, the better and more power efficient the device. There are other uses for the resonator device of the present invention, which also require similar low power consumption.
The physical principle of the invention is analyzed as follows:
according to the theory [1] of the extrusion film damping, when the gas compression effect is neglected, the damping coefficient of the rectangular flat extrusion film is as follows:
Figure BDA0002190844100000033
where eta is the gas viscosity coefficient,
Figure BDA0002190844100000041
lxand lyIs the length and width of the rectangular plate. Since the first term of the series is absolutely large, only the first term is taken, one
Figure BDA0002190844100000042
In the formula, the area of the rectangular polar plate is A ═ lxly。
The electrostatic driving force is also proportional to the plate area a. Reducing the area a not only reduces the damping but also directly reduces the electrostatic force, which is not allowed in many operating conditions, especially when the actuator is used. Therefore, willWithout changing the rectangular plate area A, discussx、lyAnd damping coefficient cdampingThe relationship (2) of (c). By using
Figure BDA0002190844100000043
Then c isdampingCan be written as
Figure BDA0002190844100000044
In the formula (I), the compound is shown in the specification,
Figure BDA0002190844100000045
FIG. 3 is a schematic view ofFor variable quantity give
Figure BDA0002190844100000047
The amplitude curve of (d). The curve shows that:
(1) when the
Figure BDA0002190844100000048
When the temperature of the water is higher than the set temperature,
Figure BDA0002190844100000049
with a maximum value of 0.5. At this time, the process of the present invention,
Figure BDA00021908441000000410
this indicates that: when the area A is not changed, the square vibrator (l)y＝lz) With maximum squeeze film damping.
(2) When the
Figure BDA00021908441000000411
When the temperature of the water is higher than the set temperature,
Figure BDA00021908441000000412
there is a minimum value. Due to the fact that
Figure BDA00021908441000000413
Therefore, squeeze film damping is minimal when the transducer length is much greater than the width. In addition, when
Figure BDA00021908441000000414
When the temperature of the water is higher than the set temperature,
Figure BDA00021908441000000415
there is also a minimum value. At this time, the process of the present invention,
Figure BDA00021908441000000416
namely: when the width of the vibrator is far larger than the length of the vibrator, the damping of the extrusion film is minimum. For a constant area rectangle,/y＜＜lxAnd lx＜＜lyAre equivalent and need not be differentiated.
Conventional transducers are often rectangular or square with an aspect ratio close to 1 because of their low aspect ratio. The device has the advantages of large squeeze film damping, low quality factor and low application price. In the invention, the difference between the internal pressure and the external pressure of the extrusion film gap of the device with large length and width is small, and the device has low extrusion film damping. However, the smaller the transducer width, the better. The device is driven by electrostatic force, and the electrostatic field between the upper and lower polar plates has 'edge effect' [3 ]]. "edge effects" lead to a decrease in electrostatic driving force [3]. Only when the width of the vibrator is larger than or equal to the polar plate gap g020 times higher, the "edge effect" is negligible. Therefore, the width of the vibrator of the present invention is: ly＝20·g0. Then, the length is:
Figure BDA0002190844100000051
has an aspect ratio of
Figure BDA0002190844100000052
The invention has the beneficial effects that: the rectangular vibrator used has a sufficiently large aspect ratio.
The structure effectively reduces the pressure difference between the inside and the outside of the extrusion film, thereby effectively reducing the damping of the extrusion film, having high energy loss and obviously improving the quality factor. The device has high application value. When the micro-actuator is used as a micro-actuator, the damping force is small, and the response of the vibrator is fast.
Drawings
Figure 1 is a front view of the present invention.
FIG. 2 top view of the present invention.
FIG. 3
Figure BDA0002190844100000053
Is measured in a curve of the amplitude of (c).
FIG. 4 is a top view of a plate edge-to-edge support with two flexible beams according to the present invention.
FIG. 5 is a top view of the same side supporting scheme of the flat plate with two elastic beams according to the present invention.
Fig. 6 is a plan view of the present invention with four resilient support beams.
Wherein, the vibrator comprises 1-a substrate, 2-a fixed support, 3-an elastic support beam and 4-a rectangular vibrator.
Detailed Description
In order to make the purpose and technical solutions of the embodiments of the present application clearer, the technical solutions of the present application will be clearly and completely described below in conjunction with the embodiments of the present application.
A low squeeze film damping microresonator device having a large length-to-width ratio structure as shown in fig. 1 and 2 includes a rectangular vibrator 4 having a large length-to-width ratio, an elastic support beam 3, a fixed support 2, and a substrate 1; one end of the elastic supporting beam 3 is connected with the fixed support 2, and the other end of the elastic supporting beam is vertically connected with the rectangular vibrator 4; the rectangular array 4 is supported and fixed by the elastic supporting beam 3; the fixed support 2 is fixedly arranged on the upper surface of the substrate 1; a driving voltage is applied between the rectangular vibrator 4 and the substrate 1;
the rectangular vibrator 4 vibrates perpendicular to the plane of the substrate 1 and along the z direction under the action of electrostatic force. In fig. 2, the elastic support beam 3 is perpendicular to the midpoint of the broad side of the rectangular vibrator 4. In fig. 1, the elastic support beam 3 is perpendicular to the thickness side of the rectangular vibrator 4, but the foot may not be the midpoint of the thickness side.
The width of the rectangular vibrator 4 is: ly＝20·g0；g0Is the size of the gap between the rectangular vibrator and the substrate 1; the length of the rectangular oscillator 4 is as follows:
Figure BDA0002190844100000061
where a is the area of the rectangular vibrator.
The aspect ratio of the rectangular vibrator 4 is:
Figure BDA0002190844100000062
the specific effects of the present invention are shown in the following two examples.
Example one: one required driving electrode area A is 900 μm2And a polar plate gap g0The length and width of the oscillator obtained by the method of the invention are as follows: ly＝20g0＝20μm；
Figure BDA0002190844100000071
As shown in FIG. 3, the vibrator has
Figure BDA0002190844100000072
As a comparison, a square resonator obtained by a conventional method was used,. lx＝ly30 μm. The square vibrator has
Figure BDA0002190844100000073
It is clear that the squeeze film damping of the square vibrator is significantly larger than the vibrator of the present invention. The squeeze film damping value of the vibrator is 0.6 times of that of a square.
Example two: for a required drive electrode area a 900 μm2And a gap g0The length and width of the oscillator obtained by the method of the invention are as follows: ly＝20g0＝10μm；
Figure BDA0002190844100000074
As shown in FIG. 3, the vibrator has
Figure BDA0002190844100000075
Square vibration obtained by conventional methodHas the advantages of
Figure BDA0002190844100000076
Obviously, the squeeze-film damping of the present vibrator is only 0.2 times that of the square vibrator.
As shown in fig. 4: a low-extrusion film damping micro-resonance device with a large length-width ratio structure comprises a rectangular oscillator 4 with a large length-width ratio, an elastic supporting beam 3, a fixed support 2 and a substrate 1; the left end and the right end of the rectangular vibrator 4 are fixedly connected with the elastic supporting beam 3; the other end of each supporting beam 3 is connected and fixed with a fixed support 2; each fixed support 2 is fixedly arranged on the upper surface of the substrate 1; a driving voltage is applied between the rectangular vibrator 4 and the substrate 1.
The width of the rectangular vibrator 4 is: ly＝20·g0；g0Is the size of the gap between the rectangular vibrator and the substrate 1; the length of the rectangular oscillator 4 is as follows:
Figure BDA0002190844100000077
where a is the area of the rectangular vibrator. The aspect ratio of the rectangular vibrator 4 is:
Figure BDA0002190844100000081
as shown in fig. 5: a low-extrusion film damping micro-resonance device with a large length-width ratio structure comprises a rectangular oscillator 4 with a large length-width ratio, an elastic supporting beam 3, a fixed support 2 and a substrate 1; one side of the rectangular vibrator 4 is connected with two elastic supporting beams 3, and the other end of each supporting beam 3 is connected and fixed with a fixed support 2; each fixed support 2 is fixedly arranged on the upper surface of the substrate 1; a driving voltage is applied between the rectangular vibrator 4 and the substrate 1.
The width of the rectangular vibrator 4 is: ly＝20·g0；g0Is the size of the gap between the rectangular vibrator and the substrate 1; the length of the rectangular oscillator 4 is as follows:
Figure BDA0002190844100000082
where a is the area of the rectangular vibrator. The aspect ratio of the rectangular vibrator 4 is:
Figure BDA0002190844100000083
as shown in fig. 6: a low-extrusion film damping micro-resonance device with a large length-width ratio structure comprises a rectangular oscillator 4 with a large length-width ratio, an elastic supporting beam 3, a fixed support 2 and a substrate 1; two sides of the rectangular vibrator 4 are respectively connected and fixed with the two elastic supporting beams 3; the other end of each supporting beam 3 is connected and fixed with a fixed support 2; each fixed support 2 is fixedly arranged on the upper surface of the substrate 1; a driving voltage is applied between the rectangular vibrator 4 and the substrate 1.
The width of the rectangular vibrator 4 is: ly＝20·g0；g0Is the size of the gap between the rectangular vibrator and the substrate 1; the length of the rectangular oscillator 4 is as follows:
Figure BDA0002190844100000084
where a is the area of the rectangular vibrator. The aspect ratio of the rectangular vibrator 4 is:

Claims (3)

1. a low squeeze film damping micro-resonance device with a large length-width ratio structure is characterized in that: comprises a rectangular vibrator (4) with a large length-width ratio, an elastic supporting beam (3), a fixed support (2) and a substrate (1); one end of the elastic supporting beam (3) is connected with the fixed support (2) and the other end is vertically connected with the rectangular vibrator (4); the rectangular array (4) is supported and fixed by the elastic supporting beam (3); the fixed support (2) is fixedly arranged on the upper surface of the substrate (1); a driving voltage is applied between the rectangular vibrator (4) and the substrate (1); the width of the rectangular oscillator (4) is as follows: ly＝20·g0；g0Is the size of the gap between the rectangular vibrator and the substrate (1); the length of the rectangular oscillator (4) is as follows:
Figure FDA0002190844090000011
where a is the area of the rectangular vibrator.
2. A low squeeze film damping micromechanical resonator with a large aspect ratio structure according to claim 1, characterized in that: the aspect ratio of the rectangular oscillator (4) is as follows:
Figure FDA0002190844090000012
3. a low squeeze film damping micromechanical resonator with a large aspect ratio structure according to claim 1, characterized in that: the number of the elastic supporting beams (3) supporting the supporting rectangular vibrators (4) is more than or equal to 1; one end of each elastic supporting beam (3) is fixedly connected with the fixed support (2).
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113292035A (en) * 2021-04-22 2021-08-24 东南大学 Large-extrusion-film damping torsion type micro-mechanical actuator

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109245602A (en) * 2018-10-12 2019-01-18 东南大学 A kind of low squeeze-film damping micro-resonator
CN109911841A (en) * 2019-03-19 2019-06-21 东南大学 A kind of maximum capacity plate antenna microactrator of squeeze-film damping

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109245602A (en) * 2018-10-12 2019-01-18 东南大学 A kind of low squeeze-film damping micro-resonator
CN109911841A (en) * 2019-03-19 2019-06-21 东南大学 A kind of maximum capacity plate antenna microactrator of squeeze-film damping

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113292035A (en) * 2021-04-22 2021-08-24 东南大学 Large-extrusion-film damping torsion type micro-mechanical actuator

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