CN114598294A - Torsional micromechanical resonator with torsional-bending coupling resonance - Google Patents
Torsional micromechanical resonator with torsional-bending coupling resonance Download PDFInfo
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- CN114598294A CN114598294A CN202210249410.4A CN202210249410A CN114598294A CN 114598294 A CN114598294 A CN 114598294A CN 202210249410 A CN202210249410 A CN 202210249410A CN 114598294 A CN114598294 A CN 114598294A
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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
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- H03H9/02244—Details of microelectro-mechanical resonators
- H03H9/02259—Driving or detection means
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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
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Abstract
The invention relates to a torsional-bending coupling resonance micromechanical resonator, which comprises a substrate, a driving electrode and an induction electrode which are arranged on the substrate, and a movable polar plate which is arranged above the driving electrode and the induction electrode, wherein two ends of the movable polar plate are respectively connected with one end of a torsional supporting beam, the other ends of the two torsional supporting beams are respectively connected with a fixed support, the two fixed supports are arranged on the substrate at intervals, the two torsional supporting beams have the same structural size and are overlapped along the axial line of the length direction, the movable polar plate is rectangular or circular, the cross section of the torsional supporting beam is square, the materials of the torsional supporting beam and the movable polar plate are the same, and the torsional vibration natural frequency of the movable polar plate is equal to the bending vibration natural frequency of the torsional supporting beams. The invention needs small driving force, so that the invention can obtain larger amplitude with smaller driving force, save driving energy, obviously reduce driving requirement and improve resonator performance.
Description
Technical Field
The present invention relates to the field of micro-electromechanical systems (MEMS), and in particular to torsional micromechanical resonators for torsional-bending coupled resonance.
Background
As shown in fig. 1, a prior art torsional micro-mechanical resonator (see document [1]) is mostly composed of a torsional vibrator (stiff mass), an elastic torsional support beam (spring element) and a stiff substrate, and is generally made of single crystal silicon or polycrystalline silicon. The torsional microresonator device vibrates at a torsional natural frequency. The torsion vibrator is generally a rectangular flat plate structure. An alternating current driving voltage is applied between the rectangular flat plate and the driving polar plate, the supporting beam generates torsional elastic deformation, and the sensing electrode senses the capacitance variation on the left side and outputs charges or current.
Torsional resonators generally assume that the support beam is only torsionally elastically deformed, as shown in fig. 2 (a). However, the electrostatic driving force not only generates a torsional moment effect but also is a lateral load, and acts directly on the support beam (see documents [1] to [3 ]). Therefore, the support beam is deformed not only by torsion but also by bending, as shown in fig. 2 (b). The conventional torsional resonator has two separated peaks in the frequency response of the outermost amplitude of the torsional array due to the defects of the structural design, so that a larger driving force is required to obtain a larger amplitude, and the required driving energy is high.
Literature
[1] Joji 22773, microsystems design and manufacture, university of qinghua press, 2008.
[2] Tai yongco, torsional MEMS resonator device torsional-bending coupling thermoelastic damping model, doctrine of doctrines, southeast university, 2014.
[3]W.T.Thomson，M D Dahleh，Theory of vibration with applications(Fifth Edtion)，Prentice Hall，2005.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a torsional micromechanical resonator of torsional-bending coupling resonance, aiming at improving the performance of the resonator by directly utilizing a torsional-bending coupling vibration structure.
The technical scheme adopted by the invention is as follows:
a torsional-bending coupling resonance micromechanical resonator comprises a substrate, a driving electrode and an induction electrode which are arranged on the substrate, and a movable polar plate which is arranged above the driving electrode and the induction electrode, wherein two ends of the movable polar plate are respectively connected with one end of a torsional supporting beam, the other end of each torsional supporting beam is respectively connected with a fixed support, the two fixed supports are arranged on the substrate at intervals, the two torsional supporting beams are identical in structural size and coincide along the axis of the length direction, the movable polar plate is rectangular or circular, the cross section of each torsional supporting beam is square, the torsional supporting beams and the movable polar plate are made of the same material, and the torsional vibration natural frequency of the movable polar plate is equal to the bending vibration natural frequency of the torsional supporting beams.
The further technical scheme is as follows:
the movable polar plate is rectangular, the connecting points of the movable polar plate and the two torsion supporting beams are respectively positioned at two ends of the central axis of the movable polar plate along the width y direction, the axes of the two torsion supporting beams along the length direction coincide with the central axis of the movable polar plate along the width y direction, the thickness of the torsion supporting beam is equal to that of the movable polar plate, and the length L of the torsion supporting beam is equal to the length L of the movable polar platexIn a relationship of
v is the Poisson's ratio of the material.
The movable polar plate is rectangular, the connecting points of the movable polar plate and the two twisting supporting beams are respectively positioned at two ends of one side edge of the movable polar plate along the width y direction, the axes of the two twisting supporting beams along the length direction are superposed with one side edge of the movable polar plate along the width y direction, the thickness of the twisting supporting beam is equal to that of the movable polar plate, and the length L of the twisting supporting beam is equal to the length L of the movable polar platexIn a relationship of
v is the Poisson's ratio of the material.
The movable polar plate is circular, the connecting points of the movable polar plate and the two twisting supporting beams are respectively positioned at two ends of the diameter of the movable polar plate, the thickness of the twisting supporting beams is equal to that of the movable polar plate, and the relationship between the length l of the twisting supporting beams and the radius R of the movable polar plate is
v is the Poisson's ratio of the material.
The torsion supporting beam and the movable polar plate are made of silicon.
The invention has the following beneficial effects:
the natural frequency of the torsional vibration of the movable polar plate is equal to the natural frequency of the bending vibration of the torsional support beam, two resonance peaks in the amplitude frequency response of the movable polar plate are superposed, namely, the torsional-bending simultaneous coupling resonance, the vibration amplitude is obviously improved compared with the conventional structure, the torsional support beam simultaneously generates torsional and bending deformation, and compared with the conventional structure, the required driving force is much lower, so that the relatively large amplitude can be obtained by using smaller driving force, the driving energy is saved, the driving requirement is reduced, and the performance of the resonator is obviously improved.
Drawings
Fig. 1 is a schematic diagram of a conventional torsional micromechanical resonator structure in the prior art.
Fig. 2 is a schematic view showing the position of the torsion plate when only the torsional deformation (a) is considered and the torsional deformation and the bending deformation (b) are considered at the same time.
Fig. 3 is a schematic structural diagram of a torsional micromechanical resonator according to embodiment 1 of the present invention.
Fig. 4 is a schematic structural diagram of a torsional micromechanical resonator according to embodiment 2 of the present invention.
Fig. 5 is a schematic structural diagram of a torsional micromechanical resonator according to embodiment 3 of the present invention.
Fig. 6 shows the result of comparing the frequency response of the amplitude of the outermost side of the movable plate of example 1 of the present invention with that of the conventional micromechanical resonator.
In the figure: 1. a substrate; 2. a drive electrode; 3. an induction electrode; 4. a movable polar plate; 5. twisting the support beam; 6. and (7) fixing and supporting.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
A torsional micromechanical resonator of the present application, which is a torsional-flexural coupled resonator, is shown in figure 3,
the device comprises a substrate 1, a driving electrode 2 and an induction electrode 3 which are arranged on the substrate 1, and a movable polar plate 4 which is arranged above the driving electrode 2 and the induction electrode 3, wherein two ends of the movable polar plate 4 are respectively connected with one end of a torsion supporting beam 5, the two torsion supporting beams 5 are the same in structural size and are overlapped along the axial line of the length direction, the other ends of the two torsion supporting beams 5 are respectively connected with a fixed support 6, and the two fixed supports 6 are respectively arranged at two ends of the substrate;
the movable polar plate 4 is rectangular or round, the cross section of the torsion supporting beam 5 is square, the materials of the torsion supporting beam 5 and the movable polar plate 4 are the same, and the torsional vibration natural frequency of the movable polar plate 4 is equal to the bending vibration natural frequency of the torsion supporting beam 5.
Wherein, a driving voltage is applied between the driving electrode 2 and the movable polar plate 4, the movable polar plate 4 is rigid, and the two torsion supporting beams 5 are twisted and deformed to play the role of a torsion spring. The movable polar plate 4 generates torsion-bending coupling vibration deformation under the action of driving voltage (input of a resonator), the capacitance change of the induction electrode is caused by the deformation of the movable polar plate 4, and the capacitance change of the induction electrode 3 is measured. The capacitance variation of the sensing electrode 3 is the output of the resonator.
The technical solution and design principle of the present application are described in detail with specific embodiments below.
Example 1
Fig. 3 is a schematic structural diagram of a torsional micromechanical resonator with a rectangular symmetric movable plate. Fig. 3 (a) and (b) are a side view and a plan view, respectively. The movable polar plate 4 is a rectangle, the connection points of the movable polar plate 4 and the two torsion supporting beams 5 are respectively positioned at two ends of the central axis of the movable polar plate 4 along the width y direction, the axes of the two torsion supporting beams 5 along the length direction are superposed with the central axis of the movable polar plate 4 along the width y direction, the cross section of the torsion supporting beam 5 is square, namely, the width b of the torsion supporting beam 5 is equal to the thickness H, and the thickness H of the torsion supporting beam 5 is equal to the thickness H of the movable polar plate 4. The length L of the torsion supporting beam 5 and the length L of the movable polar plate 4xIn a relationship of
v is the Poisson's ratio of the material.
How the length relationship is derived is explained in detail below.
The length, width and thickness directions of the movable plate 4 in this embodiment are the x-axis, y-axis and z-axis, respectively. The length, width and thickness of the torsion support beam 5 are l, b and h, respectively. The length, width and thickness of the movable polar plate 4 are respectively Lx、LyAnd H. The moment of electrostatic force acts on the movable polar plate 4 to cause the two elastic torsion supporting beams 5 to generate torsion-bending coupling elastic deformation, and the mass m of the movable polar plate 4 and the moment of inertia J around the y axisyThe method comprises the following steps: where m is ρ LxLyH，
Where ρ is the density of the movable plate 4;
in order to reduce the manufacturing cost and simplify the device geometry and the material type, the material of the torsion support beam of the embodiment is the same as that of the movable polar plate, and the torsion support beam and the movable polar plate have the same elastic modulus E and density rho. The torsion supporting beam is square, namely b is equal to H, and the thickness of the supporting beam is equal to that of the movable polar plate, namely H is equal to H.
The torsional stiffness of a torsional support beam with a square cross-section is:
it can be derived that the natural frequency of torsional vibration of the movable plate supported by the two support beams is:
in the formula (I), the compound is shown in the specification,
formula shear modulus, E and v material elastic modulus and poisson's ratio.
The bending stiffness of a square section torsion support beam is:
the moving plate is a concentrated mass supported by two support beams, so the natural frequencies of bending vibration of the two torsion support beams are:
this embodiment requires that the natural frequency of the torsional vibration must be equal to the natural frequency of the bending vibration, i.e., ωTorsion bar＝ωBendNamely:
for the most commonly used silicon materials, the poisson ratio v is 0.22,
yield L0.6LxI.e. the length L of the active plate is the torsion supporting beam L of the silicon materialx0.6 times of the total weight of the powder. Specifically, the length, width and thickness of the active plate in this example 1 are 500 μm, 300 μm and 10 μm respectively and the initial electrode pitch is 10 μm. The width and thickness of the twisted support beam were also 10 μm. The length of the torsion supporting beam is 0.6 times of the length of the movable polar plate, namely 300 mu m. The driving electrodes were 250 μm and 300 μm in length and width, respectively. The frequency response plot of the outermost amplitude of the active plate is shown in fig. 6.
By way of comparison, a frequency response plot of a conventional resonator structure designed in accordance with conventional methods is given in fig. 6. The length, width and thickness of the torsion support beam of the conventional resonator structure shown in fig. 1, which is designed in a conventional manner, are 600 μm, 7.07 μm and 2.83 μm, respectively. Fig. 1 (a) and (b) are a side view and a plan view, respectively. The conventional structure has the same torsional stiffness as the structure of the present embodiment, but the bending stiffness is different, so the frequency response of the conventional structure has two separate peaks. The torsional natural frequency of the present embodiment is equal to the bending natural frequency, and the two resonance peaks are coincident, so that the amplitude of the resonator of the present application is about 45% higher than that of the conventional structure at the torsional frequency, that is, the driving force of the resonator amplitude of the present application can be 45% lower than that of the conventional structure, so that the driving cost is greatly reduced.
Example 2
Fig. 4 is a schematic structural diagram of a torsional micromechanical resonator with an asymmetric structure of the movable plate 4. Fig. 4 (a) and (b) are a side view and a plan view, respectively. The movable polar plate 4 is rectangular, the connecting points of the movable polar plate 4 and the two twisting support beams 5 are respectively positioned at two ends of the central axis of the movable polar plate 4 along the width y direction, the axes of the two twisting support beams 5 along the length direction are superposed with one side edge of the movable polar plate 4 along the width y direction, the cross section of each twisting support beam 5 is square, the thickness of each twisting support beam 5 is equal to that of the movable polar plate 4, and the length L of each twisting support beam 5 is equal to the length L of the movable polar plate 4xIn a relationship of
v is the Poisson's ratio of the material.
How the length relationship is derived is explained in detail below.
As is clear from fig. 4, the difference from example 1 is that the torsion axis of the movable plate 4 is on the short side. The other dimensions, directions, signs, and the like are the same as those of example 1, and the torsional rigidity and the bending rigidity of the torsion support beam 5 are not changed. The mass of the movable plate 4 is still m ═ ρ LxLyh, moment of inertia J about y-axisyThe method comprises the following steps:
the natural frequency of the torsional vibration of the movable polar plate is as follows:
the natural frequency of bending vibration of the torsional support beam is still:
this embodiment requires that the natural frequency of the torsional vibration must be equal to the natural frequency of the bending vibration, i.e., ωTorsion bar＝ωBendTo obtain:
for the most commonly used silicon materials, the poisson ratio v is 0.22,
that is, the length L of the torsional support beam of the silicon material is the length L of the movable polar platex1.2 times of (1), i.e. L1.2Lx。
Example 3
Fig. 5 is a schematic structural diagram of a torsional micromechanical resonator with a circular structure of the movable plate 4. Fig. 5 (a) and (b) are a side view and a plan view, respectively. The movable polar plate 4 is round, the connecting points of the movable polar plate 4 and the two twisting supporting beams 5 are respectively positioned at the two ends of the diameter of the movable polar plate 4, the cross section of each twisting supporting beam 5 is square, the thickness of each twisting supporting beam 5 is equal to that of the movable polar plate 4, and the relationship between the length l of each twisting supporting beam 5 and the radius R of the movable polar plate is
v is the Poisson's ratio of the material.
How the length relationship is derived is explained in detail below.
Under the condition that other dimension directions, signs and the like are the same as those of the embodiment 1, as shown in fig. 5, the rectangular pole plate 4 which does twisting motion is of a circular structure, the twisting axis passes through the circle center, and the dimension of the two supporting beams is unchanged. At this time, the mass and the inertia of the movable plate 4 about the y-axis are m ═ ρ π R, respectively2h，
The natural frequency of the torsional vibration of the movable pole plate 4 is:
the natural frequencies of the bending vibration of the torsion support beam 5 are:
the natural frequency of the torsional vibration of the movable pole plate 4 of the present embodiment must be equal to the natural frequency of the bending vibration, ω, of the torsional support beam 5Torsion bar＝ωBendTherefore, the following steps are obtained:
for the most commonly used silicon materials, the poisson ratio v is 0.22,
at this time, the length l of the torsion support beam 5 must be 1.04 times the radius of the movable pole plate 4, that is: l is 1.04R.
Those of ordinary skill in the art will understand that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A torsional micromechanical resonator with torsional-bending coupling resonance comprises a substrate (1), a driving electrode (2) and a sensing electrode (3) which are arranged on the substrate (1), and a movable polar plate (4) which is arranged above the driving electrode (2) and the sensing electrode (3), wherein two ends of the movable polar plate (4) are respectively connected with one end of a torsional supporting beam (5), the other ends of the two torsional supporting beams (5) are respectively connected with a fixed support (6), the two fixed supports (6) are arranged on the substrate at intervals, the two torsional supporting beams (5) have the same structural size and are coincided along the axial line of the length direction, the torsional micromechanical resonator is characterized in that the movable polar plate (4) is rectangular or circular, the cross section of the torsional supporting beam (5) is square, and the torsional supporting beam (5) and the movable polar plate (4) are made of the same material, the natural frequency of the torsional vibration of the movable polar plate (4) is equal to the natural frequency of the bending vibration of the torsional support beam (5).
2. The torsional-bending coupled resonant micromechanical resonator according to claim 1, wherein the movable plate (4) is rectangular, the connection points of the movable plate (4) and the two torsional supporting beams (5) are respectively located at two ends of the central axis of the movable plate (4) along the width y direction, the axes of the two torsional supporting beams (5) along the length direction are coincident with the central axis of the movable plate (4) along the width y direction, the thickness of the torsional supporting beams (5) is equal to that of the movable plate (4), and the length L of the torsional supporting beams (5) is equal to the length L of the movable plate (4)xIn a relationship of
v is the Poisson's ratio of the material.
3. The torsional-bending coupled resonant micromechanical resonator according to claim 1, wherein the movable plate (4) is rectangular, the connection points of the movable plate (4) and the two torsional supporting beams (5) are respectively located at two ends of one side of the movable plate (4) along the width y direction, the axes of the two torsional supporting beams (5) along the length direction are overlapped with one side of the movable plate (4) along the width y direction, the thickness of the torsional supporting beams (5) is equal to that of the movable plate (4), and the length l of the torsional supporting beams (5) is equal to that of the movable plate (4)LxIn a relationship of
v is the Poisson's ratio of the material.
4. The torsional-torsional coupled resonant micromechanical resonator according to claim 1, characterized in that the movable plate (4) is circular, the connection points of the movable plate (4) and the two torsional supporting beams (5) are respectively located at two ends of the diameter of the movable plate (4), the thickness of the torsional supporting beams (5) is equal to the thickness of the movable plate (4), and the relationship between the length l of the torsional supporting beams (5) and the radius R of the movable plate is
v is the Poisson's ratio of the material.
5. Torsional-micromechanical resonator of the torsional-flexural coupled resonance according to claim 1, characterized in that the material of the torsional support beam (5) and the movable plate (4) is silicon.
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| CN202210249410.4A CN114598294A (en) | 2022-03-11 | 2022-03-11 | Torsional micromechanical resonator with torsional-bending coupling resonance |
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| CN202210249410.4A CN114598294A (en) | 2022-03-11 | 2022-03-11 | Torsional micromechanical resonator with torsional-bending coupling resonance |
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