WO2023065834A1 - 一种适用于mems模态局部化传感器的环状耦合系统 - Google Patents

一种适用于mems模态局部化传感器的环状耦合系统 Download PDF

Info

Publication number
WO2023065834A1
WO2023065834A1 PCT/CN2022/115835 CN2022115835W WO2023065834A1 WO 2023065834 A1 WO2023065834 A1 WO 2023065834A1 CN 2022115835 W CN2022115835 W CN 2022115835W WO 2023065834 A1 WO2023065834 A1 WO 2023065834A1
Authority
WO
WIPO (PCT)
Prior art keywords
coupling
ring
resonant
stiffness
coupling beam
Prior art date
Application number
PCT/CN2022/115835
Other languages
English (en)
French (fr)
Inventor
郝永存
祖陆晗
常洪龙
Original Assignee
西北工业大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 西北工业大学 filed Critical 西北工业大学
Priority to GBGB2402969.6A priority Critical patent/GB202402969D0/en
Publication of WO2023065834A1 publication Critical patent/WO2023065834A1/zh

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
    • G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
    • G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
    • G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
    • G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
    • G01P15/097—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values by vibratory elements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
    • G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
    • G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
    • G01P2015/0862—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values being provided with particular means being integrated into a MEMS accelerometer structure for providing particular additional functionalities to those of a spring mass system

Definitions

  • the invention relates to a ring coupling system suitable for MEMS mode localized sensors, belonging to the field of MEMS sensors.
  • MEMS Micro-Electro-Mechanical System
  • sensors generally refer to sensor systems whose internal structure is on the order of microns or even nanometers, including sensing, control and actuators.
  • MEMS sensors can be classified based on various physical quantities such as optics, electricity, heat, magnetism, acoustics, and mechanics.
  • the resonant sensor hereinafter referred to as resonator
  • the main structure of the traditional resonant sensor includes: resonant beam, sensitive structure, driving structure and detection structure.
  • the detection principle is: after the sensitive structure senses the change of the external physical quantity, it will generate an inertial force acting on the resonant beam, which will change the stiffness of the resonant beam, thereby changing the resonant frequency of the resonant beam.
  • the external physical information of the response can be measured by detecting the change of the resonant frequency.
  • the resonant sensor based on the mode localization phenomenon is a new type of resonant sensor, which is sensitive to the change of external parameters by detecting the amplitude ratio of two resonant beams in the resonant state.
  • the mode-localized sensor can improve the sensitivity by more than 2 orders of magnitude.
  • the design of the coupling structure is very important, and its coupling stiffness will directly affect the bandwidth and output sensitivity of the sensor's measurement signal.
  • the two resonant beams are coupled in series by means of electrostatic coupling or mechanical coupling.
  • Electrostatic coupling has the characteristic of adjustable coupling stiffness, but its structure itself is easily affected by the feedthrough capacitance, which makes the coupling stiffness drift.
  • mechanical coupling is usually used in the design.
  • the mechanical coupling stiffness mainly depends on the position and geometry of the coupling beams.
  • the coupling beams were all straight beams, that is, one or more homogeneous straight beams with equal cross-sections were used to connect several resonant beams along the normal direction of the resonant beams. The point is generally located near the anchor point where the resonant beam is fixed.
  • the coupling system mainly includes a ring coupling beam and two coupling stiffness adjusting electrodes.
  • the change range of the coupling stiffness of the annular coupling beam is smaller at the same lateral etching depth, and the annular coupling beam proposed by the present invention is adopted under the condition that the processing level remains unchanged.
  • the sensitivity of the coupling beam to processing errors can be reduced, and the stability and consistency of sensor performance can be further improved.
  • the two coupling stiffness adjustment electrodes arranged outside the ring-shaped coupling beam can realize the adjustment function of the mechanical coupling stiffness, which broadens the range of the mode localization sensor.
  • the purpose of the present invention is to provide a ring coupling system suitable for MEMS mode localized sensors, reduce the sensitivity of coupling beams to process errors, and realize the adjustment of mechanical coupling stiffness at the same time.
  • the present invention proposes a ring coupling system suitable for MEMS mode localized sensors, the main structure of which includes: ring coupling beam 203 and coupling stiffness adjustment electrodes 205 and 206 .
  • the ring-shaped coupling beam has a characteristic of central symmetry.
  • the specific structure of the ring-shaped coupling beam can be a circular ring, a square ring, a rectangular ring or any other closed structure that can be defined as a ring in engineering practice;
  • the ring width w of the ring-shaped coupling beam can be equal in width , can also be of unequal width, and the setting of its specific width should not affect the judgment of its "ring" feature, but in engineering practice, the ring width w of the ring coupling beam should satisfy: 500nm ⁇ w ⁇ 10*d, where d is the width of the resonant beams 201 and 202 ; so that they can meet the limitation of the processing technology and ensure a certain coupling effect.
  • the ring-shaped coupling beam 203 realizes mechanical coupling by connecting two resonant beams 201 and 202 .
  • the resonant beams 201 , 202 are fixedly connected via a central fixed anchor point 204 and distributed symmetrically about the center.
  • the central symmetrical point of the ring-shaped coupling beam 203 coincides with the central symmetrical point of the resonant beams 201 and 202, and directly intersects with the resonant beam 201 and the resonant beam 202 to form an integral structure; the resonant beam 201 and the fixed anchor
  • the intersecting points of the point 204 and the inner diameter of the annular coupling beam 203 are respectively defined as A0 and A1
  • the intersecting points of the resonant beam 202 and the fixed anchor point 204 and the inner diameter of the annular coupling beam 203 are respectively defined as B0 and B1.
  • the distance between the points A0 and A1 is defined as R1
  • the distance between the points B0 and B1 is defined as R2.
  • the coupling stiffness adjustment electrodes 205 , 206 together with the annular coupling beam 203 form coupling adjustment capacitors 207 , 208 .
  • an electrostatic force is generated to change the stress distribution in the annular coupling beam 203 , thereby realizing the adjustment of its coupling stiffness.
  • the effective plate length and capacitor spacing of the coupling adjustment capacitors 207, 208 are closely related to the width of the coupling beam 203, and the setting of specific parameters thereof should be based on a certain stiffness adjustment effect.
  • the potential difference between the coupling adjustment electrodes 205 and 206 and the annular coupling beam 203 generally does not exceed 150V.
  • the present invention adopts the ring-shaped coupling beam design. Compared with the traditional mechanical coupling beam, the sensitivity of the coupling beam to lateral etching can be greatly reduced, and the stability of the sensor can be further improved under the condition that the processing accuracy level remains unchanged.
  • the coupling stiffness adjustment electrode for the ring-shaped coupling beam is designed, and the potential difference between the ring-shaped coupling beam and the ring-shaped coupling beam is generated by adjusting the potential of the coupling stiffness adjustment electrode, thereby generating electrostatic force and changing the internal force of the ring-shaped coupling beam. Stress distribution to achieve adjustment of mechanical coupling stiffness.
  • Fig. 1 is a schematic diagram of a spring-mass model of a resonant system.
  • 101 is equivalent mass block 1
  • 102 is equivalent mass block 2
  • 103 is equivalent damping block 1
  • 104 is equivalent damping block 2
  • 105 is equivalent coupling beam
  • 106 is equivalent stiffness 1
  • 107 is equal 108 is the equivalent resonator 1
  • 109 is the equivalent resonator 2.
  • Fig. 2 is a schematic diagram of the coupling beam designed by the present invention.
  • 201 is the resonant beam of resonator 1
  • 202 is the resonant beam of resonator 2
  • 203 is the annular coupling beam
  • 204 is the central fixed anchor point
  • 205 is the lower side coupling stiffness adjustment electrode
  • 206 is the upper side coupling stiffness
  • the adjustment electrode, 207 is the coupling adjustment capacitance jointly formed by the lower coupling stiffness adjustment electrode 205 and the annular coupling beam 203
  • 208 is the coupling adjustment capacitance jointly formed by the upper coupling stiffness adjustment electrode 206 and the annular coupling beam 203 .
  • Fig. 3 (a) is the simulation result of the working mode when the annular coupling beam designed by the present invention is suitable for the mode localization sensor
  • Fig. 3 (b) is the straight beam coupling beam suitable for the mode localization sensor as a comparison The simulation results of the working mode.
  • Fig. 4 (a) is the ring-shaped coupling beam designed by the present invention when the coupling stiffness adjustment voltage is not applied, the simulation results of the first two order working modes of the sensor, and Fig. 4 (b) is the ring-shaped coupling beam designed by the present invention Simulation results for the first two orders of operation of the sensor when the coupling stiffness adjustment voltage is applied.
  • Fig. 5 is a simulation result of the relationship between the voltage value and the frequency difference of the first two working modes of the sensor when the coupling stiffness adjustment voltage is applied to the annular coupling beam designed by the present invention.
  • Fig. 6 is a specific embodiment of the annular coupling beam designed by the present invention on the MEMS mode localized accelerometer.
  • 201 is the resonant beam of resonator 1
  • 202 is the resonant beam of resonator 2
  • 203 is the annular coupling beam
  • 204 is the central fixed anchor point
  • 205 is the lower side coupling stiffness adjustment electrode
  • 206 is the upper side coupling stiffness Adjusting electrodes
  • 601 is quality block 1
  • 602 is mass block 2
  • 603 is resonance stiffness adjustment electrode 1 of resonance beam 1
  • 604 is resonance stiffness adjustment electrode 2 of resonance beam 1
  • 605 is resonance stiffness adjustment electrode 3 of resonance beam 1
  • 606 is the resonance stiffness adjustment electrode 4 of the resonance beam 1
  • 607 is the resonance stiffness adjustment electrode 1 of the resonance beam 2
  • 608 is the resonance stiffness adjustment electrode 2 of the resonance beam
  • 609 is the resonance stiffness adjustment electrode 3 of the resonance beam 2
  • 610 Resonant stiffness adjustment electrode 4 of resonant beam 2
  • 611 is differential detection electrode 1 of resonant beam 1
  • 612 is differential detection electrode
  • Fig. 7 is a schematic diagram of a part of the specific and feasible structure of the annular coupling beam designed in the present invention.
  • the ring-shaped coupling beam includes but not limited to several ring-shaped coupling structures shown in the figure.
  • Fig. 1 is a schematic diagram of a simplified spring-mass model of a resonant system.
  • the resonant system consists of an equivalent resonator 1 108, an equivalent resonator 2 109, an equivalent coupling beam and fixed anchor points.
  • Fig. 1 is a schematic diagram of a simplified spring-mass model of a resonant system.
  • the resonant system consists of an equivalent resonator 1 108, an equivalent resonator 2 109, an equivalent coupling beam and fixed anchor points.
  • the spring model is used as the stiffness model 105 of the mechanical coupling beam, which represents the stiffness k c of the equivalent coupling beam, and its mass is negligible; the spring model is used as the stiffness model 106 of resonator 1 and the stiffness model of resonator 2 107 respectively represent the stiffnesses k 1 and k 2 of the equivalent resonator 1 108 and the equivalent resonator 2 109; the mass blocks 101 and 102 are used to equivalently represent the equivalent resonator 1 108 and the equivalent resonator 2 109 respectively Masses m 1 and m 2 .
  • the two-degree-of-freedom resonant system has two vibration modes, the same-direction motion is the same-direction mode, and the reverse motion is the reverse mode.
  • x 1 and x 2 represent the displacements of the equivalent model 108 of resonator 1 and the equivalent model 109 of resonator 2, respectively
  • u 1 and u 2 represent the amplitude ratios of the co-directional mode and the reverse mode, respectively.
  • the vibration equation of the coupled system is obtained according to Newton's second law:
  • the two natural frequencies of the two-degree-of-freedom mode localized sensor can be obtained by solving the above equation. Assuming that the structural parameters of the two resonators under the initial conditions are exactly the same, the two resonant frequencies of the resonator can be obtained as:
  • Fig. 2 is a schematic diagram of the coupling beam designed by the present invention.
  • 201 is the resonant beam of resonator 1
  • 202 is the resonant beam of resonator 2
  • 203 is the annular coupling beam
  • 204 is the central fixed anchor point
  • 205 is the lower side coupling stiffness adjustment electrode
  • 206 is the upper side coupling stiffness
  • the adjustment electrode, 207 is the coupling adjustment capacitance jointly formed by the lower coupling stiffness adjustment electrode 205 and the annular coupling beam 203
  • 208 is the coupling adjustment capacitance jointly formed by the upper coupling stiffness adjustment electrode 206 and the annular coupling beam 203 .
  • ⁇ is the frequency difference between the first two working modes of the resonator. Because It hardly changes with the change of the coupling stiffness, so it can be considered that the coupling stiffness is positively correlated with the frequency difference of the working mode, and the variation of the coupling stiffness can be characterized by the frequency difference of the working mode. According to the article A High Resolution Differential Mode-Localized MEMS Accelerometer published in JMEMS by A Seshia et al. of Cambridge University in 2019, the operating bandwidth of the mode localized sensor is positively correlated with the frequency difference of the operating mode, that is, the coupling stiffness will affect the sensor Measured bandwidth level.
  • the etching gas under the action of a high-frequency electric field generates molecular radicals (including atoms, molecules or atomic groups, etc.) through glow discharge, and performs ion bombardment and chemical The reaction generates volatile gases, and finally a micromechanical structure is obtained.
  • the alternation of etching and passivation will produce a groove with a depth of 50-500nm and a width of 1 ⁇ m on the side wall of the silicon structure. Under the influence of this effect, the width of the coupling beam is reduced, and the coupling stiffness is reduced, so that the mode is locally
  • the design parameters of the chemical sensor deviate from the expected level.
  • the ring-shaped coupling beam proposed by the present invention can replace the original straight beam coupling beam, and reduce the influence caused by the reduction of coupling stiffness caused by lateral etching.
  • Fig. 3 (a) shows the simulation mode shape of the working mode when the annular coupling beam designed by the present invention is suitable for the mode localized sensor
  • Fig. 3 (b) shows that the straight beam coupling beam as a comparison is suitable for the mode Operating modal simulation shapes when the sensor is localized.
  • the frequency differences of the first two working modes of the resonator are exactly the same.
  • the frequency difference variation of the mechanical coupling beam after the process error is generated by lateral etching during the process of the modal localization sensor is simulated, and the table is as follows:
  • the coupling stiffness is the core index of structural design, which directly affects the sensitivity, bandwidth and other performance of the sensor.
  • the mechanically coupled beam has the advantages of simple design and stable coupling stiffness, but its coupling stiffness often depends on its structural design, and it is difficult to achieve flexible stiffness adjustment.
  • the ring-shaped coupling beam and the coupling stiffness adjustment electrode proposed by the present invention combine the characteristics of mechanical coupling and electrostatic coupling to realize the flexible adjustment of the mechanical coupling stiffness.
  • the coupling stiffness can be characterized by the frequency difference of the first two operating modes of the modal localized sensor.
  • Figure 4(a) shows that the resonant frequencies of the first two operating modes of the modal localized sensor are : 35830Hz, 35841Hz, the frequency difference is 11Hz.
  • Figure 4(b) shows that after applying the same structure as in Figure 4(a) and applying the coupling stiffness adjustment voltage, the resonant frequencies of the first two working modes become: 36508Hz and 36624Hz, and the frequency difference increases to 116Hz.
  • Figure 5 shows the relationship between the applied coupling stiffness adjustment voltage and the frequency difference of the first two working modes of the sensor.
  • the ring-shaped coupling beam designed by the invention can effectively adjust the coupling stiffness of the mode localized sensor, thereby widening its use range.
  • the embodiment shown in FIG. 6 provides a two-degree-of-freedom MEMS mode-localized acceleration sensor structure using a ring-shaped coupling beam.
  • the ring-shaped coupling beam 203 realizes mechanical coupling by connecting two groups of completely identical resonant beams 201 and 202 that are centrally symmetrical. Mass blocks 601 and 602 sensitive to external acceleration are connected to the outer sides of the two resonant beams.
  • the first resonant beam 201 and the second resonant beam 202 are supported by a central fixed anchor point 204; the central symmetric point of the annular coupling beam 203 coincides with the centrally symmetric central symmetric point of the first resonant beam 201 and the second resonant beam 202.
  • the mass blocks 601 and 602 generate axial stress on the first resonant beam 201 and the second resonant beam 202 under the action of acceleration, thereby changing the resonant state of the resonator.
  • Resonance stiffness adjustment electrodes 603, 604 are arranged on the upper side of the first resonant beam 201, and resonance stiffness adjustment electrodes 605, 606 are arranged on the lower side; resonance stiffness adjustment electrodes 607, 608 are arranged on the upper side of the second resonant beam 202, Resonance stiffness adjustment electrodes 609, 610 are provided on the lower side.
  • the resonance stiffness adjusting electrode is used to adjust the initial working point of the mode localized sensor, so as to prevent it from working in a working region with poor nonlinearity.
  • Coupling stiffness adjustment electrodes 205, 206 are arranged on the outer side of the ring-shaped coupling beam. By changing the voltage of the coupling stiffness adjustment electrodes 205, 206, an electrostatic force is generated to act on the ring-shaped coupling beam 203, thereby changing its coupling stiffness.
  • the mass blocks 601, 602 When external disturbances are input, the mass blocks 601, 602 generate axial disturbances to the resonant beams 201, 202.
  • the stiffness change of resonant beam 1 201 is ⁇ k1
  • the stiffness change of resonant beam 2 202 is ⁇ k2.
  • the detection signals of the two resonant beams are respectively differentiated, and the vibration amplitude information of the two resonant beams can be obtained through circuit processing, and the final output amplitude ratio signal can be obtained by inputting the two amplitude signals into the divider.
  • This differential detection method can not only eliminate the interference of the feedthrough capacitor signal, make the detection of amplitude and frequency more accurate, but also double the output signal strength, thereby greatly improving the signal-to-noise ratio of the sensor output signal.
  • the vibration amplitude of resonant beam 1 201 is equal to the vibration amplitude of resonant beam 2 202, and the amplitude ratio output is 1; after being disturbed, due to the phenomenon of mode localization, the amplitude of resonant beam The ratio output changes greatly, so as to realize the detection of acceleration.
  • the ring-shaped coupling beam proposed by the present invention is not only suitable for two-degree-of-freedom mode localization sensors, but also three-degree-of-freedom, four-degree-of-freedom or more Mode localized sensors with high degrees of freedom all fall within the protection scope of the claims of the present invention.
  • ring should be understood in a broad sense, for example, it can be a ring, a square ring, a rectangular ring or any other ring in engineering practice. It can be defined as a ring-shaped closed structure; the ring width w of the ring-shaped coupling beam can be equal or unequal, and the setting of its specific width should not affect the judgment of its "ring” feature . Those of ordinary skill in the art can understand the specific meanings of the above terms in the present invention in specific situations.
  • the ring coupling structure includes but not limited to several ring coupling structures shown in FIG. 7 .

Abstract

一种适用于MEMS模态局部化传感器的环状耦合系统，主要结构包括：环状耦合梁（203），耦合刚度调节电极（205、206）。环状耦合梁（203）是圆环、正方环、矩环或者其他封闭结构；环状耦合梁（203）通过连接两个谐振梁（201、202）实现机械耦合。相较于传统的机械耦合梁，本环状耦合系统可以使耦合梁对侧向刻蚀的敏感程度大幅度降低，在加工精度水平不变的情况下可以进一步提高传感器的稳定性和一致性；同时设计了针对环状耦合梁（203）的耦合刚度调节电极（205、206），通过调节耦合刚度调节电极（205、206）的电势产生与环状耦合梁（203）的电势差，从而产生静电力，改变环状耦合梁（203）内部的应力分布，以实现机械耦合刚度的调节。

Description

一种适用于MEMS模态局部化传感器的环状耦合系统 技术领域
本发明涉及一种适用于MEMS模态局部化传感器的环状耦合系统，属于MEMS传感器领域。
背景技术
MEMS(Micro-Electro-Mechanical System)传感器一般指内部结构在微米甚至纳米量级，包含感应、控制和执行元件的传感器系统。按照敏感机理的不同，MEMS传感器可基于光学、电学、热学、磁学、声学、力学等各种物理量进行种类划分。其中基于检测物体振动状态变化的谐振式传感器(下文或称谐振器)因为具有相对较高的灵敏度、数字输出、大动态范围和高抗干扰能力等特点，已成为MEMS传感器的重要发展趋势之一。传统谐振式传感器的主要结构包括：谐振梁、敏感结构、驱动结构和检测结构。其检测原理为：敏感结构在感应到外界物理量的变化后，产生作用在谐振梁上的惯性力，使谐振梁刚度发生变化，从而改变谐振梁的谐振频率。通过检测谐振频率变化即可测得响应的外界物理信息。
基于模态局部化现象的谐振式传感器是一种新型谐振式传感器，其通过检测两个谐振梁谐振状态下的幅值比来敏感外界参数变化。与传统的谐振式传感器相比，模态局部化传感器可以将灵敏度提高2个数量级以上。在模态局部化传感器中，耦合结构的设计非常重要，其耦合的刚度会直接影响传感器测量信号的带宽和输出灵敏度。在耦合结构的作用下，两个谐振梁以静电耦合或机械耦合的方式串联耦合。静电耦合具有耦合刚度可调节的特点，但其结构本身易受到馈通电容的影响，从而使耦合刚度产生漂移。为了提高耦合刚度的稳定性，在设计中通常采用机械耦合的方式。机械耦合刚度主要取决于耦合梁的位置和几何特性。在以往的模态局部化传感器设计中，耦合梁均为直梁，即使用一根或多根均质等截面直型梁沿谐振梁的法向连接若干个谐振梁， 其与谐振梁的连接点一般位于谐振梁固接处靠近锚点的位置。在各项异性刻蚀加工工艺中，所述耦合梁的侧壁会不可避免地产生50～500nm的侧向刻蚀，从而使耦合梁的宽度变窄，耦合刚度减小，进而导致传感器的设计指标偏离预期水平。同时，采用直梁耦合的模态局部化传感器不易实现耦合刚度调节。为了降低上述工艺加工误差造成的影响，同时实现机械耦合刚度的调节，本发明提出了一种新型的环状耦合系统。所述耦合系统主要包括一种环状耦合梁和两个耦合刚度调节电极。与直梁耦合梁相比，所述环状耦合梁在同样的侧向刻蚀深度下耦合刚度的变化幅度更小，在工艺加工水平不变的情况下，采用本发明提出的环状耦合梁可以降低耦合梁对加工误差的敏感程度，进一步提升传感器性能的稳定性和一致性。同时，在环状耦合梁外侧布置的两个耦合刚度调节电极可以实现机械耦合刚度的调节功能，拓宽了模态局部化传感器的量程。
发明内容
本发明的目的是：提供一种适用于MEMS模态局部化传感器的环状耦合系统，降低耦合梁对工艺加工误差的敏感程度，同时实现机械耦合刚度的调节。为了实现上述发明目的，本发明提出了一种适用于MEMS模态局部化传感器的环状耦合系统，其主要结构包括：环状耦合梁203，耦合刚度调节电极205、206。
所述环状耦合梁具有中心对称的特性。所述环状耦合梁的具体结构可以是圆环、正方环、矩环或者其他任意在工程实践中可以被定义为环状的封闭结构；所述环状耦合梁的环宽w可以为等宽，也可以为不等宽，其具体宽度的设定不应影响对其“环状”特征的判定，但在工程实践中，所述环状耦合梁的环宽w应满足：500nm<w<10*d，其中d为谐振梁201、202的宽度；使得其同时满足加工工艺的限制并保证一定的耦合效果。
所述环状耦合梁203通过连接两个谐振梁201、202实现机械耦合。在一般的模态局部化传感器设计中，谐振梁201、202经由中央固定锚点204固定连接并呈中心对称分布。所述环状耦合梁203的中心对称点与谐振梁201、202呈中心对称分布的中心对称点重 合，并与谐振梁201、谐振梁202直接相交为一整体结构；将谐振梁201与固定锚点204、环状耦合梁203内径的相交点分别定义为A0，A1，将谐振梁202与固定锚点204、环状耦合梁203内径的相交点分别定义为B0，B1。将所述点A0，A1之间的距离定义为R1，将所述点B0，B1之间的距离定义为R2。所述距离R1、R2应满足关系R1＝R2<10*d，以满足一定的耦合效果。
所述耦合刚度调节电极205、206与环状耦合梁203共同构成耦合调节电容207、208。通过改变耦合刚度调节电极205、206的电势形成与环状耦合梁203的电势差，从而产生静电力改变环状耦合梁203内的应力分布，从而实现其耦合刚度的调节。所述耦合调节电容207、208的有效极板长度和电容间距与耦合梁203的宽度密切相关，其具体参数的设定应以产生一定的刚度调节效果为标准。在具体的工程实践中，耦合调节电极205、206与环状耦合梁203之间的电势差一般不超过150V。
本发明的有益效果是：
本发明采用了环状耦合梁设计，相较于传统的机械耦合梁，可以使耦合梁对侧向刻蚀的敏感程度大幅度降低，在加工精度水平不变的情况下可以进一步提高传感器的稳定性和一致性；同时设计了针对所述环状耦合梁的耦合刚度调节电极，通过调节耦合刚度调节电极的电势产生与环状耦合梁的电势差，从而产生静电力，改变环状耦合梁内部的应力分布，以实现机械耦合刚度的调节。
附图说明
图1是谐振系统弹簧-质量块模型示意图。
图中，101为等效质量块一，102为等效质量块二，103为等效阻尼一，104为等效阻尼二，105为等效耦合梁，106为等效刚度一，107为等效刚度二，108为等效谐振器一，109为等效谐振器二。
图2是本发明所设计的耦合梁的示意图。
图中，201为谐振器一的谐振梁，202为谐振器二的谐振梁，203为环状耦合梁，204为中央固定锚点，205为下侧耦合刚度调节电极，206为上侧耦合刚度调节电极，207为下侧耦合刚度调节电极205与环状耦合梁203共同构成的耦合调节电容，208为上侧耦合刚度调节电极206与环状耦合梁203共同构成的耦合调节电容。
图3(a)是本发明所设计的环状耦合梁适用于模态局部化传感器时的工作模态仿真结果，图3(b)是作为对比的直梁耦合梁适用于模态局部化传感器时的工作模态仿真结果。
图4(a)是本发明所设计的环状耦合梁在不施加耦合刚度调节电压时，传感器的前两阶工作模态仿真结果，图4(b)是本发明所设计的环状耦合梁在施加耦合刚度调节电压时，传感器的前两阶工作仿真结果。
图5是本发明所设计的环状耦合梁在施加耦合刚度调节电压时，电压值与传感器前两阶工作模态频差关系的仿真结果。
图6是本发明所设计的环状耦合梁在MEMS模态局部化加速度计上的具体实施例。
图中，201为谐振器一的谐振梁，202为谐振器二的谐振梁，203为环状耦合梁，204为中央固定锚点，205为下侧耦合刚度调节电极，206为上侧耦合刚度调节电极，601为质量块一，602为质量块二，603为谐振梁一的谐振刚度调节电极一，604为谐振梁一的谐振刚度调节电极二，605为谐振梁一的谐振刚度调节电极三，606为谐振梁一的谐振刚度调节电极四，607为谐振梁二的谐振刚度调节电极一，608为谐振梁二的谐振刚度调节电极二，609为谐振梁二的谐振刚度调节电极三，610为谐振梁二的谐振刚度调节电极四，611为谐振梁一的差分检测电极一，612为谐振梁一的差分检测电极二，613为谐振梁二的差分检测电极一，614为谐振梁二的差分检测电极二，615为谐振梁一的驱动电极、616为谐振梁二的驱动电极。
图7是本发明所设计的环状耦合梁的部分具体可行结构示意图。所述环状耦合梁包 括但不限于图中所示的几种环状耦合结构。
具体实施方式
在详细介绍本发明之前，先介绍本发明涉及的模态局部化原理，和将该原理应用于MEMS传感器的理论基础。图1为谐振系统简化弹簧-质量模型示意图，该谐振系统由等效谐振器一108、等效谐振器二109、等效耦合梁及固定锚点组成。在图1中，用弹簧模型作为机械耦合梁的刚度模型105，表示等效耦合梁的刚度k c，其质量忽略不计；用弹簧模型作为谐振器一的刚度模型106、谐振器二的刚度模型107，分别表示等效谐振器一108、等效谐振器二109的刚度k 1和k 2；用质量块101、102来分别等效表示等效谐振器一108、等效谐振器二109的质量m 1和m 2。该双自由度谐振系统具有两个振动模态，同向运动为同向模态，反向运动为反向模态。下文中x 1和x 2分别表示谐振器一的等效模型108和谐振器二的等效模型109的位移，u 1和u 2分别表示同向模态和反向模态的振幅比。根据牛顿第二定律得到该耦合系统的振动方程：
Figure PCTCN2022115835-appb-000001
该式具有一个特解为：
Figure PCTCN2022115835-appb-000002
将其代入得到关于振幅的线性方程组：
Figure PCTCN2022115835-appb-000003
对于N自由度的耦合系统，应该具有N个振动模态，N个谐振频率。解上述方程可以得到二自由度模态局部化传感器的两个自然频率，假设初始条件下的两个谐振器的结构参数完全相同，则可以得到谐振器的两个谐振频率为：
Figure PCTCN2022115835-appb-000004
Figure PCTCN2022115835-appb-000005
此时谐振器的输出振幅比为：
Figure PCTCN2022115835-appb-000006
Figure PCTCN2022115835-appb-000007
图2是本发明所设计的耦合梁的示意图。图中，201为谐振器一的谐振梁，202为谐振器二的谐振梁，203为环状耦合梁，204为中央固定锚点，205为下侧耦合刚度调节电极，206为上侧耦合刚度调节电极，207为下侧耦合刚度调节电极205与环状耦合梁203共同构成的耦合调节电容，208为上侧耦合刚度调节电极206与环状耦合梁203共同构成的耦合调节电容。通过调节耦合刚度调节电极205、206的电势，产生其与环状耦合梁203间的电势差，从而产生静电力改变环状耦合梁的内部应力分布，从而改变其耦合刚度。
在模态局部化传感器的设计中，耦合梁的设计至关重要。由公式(4)、(5)可知，耦合梁的耦合刚度可以通过谐振器的前两阶谐振频率来表示：
Figure PCTCN2022115835-appb-000008
其中Δω为谐振器前两阶工作模态的频差。由于
Figure PCTCN2022115835-appb-000009
几乎不随耦合刚度的变化而改变，故可以认为耦合刚度与工作模态频差呈正相关的关系，耦合刚度的变化量可以使用工作模态频差来表征。根据剑桥大学A Seshia等人2019年发表在JMEMS的文章A High Resolution Differential Mode-Localized MEMS Accelerometer，模态局部化传感器的工作带宽与工作模态的频差呈正相关，即耦合刚度的大小会影响传感器测量的带宽水平。
在传感器的各向异性刻蚀工艺中，处于高频电场作用下的刻蚀气体通过辉光放电 产生分子游离基(包括原子、分子或原子团等)，并对被刻蚀材料进行离子轰击和化学反应生成挥发性气体，最终获得微机械结构。刻蚀和钝化的交替进行会在硅结构的侧壁产生深50～500nm，宽1μm的凹槽，在该效应的影响下，耦合梁的宽度减小，耦合刚度降低，从而使模态局部化传感器的设计参数偏离预期水平。
针对上述问题，本发明提出了的环状耦合梁可以替代原有的直梁耦合梁，降低侧向刻蚀导致的耦合刚度减小所造成的影响。图3(a)示出本发明所设计的环状耦合梁适用于模态局部化传感器时的工作模态仿真振型，图3(b)示出作为对比的直梁耦合梁适用于模态局部化传感器时的工作模态仿真振型。在谐振器前两阶工作模态频差完全相同的情况下。通过有限元仿真模拟模态局部化传感器在工艺加工过程中，机械耦合梁受到侧向刻蚀产生工艺误差后的频差变化量，得到表格如下：
表1环状耦合梁与直梁耦合梁对侧向刻蚀敏感程度的对比
Figure PCTCN2022115835-appb-000010
表1中基于有限元仿真计算的对比结果表明，相较于采用直梁耦合梁的模态局部化传感器，本发明提出的采用环状耦合梁的模态局部化传感器在相同的侧向刻蚀水平下，频差变化的误差量更小，根据公式(8)可知其耦合刚度的变化误差量更小，故采用 环状耦合梁可以减弱工艺加工时侧向刻蚀对模态局部化传感器设计的不利影响。
在模态局部化传感器中，耦合刚度作为结构设计的核心指标，直接影响了传感器的灵敏度、带宽等性能。相较于静电耦合梁，机械耦合梁具有设计简单、耦合刚度稳定的优点，但其耦合刚度往往取决于其结构设计，不易实现灵活的刚度调节。为了实现机械耦合刚度的调节，提升传感器的适用性，本发明提出的环状耦合梁及耦合刚度调节电极结合了机械耦合和静电耦合的特性，实现了机械耦合刚度的灵活调节。所述耦合刚度可以用模态局部化传感器前两阶工作模态的频差来表征，图4(a)示出在特定结构设计下模态局部化传感器的前两阶工作模态谐振频率为：35830Hz、35841Hz，频差为11Hz。图4(b)示出在与图4(a)所用相同结构并施加耦合刚度调节电压后，前两阶工作模态谐振频率变为为：36508Hz、36624Hz，频差增加到116Hz。图5示出了所施加的耦合刚度调节电压与传感器前两阶工作模态频差的关系。采用本发明设计的环状耦合梁可以有效地调节模态局部化传感器的耦合刚度，从而拓宽其使用量程。
图6示出的实施例提供一个使用了环状耦合梁的二自由度MEMS模态局部化加速度传感器结构。环状耦合梁203通过连接呈中心对称的两组完全相同的谐振梁201、202实现机械耦合。两个谐振梁外侧连接敏感外界加速度的质量块601、602。谐振梁一201与谐振梁二202通过中心固定锚点204支撑；所述环状耦合梁203的中心对称点与谐振梁一201和谐振梁二202的呈中心对称的中心对称点重合。所述质量块601、602在加速度的作用下对谐振梁一201和谐振梁二202产生轴向应力，从而改变谐振器的谐振状态。所述谐振梁一201的上侧设置有谐振刚度调节电极603、604，下侧设置有谐振刚度调节电极605、606；所述谐振梁二202的上侧设置有谐振刚度调节电极607、608，下侧设置有谐振刚度调节电极609、610。所述谐振刚度调节电极用于调整模态局部化传感器的初始工作点，从而避免其工作在非线性度较差的工作区域中。所述环状耦合梁的外侧设置有耦合刚度调节电极205、206，通过改变耦合刚度调节电极 205、206的电压产生静电力作用于环状耦合梁203上，从而改变其耦合刚度。
当有外界扰动输入时，质量块601、602产生对谐振梁201、202的轴向扰动。使得谐振梁一201的刚度变化为Δk1，而谐振梁二202的刚度变化为-Δk2。由于谐振梁一201和谐振梁二202的结构完全相同，根据胡克定律，Δk1＝Δk2＝Δk，两个谐振梁的刚度差为2Δk，则两个原本完全对称的谐振梁出现了等效刚度不匹配，诱发了模态局部化效应，从而获得更高信噪比的信号，并经由差分检测电极611、612、613、614进行差分检测。将两个谐振梁的检测信号分别进行差分，经过电路处理即可得到两个谐振梁的振动幅值信息，将两路幅值信号输入除法器即可得到最终输出的幅值比信号。这种差分检测的方式，不仅可以消去馈通电容信号干扰，使振幅和频率的检测更加准确，还可以使输出信号强度增大一倍，从而大幅提升传感器输出信号的信噪比。在初始状态下，谐振梁一201的振动幅值与谐振梁二202的振动幅值相等，幅值比输出为1；在受到扰动后，由于模态局部化现象的产生，谐振梁的幅值比输出大幅度改变，从而实现加速度的检测。
通过改变耦合刚度调节电极205、206的电压产生其与环状耦合梁203间的电势差，从而产生静电力，改变环状耦合梁203内的应力分布，进而改变其耦合的刚度。
所述实施例的具体设计参数如下表：
表2所述使用环状耦合系统的模态局部化传感器实施例设计参数
Figure PCTCN2022115835-appb-000011
Figure PCTCN2022115835-appb-000012
在本发明的描述中，需要说明的是，本发明所提出的环状耦合梁不仅适用于二自由度模态局部化传感器，在本发明的基础上设计的三自由度、四自由度或更高自由度的模态局部化传感器均落入本发明权利要求书的保护范围之内。
在本发明的描述中，需要说明的是，除非另有明确的规定和限定，术语“环状”应作广义理解，例如，可以是圆环、正方环、矩环或者其他任意在工程实践中可以被定义为环状的封闭结构；所述环状耦合梁的环宽w可以为等宽，也可以为不等宽，其具体宽度的设定不应影响对其“环状”特征的判定。对于本领域的普通技术人员而言，可以在具体情况理解上述术语在本发明中的具体含义。所述环状耦合结构包括但不限于图7示出的若干种环状耦合结构。
以上内容仅为说明本发明的技术思想，不能以此限定本发明的保护范围，凡是按照本发明提出的技术思想，在技术方案基础上所做的任何改动，均落入本发明权利要求书的保护范围之内。

Claims (3)

  1. 一种适用于MEMS模态局部化传感器的环状耦合系统，其特征在于，主要包括：环状耦合梁203，耦合刚度调节电极205、206；
    所述环状耦合梁具有中心对称的特性；所述环状耦合梁203通过连接两个谐振梁201、202实现机械耦合；谐振梁201、202经由中央固定锚点204固定连接并呈中心对称分布；所述环状耦合梁203的中心对称点与谐振梁201、202呈中心对称分布的中心对称点重合，并与谐振梁201、谐振梁202直接相交为一整体结构；将谐振梁201与固定锚点204、环状耦合梁203内径的相交点分别定义为A0，A1，将谐振梁202与固定锚点204、环状耦合梁203内径的相交点分别定义为B0，B1；将所述点A0，A1之间的距离定义为R1，将所述点B0，B1之间的距离定义为R2；所述距离R1、R2应满足关系R1＝R2<10*d。
    所述耦合刚度调节电极205、206与环状耦合梁203共同构成耦合调节电容207、208；通过改变耦合刚度调节电极205、206的电势形成与环状耦合梁203的电势差，从而产生静电力改变环状耦合梁203内的应力分布，从而实现其耦合刚度的调节。
  2. 一种如权利要求1所述的适用于MEMS模态局部化传感器的环状耦合系统，其特征在于，所述环状耦合梁203的具体结构是圆环、正方环、矩环或者其他环状封闭结构；所述环状耦合梁的环宽w可以为等宽，也可以为不等宽，其具体宽度的设定不应影响对其“环状”特征的判定，但在工程实践中，所述环状耦合梁的环宽w应满足：500nm<w<10*d，其中d为谐振梁201、202的宽度；使得其同时满足加工工艺的限制并保证一定的耦合效果。
  3. 一种如权利要求1所述的适用于MEMS模态局部化传感器的环状耦合系统，其特征在于，所述耦合调节电极205、206与环状耦合梁203之间的电势差不超过150V。
PCT/CN2022/115835 2021-06-21 2022-08-30 一种适用于mems模态局部化传感器的环状耦合系统 WO2023065834A1 (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
GBGB2402969.6A GB202402969D0 (en) 2021-06-21 2022-08-30 Annular coupling system suitable for mems modal localization sensor

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
CN202110686469 2021-06-21
CN202111236440.3 2021-10-23
CN202111236440.3A CN114217093B (zh) 2021-06-21 2021-10-23 一种适用于mems模态局部化传感器的环状耦合系统

Publications (1)

Publication Number Publication Date
WO2023065834A1 true WO2023065834A1 (zh) 2023-04-27

Family

ID=80696075

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2022/115835 WO2023065834A1 (zh) 2021-06-21 2022-08-30 一种适用于mems模态局部化传感器的环状耦合系统

Country Status (3)

Country Link
CN (1) CN114217093B (zh)
GB (1) GB202402969D0 (zh)
WO (1) WO2023065834A1 (zh)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114217093B (zh) * 2021-06-21 2024-04-26 西北工业大学 一种适用于mems模态局部化传感器的环状耦合系统

Citations (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20040207492A1 (en) * 2002-12-17 2004-10-21 Nguyen Clark T.-C. Micromechanical resonator device and method of making a micromechanical device
JP2008259100A (ja) * 2007-04-09 2008-10-23 Sanyo Electric Co Ltd マイクロメカニカル共振器
US20110063052A1 (en) * 2008-05-19 2011-03-17 Nxp B.V. mems resonator
US7990232B1 (en) * 2007-06-06 2011-08-02 Rf Micro Devices, Inc. Anchor/support design for MEMS resonators
CN103697875A (zh) * 2013-12-13 2014-04-02 上海交通大学 管脚式压电固体波动模态匹配陀螺
US20160118955A1 (en) * 2014-10-22 2016-04-28 Micrel, Inc. Multiple coil spring mems resonator
WO2016206152A1 (zh) * 2015-06-26 2016-12-29 清华大学 一种单锚定点四质量块mems谐振式陀螺仪
CN106289214A (zh) * 2016-10-21 2017-01-04 中北大学 一种抗高冲击s形弹性梁mems环形振动陀螺谐振子结构
CN106643685A (zh) * 2016-11-07 2017-05-10 中北大学 一种全新的u形折叠梁硅微环形振动陀螺
CN107425276A (zh) * 2017-07-21 2017-12-01 西安交通大学 一种具有滤波特性的圆极化缝隙天线
CN109110724A (zh) * 2018-09-30 2019-01-01 南京理工大学 一种应用于mems力敏感器件的二级应力隔离结构
CN209024198U (zh) * 2018-09-30 2019-06-25 南京理工大学 一种应用于mems力敏感器件的二级应力隔离结构
US20200412325A1 (en) * 2019-06-27 2020-12-31 Aac Acoustic Technologies (Shenzhen) Co., Ltd. Differential resonator and mems sensor
CN112953433A (zh) * 2021-04-21 2021-06-11 中国科学院半导体研究所 一种多梁耦合的微机电谐振器
CN114217093A (zh) * 2021-06-21 2022-03-22 西北工业大学 一种适用于mems模态局部化传感器的环状耦合系统

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106629571B (zh) * 2016-09-20 2019-04-09 西北工业大学 一种基于模态局部化效应的弱耦合mems谐振式加速度计
CN107643423B (zh) * 2017-10-26 2020-05-12 西北工业大学 一种基于模态局部化效应的三自由度弱耦合谐振式加速度计
CN111192812B (zh) * 2020-01-07 2022-11-25 北京北方华创微电子装备有限公司 电感耦合装置和半导体处理设备

Patent Citations (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20040207492A1 (en) * 2002-12-17 2004-10-21 Nguyen Clark T.-C. Micromechanical resonator device and method of making a micromechanical device
JP2008259100A (ja) * 2007-04-09 2008-10-23 Sanyo Electric Co Ltd マイクロメカニカル共振器
US7990232B1 (en) * 2007-06-06 2011-08-02 Rf Micro Devices, Inc. Anchor/support design for MEMS resonators
US20110063052A1 (en) * 2008-05-19 2011-03-17 Nxp B.V. mems resonator
CN103697875A (zh) * 2013-12-13 2014-04-02 上海交通大学 管脚式压电固体波动模态匹配陀螺
US20160118955A1 (en) * 2014-10-22 2016-04-28 Micrel, Inc. Multiple coil spring mems resonator
WO2016206152A1 (zh) * 2015-06-26 2016-12-29 清华大学 一种单锚定点四质量块mems谐振式陀螺仪
CN106289214A (zh) * 2016-10-21 2017-01-04 中北大学 一种抗高冲击s形弹性梁mems环形振动陀螺谐振子结构
CN106643685A (zh) * 2016-11-07 2017-05-10 中北大学 一种全新的u形折叠梁硅微环形振动陀螺
CN107425276A (zh) * 2017-07-21 2017-12-01 西安交通大学 一种具有滤波特性的圆极化缝隙天线
CN109110724A (zh) * 2018-09-30 2019-01-01 南京理工大学 一种应用于mems力敏感器件的二级应力隔离结构
CN209024198U (zh) * 2018-09-30 2019-06-25 南京理工大学 一种应用于mems力敏感器件的二级应力隔离结构
US20200412325A1 (en) * 2019-06-27 2020-12-31 Aac Acoustic Technologies (Shenzhen) Co., Ltd. Differential resonator and mems sensor
CN112953433A (zh) * 2021-04-21 2021-06-11 中国科学院半导体研究所 一种多梁耦合的微机电谐振器
CN114217093A (zh) * 2021-06-21 2022-03-22 西北工业大学 一种适用于mems模态局部化传感器的环状耦合系统

Also Published As

Publication number Publication date
CN114217093A (zh) 2022-03-22
GB202402969D0 (en) 2024-04-17
CN114217093B (zh) 2024-04-26

Similar Documents

Publication Publication Date Title
EP3615944B1 (en) High performance micro-electro-mechanical systems accelerometer
CN109061226B (zh) 静电负刚度式加速度计的设计方法
CN107643423B (zh) 一种基于模态局部化效应的三自由度弱耦合谐振式加速度计
US5392650A (en) Micromachined accelerometer gyroscope
CN109596115B (zh) 一种嵌套环式振动陀螺非线性效应抑制方法
CN103256941A (zh) 一种mems陀螺仪高阶温度补偿的实用方法
KR101927647B1 (ko) 3축 mems 자이로스코프
WO2020253795A1 (zh) 基于模态局部化效应的微弱磁场测量装置及方法
GB2505875A (en) Dual and triple axis inertial sensors and methods of inertial sensing
WO2023065834A1 (zh) 一种适用于mems模态局部化传感器的环状耦合系统
Li et al. A mode localization based resonant MEMS tilt sensor with a linear measurement range of 360°
CN104406579A (zh) 微机电可变形结构和三轴多自由度微机电陀螺仪
Hou et al. A quadrature compensation method to improve the performance of the butterfly vibratory gyroscope
JP2005504976A (ja) セルフテスト機能及び最適化方法を備えたマイクロマシニング型のセンサ
JP2015219233A (ja) 質量負荷型コリオリ振動ジャイロスコープ
CN112906185B (zh) 一种基于人工智能的mems惯性传感器异构阵列及其设计方法
CN110307832A (zh) 一种基于杠杆效应位移放大音叉式微机械陀螺仪
CN111780737B (zh) 一种基于音叉驱动效应的高精度水平轴硅微陀螺仪
Zhao et al. Temperature-insensitive silicon resonant pressure sensor by thermal stress control
Ruan et al. A mode-localized tilt sensor with resolution of 2.4 e-5 degrees within the range of 50 degrees
Han et al. High-accuracy differential resonant pressure sensor with linear fitting method
CN204188169U (zh) 微机电可变形结构和三轴多自由度微机电陀螺仪
Yilmaz et al. Effects of imperfections on solid-wave gyroscope dynamics
US10775171B2 (en) MEMS gyroscope with improved rejection of a quadrature error
Chang Serial and Parallel Connections of Micromechanical Resonators for Sensing: Theories and Applications

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 22882451

Country of ref document: EP

Kind code of ref document: A1