CN102608356B - A kind of double-shaft micromechanical resonant accelerometer structure and production method - Google Patents

A kind of double-shaft micromechanical resonant accelerometer structure and production method Download PDF

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CN102608356B
CN102608356B CN201210059387.9A CN201210059387A CN102608356B CN 102608356 B CN102608356 B CN 102608356B CN 201210059387 A CN201210059387 A CN 201210059387A CN 102608356 B CN102608356 B CN 102608356B
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resonance
corrosion
leg type
crab leg
resonance beam
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CN102608356A (en
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韩建强
冯日盛
李琰
李森林
李青
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China Jiliang University
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Abstract

The invention discloses a kind of double-shaft micromechanical resonant accelerometer structure and production methods, belong to microelectromechanical systems field.The resonance beam (1) of composition resonance type accelerometer is located at substrate top surface, and the neutral surface of crab leg type supporting beam (2) is with the center of gravity of mass block (3) in same plane.Resonance beam (1) and crab leg type supporting beam (2) is by five photoetching and anisotropic wet etching process is produced on same silicon chip three times.First, back side photoetching has mask corrosion technique to corrode silicon to certain depth from resonance beam (1) back side.Then positive and negative photoetching removes in etching tank (8) except resonance beam (1) and crab leg type supporting beam (2) are with the corrosion masking layer (9) of outer portion, has mask corrosion silicon to another depth.Finally, it removes the corrosion masking layer (9) of crab leg type supporting beam (2) positive and negative, mask and is combined without mask corrosion and realizes that resonance beam (1) and crab leg type supporting beam (2) while are molded.The double-shaft micromechanical resonant accelerometer has smaller intersecting axle interference and higher sensitivity.

Description

A kind of double-shaft micromechanical resonant accelerometer structure and production method
Technical field
The present invention relates to a kind of double-shaft micromechanical resonant accelerometer structure and production method, especially a kind of utilization The resonance beam and crab leg type support beam group that mask-makes without mask corrosion technology at double-shaft micromechanical resonant accelerometer Structure and production method belong to the field microelectromechanical systems (Micro-Electro-Mechanical Systems, MEMS).
Background technology
Micro accelerometer is a kind of important mechanical quantity sensor.It begins to study early in end of the sixties in last century people One-dimensional minitype silicon accelerometer.Start the large-scale production of one-dimensional micro accelerometer the end of the eighties.The nineties is entered, with The development of science and technology and military, commercial market demand, begin one's study three-dimensional micro accelerometer, is applied to military, automobile The fields such as electronics, industrial automation, robot technology, consumer electronics product.Due to micro accelerometer have it is small, again Amount is light, power consumption and it is at low cost, overload capacity is strong, it is easy of integration, can large-scale mass production the advantages that, not only become micro-inertia measuring The core element of combination is also applied to rapidly vehicle control, high-speed railway, robot, industrial automation, mine locating, toy, medical treatment Equal civil fields.
Micro accelerometer is the sensor that acceleration is measured using the inertia force of sensing quality.According to signal detecting mode Dividing can be pressure resistance type, condenser type, tunnel current formula, resonant mode, heat convection type, piezoelectric accelerometer.The nineties in last century with Afterwards, with the demand of the continuous development of MEMS technology and military affairs, commercial market, the acceleration test of single direction cannot Meets the needs of various aspects, accelerometer develops to three-dimensional, is satellite navigation, guided missile for detecting steric acceleration The civilian projects services such as military defense projects and automobile shockproof protection, self-actuating brake, medical treatment such as guidance, shell orientation.Three axis are miniature to be added Speedometer can measure three mutually orthogonal axial accelerations simultaneously.Its measuring principle includes condenser type, pressure resistance type, piezoelectric type And heat convection type, it can be divided into multimass block and single mass system according to mass block number.
Resonant mode acceleration transducer changes axial stress and the strain of resonator using inertia force, so as to cause resonance frequency Rate changes, and the variable quantity for detecting resonant frequency obtains the size of acceleration.Resonant mode acceleration transducer can be by tested acceleration Degree is converted directly into stability and the higher frequency signal of reliability, and distortion is not likely to produce in transmission process, nothing It need to can be with digital display circuit interface through A/D converter.In addition, resonant mode acceleration transducer wide dynamic range, sensitivity and point Resolution is high, stability is good, high certainty of measurement, has reached the noise level of the sensitivity and 2 μ g of 1KHz/g, disclosure satisfy that accelerating Spend the high performance requirements of sensor.Electric heating excitation/piezoresistive detection resonant mode of Christian Burrer reports in 1996 accelerates Degree sensor is made of mass block, support cantilever beam and resonance beam.Sensitive-mass block is suspended on parallel and right with center axis One end of two supporting beams claimed, the supporting beam other end are fixed on substrate.Resonance beam one end is connected with sensitive-mass block, another End is fixed on substrate.When the acceleration effect for having vertical substrates surface is when on sensitive-mass block, mass block will be in Vertical Square To movement, causes resonance beam to generate stretching or compression strain, change the intrinsic frequency of resonance beam, sensitivity 250Hz/g.
The same year D.W.Burns combination micromechanics and surface micromechanical process have made a kind of static excitation/piezoresistive detection The micro- beam resonant mode acceleration transducer of polysilicon, sensor include mass block, upper-lower seal lid, support spring beam, two it is same The varistor composition of the resonance beam and detection resonance beam strain of axis.Mass block and spring beam are symmetrical structure to reduce intersecting axle Interference, upper and lower seal cover board for mass block provide extrusion die damping and overload protection.Apply Dc bias in sealing shell. Apply small size alternating voltage, the static-electronic driving resonance beam vibration of generation in the driving electrodes of resonance beam.The clamped end of resonance beam Varistor measures strain caused by beam vibration, feeds back to driving electrodes after amplification, makes resonance beam vibration in resonant frequency.Two Resonance beam is operated in differential mode, and acceleration makes the resonant frequency of a resonance beam increase, another reduction is sensitive to improve It spends and common-mode signal (such as Temperature cross-over sensitivity) is inhibited.The range of sensor can pass through the size tune of supporting beam Section.To the range of 20g, length, the width and thickness of resonance beam are respectively 200 μm, 40 μm and 2 μm, resonant frequency 500KHz, Z axis acceleration detection high sensitivity reaches 1750Hz/g.
Seoul national universities of South Korea Byeung-leul Lee in 2000 etc. have developed one kind using surface micromechanical process The differential resonant mode single-axis acceleration sensors (DRXL) of inertial navigation grade, sensing element are the torsion beam resonance of static excitation Device.The acceleration analysis of vertical direction utilizes electrostatic stiffness mediating effect+6, changes spring beam by the inertia force that acceleration generates The electrostatic force born realizes the change to stiffness coefficient, so as to cause the variation of resonant frequency, and complementary using two shapes Mass block realizes variate.Acceleration transducer carries the double-ended tuning fork of mass block using end in face, is changed using inertia force The axial force for becoming tuning fork, to change resonant frequency.The resonant frequency of acceleration is 23.4KHz in face, and sensitivity is up to 128Hz/g, bandwidth 110Hz, precision are 5.2 μ g;The resonant frequency of vertical direction is 12KHz, and sensitivity is up to 70Hz/ G, bandwidth 100Hz, precision are 2.5 μ g.
Trey A.Roessig in 1997 have made a kind of new structural resonant mode acceleration using surface micromechanical process Spend sensor.Sensor includes mass block, two double-ended tuning forks and supporting beam, the branch that double-ended tuning fork passes through power enlarged structure both ends Hold tuning fork connection.Tuning fork is driven by the comb capacitance of transverse movement to be vibrated in resonant frequency, and is fed back as resonance circuit The part in circuit, to maintain to vibrate.When acceleration effect is on mass block, the effect of double-ended tuning fork axial direction is generated Power changes the potential energy of system, to change the vibration frequency of tuning fork.The differential output of two double-ended tuning forks can eliminate common mode mistake Influence (such as temperature and intersecting axle interference) of the first order component of difference to frequency.The resonant frequency of the clamped tuning fork resonator of both-end is 68KHz, sensitivity 45Hz/g.The research group in 2002 reports a kind of improved device of structure again, after Vacuum Package Background noise of the device in 300Hz be
2005, V.Ferrari et al. reported a kind of electric heating excitation/piezoresistive detection resonance made using bulk silicon technological Formula accelerometer.The acceleration of chip plane induces minor resistant genes axial stress, changes the resonant frequency of micro- beam in proportion.Micro- beam Resonant frequency is 700KHz.In 0~3KHz frequency ranges, measurement sensitivity 35Hz/g.Circuit compensation is introduced in test system Link compensates the Cross-talk effects of input and output, effectively reduces the crosstalk effect of input and output.
One of the difficult point that resonant mode acceleration transducer makes is how made between frame and mass block not same The supporting beam and resonance beam of one plane, it is desirable that resonance beam is located at substrate top surface, and the neutral surface of supporting beam will be with mass block Center of gravity is in same plane.Otherwise larger intersecting axle interference and measurement error can be introduced.Christian to solve this problem Burrer et al. makes resonance beam and the top half of mass block on a wafer, and made on another substrate supporting beam and The two, is then bonded together by the lower half portion of mass block.It has disadvantages such that bonding face is easy to crack.D.W.Burns Supporting beam is made in chip tow sides using the method for heavy doping etch stop, realizes supporting beam neutral surface and mass block weight The heart is in same plane.Dense boron doping and etch stop are needed using the resonance type accelerometer mechanical structure that this method is realized, Support cantilever thickness smaller.
Common minor resistant genes acceleration is in respect of beam type, two fixed ends beam type, double-tone V shape.Beam type makes letter Single, one axial stress transformation efficiency of inertia force is high, but symmetry is poor, and there are the interference of larger intersecting axle, are not easy to realize differential defeated Go out structure with error caused by the extraneous factors such as suppression common mode signal and temperature.Double-tone V shape uses differential output structure, passes through Lever principle amplifies axial stress, and one axial stress transformation efficiency of inertia force is low, and sensitivity is low.Two fixed ends beam type sensitivity It is general also smaller.The sensitivity for improving resonant mode acceleration transducer is the key that resonant mode acceleration transducer development.
Invention content
It is an object of the invention to invent a kind of novel double-shaft micromechanical resonant accelerometer structure and making side Method.The double-shaft micromechanical resonant accelerometer is by resonance beam (1), crab leg type supporting beam (2), mass block (3), frame (4), vibrator (5), detecting element (6) and metal lead (7) composition.Resonance beam (1) and crab leg type supporting beam (2) are located at matter " mouth " font etching tank (8) between gauge block (3) and frame (4) is interior, the clamped side in mass block (3) in one end, and the other end is solid Branch is in frame (4) inner wall.Resonance beam (1) is located at sensor chip upper surface, the neutral surface and mass block of crab leg type supporting beam (2) (3) center of gravity is in same level.
The operation principle of double-shaft micromechanical resonant accelerometer according to the present invention:Make in X-axis positive acceleration Under, mass block (3) is moved in X-direction.Axial tension stress increase or axial suffered by one of resonance beam (1) of X-direction Compression reduces, and resonant frequency increases;Another resonance beam (1) axial tension stress of X-direction reduces or axial compression stress increases, Resonant frequency reduces.The size and Orientation of the difference reflection X-axis acceleration of two resonance beam (1) resonant frequencies of X-direction.Together Sample, so that mass block (3) is moved in Y direction under Y-axis acceleration effect, one of resonance beam (1) of Y direction is axially drawn and answered Power increases or axial compression stress reduces, and resonant frequency increases;Another resonance beam (1) axial tension stress of Y direction reduces or axis Increase to compression, resonant frequency reduces, the difference reflection Y-axis acceleration of two resonance beam (1) resonant frequencies of Y direction Size and Orientation.
The X-axis acceleration signal of double-shaft micromechanical resonant accelerometer according to the present invention can also be only with one Resonance beam (1) detects, and the size and Orientation of reflection X-axis acceleration, but detection sensitivity are increasedd or decreased according to its resonant frequency It is smaller.Similarly, Y-axis acceleration signal can also be detected only with a resonance beam (1), be increasedd or decreased according to its resonant frequency Reflect the size and Orientation of Y-axis acceleration.
The resonance beam (1) of double-shaft micromechanical resonant accelerometer according to the present invention is either two fixed ends list Three beam resonator of two fixed ends twin beams resonator or two fixed ends can also be used in beam resonator.Can slot on beam or trepanning with It improves quality factor or realizes electric isolation.Two fixed ends twin beams resonator is made of two parallel beams, and the end of beam merges, And it is clamped with substrate.When making two prong reverse phase vibrations by energisation mode appropriate, generated in their combined region Stress and torque direction on the contrary, offset each other, therefore total, the vibration minimum with extraneous energy coupling that pass through clamped end The energy loss of system is small, has higher Q values.The width of the intermediate beam of triple-beam structure resonance beam is equal to adjacent two beam in left and right The sum of width, and three is mutually interconnected into an entirety in end via energy isolated area.When the antisymmetry for selecting three beam resonators When resonance mode of the three rank mode of oscillations of phase as beam, two beams on intermediate beam and both sides are in clamped end generated reaction force With torque because direction of vibration is mutually cancelled out each other instead, vibrational energy is stored in resonator inside, to reduce energy loss, plays Propose the effect of high q-factor.
The resonance beam (1) of double-shaft micromechanical resonant accelerometer according to the present invention is using electric heating excitation, photo-thermal One of excitation, inverse piezoelectric excitation, electromagnetic excitation, static excitation excitation, are at resonant condition, the resonant frequency letter that it is exported It number is realized using piezoresistive detection, electromagnetic detection, piezoelectric detection, optical interference, one of capacitance detecting.
The technical solution adopted in the present invention is to achieve the above object:Resonance beam (1) and crab leg type supporting beam (2) pass through Five photoetching and anisotropic wet etching process is produced on same silicon chip three times.First, back side photoetching has mask corrosion work Skill corrodes silicon to certain depth from resonance beam (1) back side.Then positive and negative photoetching, wet etching or dry etching etching tank (8) In except resonance beam (1) and crab leg type supporting beam (2) are with the corrosion masking layer (9) of outer portion, there is mask corrosion technique to corrode silicon and arrive Another depth.The corrosion masking layer (9) of crab leg type supporting beam (2) positive and negative is finally removed, mask-is combined reality without mask corrosion It is molded while existing resonance beam (1) and crab leg type supporting beam (2).
Double-shaft micromechanical resonant accelerometer according to the present invention is realized by following basic process steps:
1) original silicon chip is (100) face twin polishing silicon chip, and thickness H, thermal oxide, CVD method are on silicon chip Make corrosion masking layer (9), masking layer and insulation film when which is also doping simultaneously.
2) photoetching, burn into diffusion, thin film deposition processes are combined the vibrator (5) for making resonance beam (1), vibration detection Element (6) and metal lead (7).
3) back side photoetching forms resonance beam back of the body corrosion window (10), sustained release hydrofluoric acid solution corrosion resonance beam back of the body corrosion window Corrosion masking layer in mouth (10), the length and width that resonance beam carries on the back corrosion window (10) is respectively L and b+2 (H-h) Ctg54.7, wherein L are etching tank (8) width, b be 5) in step process resonance beam (1) mask width, h is resonance beam (1) Design thickness.
4) corrode silicon, corrosion depth H-h-H in potassium hydroxide solution2- 0.263 (H-d+0.471w), wherein H27) it is Walk depth when anisotropic etch, w be the 5) after step photoetching crab leg type supporting beam (2) masking layer width, d is crab leg type branch Support the design thickness of beam (2).
5) figure of positive photoetching resonance beam (1) and crab leg type supporting beam (2), is sustained hydrofluoric acid solution corrosive attack slot (8) except resonance beam (1) and crab leg type supporting beam (2) are with the corrosion masking layer of outer portion, etching mask figure such as Fig. 2 institutes in front Show.
6) figure of back side photoetching crab leg type supporting beam (2) is sustained in hydrofluoric acid solution corrosive attack slot (8) back side and removes crab For leg type supporting beam (2) with the corrosion masking layer of outer portion, etching mask figure is as shown in Figure 2.
7) corrode silicon, corrosion depth H in potassium hydroxide solution2> d/2.
8) positive photoetching, sustained release hydrofluoric acid solution corrode the corrosion masking in addition to resonance beam (1) in front etch slot (8) Layer;Reverse side photoetching, sustained release hydrofluoric acid solution corrode the corrosion masking layer in back side etching tank (8).
9) corrode silicon in potassium hydroxide solution, resonance beam (1) and crab when vertical etches depth is 0.263 (H-d+0.471w) Leg type supporting beam (2) while reaching design thickness.
The section of the crab leg type supporting beam (2) made using the above method is prismatic, side angle be 50.48 ° and 129.52 °, effective length is ctg54.7 ° of L- (H-d);The length effective length of resonance beam (1) is L-2 (H-h) Ctg54.7 °, the angle of resonance beam (1) side and bottom surface is 25.24 °, and the width of bottom is b+0.56H+1.416h+ 0.622d-2.364H2-0.293w-1.192H1, the width b+0.56H+5.659h-2.364H at upper bottom2-0.293w-1.192H1, Section is isosceles triangle when the width of bottom is equal to zero, and the width at upper bottom is 4.24h.
The advantages of double-shaft micromechanical resonant accelerometer structure according to the present invention and preparation method thereof, is: It is produced on same silicon chip not in conplane resonance beam (1) and crab leg type supporting beam (2), resonance beam (1) is located on substrate Surface, and the center of gravity of the neutral surface of crab leg type supporting beam (2) and mass block (3) makes the resonant mode of making accelerate in same plane There is degree meter smaller intersecting axle to interfere.In addition, using smaller crab leg type supporting beam (2) the support mass block of rigidity, in opposite Acceleration has higher measurement sensitivity.
Description of the drawings
Fig. 1 is the structural schematic diagram of double-shaft micromechanical resonant accelerometer according to the present invention.
Fig. 2 is double-shaft micromechanical resonant accelerometer basic process steps 5 according to the present invention) and step 6) Mask figure, wherein shadow region are the region that masking layer is corroded.
Fig. 3 is the making at double-shaft micromechanical resonant accelerometer visual angles AA along Fig. 1 as the embodiment of the present invention Process flow chart.Wherein resonance beam (1) is using electric heating excitation, varistor detection.
In figure:
1- resonance beam 2- crab leg type supporting beam 3- mass blocks
4- frame 5- vibrator 6- detecting elements
7- metal lead 8- etching tanks 9- corrodes masking layer
10- resonance beams carry on the back corrosion window 11- resonance beam mask 12- crab leg type supporting beam masks
13- crab leg type supporting beams turning point convex corner compensation mask
Specific implementation mode
Below in conjunction with the accompanying drawings 3 and embodiment 1 the present invention will be further described, but be not limited to the embodiment.
Embodiment 1:Original silicon chip (3) thickness is 380 microns, and resonance beam (1) thickness is 10 microns, crab leg type supporting beam (2) thickness is 50 microns, 661 microns of etching tank (8) width.Wherein resonance beam is using electric heating excitation, varistor detection.Foundation Above-mentioned data are as follows come the fabrication processing determined:
1) thermal oxide makes the silica membrane of 1.5 microns of thickness in the silicon chip tow sides of (100) crystal orientation.(see attached Fig. 3 [1])
2) photoetching, burn into diffusion, thin film deposition processes are combined the vibrator for making resonance beam (1) on silicon chip and shake Dynamic detecting element.(see attached drawing 3 [2])
3) back side photoetching forms resonance beam back of the body corrosion window (10).Resonance beam carries on the back the length of corrosion window (11) (along resonance Beam (1) length direction) and width (along resonance beam (1) width direction) compared with the length and width of resonance beam (1) be respectively 660 microns With 724 microns.The corrosion masking layer being sustained in hydrofluoric acid solution corrosion resonance beam back of the body corrosion window (10).(see attached drawing 3 [3])
4) corrode silicon, 130 microns of vertical etches depth in 40% potassium hydroxide solution.(see attached drawing 3 [4])
5) figure of positive photoetching resonance beam (1) and crab leg type supporting beam (2), is sustained hydrofluoric acid solution corrosive attack slot (8) except resonance beam (1) and crab leg type supporting beam (2) are with the corrosion masking layer of outer portion in front.The masking slice width of resonance beam (1) Degree is 120 microns.(see attached drawing 3 [5])
6) figure of back side photoetching crab leg type supporting beam (2) is sustained in hydrofluoric acid solution corrosive attack slot (8) back side and removes crab Leg type supporting beam (2) is with the corrosion masking layer of outer portion.(see attached drawing 3 [6])
7) corrode silicon in 40% potassium hydroxide solution, corrosion depth is equal to 120 microns.(see attached drawing 3 [7])
8) positive photoetching, sustained release hydrofluoric acid solution corrode the corrosion masking in addition to resonance beam (1) in front etch slot (8) Layer.Reverse side photoetching, sustained release hydrofluoric acid solution corrode the corrosion masking layer in back side etching tank (8).(see attached drawing 3 [8])
9) corrode silicon in 40% potassium hydroxide solution, resonance beam (1) and the support of crab leg type when corrosion depth is equal to 120 microns Beam (2) while reaching design thickness.(see attached drawing 3 [9])
Width using the upper bottom of the resonance beam (1) of above-mentioned processing step corrosion is 137 microns, and the width of bottom is 94.5 The effective length (that is, thickness is 10 micron fractions) of micron, resonance beam (1) is 137 microns.Crab leg type supporting beam (2) it is effective Length is that (that is, thickness is 50 micron fractions) is 427 microns.

Claims (2)

1. a kind of double-shaft micromechanical resonant accelerometer, it is characterised in that:The double-shaft micromechanical resonant accelerates Degree meter is by resonance beam (1), crab leg type supporting beam (2), mass block (3), frame (4), vibrator (5), detecting element (6) and metal Lead (7) forms, and resonance beam (1) and crab leg type supporting beam (2) are located at " mouth " font between mass block (3) and frame (4) Etching tank (8) is interior, the clamped side in mass block (3) in one end, and the other end is clamped in frame (4) inner wall;Resonance beam (1), which is located at, to be passed Sensor chip upper surface, the neutral surface of crab leg type supporting beam (2) is with the center of gravity of mass block (3) in same level;
It is realized by following basic process steps:
1) original silicon chip is (100) face twin polishing silicon chip, and thickness H, thermal oxide, CVD method make on silicon chip Corrode masking layer (9), masking layer and insulation film when which is also doping simultaneously;
2) photoetching, burn into diffusion, thin film deposition processes are combined vibrator (5), the vibration detecting element for making resonance beam (1) (6) and metal lead (7);
3) back side photoetching, forms resonance beam back of the body corrosion window (10), and sustained release hydrofluoric acid solution corrosion resonance beam carries on the back corrosion window (10) length and width of the corrosion masking layer in, resonance beam back of the body corrosion window (10) is respectively ctg54.7 ° of L and b+2 (H-h), Wherein L is etching tank (8) width, b be the 5) in step process resonance beam (1) mask width, h is that the design of resonance beam (1) is thick Degree;
4) corrode silicon, corrosion depth H-h-H in potassium hydroxide solution2- 0.263 (H-d+0.471w), wherein H2Be 7) step it is each Depth when anisotropy is corroded, w be the 5) after step photoetching crab leg type supporting beam (2) masking layer width, d is crab leg type supporting beam (2) design thickness;
5) mask pattern of positive photoetching resonance beam (1) and crab leg type supporting beam (2), is sustained hydrofluoric acid solution corrosive attack slot (8) except resonance beam (1) and crab leg type supporting beam (2) mask are with the corrosion masking layer of outer portion in front;
6) figure of back side photoetching crab leg type supporting beam (2) is sustained in hydrofluoric acid solution corrosive attack slot (8) back side the crab leg type that removes Supporting beam (2) is with the corrosion masking layer of outer portion;
7) anisotropic etch silicon in potassium hydroxide solution, corrosion depth H2> d/2;
8) positive photoetching, sustained release hydrofluoric acid solution corrode the corrosion masking layer in front etch slot (8) in addition to resonance beam (1); Reverse side photoetching, sustained release hydrofluoric acid solution corrode the corrosion masking layer in back side etching tank (8);
9) corrode silicon in potassium hydroxide solution, resonance beam (1) and crab leg type when vertical etches depth is 0.263 (H-d+0.471w) Supporting beam (2) while reaching design thickness.
2. double-shaft micromechanical resonant accelerometer according to claim 1, it is characterised in that:Made crab leg type The section of supporting beam (2) is diamond shape, and side angle is 50.48 ° and 129.52 °, and effective length is ctg54.7 ° of L- (H-d); The length effective length of resonance beam (1) is ctg54.7 ° of L-2 (H-h), and the angle of resonance beam (1) side and bottom surface is 25.24 °, Its width gone to the bottom is b+0.56H+1.416h+0.622d-2.364H2-0.293w-1.192H1, the width b+0.56H+ at upper bottom 5.659h-2.364H2-0.293w-1.192H1, section is isosceles triangle when the width of bottom is equal to zero, and the width at upper bottom is 4.24h。
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