MEMS技術(shù)第五講機(jī)電耦合模型解讀課件

1、 MEMS和微系統(tǒng)設(shè)計(jì)課程的基本目的掌握MEMS設(shè)計(jì)的基本過程掌握mems機(jī)電及其耦合分析的基本理論掌握機(jī)電結(jié)構(gòu)微器件的性能分析方法了解熱、流體的基本理論了解MEMS的發(fā)展前沿知識(shí)培養(yǎng)對(duì)MEMS的興趣課程內(nèi)容MEMS概述及MEMS設(shè)計(jì)的概述工藝簡(jiǎn)要回顧系統(tǒng)設(shè)計(jì)、工藝設(shè)計(jì)及版圖設(shè)計(jì)主要的機(jī)械、電子元件及其設(shè)計(jì)基礎(chǔ)多域耦合設(shè)計(jì)：以機(jī)電耦合為例子器件性能的估計(jì)簡(jiǎn)單的其他域的元件及其簡(jiǎn)要設(shè)計(jì)要點(diǎn)設(shè)計(jì)實(shí)例 本章提綱力電耦合的靜態(tài)分析 彈簧與電阻 薄膜與電容 彈簧與電容 二階動(dòng)態(tài)系統(tǒng) 與測(cè)試電路的耦合Transversal deflection of a beamwith a load at the en

2、d with:xwdBLBFz(187,1)(187,2)Rectangular beam:(187,3)I := Area moment of inertia of the beam B := Strain at the surface of the beamF := Force acting at the end of the beam dB := Thickness of beam w := Deflection of beam bB := Width of beam LB := Length of beam EB := Youngs modulus of beam187* W. Bei

3、tz, K.-H. Grote, Dubbel, Taschenbuch fr den Maschinenbau”*(187,4)(187,5)Aria momentum of inertia(188,1)(188,2)Rectangular:(188,3)I := Area moment of inertia of the beam EB := Youngs modulus of the beam FB := Elastic force of the beam at its end w := Deflection of the beam dB, bB, LB, RB := Thickness

4、, width, length, and radius of the beam, respectively188More aria momentums of inertia are found in books like: W. Beitz, K.-H. Grote, Dubbel, Taschenbuch fr den Maschinenbau” orR.D. Blevins, Formulas for Natural Frequency and Mode Shape“, Krieger, Malaba, FL (1987)bBdB(187,3)Circular:RBTrapezoid sh

5、aped:dBebB,1bB,2(188,4)with:(188,5)Strain on the surface of a beam loaded at its end xwdBLBFz(189,1)Rectangular beam:(187,3) :(189,2)189* W. Beitz, K.-H. Grote, Dubbel, Taschenbuch fr den Maschinenbau”*I := Area moment of inertia of the beam EB := Youngs modulus of the beam F := Force acting at the

6、end of the beam B := Strain at the surface of the beam w := Deflection of the beam dB, bB, LB : Thickness, width, and length of the beam, respectivelyRectangular beam clamped on one side and loaded at the other end xwdBLBFz(189,2):x m x mw m(187,1), (187,3):LB=800mbB=40mdB=20mEB=140GPaF=1mN190EB :=

7、Youngs modulus of the beam B := Strain at the surface of the beam F := Force acting at the end of the beamdB, bB, LB, w := Thickness, width, length, and deflection of the beam, respectivelyTransversal deflection of a beamloaded at the end The strain at the surface of a beam clamped at one end and lo

8、aded at the other end in transversal direction is largest at the fixed end.Strain and deflection are not a functions of an initial stress of the beam. Rectangular beam:(189,2):Strain and deflection are proportional to the force (linear characteristic curve).(187,1), (187,3):191xwdBLBFzEB := Youngs m

9、odulus of the beam B := Strain at the surface of the beam F := Force acting at the end of the beamdB, bB, LB, w := Thickness, width, length, and deflection of the beam, respectivelyTransversal deflection of a beamloaded at the endRectangular beam :Because of the transverse strain the beam gets narro

10、wer on the side with tensile stress and wider on the opposite side. (With the exception of the region next to the clamping)Cross-section of the beam:Without loadWith loadbBbB (1 B B)dB192xwdBLBFz(189,2):EB := Youngs modulus of the beam B := Poissons ratio of the beam B := Strain at the surface of th

11、e beam F := Force acting at the end of the beamdB, bB, LB, w: Thickness, width, length, and deflection of the beam, respectivelyThe effect of crystal orientation on elastic propertiesOnly isotropic materials have been considered so far. *J.J. Wortman, R.A. Evans, Youngs Modulus, Shear Modulus, and P

12、oissons Ratio in Silicon and Germanium“, J. Appl. Phys. 36 (1965) 153 - 156Youngs modulus GPa of silicon and germanium as a function of the orientation in the (100)-plane*However, membranes from mono-crystalline silicon are anisotropic.115Youngs modulus GPa of mono-crystalline silicon and germanium

13、as a function of crystal orientation*J.J. Wortman, R.A. Evans, Youngs Modulus, Shear Modulus, and Poissons Ratio in Silicon and Germanium“, J. Appl. Phys. 36 (1965) 153 - 156(100)-plane*(110)-plane1501005005010015015010050050100150116Poisons ratio of silicon and germanium as a function of crystal or

14、ientation*J.J. Wortman, R.A. Evans, Youngs Modulus, Shear Modulus, and Poissons Ratio in Silicon and Germanium“, J. Appl. Phys. 36 (1965) 153 - 156(100)-plane*(110)-plane00,10,20,30,30,20,100,30,20,10,10,20,3117Alignment of strain gauges form p-silicon on (100) -wafers(100)Freely stretched membraneS

15、train gauges from p-siliconThe edges of v-grooves in (100)-wafers are orientated in -direction.In -direction the piezo effect of p-silicon is largest. 140一個(gè)簡(jiǎn)單計(jì)算 計(jì)算最大的電阻變化率及其電壓變化率，假定梁及電阻的分布如上頁所示本章提綱力電耦合的靜態(tài)分析 彈簧與電阻 薄膜與電容 彈簧與電容 二階動(dòng)態(tài)系統(tǒng) 與測(cè)試電路的耦合Capacitive measurement of membrane deflectionCapacity C of a

16、 capacitor:Cel := Electrical capacity 0 := Absolute permittivity r := Relative permittivity AC := Inner area of capacitor plates dC := Distance of capacitor platesCapacity CPressure differenceExample pressure sensor:The capacitive measurement of the deflection of a membrane results in no linear sign

17、al.The characteristic curve of a membrane is much more complex than the one of a capacitor.147(147,1)Capacitive measurement (Linearization)Characteristic curve of a pressure sensor calculated by Finite ElementsCapacity CPressure difference* L. Rosengren, J. Sderkvist, L. Smith, ”Micromachined sensor

18、 structures with linear capacitive response”, Sensors and Actuators A 31 (1992) 200 - 205Membrane touches the substrate*148Capacitive measurement (Linarizeation)* L. Rosengren, J. Sderkvist, L. Smith, ”Micromachined sensor structures with linear capacitive response”, Sensors and Actuators A 31 (1992

19、) 200 - 205*Top end of the comb structure is conductive.149Characteristic curve of a pressure sensor calculated by Finite ElementsMembrane shapes (thick membrane or plate clamped at its circumference) Bending moments are dominating.w0 dM(82,1)dMw082r(82,2)Circular plate bulged up by a pressure diffe

20、rence:w(r) := Deflection of membrane w0 := Deflection of the center of the membrane dM := Thickness of membrane 2 RM := Diameter of membrane2 RMMembrane shapes (thin membrane) w0Mechanical stress is dominating.w(r) := Deflection of membrane w0 := Deflection of the center of the membrane dM := Thickn

21、ess of membrane 2 RM := Diameter of membranew0 dM(84,1)84(84,2)Circular membrane bulged up by a pressure difference:Overview on the deflection of membranes114RM, M, dM, EM, w0, 0 := Radius, Poissons ratio, thickness, Youngs modulus, central deflection, and initial stress of the membrane, respectivel

22、y aM := Length of a square membrane p := Pressure drop over the membraneThin, circular,exactlyThin, square,exactlyThick, circular, without 0, exactlyThick, square,without 0, exactlyIn general, circular,rough approximation如何計(jì)算壓力對(duì)應(yīng)電容的變化？本章提綱力電耦合的靜態(tài)分析 彈簧與電阻 薄膜與電容 彈簧與電容 二階動(dòng)態(tài)系統(tǒng) 與測(cè)試電路的耦合Spring-Suspended C

23、apacitor: Voltage-Control CaseVoltage increaseGap decreaseForce increaseStability Analysis Range of stability: examine net (attractive) force on plateIf we increase the gap by dg,the increment 0 or the plate collapses Pull-in Voltage VplSolve for point at which plate goes unstable:Substitution for k

24、 leads to:本章提綱力電耦合的靜態(tài)分析 彈簧與電阻 薄膜與電容 二階動(dòng)態(tài)系統(tǒng) 與測(cè)試電路的耦合電子二階系統(tǒng)及機(jī)電二階系統(tǒng)的等效Mechanical-to-electrical correspondence in the current analogy:Mechanical Variable Electrical VariableDamping, cResistance, RStiffness-1, k-1Capacitance, CMass, mInductance, LForce, fVoltage, VVelocity, vCurrent, IBandpass Biquad tra

25、nsfer functionLecture OutlineReading: Senturia, Chpt. 6, Chpt. 14Lecture Topics:Input ModelingForce-to-Velocity Equiv. CircuitInput Equivalent Circuit.Current ModelingOutput Current Into Ground Input CurrentComplete Electrical-Port Equiv. CircuitImpedance & Transfer FunctionsElectromechanical Analog

26、iesForce-to-Velocity RelationshipThe relationship between input voltage v1 and force Fd1:When displacement x is the mechanical output variable:When velocity v is the mechanical output variable:Force-to-Velocity Equiv. CktCombine the previous lumped LCR mechanical equivalent circuit with a circuit mo

27、deling the capacitive transducer circuit model for oltage-to-velocityEquiv. Circuit for a Linear TranducerA TransducerConverts energy from one domain (e. g., electrical) to another (e. g., mechanical)has at least two portsis not generally linear, but is virtually linear when operated with small sign

28、als (i.e., small displacements)Equiv. Circuit for a Linear TranducerFor physical consistency, use a transformer equivalent circuit to model the energy conversion from the electrical domain to mechanical domainElectromechanical Equivalent CircuitE2=Fd1, e1=v1, just need 1:From the matrix: e2=e1Output

29、 Current Into GroundWhen the mass moves with time-dependent displacement x(t), the electrode-to-mass capacitors C1(x,t) and C2(x,t) vary with timeThis generates an output current:Output Current Into GroundAgain, model with a transformer:Output Current Into GroundInput Current Expression (Cont)Input

30、Current Expression (Cont)Static electrode-to-mass overlap capacitanceOutput Current Into GroundWhat is the impedance seen looking into port 1 with port 2 shorted to ground?Input Impedance Into Port 2What is the impedance seen looking into port 2 with port 1 shorted to ground?Note: there are not the

31、same as Lx1,Cx1,1/2Rx1!Port 1 to 2 TransG Across the CircuitWhat is the transconductance from port 1 to port 2 with port 2 shorted to ground?Port 1 to 2 vi-to-i0 Transfer FunctionSeparate freq. response f magnitude:Condensed Equiv. Circuit (Symmetrical)Holds for the symmetrical case, where port 1 an

32、d port 2 are identicalPhasing of SignalsBelow: plots of resonance electrical and mechanical signals vs. time, showing the phasings between them如何設(shè)計(jì)傳感器的基本性能量程靈敏度頻率分辨率本章提綱力電耦合的靜態(tài)分析 彈簧與電阻 薄膜與電容 二階動(dòng)態(tài)系統(tǒng) 與測(cè)試電路的耦合Reading: Senturia, Chpt. 14Lecture Topics:Detection CircuitsVelocity sensingPosition SensingVe

33、locity-to-Voltage conversionTo convert velocity to a voltage, use a resistive loadVelocity-to-Voltage conversionTo convert velocity to a voltage, use a resitive loadVelocity-to-Voltage conversionTo convert velocity to a voltage, use a resistive loadSince this structure has completely symmetrical I/O

34、 ports:Brute force approach:Position-to-Voltage conversionTo sense position (i.e., displacement), use a capacitive loadBrute force approach:Position-to-Voltage conversionTo shense position (i.e., displacement), use a capacitive loadVelocity-to-Voltage conversionTo convert velocity to a voltage, use a resitive loadProblems Wit