1、 MEMS和微系统设计课程内容n MEMS概述及 MEMS设计的概述n 工艺简要回顾n 系统设计、工艺设计及版图设计n 主要的机械、电子元件及其设计基础n 多域耦合设计：以机电耦合为例子n 器件性能的估计n 简单的其他域的元件及其简要设计要点n 设计实例 第 4讲主要内容 (3)1、弹簧设计原理及计算例子2、薄膜设计原理及计算例子3、电容设计原理及计算例子4、电阻设计原理及计算例子5、压电模型n电容变化n静电力图 2-17电容式微传感器的基本结构 平行板电容器的电容为电容敏感原理 式中A为极板面积为真空介电常数 为极板间介质的相对介电常数当介质为空气时， ； 为两极板间距离间隙变化型：改变两极
2、板间隙面积变化型：改变形成电容的有效面积 A介质变化型：改变两极间介质的介电常数间隙变化型电容式微传感器利用泰勒级数展开，由麦克劳林公式可得 略除高阶无穷小项，得这时传感器的灵敏度和非线性误差分别为：采用差动电容结构可以大大减小传感器输出的非线性 ： (2-12)(2-13) (2-14)(2-15)在小位移情况下，外加作用和成比例关系，可见电容的倒数差及电容的差除和都与输入作用力成线性关系。式 (2-14)表明，用电容的差除和表达传感器的性能，其输出还要受到介质介电常数的影响。式 (2-15)表明电容差除和只受电容极板间隙和间隙变化的影响。目前，硅电容变送器普遍采取式 (2-15)的方法来描
3、述传感器的性能。其他的电容变化形式n 变面积电容器A example: calculate to C and the shift of C两种电容变化形式的变化量对比（电容原值、导线的电容值、电容变化值）Wire： L=1m, r=0.2mm, d=1mmgap=g=1Thickness=t=2finger length=L=100overlap length x=75电容 readout 位置检测和速度检测Why modulate v(t)?Ideal buffer: cin=0Matched Air-Gap Reference Capacitors Simple Capacitor Div
4、ider (con.)matched air-gap reference capacitoroffset signalCapacitor Divider With Differential ExcitationWhy modulate v+ and v- ?Ideal buffer: cin=0Impedance divider with superposition:Improved Capacitive Divider (cont.)no offset! distortionThe capacitive Half -BridgeImpedance divider with superposi
5、tion:The capacitive Half Bridge (cont.)Simplify expression:No offset， 2x signal increaseParasitic CapacitancesSurface micromachined z-axis parallel-plate capacitorEquivalent circuitCpp (x): nominal | plate sense capacitorCf1 (x): fringe capacitance (varies with plate displacement)Cf2 :fringe capacit
6、ance between upper plate (connected to anchor plane) and lower plate slight dependence on xCpu :parasitic capacitance from upper plate to substrate Cpl : parasitic capacitance from lower plate to substrate Velocity SensingFundamental current-voltage relationship for a time-varying capacitor:Consider
7、 special case: v=vp =constantused in high-quality capacitance microphonesVelocity Sensing (cont.)Sense capacitors time variation:Parallel-plate sense capacitor with gap go :Harmonic motion:Some NumbersSurface micromachined capacitor: Is this real?noise in buffer ampWorld Record CapacitivePosition-Se
8、nse Resolution*Analog Devices ADRS-150 vibratory rate gyroscope John Geen ,Steve Sherman, John Chang, and Steve Lewis, IEEE J. Solid-State Circuits, 37, Dec. 2002, 1860-1866Full scale Corillis-induced displacement=20Sense capacitance 1000fFMinimum detectable capacitance change 12 zF =0.012 aFNominal
9、 sense gap = 1.6 m Minimum displacement: 16 fm !* Surface micromachining class audio frequency band EE C245-ME C218 Fall 2003 Lecture 12Is ADL Splitting Electrons?At V+ =5V, the charge on the sense capacitor is:qs =c+ v+ =(1000fF)(5V)=5000fCNumber of electrons at Minimum detectable change in sense c
10、harge:Minimum detected change in number of electrons:n电容变化n静电力变间隙电容驱动器的基本理论Basic physics of Electrostatic ActuationTwo ways to change the energy:1.Change the charge q2.change the separation xNote: we assume that the plates are supported elastically ,so they dont collapse . Charge-Control Case (cont.)Stored energy:Force (attractive ,internal):Voltage:Independent of the gap!constantElectrostatic Force (Voltage Control)Find co-energy in terms of voltageVariation of co-energy with respect to gap yields v.s. force:Variation of co-energy with respect to voltage yields chargeas expected
