EE C245 - ME C218 Introduction to MEMS Design Fall Today s Lecture

Transcription

1 EE C45 ME C18 Introduction to MEMS Desin all 3 Roer Howe and Thara Srinivasan Lecture 1 Electrostatic Actuators I Today s Lecture Enery in electromechanical systems define carefully Parallelplate electrostatic actuators: snapdown Why is electrostatic actuation important in MEMS? Linearization of the squarelaw electrostatic force: differential electrostatic actuation Readin: Senturia, S. D., Microsystem Desin, Kluwer Academic Publishers, 1, Chapter 6, pp

2 Basic Physics of Electrostatic Actuation Two ways to chane the enery: e e q q 1. Chane the chare q. Chane the separation x W(q,) q e Note: we assume that the plates are supported elastically, so they don t collapse. H. H. Woodsen and J. R. Melcher, Electromehcanical Dynamics Part I, Chapter 3, Wiley, ChareControl Case Stored enery: work done in increasin ap after charin capacitor at zero ap W d e Electrostatic force as a function chare ρ(x) E(x) q q W(q,) x x 4

3 ChareControl Case (Cont.) Stored enery: q q W d εa εa constant orce (attractive, internal): oltae: 5 oltaecontrol Case Practical situation: we control (since charecontrol on the typical subp MEMS actuation capacitor is a major challene for electronics desiners) Can we find e as a partial derivative of the stored enery W W(,) with respect to with held constant? No! Answer: apply Leendre transformation and define the coenery W (,) W (, ) q W 6 3

4 oltaecontrol Case (Cont.) Evaluate the coenery: W q(, ) d W (,) oltae in terms of chare at ap: 7 Electrostatic orce (oltae Control) ind coenery in terms of voltae W q(, ) d ariation of coenery with respect to ap yields e.s. force: W (, ) e ariation of coenery with respect to voltae yields chare: W (, ) q 8 4

5 5 9 SprinSuspended Capacitor: ChareControl Case q q e k z q e q W ), ( e kz 1 SprinSuspended Capacitor: oltaecontrol Case 1 ), ( A W q e ε e kz q q e k z k z e o o /

6 Stability Analysis Rane of stability: examine net (attractive) force on plate εa net k ( ) o If we increment the ap by d, the increment d net > or the plate collapses d net net d 11 PullIn oltae PI Solve for point at which plate oes unstable: εa k PI 3 PI net εapi PI Substitution for k leads to: k( o PI ) net 1 6

7 Graphical Solution for Plate Stability Plot normalized electrostatic and sprin forces vs. normalized displacement 1(/ o ) 1.8 forces displacement 13 So Why are Electrostatic Actuators Important in MEMS, Anyway? Easy to make in micromachinin processes, since conductors and air aps are all that s needed Eneryconservin only parasitic enery loss throuh i R losses in conductors and interconnects Pullin phenomenon can be exploited to make a hysteretic actuator simplifies control Multiple plate structures (combs, 3D) can be used to tailor the force(displacement,voltae) function Scalin of the electrostatic force is favorable due to Paschen s curve Same structure can be used for position sensin 14 7

8 Paschen s Curve Air, o C vacuum limit: field emission at E 1 /nm 1 /µm 15 Linearizin the oltae SquareLaw Polarize the capacitor by applyin a DC offset voltae P toether with a (small) sinal voltae v si (t) << P q(t) e (t) q(t) 1 C 1 C e v ( P v si ( t)) v(t) P v si (t) 16 8

9 The Differential Electrostatic Actuator q l (t) q(t) el (t) er (t) q r (t) Net force on suspended center electrode is the difference net er (t) el (t) v L (t) P v(t) v R (t) P v(t) 17 SecondOrder Effects Assumption was that the aps were both correct only if the fabrication technoloy is perfect and the movin electrode is stationary Allow for ap difference: residual DC and v are present Is there a way to ensure linearization? 18 9

10 Pulse Linearization Applied voltae is limited to discrete levels (e.., 1 and 3 ) applied at a clock rate much hiher than the mechanical resonant frequency The electrostatic force is either zero or a value that is precisely set by the capacitance and the voltae The density of pulses determines the force, with the system bandwidth filterin out the hih frequency components EE: simadelta feedback ME: banban control 19 1