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

Transcription

1 EE C45 - ME C18 Introduction to MEMS Design Fall 003 Roger Howe and Thara Srinivasan Lecture 11 Electrostatic Actuators II Today s Lecture Linear (vs. displacement) electrostatic actuation: vary overlap area: electrostatic comb drive Electrostatic springs: positive (comb levitation) Second-order effects in electrostatic actuators: charged dielectrics, work functions, depletion, and Casimir Reading: 1. W. C. Tang, M. G. Lim, and R. T. Howe, Electrostatic comb drive levitation and control method, Journal of Microelectromechanical Systems, 1, (199).. B. D. Jensen, S. Mutlu, S. Miller, K. Kurabayashi, and J. J. Allen, Shaped comb fingers for tailored electromechanical restoring force, Journal of Microelectromechanical Systems, 1, (003). 3. Kudrle, T. D., et al, Pull-in suppression and torque magnification in parallel plate electrostatic actuators with side electrodes, 1th Int. Conf. on Solid-State Sensors, Actuators, and Microsystems (Transducers 03), Boston, Mass., June 8-1, 003, pp

2 Interdigitated Comb Drive Common bias: DC offset V P connected to shuttle through poly0 ground plane William Tang, Ph.D. EECS Dept., 1990 (this device by Clark Nguyen, Ph.D. 1994) 3 Electrostatic Force: a First Pass* t g stator (fied electrode) rotor (not but moving) L gap = g, thickness = t L = finger length = overlap length W. C. Tang, Ph.D. EECS Dept.,

3 First-Pass Electrostatic Force (Cont.) Neglect fringing fields Parallel-plate capacitance between stator and rotor W (, V ) = q(, V ) dv = F e rs V rs 0 W = = 5 Comb Drive Force: a Second Pass Energy must include capacitance between the stator and rotor and the underlying ground plane, which is typically biased at the stator voltage V s why? t g L z o + - V s + - V r 6 3

4 Comb-Drive Force with Ground Plane Correction Finger displacement changes capacitances from stator and rotor to the ground plane modifies the electrostatic energy F e, W = = 1 dc d sp V s + 1 dc d rp V r + 1 dc d rs ( V V ) s r Gary Fedder, Ph.D., pp , Capacitance Epressions Consider case where V r = V p = 0 V C sp depends on whether or not fingers are engaged Gary Fedder, Ph.D., pp ,

5 Simulation (D Finite Element) Gary Fedder, Ph.D., p. 13, Vertical Force (Levitation) F e, z W = = z F e, z Consider V r = 0 V as shown: = W. C. Tang, JMEMS, 199 (reader) 10 5

6 Levitation Force electrical spring const. Fe, z ke( ze z) constant Levitation force adds to the mechanical spring constant in the z direction increases the resonant frequency Gary Fedder, Ph.D., p. 1, Vertical Resonant Frequency Must account for electrical springs in finding MEMS resonant frequencies comb (-ais) k e = 0 comb (z-ais) k e > 0 parallel plate k e < 0 W. C. Tang, JMEMS, 199 (reader) 1 6

7 Relative Forces for Surface Microstructures L gap = g = 1 µm, thickness = t = µm finger length = L =100 µm overlap length = 75 µm y V r = 0 V V 1 V Comb drive (-direction) (V 1 = V = V s = 1V) F e, = Differential plate (y-direction) (V 1 = 0 V, V = 1V) F e, y = 13 Levitation Suppression Pattern Poly 0 into differentially biased electrodes to minimize field lines terminating on top of comb Penalty: -ais force is reduced W. C. Tang, JMEMS, 199 (reader) 14 7

8 Eperimental Measurements Shuttle is pulled down (toward the substrate) with zero applied voltage Why? W. C. Tang, JMEMS, 199 (reader) 15 Charged Dielectrics: No Applied Voltage Needed! Minimize eposed dielectrics! Nitride charge inferred from deflection and simulated field distribution is consistent with typical values W. C. Tang, JMEMS, 199 (reader) 16 8

9 Work Function Differences Eample: p + structure over n + poly 0 electrode z p + poly-si n + poly-si Equilibrium band diagram How is charge echanged to reach equilibrium? Answer: 17 Depletion Effects in Silicon n type silicon (SOI structure) ρ() V qn d -X d g E() -X d g 18 9