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, 170-178 (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, 373-383 (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. 360-363. 1
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., 1990 4
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
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. 119-1, 1994 7 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. 119-1, 1994 8 4
Simulation (D Finite Element) Gary Fedder, Ph.D., p. 13, 1994 9 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
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, 1994 11 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
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
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
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