EE 245: Introduction to MEMSLecture 23: Comb DriveCTN 11/12/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 38Typical Drive & Sense ConfigurationxyzEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 39Comb-Drive Force Equation (2ndPass)• In our 1stpass, we neglectedª Fringing fieldsª Parallel-plate capacitance between stator and rotorª Capacitance to the substrate• All of these capacitors must be included when evaluating the energy expression!StatorRotorGround PlaneEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 40• Finger displacement changes not only the capacitance between stator and rotor, but also between these structures and the ground plane → modifies the capacitive energyComb-Drive Force With Ground Plane Correction[Gary Fedder, Ph.D., UC Berkeley, 1994]EE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 41Capacitance Expressions• Case: Vr= VP= 0V• Cspdepends on whether or not fingers are engaged[Gary Fedder, Ph.D., UC Berkeley, 1994]Region 2Region 3Capacitance per unit lengthEE 245: Introduction to MEMSLecture 23: Comb DriveCTN 11/12/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 42• Finger displacement changes not only the capacitance between stator and rotor, but also between these structures and the ground plane → modifies the capacitive energyComb-Drive Force With Ground Plane Correction[Gary Fedder, Ph.D., UC Berkeley, 1994]EE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 43Simulate to Get Capacitors → Force• Below: 2D finite element simulation20-40% reduction of Fe,xEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 44Vertical Force (Levitation)• For Vr= 0V (as shown):()222,212121rsrsrrpsspzeVVdzdCVdzdCVdzdCzWF −++=∂′∂=()2,,21srsespzeVdzCCdNxF⎥⎦⎤⎢⎣⎡′+′=EE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 45Simulated Levitation Force• Below: simulated vertical force Fzvs. z at different VP’s [f/ Bill Tang Ph.D., UCB, 1990] ª See that Fzis roughly proportional to –z for z less than zo()()zzkzzzVFoeooPzz−=−≈2γ→ it’s like an electrical stiffness that adds to the mechanical stiffnessElectrical StiffnessEE 245: Introduction to MEMSLecture 23: Comb DriveCTN 11/12/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 46Vertical Resonance Frequency• Signs of electrical stiffnesses in MEMS:Comb (x-axis) → ke= 0Comb (z-axis) → ke> 0Parallel Plate → ke< 0zezzozkkk +=ωω2Vzkoze⎟⎟⎠⎞⎜⎜⎝⎛=γwhereωz/ωzoVertical resonance frequency at VP= 0VVertical resonance frequencyLateral resonance frequency=EE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 47Suppressing Levitation• Pattern ground plane polysilicon into differentially excited electrodes to minimize field lines terminating on top of comb• Penalty: x-axis force is reducedEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 48Force of Comb-Drive vs. Parallel-Plate• Comb drive (x-direction)ª V1= V2= VS= 1V• Differential Parallel-Plate (y-direction)ª V1= 0V, V2= 1VParallel-plate generates a much larger force; but at the cost of
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