Transducers. Today: Electrostatic Capacitive. EEL5225: Principles of MEMS Transducers (Fall 2003) Instructor: Dr. Hui-Kai Xie

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1 EEL55: Principles of MEMS Transducers (Fall 3) Instructor: Dr. Hui-Kai Xie Last lecture Piezoresistive Pressure sensor Transducers Today: Electrostatic Capacitive Reading: Senturia, Chapter 6, pp EEL55: Principles of MEMS Transducers (Fall 3) Lecture by H.K. Xie 1/15/3

2 Electrostatic Transducer Sensor Actuator Advantages Capacitive Transducers Reciprocal sensor and actuator in same device Negligible temperature dependence High accuracy Challenges Small signal magnitude Effect of parasitic capacitance Potential undesired electrostatic actuation MEMS Applications accelerometers gyroscopes actuators voltage controlled capacitance EEL55: Principles of MEMS Transducers (Fall 3)

3 Capacitive Transducers Geometrical configurations Parallel plate ertical Parallel Anchor Interdigitated comb finger Transverse comb Longitudinal comb ertical comb 3 EEL55: Principles of MEMS Transducers (Fall 3)

4 Parallel Plate = movable plates plates of area S = fied plates 4 The capacitance can be epressed as: Ct EEL55: Principles of MEMS Transducers (Fall 3) 1 1 () 1 C 1, () t ε S ε S ε S t () t () = = = = ε S where C = is the capacitance at rest, : gap at rest, and (t): gap change.

5 Capacitive Transducers The voltage, t ( ), is related to the charge on the parallel plate of the capacitor, Qt ( ), through the capacitance, Ct ( ). Qt () Qt () t () t () = = 1 Ct () C t ( ) = "behavior at rest" + "electromechanical coupling" By first principles, we find the electrostatic force from potential energy stored in this capacitor: Q Q * 1 P P Q Q W = Qd = Cd = C = W = dq = dq = C C 5 EEL55: Principles of MEMS Transducers (Fall 3)

6 Charging Capacitor at Fied Gap Q Q Q Q Q WP = dq = dq = = C C ε S W * P Parallel Plate C Q C ε S = = = C Q Lifting up one electrode at Fied Charge WP Q W F(, Q) = = P = F( ) d ε S Electrostatic force: F E WP = F(, Q) = = Q ε S Note: Electrostatic force always tries to narrow the gap. F() +Q -Q F E () 6 EEL55: Principles of MEMS Transducers (Fall 3)

7 Parallel Plate Lifting up one electrode at Fied oltage W * (, ) = Q W( Q, ) dw * (, ) = Qd + dq dw ( Q, ) F() where dw ( Q, ) = dq + Fd F E () dw * (, ) = Qd F( ) d + W * (, ) F( ) = Electrostatic force: * WP 1 dc FE = F(, ) = = d Note: Electrostatic force always tries to narrow the gap. 7 EEL55: Principles of MEMS Transducers (Fall 3)

8 Parallel Plate C m =1/k movable plate = = fied plate The sum of the mechical and electrical forces is F = F + F = M E 8 EEL55: Principles of MEMS Transducers (Fall 3)

9 Electrostatic Spring Softening The electrostatic force opposes motion in the -direction as follows: F E ε ε ε = = + or 1 S S S 1 1 If << F E, FE FE, + = FE, or 9 F F = F + F = F + k E, total E M E, m FE, Ftotal FE, + km EEL55: Principles of MEMS Transducers (Fall 3) k e Electrostatic spring softening effect Equivalent electrostatic spring constant: F E, ε S = = 3

10 Pull-In ε S Fnet = FE + km = km ( ) Consider the effect of a small perturbation in the gap spacing, + δ, on the net force, δf: Fnet ε S δfnet = δ or δfnet = k 3 m δ δ F must oppose δ to avoid collapse (pull-in), net εs εs which requires: km > or k 3 m,min = 3 ε S Thus, Fnet = = km ma Then we obtain min = 3 ( ),min min 3 8k So, pull-in occurs at PI = at which PI = 3 7ε S 1 EEL55: Principles of MEMS Transducers (Fall 3) F M F E F E, Eample: = 1 um, C = 1 pf, E k = 1 N / m, =.54 PI

11 Capacitive Transducers Position Sensing ac input voltage parasitic electrostatic force capacitive divider need to match C r to C to minimize offset output proportional to i C S C r out Buffer The output of the capacitor divider is: - i Cs Cr Cs out = + ( ) = C + C C + C i i i s r s r εs C = sense capacitor= 1+ = + CS C C If C ref = C, then we have C = if 1. i out i i C + C + 11 EEL55: Principles of MEMS Transducers (Fall 3)

12 Capacitive Sensor Transverse comb Fleture Anchor Fied Plates Ref. Analog Devices ADXL-5 1 EEL55: Principles of MEMS Transducers (Fall 3)

13 Capacitive Sensor Transverse comb Thickness=t C s1 C s L where C and C are given by: S1 S ε Lt CS1 = N + C + ε Lt CS = N + C fringe fringe + 13 EEL55: Principles of MEMS Transducers (Fall 3)

14 Capacitive Sensor Transverse comb for sense For small displacements, C CS1 C = C CS C = + ε NLt where C = = C = + C C = sensitivity out i C fringe i out C s1 C s - i Differential Capacitive Bridge 14 EEL55: Principles of MEMS Transducers (Fall 3)

15 Transverse comb for actuation Differential force (=) F = F F 1 1 dc = d 1 ( ) ( ) Electrostatic Actuator C ( ) ( ) C = Differential force is proportional to voltage,. F 1 F F 15 EEL55: Principles of MEMS Transducers (Fall 3)

16 Electrostatic Actuator Electrostatic spring ( =) F 1 F d kel = ( F1 F) d d ε S 1 1 = d + C + = - Electrostatic Softening Effect 16 EEL55: Principles of MEMS Transducers (Fall 3)

17 Lateral comb Capacitive Transducers ε t( + ) C = d 1 ε t( + ) d W p = C = d W p ε t FE = = Note: non-linear with. d F No electrostatic E Note that the spring constant, k e = =! softening effect for longitudinal actuation! If = + sinωt dc ac εt εt F = + t = + t+ t d d εt = ( dc +.5ac + dcac sinωt.5ac cos ωt) d ( ) ( dc ac sin ω ) ( dc dc ac sinω ac sin ω ) Second harmonic 17 EEL55: Principles of MEMS Transducers (Fall 3)

18 ertical Comb X-ais sensing Z-ais sensing stator rotor stator C1 m+ z y C1 s C C m- m+ m- C1 = C (at zero displacement) C1 C (at zero displacement) 18 EEL55: Principles of MEMS Transducers (Fall 3)

19 ertical Comb Mawell D Field Simulation Capacitance (af/finger/mm) C1 C Normalized diff. capacitance C-C1 C+C1 Z (µm) Z (µm) C1 and C have high nonlinearity However, their normalized difference has wide linear range A large offset eists 19 EEL55: Principles of MEMS Transducers (Fall 3)

20 ertical Comb Wiring for -ais actuation But we can make wiring like this Fz Fz z y F F = 1 F dc d Total of 5 different combinations F z = 1 dc dz EEL55: Principles of MEMS Transducers (Fall 3)

21 ertical Comb C Z-ais spring z 1 C1 Z-ais comb Capacitance (af/µm) C C1 dc dz dc1 dz Z-ais displacement (µm) Capacitance gradient (af/µm ) Z-ais displacement (µm) Simulation Eperimental data Applied voltage, 1 () 1 EEL55: Principles of MEMS Transducers (Fall 3) H. Xie, et al, MSM, San Diego