Capacitive Sensor Interfaces Bernhard E. Boser Berkeley Sensor & Actuator Center Dept. of Electrical Engineering and Computer Sciences University of California, Berkeley Capacitive Sensor Interfaces 1996 B. Boser 1
Example: Vibratory Gyroscope Electrostatic Interfaces for: vibration (about z-axis) x/y-axis tilt x/y-axis force feedback x/y-axis frequency tuning quadrature error cancellation... Ref: T. Juneau et al., Micromachined Dual Input Axis Angular Rate Sensor, Solid-State Sensor and Actuator Workshop, Hilton Head, SC, June 1996. Capacitive Sensor Interfaces 1996 B. Boser
Outline Capacitor Basics MEMS Capacitor Configurations parallel plate transverse comb lateral comb Simulation Summary Capacitive Sensor Interfaces 1996 B. Boser 3
Capacitor Basics Definition: C = Q V Energy: E = 1 CV Force: F = E x = 1 C x V Spring Constant: k F = x Figure of Merit (for sensing): FM = C x C Capacitive Sensor Interfaces 1996 B. Boser 4
Capacitors in MEMS always present no special fabrication steps required must deal with in any case versatile sensor & actuator negligible temperature coefficient high accuracy: position measurements <.1Å demonstrated challenges small signals, parasitics undesired electrostatic actuation Capacitive Sensor Interfaces 1996 B. Boser 5
Outline Capacitor Basics MEMS Capacitor Configurations parallel plate transverse comb lateral comb Simulation Summary Capacitive Sensor Interfaces 1996 B. Boser 6
Parallel Plate Capacitor x V Area A x µm Ref: D. Young et al., A Micromachined Variable Capacitor for Monolithic Low-Noise VCOs, Solid-State Sensor and Actuator Workshop, Hilton Head, SC, June 1996. MEMS Applications accelerometers gyroscopes actuators varactor replacement Capacitive Sensor Interfaces 1996 B. Boser 7
Parallel Plate Capacitor (cont.) ε A Capacitance C = 14 ff x + x Sensitivity -14 ff/µm Force F= -18 µn Spring Constant k= 35 N/m Figure of Merit = -1µm -1 C C = x x + x 1 CV x + x CV ( x + x) 1 FM x + x Example (for x = 1 µm, A = (4 µm), V = 5 V (constant), ε = 8.85 af/µm) large capacitance & force (large area) nonlinear electrostatic spring Capacitive Sensor Interfaces 1996 B. Boser 8
Application: Position Sensing C s + V t sinω C s = ε A C C x + x x x x, C x = ( x << x ) V out C ref = C C ref V t sinω Buffer V out V C C ref FM x + signal C offset minimize offset: match C ref to C output proportional to x (x << x ) sense voltage V : parasitic force Capacitive Sensor Interfaces 1996 B. Boser 9
Matching C ref to C anchor parallel plate capacitor (top view) stiff suspension suspension sense capacitor C s reference capacitor C ref Ref.: W. Yun et al., Surface micromachined, digitally force-balanced accelerometer with integrated CMOS detection circuitry, Solid-State Sensor and Actuator Workshop, Hilton Head, 199, pp. 1-5. Capacitive Sensor Interfaces 1996 B. Boser 1
Pull-In Voltage x +x F el F mech = -k mech x V -k el /k mech 1 1/3 -x/x k xx + x F = F V = mech el mech ( ) C x k = k el mech x + x Capacitive Sensor Interfaces 1996 B. Boser 11
Pull-In Voltage (cont.) electrostatic force always positive, F el pull-in occurs when x x > 3 k el > k mech V > x km 3 15. C e.g. x = 1µm, C = 1pF, k m = 1N/m Æ V <.54 V to avoid pull-in Capacitive Sensor Interfaces 1996 B. Boser 1
Voltage versus Charge constant voltage constant charge V = const C C E = 1 CV E = 1 Q C F = 1 CV x + x F = 1 Q A ε k CV = ( x + x) force dependent on x (quadratic in V) k = force independent of x, no pull-in (quadratic in Q) Capacitive Sensor Interfaces 1996 B. Boser 13
Outline Capacitor Basics MEMS Capacitor Configurations parallel plate transverse comb lateral comb Simulation Summary Capacitive Sensor Interfaces 1996 B. Boser 14
Transverse Comb flexture anchor Fixed Plates N Unit Cells Ref: Analog Devices ADXL-5 Capacitive Sensor Interfaces 1996 B. Boser 15
Transverse Comb (cont.) N movable fingers x L C s1 C s A A t x +x A Anchor A x = C s1 = ε N x Lt + x + C fringe x > C s = ε N x Lt x + C fringe Capacitive Sensor Interfaces 1996 B. Boser 16
Transverse Comb (cont.) C C s1 x= C x x C = C + s x= C x x ε NLt x C C x Capacitance C x= = + C fringe 15 ff C x Sensitivity 15 ff/µm fringe Figure of Merit 1.8µm -1 1 C FM x C Example for x = 1 µm, L = 15 µm, t = µm, N = 4, V = 5 V (constant), C fringe /C =. Capacitive Sensor Interfaces 1996 B. Boser 17
Differential Force (x=) F 1 C s1 F C s x= +V V x -V F = F F 1 C 1 x V V x V + V x! CVV x x " $ # e.g. F/V x = 1.5µN/V for V = 5V, C = 15fF, x = 1µm linear voltage-force relationship Capacitive Sensor Interfaces 1996 B. Boser 18
Electrostatic Spring (V x = ) x k el = d dx F ( F ) 1 F 1 F C s1 C s = d dx ε AV 1 1 ( x + x) ( x x) +V V x = -V CV x << x x e.g. k el = -.1 N/m for V = 1V, C = 1fF, x = 1µm Capacitive Sensor Interfaces 1996 B. Boser 19
Resonant Frequency Shift linear second order mechanical system: ω r = = k m k mech + k m el e.g. ω = 5 krad/sec m =.1 µg k mech = m ω =.5 N/m k el = -.1 N/m = ω + 1 k k el mech ω r /ω =.78 substantially reduced resonance negative ω r possible Capacitive Sensor Interfaces 1996 B. Boser
Differential Position Sensing C s1 + V t sinω V out V out C V x x = V FM x C C s V t sinω Buffer V out /x = V o x FM = 4V/µm = 4µV/Å output proportional to x for x << x sense force almost canceled: F 1 F Capacitive Sensor Interfaces 1996 B. Boser 1
Outline Capacitor Basics MEMS Capacitor Configurations parallel plate transverse comb lateral comb Simulation Summary Capacitive Sensor Interfaces 1996 B. Boser
Lateral Comb lateral comb drive resonator Ref.: W. Tang, Electrostatic comb drive for resonant sensor and actuator applications, Ph.D. Thesis, UC Berkeley, EECS, 199. Capacitive Sensor Interfaces 1996 B. Boser 3
Lateral Comb Geometry rotor (movable) C p top view C x x stator (anchored) cross-section t d x Capacitive Sensor Interfaces 1996 B. Boser 4
Capacitance per Finger = x Mutual Capacitance: ( + ) ε C = N tx x d + NC, p parasitic Capacitive Sensor Interfaces 1996 B. Boser 5
Lateral Comb ε C N tx + = x ( ) d C ε N t x d N t = 1 ε d [ + C p ] Capacitance 9 ff Sensitivity 1.8 ff/µm Force F V fn Spring Constant k= 1 FM x + x Figure of Merit.µm -1 Example (for x = 5 µm, t = µm, d = 1 µm, N = 1, V = 5V, C p = ) Capacitive Sensor Interfaces 1996 B. Boser 6
Lateral Comb Characteristics linear: C proportional to x no electrostatic spring main application: linear forcer, e.g. in resonator (use differential setup to cancel nonlinearity in voltage) challenges: parasitics introduce nonlinearity poor sensitivity dc/dx small forces for standard supply voltages (5V) Capacitive Sensor Interfaces 1996 B. Boser 7
Exact Analysis of Lateral Force W.A. Johnson et al., Electrophysics of Micromechanical Comb Actuators, IEEE J. Electromech. Systems, pp. 49-59, March 1995. (includes fringing field effects) G. Fedder, Simulation of Microelectromechanical Systems, Ph.D. thesis, UC Berkeley, EECS, 1994. Capacitive Sensor Interfaces 1996 B. Boser 8
Levitation Effects F z Ref: W. Tang, Electrostatic Comb Drive for Resonant Sensor and Actuator Applications, Ph.D. thesis, UC Berkeley, EECS, 199. Capacitive Sensor Interfaces 1996 B. Boser 9
Levitation Force Capacitive Sensor Interfaces 1996 B. Boser 3
Levitation Suppression sliced ground-plane reduces levitation force by order-of-magnitude Capacitive Sensor Interfaces 1996 B. Boser 31
Lateral Comb Resonator Ref: C. Nguyen, Micromechanical Signal Processors, Ph.D. thesis, UC Berkeley, EECS, 1994. Capacitive Sensor Interfaces 1996 B. Boser 3
Electrostatic Solvers: Fastcap Simulation http://rle-vlsi.mit.edu/projects.html Maxwell Ansoft, Pittsburgh, Pennsylvania, 1991. General Text Systems, H. H. Woodsen and J. R. Melcher: Electromechanical Dynamics, Part I: Discrete R. E. Krieger Publishing, Malabar, Florida 395, 199. Reprinted from J. Wiley edition of 1968. Self-Consistent Electromechanical Simulation: Simultaneous solution of electrostatic and mechanical equations required for large displacements x: MEMCAD. http://www-mems.mit.edu/groups/senturiagroup.html Capacitive Sensor Interfaces 1996 B. Boser 34
Fastcap Example: Transverse Comb x V sense C s-sub C sense V pm C 1 C fb proof mass V pm C f-sub V fb substrate GND feedback tines V fb sense tines V sense Capacitive Sensor Interfaces 1996 B. Boser 35
Boundary Element (BEM) Generation cubegen -n1 -xo -yo -zo -xh4 -yh115 -zh -natine_pm > tine_pm.qui cubegen -n1 -xo -yo -zo -xh4 -yh144 -zh -natine_sense > tine_sense.qui cubegen -n1 -xo -yo -zo -xh4 -yh14 -zh -natine_drive > tine_drive.qui cubegen -n1 -xo -yo -zo -xh8 -yh1 -zh -naendtine > endtine.qui cubegen -n1 -xo -yo -zo -xh34 -yh -zh -naproofmass > proofmass.qui capgen -p1 -n -w45 -nasubstrate > subst.qui Capacitive Sensor Interfaces 1996 B. Boser 36
BEM Assembly * PROOF MASS C tine_pm.qui 1. + C tine_pm.qui 1 15. + C tine_pm.qui 1 3. + C proofmass.qui 1. -19.99 * * SENSE TINES C tine_sense.qui 1 1 5 + C tine_sense.qui 1 5 5 + C endtine.qui 1 1 148.99 + C endtine.qui 1 5 148.99 * * FEEDBACK TINES C tine_drive.qui 1 5 5 + C tine_drive.qui 1 5 + C endtine.qui 1 1 18.99 + C endtine.qui 1 16 18.99 * * SUBSTRATE C subst.qui 1-5.5 - -1.6 + C subst.qui 1-5.5 5-1.6 + C subst.qui 1-5.5 7-1.6 File lsensor_..bem x =. µm (one file for each x) Capacitive Sensor Interfaces 1996 B. Boser 37
Run Fastcap One simulation run for each x = -.5µm to +.5µm: fastcap -lsensor_-.5.bem > out-.5 fastcap -lsensor_-.4.bem > out-.4 fastcap -lsensor_-.3.bem > out-.3 fastcap -lsensor_-..bem > out-. fastcap -lsensor_-.1.bem > out-.1 fastcap -lsensor_..bem > out. fastcap -lsensor_.1.bem > out.1 fastcap -lsensor_..bem > out. fastcap -lsensor_.3.bem > out.3 fastcap -lsensor_.4.bem > out.4 fastcap -lsensor_.5.bem > out.5 Capacitive Sensor Interfaces 1996 B. Boser 38
Fastcap Output out. ( x =.µm) Running fastcap. (15Jul9) Input: sensor_-..lst Input surfaces: GROUP1 tine_pm.qui, conductor title: `4mX115mXm cube (n=1 e=.1)' outer permittivity: 1 number of panels: 174 number of extra evaluation points: translation: (. ) tine_pm.qui, conductor title: `4mX115mXm C s-sub 5.986fF C f-sub 6.63fF C sense 6.6fF V pm C fb 5.548fF V sense C 1 7.71fF V fb CAPACITANCE MATRIX, femtofarads V pm V sense V fb GND V pm 8.81-6.6-5.548-16.54 V sense -6.6 19.9-7.71-5.896 V fb -5.548-7.71 19.9-6.63 GND -16.54-5.896-6.63 3.58 Capacitive Sensor Interfaces 1996 B. Boser 39
BEM Analysis Summary (Matlab) C 1 Capacitnace [ff] C s-sub (levitation!) C sense C sense 41. ff / µ m x Proof Mass Displacement x [µm] Capacitive Sensor Interfaces 1996 B. Boser 4
Summary capacitive interfaces: position sensing electrostatic forcer interface types: parallel plate: large C, negative spring, asymmetric transverse comb: symmetric, good position sense, ω r tuning lateral comb: linear forcer, small dc/dx Capacitive Sensor Interfaces 1996 B. Boser 41