SENSORS Tutorials: November 3, 2013 Conference: November 4-6, Sponsored by the IEEE Sensors Council,

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1 Tutorials: November 3, 2013 Conference: November 4-6, 2013 Sponsored by the IEEE Sensors Council,

2 Source: Yole Développement, Inertial Sensors in Mobile Products, 2012

4 M. Judy, Proc. Solid-State Sensors, Actuators, and Microsystems Workshop, Hilton Head Island, SC, Jun Source: Yole Développement, MEMS Packaging sample report, 2012

Dixon-Warren, Chipworks Inc. Source: www.

5 The Evolution of Compact Three Axis Accelerometers, St.J. Dixon-Warren, Chipworks Inc. Source: Source: System Plus Consulting Reverse costing sample reports

6 LGM-118 Peacekeeper ICBM IMU

7 ma in = kx x a in = m k

8 g 0 dc dx = ε w t g 0 x ( ) 2 l dc dx = ε 2n t g 0 g 0 t: thickness, n: # of fingers

9 J. Chae, et. al., Journal of Microelectromechanical Systems, Vol. 14, No 2, Apr Electrode fixed to substrate Electrode fixed to mass

11 ΔC x S a x + a 2 x S x2 x + S y a y + S z a z + C 0 Scale Factor Non-linearity Cross-Axis Sensitivity Offset Parameter Units Expression Description Resonance Frequency Hz ω 0 = k m Free-vibration frequency of accelerometer Scale Factor F/(m/s 2 Linear term of the acceleration to ) SF 1 ε A elec capacitance change sensitivity ω 0 2 Quadratic non-linearity F/(m/s 2 ) 2 SF Quadratic term of the acceleration to 2 1 ε A elec capacitance change sensitivity ω 0 4 g 0 2 g 0 3 Brownian Noise (m/s 2 )/ Hz MNEA = 4k B T ω 0 Q m Mechanical noise equivalent acceleration Pull-in Voltage V V pi = 8ω m g 0 27ε A elec Voltage required to snap-down moving device to parallel Bandwidth Hz ω 3dB Q ω 0 Approximate 3 db Bandwidth in over-damped second-order system

12 m = ρ V = ρ ( h w l) k = C n E I l t 3 I = 1 12 b3 h h b ρ E I C n 48 C n 384 C n 36 l t h l w l t l t 2 l t 1 for: l t1 = 2 l t2

13 m d 2 x dt 2 + b dx dt + kx= ma in ω 0 = k m Q = km b X(s) A in (s) = 1 s 2 + ω 0 Q s +ω 2 0 ω << ω 0 X( jω) A in ( jω) 1 ω = m 2 0 k

14 1 Q = 1 Q SFD + 1 Q TED + 1 Q anchor Q material Q 1 Q SFD Plate ΔP Air flow Air flow x 2 P x + 2 P 2 y = 12μ eff 2 h 3 dh dt h: Gap size P: Pressure µ: Coefficient of viscosity

15 b μ eff l t 3 h 3 Q h 3 λ = μ P K s λ h 2k B T m Plate μ eff μ K s 1.159

17 Q = km b n elec b n elec μ eff h 3 l t3 3 n elec µ eff l t h Damping coefficient (Ns/m) Electrode area (um 2 ) Gap, Area Larger damping Gap size (nm)

18 SF = ΔC a in 1 ω 0 2 BW 3dB Q ω 0 ε A elec g 0 2 F elec 1 2 ε A elec 3 V 2 8 k g V pull in 0 2 g 0 27 ε n sens A elec t b = μ eff l 3 g 0 3 ( m ) (nn sens + n damp

20 Output Voltage (mv) Applied acceleration (g) Output Voltage (mv) Applied acceleration (g)

22 Z-AXIS GYRO Y-AXIS GYRO X-AXIS GYRO 3-AXIS ACCEL MUX Reference Capacitor DEMUX X Y Z

23 f 0 = 1 2π k m eff

24 f 0 = 1 2 2π k + Δk m eff

25 F elec = 1 2 C x V 2 = 1 2 ε A (g 0 x) 2 V 2 F elec 1 ε A V 2 1 ± g 0 g 0 g x g x2 ±... 0 F electot = F elec1 F elec2 F electot ε A g 0 V AC V P + 2 V P 2 g 0 V 2 x

26 m d 2 x dt 2 + b dx dt + kx= ma in + F electot Mechanical Transfer Function Input Electrostatic Acceleration Force ω TOT = k 2 ε A g V 2 3 P m g 0 a in m d 2 x dt + b dx 2 dt + k 2ε A g 3 2 V P x = ma in + ε A g V V 2 ac P ω TOT a in 3 2 ε A kω 0 g V 2 4 DC

27 TCF CTE α TCE f = 1 2π k m eff w ρ l 2 w = w 0 ( 1+α ΔT) l = l 0 ( 1+α ΔT) ρ = ρ 0 ( 1 3α ΔT) TCF α = 1 f 0 df dt α 2 f = 1 2π TCF TCE = 1 f 0 k m eff E df dt TCE 2 E = E 0 ( 1+TCE ΔT) TCF -30 ppm/ºc SF ppm/g

28 f = f 0 1+ NL2 EI Differential FM Accelerometer SF KHz SF KHz

29 Vac ain ΔC+ RF ΔC+ proof-mass Vac ΔCx ΔC- TIA RF ω 3dB Q ω 0 Q <1 V out ΔC 2 R F j jω ac VV ac Magnitude [db] ω3db ωac ω ac >> ω 3dB Frequency [rad/s]

30 Vcm CP1 CP2 ain proof-mass x CN1 CN2 CP1 CN1 CP2 CN2 Sampling Phase Amplifying Phase OTA OTA V out = 1 2 V DD C F C TOT (C TOT = C P1 C N1 + C P2 C N 2 )

32 dc dx = ε A g 0 x ( ) 2 Feedback electrodes F err x 0 y = F elec FB F ext FB = m a in FB

33 a test a ref Programing Interface

35 ain go go proof-mass ΔC Amp Vtest Felec proof-mass ΔC Amp x ΔC 1 ε A elec 2 2 a in ω 0 g 0 x ΔC 2 V test 1 2M ω 0 2 ( ε A elec ) 2 4 g 0 Change in Capacitance [F] Input Stimulus

36 Integrated Self-Test proof-mass Ccal CP1 CN1 SC-AMP

37 V out = 1 2 V DD C F (C P1 C N1 + C P2 C N 2 ) = 2V DD C F ΔC + V DD 2C F (C S.P1 C S.N1 + C S.P2 C S.N 2 )

38 C eq b C + b C + b C + b C 0 b0 1 b1 2 b2 3 b3 C t 2 (C b0 + C b1 + C b2 + C b3 )+ C t1 C t 2 + C t3 C t 4 CP1 CN1 proof-mass Ceq SC-AMP Ceq

39 V out = 2V DD C F ΔC + V DD 2C F C mismatch + 0.5V DD V cal C F C offset

40 S OUT F IN 1 FB + C OFF k α FB + C OFF k mod α FB

45 Tutorials: November 3, 2013 Conference: November 4-6, 2013 Sponsored by the IEEE Sensors Council,

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