23-10-2012 NXP

MEMS resonator

Presentation by

Drs. Helger van Halewijn

1

Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan

MEMS resonator overview package

• Resonator size 500 x 700 x 150 micron • Single silicon on CMOS technology • High frequency stability, low time jitter, low temperature

drift. • Low motion damping Q-factor > 40000 (≈ 50 MHz)

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Overview of dogbone resonator

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actuation gap

anchor “mass ” of resonator

spring

3

Schematic of dogbone resonator

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Some parameters studied in COMSOL

• During production in waferfab all dimensions variations can influence the performance

• Q-factor, resonance stability 1. Dimensions resonator head 2. Anchor loss 3. Thickness Si 4. Oxidation layer 5. Air pressure (vacuum)\ 6. Thermal losses. 7. Viscous Drag 8. Electrostatic actuation+fringing 9. Mode coupling.

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Non linear resonance frequency

• Resonance frequency

1. k spring constant 2. m mass system 3. V driving voltage 4. w width 5. h height 6. g gap 23-10-2012 NXP

203

sin( ) DCel AC

DCres

V xF V tg

V whkfm mg

ηη ω

ε

= +

−=

6

Q-factor estimation

• Reciprocal addition.

• Anchor loss : Qanchor≈ 104 -107 dimension • Thermo-elastic loss Qte≈ 104-106 material • Surface loss: Qsur≈ 106-108 debris or cracks • Air damping: Qair≈ 102 – 107 vacuum quality, leakage • Viscous drag Qdrag ≈ 105-107 vacuum quality

• All seperate Q factors are estimated with COMSOL.

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1

1 1N

itot iQ Q=

=∑

7

Overview resonance mode at 56 MHz

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Acoustic loss at anchor.

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Acoustic loss: Gray domains, PML

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• Red arrows

indicate PML-layers.

• In PML complete acoustic absorption.

• Blue domains represent normal material properties.

• Eigenfrequency analyses.

Acoustic loss: dimensional variations in the structure.

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Capacitances

•Area of gate within green lines is 41084 μm2 (drain area excluded)

Fringe effects, from simple to real system

Simulated Cap = 338 fF

Dominated by drain bottom capacitance

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1. Simple hand calculation Drain C1 = 322 fF 2. Gate C2 = 1270 fF and Source C3 = 18700 fF 3. Capacitance C12=22.5 fF and C23=51 fF 4. Using mathematical formula

5. Cgate = 1264 fF 6. Comsol result is Cgate Comsol= 1266 fF OK 7. Csource and Cdrain have similar accuracies.

Calculation + Simulation Gate Capacitance

312

2312 111

CCC

CCCgate

++

++=

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Capacitance as function of resistivity

1. Results from Comsol 2. Including effects like air height and

substrates thickness 3. Resonator operates at 0.3 – 1.2 Ωcm (

equivalent to 80 – 330 S/m) 4. Capacitance variation is < 2% in resistivity

range 5. All simulations are performed with 56 MHz

Gate

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00

1.00E+01

1.00E+02

1.00E+03

1.00E+04

Conductance [S/m]

Cap

acita

nce

[F]

Y11 100 200Y11 100 300Y11 200 200Y11 200 300

Feedthrough Capacitance

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

Conductance [S/m]

Cap

acita

nce

[F]

Y11Y21 100 200Y11Y12 100 300Y11Y12 200 200Y11Y12 200 300

Drain

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04

Conductance [S/m]

Cap

acita

nce

[F]

Y22 100 200Y22 100 300Y22 200 200Y22 200 300

Asymmetric amplitude under electrical load (V bias)

• At 10 Volt, a harmonic behavior.

• At 80 Volt bias an inharmonic term can easily be seen.

• At 56 MHz, oscillation time is 40 nsec.

• COMSOL time step < 1 nsec

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Static stress due to process cycles

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Static stress at perifery due to curing procedures at various process conditions Stress concentrations in resonator legs.

•Ue 1.1 µm

•Ue 7.1 µm •Ue 13.1 µm

Q-factor of resonator under Stress

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0

50000

100000

150000

200000

250000

300000

0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05

Q fa

ctor

Underetch [μm]

Q-factor as function of Underetch and Stress

0 MPa 2.6 MPa 5.3 MPa 10.5 MPa 21.0 MPa 31.5 MPa

Thermal losses in resonator

• Q-factor can be written as:

• E = Youngs Modulus [Pa] • α = expansioncoefficient [1/m] • To = ambient temperature [K] • ρ = density [kg/m3] • ω = frequency [rad/s] • τ = thermal relaxation [s]

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2

2

11 ( )

o

therm p

E TQ C

α ωτρ ωτ

=+

Thermal losses in resonator

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Temperature fluctuations of about ±100C, at 56 MHz. This mechanism is due to material properties.

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Thickness Oxidation: Q factor and frequency shift

• Simulation with single layer.

• Mesh is adapted at layers lower than 20 nm.

• Minimum layer thickness 2.5 nm.

• In Comsol, Solid mechanics and shells are combined.

Q factor Straight resonator

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

0 10 20 30 40 50 60

SiO2 Layer thickness [nm]

Q fa

ctor

55000000

55200000

55400000

55600000

55800000

56000000

56200000

56400000

0 20 40 60

Freq

uenc

y [H

z]

SiO2 Layer thickness [nm]

Frequency Straight resonator

21

Squeezed film effect including stress

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1000

10000

100000

10 100 1000 10000 100000

Q-fa

ctor

Pressure [Pa]

Q-factor compared with measurements KIM

Q-factor 12nm

Q-factor 20nm

KIM

• Q > 40000 at appropriate conditions

• Sliding effect on large surface negligable

• Q-factor is slightly dependant on mesh size of the surface where the film damping is applied.

Overview: Influence of Polyamide Capping above resonator

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10,000

100,000

1,000,000

10,000,000

100,000,000

-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00 40.00 50.00Q

-fact

or

Frequency shift [ppm]

Q factor and Capping stress, Polyimide only

UnderEtch 5.4 [μm]

UnderEtch 1.4 [μm]

-10 MPa

-100 MPa

100 MPa

31 MPa

10MPa

Permanent frequency shifts: ≈ 20 ppm Well within specs.

Conclusion • Production steps in CMOS technlogy have their own

influence on the performance of the resonator. • COMSOL paved the way to better understanding to control

specs in production. (Q-factor, dimensions, stress and material loss factors)

• MEMS module was used together with the mechanical module. – Prestressed Analysis, eigenfrequency – Prestressed Analysis, frequency domain. – Heat module, Squeezed film and much more.

• Thanks to Dr. H van de Vlist (NXP, Nijmegen)

Dr. J. van Beek (NXP, Eindhoven) 23-10-2012

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