16313 Halewijn Presentation

7/28/2019 16313 Halewijn Presentation

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23-10-2012 NXP

MEMS resonator

Presentation by

Drs. Helger van Halewijn

1

Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan


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MEMS resonator overview package

Resonatorsize500x700x150micron

SinglesilicononCMOStechnology

Highfrequencystability,lowtimejitter,lowtemperaturedrift.

LowmotiondampingQ-factor>40000(50MHz)

23-10-2012

NXP2


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Overview of dogbone resonator

23-10-2012 NXP

actuationgap

anchormass ofresonator

spring

3


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Schematic of dogbone resonator

23-10-2012 NXP 4


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Some parameters studied in COMSOL Duringproductioninwaferfaballdimensionsvariationscaninfluencetheperformance

Q-factor,resonancestability1. Dimensionsresonatorhead

2. Anchorloss3. ThicknessSi

4. Oxidationlayer

5. Airpressure(vacuum)\

6. Thermallosses.

7. ViscousDrag

8. Electrostaticactuation+fringing

9. Modecoupling.

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Non linear resonance frequency Resonancefrequency

1. kspringconstant

2. mmasssystem

3. Vdrivingvoltage

4. wwidth

5. hheight

6. ggap

23-10-2012 NXP

2

03

sin( ) DCel AC

DC

res

V xF V t

g

V whk

f m mg

= +

=

6


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Q-factor estimation Reciprocaladdition.

Anchorloss:Qanchor104-107dimension Thermo-elasticlossQte10

4-106material

Surfaceloss:Qsur106-108debrisorcracks

Airdamping:Qair102107vacuumquality,leakage

ViscousdragQdrag105-107vacuumquality

AllseperateQfactorsareestimatedwithCOMSOL.

23-10-2012 NXP

1

1 1N

itot iQ Q=

=

7


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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 arrowsindicate PML-layers. In PML completeacousticabsorption. Blue domainsrepresent normalmaterial properties. Eigenfrequencyanalyses.


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Acoustic loss: dimensionalvariations in the structure.

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23-10-2012 NXP 12

Capacitances

Areaofgatewithingreenlinesis41084m2(drainareaexcluded)


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Fringe effects, from simple to real system

SimulatedCap

=338fF

Dominatedby

drainbottom

capacitance

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1. Simple hand calculation Drain C1 = 322 fF2. Gate C2 = 1270 fF and Source C3 = 18700 fF3. Capacitance C12=22.5 fF and C23=51 fF4. Using mathematical formula

. Cgate = 1264 fF6. Comsol result is Cgate Comsol= 1266 fF OK7. Csource and Cdrain have similar accuracies.

Calculation + Simulation Gate Capacitance

312

2312 11

1

CCC

CCCgate

+

+

++=


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23-10-2012 NXP15

Capacitance as function of resistivity

1. ResultsfromComsol

2. Includingeffectslikeairheightandsubstratesthickness

3. Resonatoroperatesat0.31.2cm(

equivalentto80330S/m)4. Capacitancevariationis


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Asymmetric amplitude underelectrical load (V bias)

At10Volt,aharmonic

behavior.

At80Voltbiasan

inharmonictermcaneasilybeseen.

At56MHz,oscillation

timeis40nsec.

COMSOLtimestep


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Static stressdue to process cycles

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17

Staticstressatperiferyduetocuring

proceduresatvariousprocessconditions

Stressconcentrationsinresonatorlegs.

Ue 1.1 m

Ue 7.1 m Ue 13.1 m


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Q-factor of resonator under Stress

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18

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

Qf

acto

r

Underetch [m]

Q-factor as funct ion of Underetch and Stress

0 MPa

2.6 MPa

5.3 MPa

10.5 MPa

21.0 MPa

31.5 MPa


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Thermal losses in resonator

Q-factorcanbewrittenas:

E=YoungsModulus[Pa]

=expansioncoefficient[1/m]

To=ambienttemperature[K]

=density[kg/m3]

=frequency[rad/s]

=thermalrelaxation[s]

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2

2

1

1 ( )

o

therm p

E T

Q C

=+


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Thermal losses in resonator

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Temperaturefluctuations ofabout 100C, at56 MHz.This mechanismis due to materialproperties.


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23-10-2012NXP

Thickness Oxidation: Q factor and frequency shift Simulationwithsingle

layer.

Meshisadaptedatlayerslowerthan20

nm.

Minimumlayer

thickness2.5nm.

InComsol,Solid

mechanicsandshells

arecombined.

Q factor Straight resonator

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

0 10 20 30 40 50 60

SiO2 Layer thickness [nm]

Qf

actor

55000000

55200000

55400000

55600000

55800000

56000000

56200000

56400000

0 20 40 60

Frequency

[Hz]

SiO2 Layer thickness [nm]

Frequency Straight reso nator

21


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Squeezed film effect including stress

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1000

10000

100000

10 100 1000 10000 100000

Q-factor

Pressure [Pa]

Q-factor compared with

measurements KIM

Q-factor 12nm

Q-factor 20nm

KIM

Q > 40000 atappropriateconditions Sliding effect onlarge surfacenegligable Q-factor is slightlydependant on meshsize of the surfacewhere the filmdamping is applied.


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Overview: Influence of Polyamide Cappingabove 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 50.00

Q-factor

Frequency shift [ppm]

Q factor and Capping stress, Polyimide only

UnderEtch 5.4 [m]

UnderEtch 1.4 [m]

-10 MPa

-100 MPa

100 MPa

31 MPa

10MPa

Permanent frequency shifts: 20 ppmWell within specs.


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Conclusion ProductionstepsinCMOStechnlogyhavetheirown

influenceontheperformanceoftheresonator.

COMSOLpavedthewaytobetterunderstandingtocontrol

specsinproduction.(Q-factor,dimensions,stressand

materiallossfactors)

MEMSmodulewasusedtogetherwiththemechanical

module.

PrestressedAnalysis,eigenfrequency

PrestressedAnalysis,frequencydomain.

Heatmodule,Squeezedfilmandmuchmore.

ThankstoDr.HvandeVlist(NXP,Nijmegen)

Dr.J.vanBeek(NXP,Eindhoven)

23-10-2012NXP

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16313 Halewijn Presentation