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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
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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.
23-10-2012 NXP 5
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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.
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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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23-10-2012 NXP 14
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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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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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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