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Sponsored byThe Institute of Electrical and Electronics Engineers (IEEE)Ultrasonics, Ferroelectrics and Frequency Control (UFFC) Society
U
2005-2006 International Distinguished Lecturer Program
Ken-ya HashimotoChiba University
Simulation of Surface Acoustic Wave Devices
Current Status and Future Prospects
Ken-ya HashimotoChiba University
[email protected]://www.em.eng.chiba-u.jp/~ken
SAW Device SimulationSAW Device Simulation! Background! COM analysis for rapid simulation! FEM/SDA analysis for parameter determination! Correction for SH-SAW simulation! Transverse-mode analysis! FEM/BEM analysis for precise simulation! Summary and remaining problems
SAW Device SimulationSAW Device Simulation! Background!!! COM analysis for rapid simulationCOM analysis for rapid simulationCOM analysis for rapid simulation!!! FEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determination!!! Correction for SHCorrection for SHCorrection for SH---SAW simulationSAW simulationSAW simulation!!! TransverseTransverseTransverse---mode analysismode analysismode analysis!!! FEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulation!!! Summary and remaining problemsSummary and remaining problemsSummary and remaining problems
Surface Acoustic WaveSurface Acoustic WaveBulk Acoustic Wave (BAW):•Longitudinal Wave (Primary Wave)
•Transverse Wave (Share Wave, Secondary Wave)
Surface Acoustic Wave (SAW):
(Rayleigh SAW)Propagation of
Seismological Waves
Vout
Vin
Piezoelectric substrate
Interdigital Transducers (IDT)
SAW
! Mass-Production by Photolithography! Low-loss, Small-Size & Low Price! Operation in VHF-UHF Range
Line width λ/4=0.5µm (f=2GHz)
SAW Transversal FiltersSAW Transversal Filters
W
wL1=N1pI
wLT
IDT-1 IDT-2
x t
pI
(a) surface deformation (b) SAW propagation
τI
pI pI pI pI pI pI pI pI pI
L2=N2pI
Delta Function ModelDelta Function Model
2/1ˆ −= ii NN
Delta Function Model Analysis
Coupling-of-Modes Analysis
Reference: Influence of Internal Reflection
Surface Acoustic Wave (SAW) Resonator
inV
Piezoelectric substrate
Interdigital Transducer (IDT)
Grating (Bragg) Reflectors
"It seems well-developed. Why further research necessary?"
System designers need devices with zero insertion loss, zero TCF, 100dB out-of-band rejection, 200%
bandwidth, one day delivery, and price minimization.
Why Fast & Precise Simulators Needed?Why Fast & Precise Simulators Needed?
! Improving Production Yields
Current Computers with Mass Memories are! Low Price, Maintenance Free, Space Saving! Working 365 days with 24 hours
! No Friction with Workers Union
! Better Understanding of Underlying Physics! Reducing Number of Trials
! Meaningful Optimal Design
What are Necessary for Simulators?What are Necessary for Simulators?
! Improving Production Yields
! Better Understanding of Underlying Physics! Reducing Number of Trials
! Meaningful Optimal Design
AccuracyAccuracySpeed
For Speedy Simulation
For Accurate Simulation
Behavior-Model Based Simulation
Full Wave Simulation
Practical Simulation ProcedurePractical Simulation Procedure
Pseudo 2D Simulation of Whole Structure
Pseudo 3D Simulation of Whole Structure
Simulation of Package Characteristics by Commercial Tools
Derivation of Simulation Parameters by 2D (X-Z)
Simulation
Derivation of Simulation Parameters by 2D (X-Y)
Simulation
3D Full Wave Simulation is not Realistic
Simulation Including Package Influence
1nH ( ≈ gold wire of 1mm length)
6Ω/mm @ 1GHz
1pF ( ≈ 1mm×1mm pad on LiNbO3 substrate)
150Ω/mm2 @ 1GHz
Influence of parasitic impedances is significant in GHz range!
SAW Device SimulationSAW Device Simulation!!! BackgroundBackgroundBackground! COM analysis for rapid simulation!!! FEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determination!!! Correction for SHCorrection for SHCorrection for SH---SAW simulationSAW simulationSAW simulation!!! TransverseTransverseTransverse---mode analysismode analysismode analysis!!! FEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulation!!! Summary and remaining problemsSummary and remaining problemsSummary and remaining problems
Pseudo 2D Simulation of SAWRPseudo 2D Simulation of SAWR
inV
Piezoelectric substrate
Interdigital Transducer (IDT)
Grating (Bragg) Reflectors
! Combination of Periodic Structures! Wide Aperture
Accurate Simulation by 1-D Model
! Equivalent Circuit Analysis! Coupling-of-Mode (COM) Analysis! p-Matrix Analysis (Hybrid Scattering Matrix)
Modeling of Element (IDT)Modeling of Element (IDT)
! Number of Independent Parameters! Simple to Use! Easy to Extend! Many Articles
Compatible (Basically Equivalent)
U-
U+
V0
δI
U++δU+
U-+δU-
COM Equation for Periodic StructureCOM Equation for Periodic Structureβu: Wavenumber(Unperturbed)κ : Reflection Coef.ζ : Transduction Coef.θu=βu-2π/pI
pI: IDT Period
044 CVjUjUjxI
VjUjUjx
U
VjUjUjx
U
u
u
ωζζ
ζθκ
ζκθ
+−−=∂∂
−++=∂
∂
+−−=∂
∂
−+
−+−
−++ Propagation
Reflection
DetectionCapacitance
Excitation
00
00
)exp()exp()()exp()exp()(
VXjAXjAXUVXjAXjAXU
pp
pp
ξθθξθθ
+++−Γ=
++Γ+−=
−+−
−++
General Solution
where θp=(θu2-κ2)0.5, Γ0=(θp-θu)/κ, ξ=ζ/(θu+κ)
dXCVjUUjdXXXII
L
L
L
L
])(4[)(0
2/
2/
2/
2/
*0 ωζζ ++−=
∂∂= −+
+
−
+
−∫ ∫
Total Current Input
L: IDT Length
[P]
V0
U+(0)U-(0)
−−=
−
+
+
−
0332313
232221
131211
0
)()0(
44)()0(
VLU
U
PPPPPPPPP
ILU
U
U+(L)U-(L)
I0
P-Matrix Expression
Reflector ReflectorIDTGap(ϕ) Gap (ϕ)
Cascade-ConnectionCascade-Connection
VinIin
Short-Circuited Grating = Short-Circuited IDT
IDT Modeling Modeling of Whole Structure
Open-Circuited Grating = Open-Circuited IDT
Gap = IDT without reflection & Excitation
SAW Device SimulationSAW Device Simulation!!! BackgroundBackgroundBackground!!! COM analysis for rapid simulationCOM analysis for rapid simulationCOM analysis for rapid simulation! FEM/SDA analysis for parameter determination!!! Correction for SHCorrection for SHCorrection for SH---SAW simulationSAW simulationSAW simulation!!! TransverseTransverseTransverse---mode analysismode analysismode analysis!!! FEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulation!!! Summary and remaining problemsSummary and remaining problemsSummary and remaining problems
3800381038203830384038503860387038803890
0 0.05 0.1 0.15 0.2Relative Al Thickness h/λ
SAW
Vel
ocity
(m/s
)
SAW velocity on Al/128oYX-LiNbO3
Complex variation at very thin film thickness
No guarantee of rapid convergence for perturbation analysis
Full Wave Analysis for Infinite Grating! Perturbation or Functional Method ⇔
inaccurate (?)! Boundary Element Method (BEM) ⇔
complex for Green function calculation! Finite Element Method (FEM) ⇔
slow convergence (?)
11.021.041.061.081.1
1.121.141.16
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Inverse of number of subdivision, 1/(N-1)
Nor
mal
ized
cap
acita
nce
Piece-wise expression
with x-0.5 dependence
BEM calculation of IDT capacitance
∑−
= −=
1
02)/2(1
)/2()(N
n
nn
wXwXAXq
Used function
Charge concentration at electrode edges ((((∝∝∝∝x-0.5))))
What should be used for
infinite case?
Full Wave Analysis for Infinite Grating! Perturbation or Functional Method ⇔
inaccurate (?)! Boundary Element Method (BEM) ⇔
complex for Green function calculation! Finite Element Method (FEM) ⇔
slow convergence (?)
! Spectrum Domain Analysis (SDA) ⇔simple analysis, fast convergence but applicable structure limited
FEM/SDA
Blφφφφtekjær's Method for infinite IDTsBlφφφφtekjær's Method for infinite IDTs
∑
∑∞+
−∞=
+∞
−∞=
−−−−
=
−−−=
n GG
gn
n GG
Gn
wXnXjXB
Xe
wXnXjAXq
)2/cos()cos()]2/1(exp[)sgn(
)(
)2/cos()cos()]2/1(exp[)(
βββββ
β
Field Expression (Rigorous for electro-statics)
How shall we include mechanical effects?
For non-piezoelectric case, Bm=-jεAm
FEM/SDA AnalysisFEM/SDA Analysis
SAW Propagation Direction
Finite Element AnalysisFor Arbitrary Electrode Cross-Section (+ Analytic Solution not Available)
Piezoelectric Substrate
Metal Electrode
Flat Substrate Surface
Analytic Solution = Fast Analysis
Spectral Domain Analysis
Boundary Condition:Minimization of Radiated Power (Error) from Boundary
Characterization of Wave Properties in Infinite Structures
Dispersion Characteristics of Rayleigh-type SAW on 128-LN. Blue: FEMSDA, Red: COMVB=4,025 m/s (Slow-shear SSBW velocity)
3880
3900
3920
3940
3960
3980
4000
0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.5200.10.20.30.40.50.60.7
Relative frequency, fp/VB
Phas
e ve
loci
ty (
m/s
)
Atte
nuat
ion
(dB
/λ)
OC
SC
h=2%λ
COM Parameter Determination by Numerical Fitting
00.10.20.30.40.50.60.7
0.47 0.48 0.49 0.5 0.51
Atte
nuat
ion
(dB
/λ)
OS
SS
3880390039203940396039804000
0.47 0.48 0.49 0.5 0.51Ph
ase
velo
city
(m/s
ec)
Relative frequency, fp/VB
SS
OSOS
SS
Relative Frequency, fp/VB
h/p=0.01h/p=0.02h/p=0.03h/p=0.04
h/p=0.01h/p=0.02h/p=0.03h/p=0.04
Dispersion Relation vs. Al Thickness
0.02
0.03
0.04
0.05
0.06
0.07
0 0.01 0.02 0.03 0.04Al Thickness/Grating-Period
Rel
ativ
e C
OM
Par
amet
ers Ku
c-110κ12
κ11
2
Change in COM Parameters with Al Thickness
Cp
K Iu ω
ζπ 22 = : Electromechanical Coupling Factor
for Perturbed Modec=VB/Vref VB=4,025 m/s (Slow Shear SSBW)
-0.08
-0.06
-0.04
-0.02
-0.00
0.02
0.04
0.0 0.2 0.4 0.6 0.8 1.0R
efle
ctiv
ity,
r
Metallization ratio, w/p
short-circuited grating
open-circuited grating
h/p=0.06
Rayleigh-type SAW on 128oYX-LiNbO3Solid Lines: FEMSDA, +×: Experiment
3.803.823.843.863.883.903.923.943.963.984.00
0.0 0.2 0.4 0.6 0.8 1.0
Effe
ctiv
e ve
loci
ty, V
e(k
m/s
)
Metallization ratio, w/p
open-circuited grating
short-circuited grating
h/p=0.06
Comparison with ExperimentComparison with Experiment
Correction of Simulation ParametersCorrection of Simulation Parameters
! Uncertainties in Substrate Material Constants (Supplier and Lot Dependent)
! Uncertainties in Film Material Constants (Fab. Process Dependent)
! Electrode Cross-Section (Fab. Process Dependent)
Although their Absolute Values may be Doubtful, Dependencies on Device Parameters might be held
SAW Device SimulationSAW Device Simulation!!! BackgroundBackgroundBackground!!! COM analysis for rapid simulationCOM analysis for rapid simulationCOM analysis for rapid simulation!!! FEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determination! Correction for SH-SAW simulation!!! TransverseTransverseTransverse---mode analysismode analysismode analysis!!! FEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulation!!! Summary and remaining problemsSummary and remaining problemsSummary and remaining problems
Properties of SH-type SAWsProperties of SH-type SAWsSimilar to Rayleigh-Type SAWs (SV+L) at First Look
•Influence of Bulk Wave Radiation
•Frequency Dependent Velocity
•Frequency Dependent Piezoelectricity
Incident SAWBragg-Reflected
SAW
Bragg-Reflected BAW
Back-Scattering to BAW
For SH-type SAW,Cutoff For BAW Back-Scattering≈SAW Resonance Frequency
Atte
nuat
ion
(dB
/ )
385039003950400040504100415042004250
0.4 0.44 0.48 0.52 0.56 0.60
0.5
1
1.5
2
2.5
3
Phas
e ve
loci
ty (
m/s
)
Relative frequency, fp/VB
λ
Dispersion in phase velocity & attenuation of SH-type SAW on SC grating on 42-LT. Blue: calculated by FEMSDA, and red: calculated by conventional COM.
Stopband BAW backscattering
Frequency
Am
plitu
de SAW Response
BAW Radiation
Stored Energy(∝ Velocity Reduction)
BackscatteredBAW cutoff
Origin of dispersion near stopband
385039003950400040504100415042004250
0.4 0.44 0.48 0.52 0.56 0.6
OCSC
Phas
e ve
loci
ty (
m/s
)
Relative frequency, fp/VB
Phase velocity of SH-type SAW for grating structure on 42-LT. Blue:calculated by FEMSDA, and red: calculated by Plessky's model.
generation detection
SAW radiationconductance + >0
generation detection
SH-typeSAW
BAWinternal reflection
BAW radiationconductance
Coupling between SAW and BAW radiation through internal reflection.
-15-10
-505
10152025
865 870 875 880 885 890 895
conductance
susceptance
Frequency (MHz)
Rel
ativ
e ad
mitt
ance
Y/G
0
Experimental (blue) and calculated (red) input admittance of finite synchronous resonator. (G0=20 mS)
Simulation of SAW Resonator for Ladder-Type Filters
Simulation of SAW Resonator for Ladder-Type Filters
-1.5
-1
-0.5
0
0.5
1
1.5
840 860 880 900 920 940 960
Rel
ativ
e ad
mitt
ance
Y/G
0
Frequency (MHz)
conductance
susceptance
Experimental (blue) and calculated (red) input admittance of finite synchronous resonator. (G0=20 mS)
Lateral Leakage BAW Radiation from Finite IDT
Slowness Surface of SH-type SAW on 36-LTSlowness Surface of SH-type SAW on 36-LT
! Beam-like Propagation (No Guided Transverse Mode)
! Power Leakage through Bus-Bar Regions
! Frequency Dependent Behavior
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 0.1 0.2 0.3Sx sec/km
S yse
c/km
1800 1900 2000
-40
-20
0
Atte
nuat
ion
[dB]
Frequency [MHz]
Metallization-ratio
50%35%
1800 1900 2000
-40
-20
0
Atte
nuat
ion
[dB]
Frequency [MHz]
Metallization-ratio
50%35%
IDT
Busbar
BusbarTransverse Leakage
Reflector
Inte
nsity
[a.u
.] High
Low
IDT
Busbar
BusbarTransverse Leakage
ReflectorIDT
Busbar
BusbarTransverse Leakage
Reflector
Inte
nsity
[a.u
.] High
Low
Inte
nsity
[a.u
.] High
Low
Laser Probe Image Impact of Metallization Ratio to Transverse Leakage
Presented at 2003 IEEE FCS By Tstutsumi, et al. (Fujitsu Labs)
COM analysis of DMS FiltersCOM analysis of DMS Filters
-100
-80
-60
-40
-20
0
800 850 900 950 1000 1050 1100Frequency (MHz)
Scat
terin
g Pa
ram
eter
(dB
)
Experiment
Simulation
S11
S21
Overestimated Propagation Loss
! Influence of DiscontinuitiesNo Practical Theory ⇒ Phenomenological Model(additional phase shift)
! Influence of BAWsModeling has not been Established yet
Difficulties in Simulation of DMS FiltersDifficulties in Simulation of DMS Filters
Discontinuities
SAW Device SimulationSAW Device Simulation!!! BackgroundBackgroundBackground!!! COM analysis for rapid simulationCOM analysis for rapid simulationCOM analysis for rapid simulation!!! FEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determination!!! Correction for SHCorrection for SHCorrection for SH---SAW simulationSAW simulationSAW simulation! Transverse-mode analysis!!! FEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulation!!! Summary and remaining problemsSummary and remaining problemsSummary and remaining problems
Frequency
Adm
ittan
ce
ωr ωa
B
GIn-harmonic Resonance
3D Simulation of Whole Structure3D Simulation of Whole Structure
Origin of Transverse
Mode
Precision Stage
Optics
IF Detector
Stage Controller RF Source
LO Source
CCD camera
Data Logger
N Divider
10
100
1k
428 430 432 434 436 438Im
peda
nce
(Ω)
Frequency (MHz)
(a) (b) (c)
SAW Resonator
20 min. for 2,620×410 pixels
1-port SAW ResonatorPeriod: 7.18 µmSubstrate: ST-Cut QuartzElectrode: Al (140 nm)
700 800 900 1000
0.3
0.2
0.1
0
-0.2
-0.1
0.5
0.4
Frequency [MHz]
Adm
ittan
ce [S
]
IDT Resonator on Cu-Grating/15oYX-LiNbO3IDT Resonator on Cu-Grating/15oYX-LiNbO3
G
B
1300Frequency, f [MHz]
700 800 900 1000 1100
0
10
20
30
50
Inse
rtion
loss
[dB
] min IL=0.5 dB
BW3dB=152MHz (15%)
40
1200
h/2p=7.2-9.3%
Wideband SAW filter on Cu/15oYX-LiNbO3 structureWideband SAW filter on Cu/15oYX-LiNbO3 structure
Presented at IEEE 2004 UFFC Conf.
Measured Field distribution by Laser Probe
340.30 MHz
373.75 MHz363.24 MHz350.00 MHz
Presented at 2005 IEEE Ultrasonics Symp.20min. for each image
Transverse Mode AnalysisTransverse Mode AnalysisIgnoring
Depth Dependence
Simplifying IDT Region as Uniform
Layer
wG
wB
wB
Region B
Region G
Region B
x
y
Mode Orthogonality + Completeness Enable us to Estimate Mode Excitation Efficiency
Res
onan
ce F
requ
ency
, fr[M
Hz]
Aperture, w/λ
Rayleigh mode
S0
S1
S2
S3
S4
S5
Calculated and Experimental Spectra of Transverse Modes
0 10 20 30
850
830
840
820
800
810
7905 15 25
Weighted Dummy Electrodes for Suppression of Transverse Modes
Scattering of Unnecessary Modes Through Coupling with Dummy Electrode Modes
1.3Frequency, f [GHz]
0.7 0.8 0.9 1 1.1
Inse
rtion
loss
[dB
]
0
10
20
30
40 1.2
W Weighted Dummy ElectrodesW/O Weighted Dummy Electrodes
1.3Frequency, f [GHz]
0.7 0.8 0.9 1 1.1
Inse
rtion
loss
[dB
]
0
10
20
30
40 1.2
SAW Filter Using Cu/15oYX-LiNbO3 Structure
SAW Device SimulationSAW Device Simulation!!! BackgroundBackgroundBackground!!! COM analysis for rapid simulationCOM analysis for rapid simulationCOM analysis for rapid simulation!!! FEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determination!!! Correction for SHCorrection for SHCorrection for SH---SAW simulationSAW simulationSAW simulation!!! TransverseTransverseTransverse---mode analysismode analysismode analysis! FEM/BEM analysis for precise simulation!!! Summary and remaining problemsSummary and remaining problemsSummary and remaining problems
Full Wave Analysis for Finite Structure! Perturbation or Functional Method ⇔
inaccurate! Boundary Element Method (BEM) ⇔
complex for Green function calculation! Finite Element Method (FEM) ⇔
slow conversion
Rigorous Analysis of arbitrary 2D structure
FEM/BEM
This simulation is time consuming but current computers are a little powerful
Structure of PitchPitch--Modulated IDT & ReflectorModulated IDT & ReflectorConventional Structure PitchPitch--Modulated StructureModulated Structure
IDT IDTREFECTOR
ModulatedModulated
ModulatedModulatedGap ControlledGap Controlled
Presented at IEEE 2004 UFFC Conf.
Relative frequency
-100
-80
-60
-40
-20
0
-0.15 -0.1 -0.05 0 0.05 0.1 0.15Scat
terin
g co
effic
ient
S21
(dB
) ModulatedConstant
Designed Results
Wideband & Without gaps between IDTsPresented at IEEE 2002 Ultrasonics Symp.
Red line: Modulated-Pitch Structure (Lg=0λ)Blue line: Unmodulated-Pitch Structure (Lg=0.3λ)
COM Analysis (BAW Ignored)
∆IL=0.1dB
Remaining Loss (1-|S21|2-|S11|2)
Presented at IEEE 2004 UFFC Conf.
∆∆∆∆IL=0.4dB
FEM/BEM Analysis (BAW Incl.)
Experimental Verification
∆IL=0.4dB
Red line: Modulated-Pitch StructureBlue line: Unmodulated-Pitch Structure (Lg=0.3λ)
Remaining Loss
Presented at IEEE 2004 UFFC Conf.
DMS Filter Using Modulated StructureDMS Filter Using Modulated Structure
Courtesy of Fujitsu Media DevicesPresented at IEEE 2004 UFFC Conf.
SAW Device SimulationSAW Device Simulation!!! BackgroundBackgroundBackground!!! COM analysis for rapid simulationCOM analysis for rapid simulationCOM analysis for rapid simulation!!! FEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determinationFEM/SDA analysis for parameter determination!!! Correction for SHCorrection for SHCorrection for SH---SAW simulationSAW simulationSAW simulation!!! TransverseTransverseTransverse---mode analysismode analysismode analysis!!! FEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulationFEM/BEM analysis for precise simulation! Summary and remaining problems
! Pseudo 2D Simulation of Whole Structure
! Derivation of Simulation Parameters by 2D (X-Z) Simulation
! Correction of Simulation Parameters! Simulation of SH-type SAW! Precise Simulation of Ladder-Type Filters! Transversal Mode Analysis! Package Modeling
What we can do ......
What we should do next?! Fast & Precise Simulation of DMS-Type Filters
(Including Frequency Dependent K2 and Attenuation)
! Pseudo 3D Simulation of Whole Structure (Including Lateral Leakage)
! Rapid Package Simulation for Optimal Design! Finding Remaining Loss Mechanism! Precise Simulation Tools for More Complicated
Structures