DESIGN AND MODELLING OF PIEZOMEMSDESIGN AND MODELLING OF PIEZOMEMS- METHODOLOGIES AND CASE STUDIES
Gerold Schropfer, [email protected]
International Workshop on Piezoelectric MEMS, May 18th-19th, 2010, Aachen
Outline
• Introduction• Modelling methodologies for PiezoMEMS• PiezoMEMS modelling case studies
ResonatorsEnergy HarvestersPZT MoveMEMS design kit
CantileversMirror
• Conclusions• Conclusions
About Coventor
Coventor:
• Coventor offers Design Tools and Platforms for MEMS and ICs
• 15 years experience
• Leader in MEMS design software
• US based
• Strong European R&D
Products:
CoventorWare™
Coventor Infrastructure
Process & Materials DataProcess & Materials Data
MEMulator-SEMulator3D
Fab Process Modeling
MEMulator-SEMulator3D
Fab Process Modeling
MEMulator-SEMulator3D
Fab Process Modeling
3D CAD Tools
SolidWorksPro-Engineer
I-DEASAutoCAD
3D CAD Tools
SolidWorksPro-Engineer
I-DEASAutoCAD
EDA Simulators
SimulinkSaber
CadenceMentor
EDA Simulators
SimulinkSaber
CadenceMentor
SEMulator3D™ MEMS+™ Platform
Introduced 2001
3D Field Solvers
Abaqus (Dassault)Fluent, Flow3D
ANSYS,Ansoft, etc.
3D Field Solvers
Abaqus (Dassault)Fluent, Flow3D
ANSYS,Ansoft, etc.
2D LayoutGDS2, CIF,
DXF (AutoCAD)
2D LayoutGDS2, CIF,
DXF (AutoCAD)
ARCHITECT3D(based on Saber)
Schematic-DrivenMEMS Design
DESIGNER2D & 3D Geometry(Physical Design)
DESIGNER2D & 3D Geometry(Physical Design)
ANALYZER3D Field Solvers
(Verification)
ANALYZER3D Field Solvers
(Verification)
INTEGRATORReduced-Order Model
Extraction
INTEGRATORReduced-Order Model
Extraction
Introduced 2005 I t d d 2009
MEMS design(previously MEMCAD, MIT spinn-off in 1995)
Introduced 2001
Virtual fabrication MEMS + IC development
Introduced 2005 Introduced 2009
MEMS Designer’s Challenges
3D Nature / Structures3D Multi-Physics
Reliability3D Multi Physics
(coupled)
Variety of MEMS Processes
Co-Design of Die and Package
Coupling of MEMS
P f D d ti
Variability in Process and Material
with Electronics
Performance Degradation (induced by fabrication or use)
Variability in PiezoMEMS Process and Materials
Design Design Design ToolToolTool
Input Data
Result Output
Material Properties Piezo-Coeff. Young's Modulus
Device Performance Membrane Deformation
Young s Modulus Stress etc.
Process Geometry Film Thickness
Resonance modes etc. System Performance
Feedback Control Noise etc
Sidewall angles etc. Layout Geometry
Length, width etc.
Noise etc.
Variability in input Uncertainty in output
Models of MEMS
Representations of MEMS are required in many contexts System/Control
),( txfkxxcxm MEMS high-level design Circuit-level MEMS+IC
MEMS detailed 3DLayout
Process Modelling
Process Modelling
http://www.synopsys.com/Tools/TCAD/CapsuleModule/sprocess_ds.pdf
Process EmulationLayout Tools: 2D Verification TCAD: Process SimulationProcess Emulation
Mapping process to model steps (very efficient)
Able to model complete process sequences
Layout Tools: 2D Verification
Feasible on an entire chip. Check design rules, verify
layout, etc. Does not capture 3D effects
TCAD: Process Simulation
Accurate but time consuming Simulates single steps
(implant, etch,…) Feasible for small areasprocess sequences
Able to model large area Fully 3-D
Does not capture 3D effects No direct link to the process.
Feasible for small areas Often 2D, rarely 3D.
Scope Fidelity
MEMS Behavioral Model Library
• Macro or behavior models (ideally analytical)Beams & Suspensions (Bernoulli Beam Theory)Plates (Rigid, Flexible MITC Plate Theory)
Sensing Electrodes and Comb Finger Drives (Conformal Mapping Theory)
• Solved in electrical circuit simulators (analogy electrical and mechanical)
[CoventorWare 2010 Architect3D reference documentation]
MEMS Behaviour Model Libraries
• Models built based on parameterized library components
IC schematic or 3D building blocks
Traditionally: Schematic entry based library Recently: 3D model library
Which aproach to use for piezoMEMS design ?
Behaviour Models:System level designEasier design automation and EDA
FEM/BEM :Geometric FlexibilityCaptures field details
integrationShort simulation time enables
Transient analysisRapid optimization
such as stress distributionAddresses physics not amenable to
behavioral modelingsuch as gas damping
Statistical analysis, such like yield or sensitivity analysis
Arbitrarily accurate via mesh refinement
MEMS-IC Co-Design(Integration of MEMS and EDA tools)
Ref. G. Schröpfer, G. Lorenz, S. Rouvillois, J.Chianetta, et al., A Novel EDA-Compatible Methodology for Design and Simulation of MEMS with IC, 7. GI/GMM/ITG-Workshop on Multi-Nature Systems, Ulm, Germany, 3 February 2009
Outline
• Introduction• Modelling methodologies for PiezoMEMS• PiezoMEMS modelling case studies
ResonatorsEnergy HarvestersPZT MoveMEMS design kit
CantileversMirror
• Conclusions• Conclusions
Film Bulk Acoustic Resonator (FBAR)
3D model of a “generic” FBARg
• RF signal across device produces longitudinal vibrations piezo layerR h fil thi k i i t l lti l f h lf th i l l th • Resonance when film thickness is integral multiple of half the signal wavelength
• At resonance sharp change in electrical impedance (frequency selective filter)• Designed for strong resonance with narrow bandwidth (wireless communication)
FBAR FEM Modelling
Animation of resonance mode
PiezoElectric strain coefficients for ZnO
Real and Imaginary charge on top and bottom electrode as a function of frequency electrode as a function of frequency
Impedance as a function of frequency
Modal Harmonic Analysis for PiezoMEMS
Modal Harmonic Analysis…• A set of vibration modes for the model are first calculated. These modes are used
to approximate the harmonic responseto approximate the harmonic response• Modal harmonic is almost always computationally less expensive than direct
harmonic
• Includes coupling between electric field strength and mechanical stress/strain
Modal Harmonic PZEFrequency Response
0,7Modal Harmonic & Direct Harmonic Comparison
Modal Harmonic
0,5
0,6Modal Harmonic
Direct Harmonic
Direct Harmonic ‐ Detailed
0,3
0,4
MaxX_
Mag
0,7d l
0,1
0,2
0,4
0,5
0,6
Mag
Modal Harmonic
Direct Harmonic
Direct Harmonic ‐Detailed
0
735000000 740000000 745000000 750000000 755000000 760000000 765000000 770000000Frequency (Hz)
0 1
0,2
0,3
0,4
MaxX_
M
0
0,1
749000000 751000000Frequency (Hz)Coventor Inc. Confidential Slide 16
Q-Factor and Damping
Resonator analysis requires Q-factor calculation, which depends on different damping mechanism:
11111
Gas DampingThermo-Elastic Damping
OTHERANCHORTEDGASTOTAL QQQQQ11111
Anchor Loss Others: Complex Harmonic Loading, structural or surface effects
Quality CADQuality Factor Explanation CAD
Solution(s)
QGAS Gas damping, can be reduced by reducing ambient pressure FEM (specific module)
Thermoelastic Damping -- As a vibrating body is strained, the M h i l FEM QTED
Thermoelastic Damping As a vibrating body is strained, the temperature changes in proportion to the strain; when temperature gradients occur, heat conduction causes irreversible energy loss
Mechanical FEM or behavior model(TED option)
QAnchor Loss -- A fraction of elastic energy is transmitted via the anchors to the surrounding support structure where it is Mechanical FEM with
Coventor Inc. Confidential Slide 17
QANCHORanchors to the surrounding support structure where it is dissipated. Also referred to as support loss, clamping loss, or attachment loss
QuietBoundary Surface BC
QOTHEROther Loss Mechanisms which may include structural dissipation (crystallographic defects) and surface effects
Mech. FEM with Rayleigh Damping Coef.
Piezoelectric Energy Harvester
•Silicon-based fabrication using AlN as piezoelectric material•Three wafer process, bonded by SU-8
harvesting capacitor
adhesivebonds
capacitor
1281 7 mm31281.7 mm
mass beam
[HOLST IMEC]
Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009
Finite Element Model for Piezoelectric Harvester
• predictsresonance frequencyresonance frequencyoutput voltage or charge under open and short circuit condition
• requires material damping• requires material damping
S. Matova, Proc. Eurosensors XXII
uit v
olta
ge /
Vop
en c
ircu
frequency / Hz
Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009
Euler-Bernoulli Beam with Piezoelectric Patch
• Non-linear Bernoulli beam with piezoelectric transducerIncludes lumped and distributed elementsActive part : potential differences → forcesSensing part : displacement → charge
• Implemented in Coventor Model Library (Architect3D)p y ( )
3.00E-06load matching
anchor
beam mass1.50E-06
2.00E-06
2.50E-06Po
wer
(W)
0.00E+00
5.00E-07
1.00E-06
RMS
P
1.0E+04 1.0E+05 1.0E+06 1.0E+07
Rload (Ohm)
Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009
Model Validation :Short Circuit
• Short circuit condition (Rload = 200 Ω)• Frequency deviation due to beam thickness variation q yand precise material parameter characterization
8.0
FEA l d i it
5 0
6.0
7.0
A)
FEA closed circuit
Measured Rload = 200 Ohm
Architect3D Rload = 200 Ohm
3.0
4.0
5.0
Cur
rent
(uA
0 0
1.0
2.0
0.5 g excitation0.0
1100 1110 1120 1130 1140 1150 1160
Frequency (Hz)Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009
Model validation : open circuit
• Short circuit condition (Rload = 5.3 MΩ)• Good match in output magnitudep g
2.5
3.0
FEA open circuit
1 5
2.0
2.5
ge (v
)
Measured Rload = 5.3 MOhm
Architect3D Rload = 5.3 MOhm
1.0
1.5
Volta
g
0.0
0.5
1100 1110 1120 1130 1140 1150 1160
0.5 g excitation
Frequency (Hz)
Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009
Circuit Elements for FEM Piezo Direct Harmonics
• Piezo harmonic analysis of MEMS incorporated into an electrical circuitresistors, inductors and capacitors
• For such applications as:• For such applications as:Energy harvesters: vibration of a piezoelectric device provides electrical current to other components in the circuitActive damping: piezoelectric material is dd d t l h i l t t t added to a larger mechanical structure to
control its motion by converting vibration energy into electrical current that is directed through a resistor and dissipated as heat
PZT
Fix
PZT
Structural Layer
Ref: Erturk, A. & Inman, D. J. A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters, J of Vibration and Acoustics, 130, 4, August 2008.
PZT Energy HarvesterPower Response
1,0E‐03
Power Response Function1,0E‐03
Power Response Function1,0E‐03
Power Response Function1,0E‐03
Power Response Function1,0E‐03
Power Response Function
1,0E‐04
1E2Ω
1,0E‐04
1E2Ω 1E3Ω
1,0E‐04
1E2Ω 1E3Ω 1E4Ω
1,0E‐04
1E2Ω 1E3Ω
1E4Ω 1E5Ω1,0E‐04
1E2Ω 1E3Ω
1E4Ω 1E5Ω
1E6Ω
1,0E‐05er (W
)
1,0E‐05er (W
)
1,0E‐05er (W
)
1,0E‐05er (W
)
1,0E‐05er (W
)
1 0E 06
,
Powe
1 0E 06
,
Powe
1 0E 06
,
Powe
1 0E 06
,
Powe
1 0E 06
,
Powe
1,0E‐061,0E‐061,0E‐061,0E‐061,0E‐06
1,0E‐07
47 47,5 48 48,5 49 49,5 50 50,5 51
Frequency (Hz)
1,0E‐07
47 47,5 48 48,5 49 49,5 50 50,5 51
Frequency (Hz)
1,0E‐07
47 47,5 48 48,5 49 49,5 50 50,5 51
Frequency (Hz)
1,0E‐07
47 47,5 48 48,5 49 49,5 50 50,5 51
Frequency (Hz)
1,0E‐07
47 47,5 48 48,5 49 49,5 50 50,5 51
Frequency (Hz)
Design Kit Motivation
DesignDesignHandbookHandbook
FoundryFoundry
… use tools to build a bridgeDesigner
MoveMEMS PZT Design Kit Experiments vs. Simulation
• Deflection of test cantilever
ModelExperiments
Canitilever 6-3 up to 30 V
25 000
5 000
10 000
15 000
20 000
Hei
ght (
nm)
0V10V20V0 V 2nd20V25V
Monte Carlo Simulation with thickness of all layers as statistical parameter (nominal distribution assumed)
-5 000
00 0.2 0.4 0.6 0.8 1 1.2
Distance (mm)
30V
Piston Mirror
• Ref. Thor Bakke, Andreas Vogl, Oleg Żero, Frode Tyholdt, Ib-Rune Johansen, and Dag Wang, A novel ultra-planar, long-stroke, and low-voltage piezoelectric micromirror JMM 2010micromirror, JMM 2010
Mirror Model with MITC shell elements
PiezoMEMSProcess Design Kit (PDK)
• Library of foundry specific process emulation files • Specific material property databases Spec c a e a p ope y da abases• Layout template file with design rule check• Parametric model library elements • Compatible to design handbooks• Combined with fabrication run, e.g. Multi-Project-Wafer
Materials’Properties
Process Parameters
Fabrication System and MEMS IC Co-design
Layout3D Model
FEM/BEM Analysis
MoveMEMS PZT Process Data MEMS IC Co design 3D Model AnalysisProcess Data
[EC NMP Project piezoVolume]
Towards a PiezoMEMS Eco System
Parametric design format provides a new standard to facilitate the communication between the partners of the eco-system
Parametric Parametric PiezoMEMS Design
MEMSUserFAB Model
P tPDK
MEMSDeveloper/Layout
Parameters
Models
PDK
Developer/Designer
Layout
Conclusions
• PiezoMEMS design requires different methods for different applications and modelling levels
FEM and behaviour models (circuit design)FEM and behaviour models (circuit design)• Knowledge of process and material properties is key
“Robust” designs compensate for process variability• In workIn work
Advanced PiezoMEMS models MoveMEMS PZT design kit are
• Recommend holistic and integrated approach g ppMEMS, electronics, packagingValidated models… to avoid inconsistencies between eco-system partners
As wanted … As packaged … As fabricated … As modeled … As designed …
Acknowledgement
“The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2010‐2013) under grant agreement n° 229196”Seventh Framework Programme (FP7/2010 2013) under grant agreement n 229196
www.piezovolume.com