Transcript Simulating MEMS - Courant Institute of Mathematical Sciences

Simulating MEMS
David Bindel
April 11, 2001
Overview
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What are MEMS?
Modeling and simulation
The SUGAR simulator
Ongoing work
Conclusion
What Are MEMS?
• “Micro Electro Mechanical Systems”
• Actually combines more domains:
– Micro Electro Mechanical Magnetic Optical
Fluidic Thermal Systems
• But MEMMOFTS is too long an acronym
(Picture of micromirror from BSAC
home page: www.bsac.berkeley.edu)
MEMS Characteristics
• Micro
– Micrometer scale features
– Still classical physics
– But constants differ from macro scale
• Electromechanical
– Involves multiple physical domains
• Systems
– Design includes subsystems, interfaces, …
MEMS Applications
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Inertial sensors: accelerometers, gyroscopes
Fluidics: ink-jet printers, biolab chips
Optics: optical switching, projectors
Pressure sensors: Automotive, medical, industrial
RF devices: cell phone, radar components
Other: Microrelays, sensors, disk heads
List taken from “Microsystem Design” by S. Senturia
MEMS Fabrication
• (Mostly) similar to IC fabrication
Deposition
• Not precision machining!
• Process characterization important
• There are standard processes
Lithography
MUMPS =
Multi-User MEMS Processes
Etch
(not sparse linear algebra package)
Modeling Approaches
• Physical simulation
– Describe physics with coupled PDEs
– Solve via finite elements, finite differences, …
• Behavioral simulation
– Characterize components by coupled ODEs
– Solve a much smaller system
Physical Modeling
• Commonly uses FEM or BEM
• Commercially successful:
Mirror simulated in
Coyote’s AutoMEMS
– Coventor (formerly MEMCAD and Coyote)
– ANSYS
• Captures second-order physical effects
• Computationally intensive
– Coyote sells SMP and cluster versions of its software
– MEMCAD’s FEM tools even more expensive
System Modeling
(Mirror prototype, KSJ Pister)
• Simple component models
– E.g. 2 nodes with 6 dof each to describe beam
– Mimics approximations of hand-analysis
– Deriving models can be problematic
• Often based in existing package
– SPICE, Simulink, MathCAD, …
• Much less expensive
• Often good enough to be useful in design
Combined Approaches
• Reduced-order models derived from FEM
– Used in other FEM simulations
– Used as black boxes in system simulation
• Coupled finite element, system models
– Rough models often based on FEM anyhow
• IC world uses both approaches
– System simulation for design feedback
– Physical simulation to check parasitics
SUGAR Simulator
• Graduate students
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S. Bhave
D. Bindel
J.V. Clark
N. Zhou
• Professors
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J. Demmel
S. Govindjee
M. Gu
K.S.J. Pister
SUGAR Simulator
• Name and heritage from SPICE
• Written (mostly) in Matlab for ease of
– Installation
– Extension
• Supported analyses:
– Static analysis
– Linearized frequency-response analysis
– Transient simulation
SUGAR architecture
• Parameterized netlists describe devices
• Convert to Matlab structure by MEX function
• Most work done in model functions
Netlist
(ASCII file
describing
device)
Compiler
Analysis,
Display
Model functions
SUGAR Simulation of ADXL-05
Describing the ADXL-05
uses mumps.net
subnet XSusp [B] [susp_len=* angle=*]
…
XSusp p1 [c(1)] [susp_len=200u angle=0]
for k=1:10 [
mass(k) XMass p1 [c(k) c(k+1)] [finger_len=100u]
]
XSusp p1 [c(11)] [susp_len=200u angle=180]
Running the Simulation
>> net = cho_load(‘adxl.net’);
>> dq = cho_dc(net);
>> cho_display(net, dq);
% Load netlist
% Do static analysis
% Display displaced device
Ongoing Work
• SUGAR installation on Millennium
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Prototype already built (CS 267 project)
User only needs a web browser
Centralized software installation and maintenance
Use load-balancing to run small sequential jobs
Possibly add parallelism for large devices,
detailed simulations, parameter studies
Ongoing Work
• Homotopy methods and equilibria
– Electrostatic devices experience “pull-in”
– Pull-in where energy min becomes a saddle
– Tell designers what voltage they can use
• Model reduction
– Simulate even tinier systems!
– Generate models for subsystems
• Based on simulations in or out of SUGAR
Ongoing Work
• Deal with multiple scales
– Model using differential-algebraic equations
– Better understand effects of multiple physical
scales on the numerics
• Expand set of models
– Contact
– Damping
– Plates
Ongoing Work
• Incorporate feedback from measurement
– To fit material parameters
– To sanity check models
• Develop suite of test structures
– To find problems in our routines
– To figure out capabilities we need
– To compare against other approaches
Ongoing Work
• Fix the things that are currently broken!
• Make it a reasonable tool for class work
– Sufficiently capable
– Documented
– Stable
Conclusions
• MEMS designers need better tools!
• Existing software handles detailed physics
– But too detailed and slow for tight design loops
• Hand analysis often good enough
– But bookkeeping is hard for large devices
• SUGAR will fill in the gap
– As a useable tool for instruction
– For rapid development of complex MEMS