simulating mems david bindel april 11, 2001. overview what are mems? modeling and simulation the...
TRANSCRIPT
Overview
• 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
• 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
Deposition
Lithography
Etch
• (Mostly) similar to IC fabrication
• Not precision machining!
• Process characterization important
• There are standard processes
MUMPS =
Multi-User MEMS Processes
(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:
– 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
Mirror simulated in Coyote’s AutoMEMS
System Modeling
• 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
(Mirror prototype, KSJ Pister)
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– S. Bhave– D. Bindel– J.V. Clark– N. Zhou
• Professors– 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 filedescribing
device)
CompilerAnalysis,Display
Model functions
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’); % Load netlist>> dq = cho_dc(net); % Do static analysis>> cho_display(net, dq); % Display displaced device
Ongoing Work
• SUGAR installation on Millennium– 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