Simulating MEMS

David Bindel

April 11, 2001

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

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’); % 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