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:

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 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’);% 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