1. Modeling MEMS Sensors [SUGAR: A Computer Aided Design Tool for MEMS ]
UC Berkeley
James Demmel, EECS & Math
Sanjay Govindjee, CEE
Alice Agogino, ME
Kristofer Pister, EECS
Roger Howe, EECS
UC Davis
Zhaojun Bai, CS
January, 2004
Interdisciplinary team: Computational theory, mechanical analysis, design methods, design fabrication and testing

2. Sugar Project Objective
“Be SPICE to the MEMS world”
open source and more
Design
Fast, Simple,
Capable
Fast simulation for quick designing
Coupling to measurement system to allow for model verification and improvement
Design optimization elements that couple to simulation engine for creation of layouts that are sent for fabrication
Primarily electro-mechanical systems poly silicon and single crystals (MUMPS test bed) with other processes in the works
Measurement
Simulation

3. SUGAR: Simulation Capabilities
Hierarchical Scripting Language
Solvers
Transient
Steady-State
Static
Sensitivity
System Assembler
Flexible parameterized inputs;
both matlab and web interfaces (jobs spun out to millenium cluster);
C guts with calls to high performance numerical libraries.
Includes design optimization routines and routines for measurement coupling;
Most models are lumped parameter but some are continuum and then reduced
Using spcialized Krylov methods
Models
MATLAB
Web Interface

4. Resonant MEMS Systems Essential element in RF MEMS signal processing
Specific signal amplification in physical and chemical sensors
Bulk Acoustic Waves for GHz
Traditional analytic design methods frustratingly inadequate; Abdelmoneum, Demirci, and Nguyen 2003

5. Checkerboard Resonator
3 energy domain problem
Wireless (RF) signal processing in the Giga-Hertz range in collaboration
With Prof. Howe’s group
Optimization of the Bode plot

6. Bode Plot Sun Ultra 10: Exact 1474 sec Reduced 28 sec
Working on algorithms for fast optimization of transfer functions
Which crucially rely on our Krylov methods 2 orders of magnitude speed ups

7. Challenges in Simulation of Resonator Based MEMS Sensors
Coupled energy domains with differing temporal and spatial scales; boundary layer effects
Accurate material models: thermoelastic damping, Akhieser mechanism, uncertainty
Radiation boundaries for semi-infinite half-spaces: anchor losses
Large sparse systems for which parallelism needs to be exploited (cluster computing)
Automated generation of reduced order models to accelerate large simulations
Breaking new ground on coupled simulation due to scaling issues; commputationally very challenging
Accounting for uncertainty is very important due to fabrication tolerance limints and model uncertainty.
Lots of equations => parallel cluster computing
reduced order modeling for second order systems using Krylov methods

8. Design Synthesis and Optimization
Beyond a quick design tool we are looking to design development and constrained optimization
Multi-objective genetic algorithms (combinatorial type problems)
Specialized gradient methods (continuous type problems)
Combinitorial for sythesis with known building blocks
Continuous methods for optimizing

9. Simulation is not enough Design synthesis is needed
Symmetric Leg Constraint case
Optimized for resonant frequency and x/y suspension stiffness
Note comb drives
Unconstrained case
Manhattan Angle and Symmetric Leg Constraints case

10. Experimental Measurements
Modeling is not enough; verification is needed
Integrated modeling and testing is the ideal
Tight coupling of simulation and testing with automatic model extraction and comparison (using SMIS)
Theory is all well an good but to be truly effective one must build
Test and improve.
Thus we have a coupled measurement component to the project
Which is tightly coupled to the simulation engine.

11. Synthesized Structures
From the input netlists we can automatically generate the CIF files
That are needed at the foundry

12. Simulation - Measurement Comparison
Generate Parameters
Refine Parameters
Sense Data
Extract Features
Correspond
Extract Features
Simulate
Once fabricated we are working on technology to perform experiments
Automatically capture the fabricated system and the run a simulation
Automatically and then match the response of the device.
This also allows us to refine the model if need be for future use
Such as parameter studies of behavior

13. Other current and future activities
Bounding sets for expected performance variation
Material parameter extraction
Single crystal Silicon models; CMOS processes; Si-Ge etc
Other reduced order models; e.g. electrostatic gap models directly from EM-field equations
Real-time dynamic experiment-simulation coupling
Advanced design synthesis and optimization technologies
Pushing hard on RF MEMS modeling
Desgin optimization
Desgin variablilty estimation
New processes (CMOS etc)
More integrated measurement and reverse coupling to design
Genetic algorithms

14. Graduate Students David Bindel, CS Jason Clark, AST David Garmire, CS
Raffi Kamalian, ME
Tsuyoshi Koyama, CEE
Shyam Lakshmin, CS
Jiawang Nie, Math
A look at the the folks that do the real work
A very inter-disciplinary team ==> challenging to coordinate and educate

15. Torsional Micro-mirror (M. Last)
Comb drives suspensions; 10K dofs; 30 seconds for the the computation of the bode plots for this system using
Reduced order modeling; Important when you want complete system simulation with perhaps 10,000 mirrors hooked together