MEMS Design usingMEMS Design usingGenetic AlgorithmsGenetic Algorithms

Carlo H. Séquin

EECS Computer Science Division

University of California, Berkeley

CS 285

Genetic AlgorithmsGenetic Algorithms

Pursue several design variations in parallel(many phenotypes in each generation)

Evaluate their “fitness” (how well they meet the various design objectives Pareto set)

Use best designs to “breed” new off-springs(by modifying / combining their genes)

Expectation: Good traits will stick around,bad solution will be weeded out ...

The “genome” is the ultimate The “genome” is the ultimate parameterization of a design,parameterization of a design,given the proper proceduregiven the proper procedure

to interpret that codeto interpret that code

Without the proper framework, the genome is meaningless. (e.g., human DNA on a planet in the Alpha-Centauri System)

An ExperimentAn Experiment

Let ME students design a MEMS resonator

Students (initially) had no IC experience

Good programmers

Excited about Genetic Algorithms

Micro-Electromechanical SystemsMicro-Electromechanical SystemsMEMSMEMS

Created with a somewhat enhanced fabrication technology used for integrated circuits.

Many nifty devices and systems have been built: motors, steerable mirrors, accelerometers, chemo sensors ...

The Design of a MEMS ResonatorThe Design of a MEMS Resonator Filters

Accelerometers

Gyroscopes

Prevent horizontaloscillations !

Resonate vertically at desired frequency

Basic MEMS ElementsBasic MEMS Elements

Beam H-shaped center mass

Comb driveAnchor to substrate

A General Set-Up for OptimizationA General Set-Up for Optimization Poly-line suspensions at 4 corners.

Adjust resonant frequency F

Get Kx Ky into OK ranges

Minimize layout area

Need an Electro-Mechanical Simulator !Need an Electro-Mechanical Simulator !

“SUGAR”

“SPICE for the MEMS World”(open source just like SPICE)

Fast,Simple,

Capable.

DESIGN

MEASUREMENT SIMULATION

A Possible PhenotypeA Possible Phenotype

Adjust resonant frequency to 10.0 ± 0.5 kHz

Bring Kx / Ky into acceptable range ( >10 )

Minimize size of bounding box; core fixed

MEMS Actually Built and MeasuredMEMS Actually Built and Measured

Genetic Algorithm in Action !Genetic Algorithm in Action !

Area = 0.181 mm2; Kx/Ky = 12

Use 4-Fold Symmetry !Use 4-Fold Symmetry !

1st-order compensation of fabrication variations

Using 4-fold SymmetryUsing 4-fold Symmetry

Faster search ! Area = 0.171 mm2; Kx/Ky = 12

X,Y-Symmetry; Axis-Aligned BeamsX,Y-Symmetry; Axis-Aligned Beams

Area = 0.211 mm2; Kx/Ky = 118

Introduce Serpentine ElementIntroduce Serpentine Element

A higher-order composite subsystemwith only five parameters: N , Lh, Wh, Lv, Wv

N=3

Wv

Lh

Wh Lv

Proper Use of Serpentine Sub-DesignProper Use of Serpentine Sub-Design

That is what we had in mind ...

Proper Use of Serpentine ElementProper Use of Serpentine Element

Area = 0.143 mm2; Kx/Ky = 11Reduce X-dimension of layoutby introducing more serpentine loops

Trying to Reduce AreaTrying to Reduce Area

Area = 0.131 mm2; Kx/Ky = 4 !!

soft Kx flare out

Increasing Stiffness KIncreasing Stiffness Kxx

Connecting bars suppress horizontal oscillations

But branched suspensions may not be expressible in genome ( = underlying data structure ).

Using Cross-Linked SerpentinesUsing Cross-Linked Serpentines

Area = 0.126 mm2; Kx/Ky = 36

PROFESSIONAL DESIG

N

Why Does the G.A. Not Find This ?Why Does the G.A. Not Find This ?

Lack of expressibility of genome.

Solution space too large, too rugged ...

Sampling is too sparse !

Samples are not driven to local optima.

““Holey” Fitness SpaceHoley” Fitness Space

Open-ended engineering problems have complicated, higher-dimensional solution / fitness spaces.

1. Generation – a random sampling20. Generation – drifting to higher ground50. Generation – clustered near high mountains

A Rugged Solution SpaceA Rugged Solution Space

No phenotype is on the top of a peakNo phenotype is on the top of a peak

Good intermediate solutions may get lostGood intermediate solutions may get lost

What really happened here ?What really happened here ?

Major improvement steps came by engineering insights.

Genetic algorithm found good solutions for the newly introduced configurations.

With few enough parameters & clear objectives, greedy optimization may be more efficient.

With complex multiple objectives, G.A. may have advantage of parallel exploration.

What Are Genetic Algorithms Good For ?What Are Genetic Algorithms Good For ?

Exploring unknown territory

Generating a first set of ideas

Showing different subsystem solutions

How can this be harnessed most effectivelyin an engineering design environment ?

Uncharted TerritoryUncharted Territory

Task: Design a robot that climbs trees !Task: Design a robot that climbs trees !

How do you get started ??How do you get started ??

Making G.A. Useful for EngineeringMaking G.A. Useful for Engineering

G.A. by itself is not a good engineering tool

G.A.

Selectivebreeding Greedy

Optimization

Selection ofgood startingphenotypes

Suggestiveediting

Visualization

OPASYNOPASYNA Compiler for CMOS Operational AmplifiersA Compiler for CMOS Operational Amplifiers

H.Y. Koh, C.H. SH.Y. Koh, C.H. Séquin, P.R. Gray, 1990équin, P.R. Gray, 1990

Synthesizing on-chip operational amplifiers to given specifications and IC layout areas.

1. Case-based reasoning (heuristic pruning)selects from 5 proven circuit topologies.

2. Parametric circuit optimization to meet specs.

3. IC Layout generation based on macro cells.

MOS Operational Amplifier (1 of 5)MOS Operational Amplifier (1 of 5)

Only five crucial design parameters !

Op-Amp Design (OPASYN, 1990)Op-Amp Design (OPASYN, 1990)

Multiple Objectives:

power dissipation (mW)

output voltage swing (V)

output slew rate (V/nsec)

open loop gain ()

settling time (nsec)

unity gain bandwidth (MHz)

1/f-noise (V*Hz-½)

total layout area (mm2)

“Cost” of Design = weighted sum of deviations

OPASYN Search MethodOPASYN Search Method

Design-parameter spaceRegular sampling followed by gradient ascent

Hard design constraints

Fitness

Cost

MOS Op-Amp LayoutMOS Op-Amp Layout

Following circuit synthesis & optimization, other heuristic optimization procedures produce layout with desired aspect ratio.

Synthesis in Established FieldsSynthesis in Established Fields

Filter design and MOS Op-Amp synthesishave well-established engineering practices.

Efficiently parameterized designs as wellasrobust and efficient design procedures exist.

Experience is captured in special-purpose programs and used for automated synthesis.

But what if we need to design something in “uncharted engineering territory” ?