1

COMSOL API based Toolbox for the Mixed-Level Modeling of

Squeeze-Film Damping in MEMS: Simulation and Experimental Validation

Martin Niessner1, Gabriele Schrag1, Jacopo Iannacci2,

Gerhard Wachutka1

1 Institute for Physics of Electrotechnology, Munich University of Technology, Germany2 Mems Research Unit, Fondazione Bruno Kessler, Italy

INSTITUTE FOR PHYSICS OF ELECTROTECHNOLOGYMUNICH UNIVERSITY OF TECHNOLOGY

Session: Numerical

Methods

& OptimizationCOMSOL Conference

2011, Stuttgart, Germany, October

26-28, 2011

2

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

3Simplification

Reynolds equation

is

employed: valid

for

I >> hgap

Problem Description

Complication

2finite size:

pressure

drop at the

boundarypBoundary

≠pAmbient

Complication

1perforations:loss

of fluid

Problem description:1. calculate pressure underneath moving plate2. calculate damping from pressure

Complication

3deformablemembranes:

h=f(x,y)

4

channel

flow:dominating

forthick

platesand/or

small

holes

orifice

model:dominating

forthin

platesand/or

large holes

Reynolds equation

finite size

effects:additional pressure

dropat the

boundary

BT

C

O

fluidic

resistor:modeling

transit

region

R R

Mixed-LevelModel (MLM)

C1 & C2: Mixed-level

Damping

Model (1/2)

Framework for the model: Generalized

Kirchhoffian

network

theory

5

C1 & C2: Mixed-level

Damping

Model (2/2)

Features: • Discretized

system-level

model• Physics-based

Boundaryresistance:

12

384.0 −Ψ⋅⋅= Bii

B lhR πη

geometry

and material parameters

only

Correction

for

rarefied

gas effects

6

C3: Modal Superposition

Deformable

membranes

are

modeled

by

a superposition

of mechanical

eigenmodes:

…

Φ1 Φ2

Φ3

Φm

h h

MAPPING

7

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

8

General Workflow

- Open .mph file- Analysis of FEM data- MLM generation- Save as .class file

- Model mechanical structure- Include residual stresses- Eigenfrequency analysis- Save as .mph

CO

MS

OL

TOO

LBO

X

JAVA

- Open .class file- Run simulation

CO

MS

OL

CO

MSO

L SER

VER

COMSOLAPI

9

Toolbox: GUI & Algorithms

algorithms fortopography

analysis

automatedgeneration ofmixed-level

model

holesboundary

Toolbox Algorithms

10

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

11

Experimental Setups

white

light interferometer(Veeco WYKO NT1100 DMEMS)

• static measurements

→ Allows

for

dynamic

measurements

at varying

ambient pressure

conditions

laser

scanning

vibrometer(Polytec MSA-500 [customized])

• dynamic measurements• pressure chamber

Q is

calculated

from

frequency

domain

(3dB-bw)

Verification

of device

dimensions

12

100

101

102

103

102

103

Pressure [mbar]

Qua

lity

fact

or

QMLMQTotalQMEAS

Experimental Data

vs. Simulation

100

101

102

103

102

103

Pressure [mbar]

Qua

lity

fact

or

QMLMQTotalQMEAS

QTOTAL QMLM QLIMIT

1 1 1= +

Microresonator RF-MEMS switch

Maximum error

at normal pressure: 7%

13

Benchmark

vs. Alternative Models

14

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

1. Problem Description and

Modeling Approach

2. COMSOL Implementation

3. Evaluation

4. Conclusion

15

Conclusion

• Toolbox for

the

modeling

of SQFD in MEMS:• Based on Generalized

Kirchhoffian

network

theory• Uses the mixed-level

modeling

approach• Employs physics-based

models• Is extendible• Exploits the functionality of the COMSOL API• Allows easy-to-use

automated

model

generation

• Experimental evaluation:• Two devices were investigated• Excellent agreement with measurements:

• Maximum error

of 7%

at normal pressure

• Benchmark:• Two alternative compact models were investigated• Minimum error

of alternative models is 26%

at normal pressure• Automatically generated mixed-level

model

performs better

16

Thank you for your attention!Thank you for your attention!

17

Sattler R, DTIP, 2004.

MLM: Details

B

12

384.0 −Ψ⋅⋅= Bii

B lhR πη

659.0

238.05.0

471.21305.01−

−−

+⋅+

⋅Ψ=ΨD

DRB

Boundary

resistance:

Sattler R, PhD thesis, 2007.

with

13

12 −Ψ⋅= Rikik

ikR hb

rR η 159.1638.91 KnR +=Ψ

Reynolds regime

resistance:

withSattler R, PhD thesis, 2007 and Veijola T, S&A, 1998.

→ Models are

physics-based→ Models have

geometry-based

and material parameters

only

(no fit!)→ Corrections

factors

account

for

rarefied

gas effects

(is

fit!)

18

Teststructures

B1 B2 B3 B4

A1 A2 A3 A4 A5 A6

Summary

of geometrical

parameters:• number of holes: 18 .. 903• hole size: 13 µm .. 20 µm• plate thickness: 5 µm .. 15 µm• perforation level: 23% .. 47%• gap: 2 µm .. 3 µm• frequency: 14 kHz .. 44 kHz

RFS

19

MLM Toolbox Implementation

of Veijola‘s

mixed-mode

model

of SQFD for

perforated

platesin COMSOL 3.5a

FormulationModeling

Autom. Model Gen.Condensation

Number

of DOFS

Flux-conservingPhysics-based

YesPossible~2300

FEM-based -> PotentialHeuristic

NoNo

>> 2300