Jie Chen and Ranga PitchumaniAdvanced Materials and Technologies Laboratory

Department of Mechanical Engineering

Virginia Tech

Blacksburg, Virginia 24061-0238

pitchu@vt.edu • http://www.me.vt.edu/amtl • (540) 231-1776

Computational Modeling of Polymer Flow in

Microcavities through a Microscreen

Paper No. IMECE2010-38675 presented at the ASME IMECE 2010 • November 18, 2010 •

Vancouver, BC, Canada

The work is being supported by a grant from the National Science Foundation through

Grant No. CBET-0934008

Advanced Materials and Technologies Laboratory

LIGA Processing Steps

DevelopmentMicromolds

Lithography:

Synchrotron

generated X-rays

X-ray Mask

(Patterned gold on

silicon)

Resist material

Metallized

Substrate

Lithography:

Exposure

Plastic replicate

via injection

molding or hot

embossing

Molding:Electrodeposition:

Microstamp

Mold Filling Planarization/Mold Dissolution

Electrodeposited

Metal

LIGA (an acronym for the German words for Lithography, Electroforming and

Molding) is a microfabrication process that can produce high aspect ratio

microstructures (HARMs) with excellent feature fidelity and sidewall tolerance.

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Demolded

Replicate

Replication of Electroforming Molds with

Integral Metallic Screen

Metallic

Screen

LIGA Stamp

CONCEPT

In practice, a porous region and a flow channel are added on top of the

screen for flow distribution and screen support

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Problem with Replicating Small Features

During filling of small microcavities adjacent to larger microcavities on a

microtool stamp, fluid preferentially fills larger cavity first; Resulting pressure

imbalance across a feature wall causes feature collapse on the microstamp tool.

Effective process development calls for designing the microfeature layout on the

stamp and the molding process and material parameters so as to elminate such

feature failures.

A fundamental understanding of the microstructural evolution during

electrodeposition onto the metallic microscreens is essential to design and

optimize the overall micropart fabrication process.

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Mathematical Model

0u

τuuu

pt

)(

)()( uτ)u( TkpρEt

E

Dτ2

|| 2u

hE

0)( ut

τuuu

pt

)(

)()()(

uτ)u( TkpEρt

E

Dτ2

|| 2up

hE

0Ft

Fu

PMMA

air

Volume of fluid

Solidification/melting

uu mushATkHt

H

)(

)1()()(

)(3

2

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Example Case of Mold Filling

PMMA volume fraction Pressure

m80LW K361WT K576inTcc/s30Q

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Stress Calculation

H

w

x

pL(y, z)

pR(y, z)

Wall width (normal

to the page): L

L H

RLb

b

dzzppdyM

wLI

I

wMσ

0 0

3

max

12

1

2

2max

6

wL

Mσ b

RIGHT the toDeflection0

LEFT the toDeflection0

max

max

σ

σ

yz

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Maximum Stresses on the Walls

Peak Stress, p

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Incomplete Fill

m80LW K338WT K536inTcc/s30Q

The stress values are higher than that in the case of higher mold temperature

and inlet temperature.

Due to incomplete fill, the stress is larger than zero at the end of fill.

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Three 3-level factors are considered

The experiments are set up based

on the Taguchi L9 orthogonal array

Outputs of interest

Fill ratio, – defined as the volume

ratio of the filled micro cavities

Peak stress, p

Design of Experiments

Levels Q [cc/s] Tw [K] Tin [K]

1 15 338 496

2 30 361 536

3 45 373 576

Fil

l fr

acti

on

Fil

l ti

me

Str

ess

WT inTQ

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Correlation and Processing Windows

A Q*aTW* bTin

* c

p A Q*dTW* eTin

* f

m80LW

m200LW

cc/s45Q

cc/s45Q

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Design Plots

1

p 2 GPa

1

p 2 GPa

1Tw = 334 K

Tin = 694.5 K

GPa421.1

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A computational model is developed for the polymer flow during the

fabrication of electroforming micromolds incorporating the temperature

dependent, non-Newtonian rheology of the polymer melt.

The mold temperature, the inlet temperature, and the inlet flow rate are

investigated as the control parameters. The mold temperature plays the

most important role in the filling process.

In some cases, full blockage is produced in the small cavities because

PMMA solidifies. Therefore, the filling process is incomplete.

In most of the cases, the peak stress appears on the wall next to the

large cavity earlier than on all the other walls.

Design plots for geometric design as well as process design were

developed from the studies.

Summary