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Computational Modeling of Polymer Flow in Microcavities through a Microscreen Jie Chen and Ranga Pitchumani Advanced 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 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


LIGA Processing Steps ď ą 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. Resist material

Lithography:

Lithography:

Exposure

Micromolds

Development X-ray Mask (Patterned gold on silicon)

Metallized Substrate Synchrotron generated X-rays

Electrodeposition:

Molding:

Electrodeposited Metal Microstamp

Mold Filling

Plastic replicate via injection molding or hot embossing

Planarization/Mold Dissolution

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Replication of Electroforming Molds with Integral Metallic Screen CONCEPT Metallic Demolded Screen Replicate LIGA Stamp

ď ą 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

ď ą 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. ď ą 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. ď ą 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 PMMA u 0 u t E t

τ

u t ( E) t

p ))

(k T

E

D

(uu) (u( ρE

air

t

p

| u |2 h 2 τ

( u) 0

τ

D

( uu)

p

τ

(u( ρ E

F t

Volume of fluid

u

p ))

F

E

τ u)

h

(k T

p

| u |2 2

τ u)

0

Solidification/melting ( H) t

( uH )

(1 )2 (k T ) Amushu ( 3 )

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Example Case of Mold Filling WL

80 m

Q 30 cc/s

PMMA volume fraction

TW

361K

Tin

576 K

Pressure

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Stress Calculation

w

Mb w 2 I

σ max I

pL(y, z)

1 L w3 12 L

H

z

pR(y, z)

Mb

H

dy pL 0

σ max

y

pR z dz

0

6M b L w2

x

Wall width (normal to the page): L

σ max

0

Deflectionto the LEFT

σ max

0

Deflectionto the RIGHT

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Maximum Stresses on the Walls Peak Stress,

p

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Incomplete Fill WL

80 m

Q 30 cc/s

TW

338K

Tin

536 K

ď ą The stress values are higher than that in the case of higher mold temperature and inlet temperature. ď ą Due to incomplete fill, the stress is larger than zero at the end of fill. Advanced Materials and Technologies Laboratory


Design of Experiments

 The experiments are set up based on the Taguchi L9 orthogonal array

Levels

Q [cc/s]

Tw [K]

Tin [K]

1

15

338

496

2

30

361

536

3

45

373

576

Tin

Fill fraction

 Three 3-level factors are considered

TW

Stress

Q

 Fill ratio, – defined as the volume ratio of the filled micro cavities  Peak stress,

p

Fill time

Outputs of interest

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Correlation and Processing Windows

WL

80 m

Q 45 cc/s

A

*a * b * c Q TW Tin

WL

200 m

Q 45 cc/s d

p

e

* A Q* TW Tin*

f

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Design Plots

1 Tw = 334 K

1 Tin = 694.5 K

p

1

2 GPa

p

1.421 GPa 2 GPa

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Summary  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. Advanced Materials and Technologies Laboratory


Computational Modeling of Polymer Flow in Microcavities