Modeling Diffusion of Sparsely Populated Acids on a Monomer/Polymer LatticeAndrew Brzezinski, Matthew DuchDept. of Materials Science & Engineering

Spring 2006

Background & Motivation

Acid generation by multi-beam laser interference Results in an FCC lattice-type illumination pattern Unit cell on the order of the wavelength of light used (=

351 – 532 nm)

sample

Background & Motivation

Acid acts as catalyst for polymerization of photoresist

Resulting structure reflects illumination intensity

Code: Initialization

Used alternate unit cell than standard FCC

400x400x566 sites Acid placement based

on sum of 13 Gaussian distributions

Acid distribution proportional to intensity

Code: MovementGet next acid from list

Polymerize?

Pick direction

Move Acid

Is target monomer?

Compare to RND

Is target polymer?

Move Acid

Pass

Fail

Code: Data Analysis

Label each lattice site Create list of bonded

sites Collapse list to

determine cluster size and number of bonds

Number of polymerized sites with 0-6 number of bonds

Total number of clusters

Bin clusters by size Largest cluster size Images of lattice

Determine Parameters Movement probability into polymerized bin Polymerization probability

Total Number of Clusters vs Time

0

500000

1000000

1500000

2000000

2500000

0 500 1000 1500 2000 2500 3000 3500

Time Step

Nu

mb

er o

f C

lust

ers

Determine ParametersLargest Cluster Size

0

10000000

20000000

30000000

40000000

50000000

60000000

0 500 1000 1500 2000 2500 3000

Time Step

Clu

ster

Siz

e

Movement probability into polymerized bin: 0.3 Polymerization probability: 0.5

Cluster Size DependenceLargest Cluster Size

0

10000000

20000000

30000000

40000000

50000000

60000000

70000000

80000000

90000000

0 500 1000 1500 2000 2500 3000

Time Step

Siz

e o

f C

lust

er 16I

8I

4I

2I

I

Bond NumbersNumber of Polymerized Sites with # Bonds

0

10000000

20000000

30000000

40000000

50000000

60000000

0 500 1000 1500 2000 2500

Time Step

Nu

mb

er o

f S

ites

0

1

2

3

4

5

6

Number of Polymerized Sites with # Bonds

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

0 1000 2000 3000 4000 5000 6000

Time Step

Nu

mb

er o

f S

ites

0

1

2

3

4

5

6

16 I0

I0

In Conclusion

Made a model to capture basic physics of polymer cross-linking

Used our model with acid distribution from interference lithography

Have shown that our model has potential to increase our understanding and control of the fabrication process