modeling diffusion of sparsely populated acids on a monomer/polymer lattice
DESCRIPTION
Modeling Diffusion of Sparsely Populated Acids on a Monomer/Polymer Lattice. Andrew Brzezinski, Matthew Duch Dept. of Materials Science & Engineering Spring 2006. Background & Motivation. sample. Acid generation by multi-beam laser interference - PowerPoint PPT PresentationTRANSCRIPT
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