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Modeling Diffusion of Sparsely Populated Acids on a Monomer/Polymer Lattice

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

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Modeling Diffusion of Sparsely Populated Acids on a Monomer/Polymer Lattice

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  1. Modeling Diffusion of Sparsely Populated Acids on a Monomer/Polymer Lattice Andrew Brzezinski, Matthew Duch Dept. of Materials Science & Engineering Spring 2006

  2. Background & Motivation sample • 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 (l= 351 – 532 nm)

  3. Background & Motivation • Acid acts as catalyst for polymerization of photoresist • Resulting structure reflects illumination intensity

  4. 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

  5. Code: Movement Get next acid from list Polymerize? Pick direction Is target monomer? Is target polymer? Fail Move Acid Compare to RND Pass Move Acid

  6. 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 Code: Data Analysis

  7. Determine Parameters • Movement probability into polymerized bin • Polymerization probability

  8. Determine Parameters • Movement probability into polymerized bin: 0.3 • Polymerization probability: 0.5

  9. Cluster Size Dependence

  10. Bond Numbers 16 I0 I0

  11. 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

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