Self-assembly of ink molecules in dip-pen nanolithography: A diffusion model

Abstract

The self-assembly of ink molecules deposited using dip-pen nanolithography (DPN) is modeled as a two-dimensional diffusion with a source (tip). A random walk simulation and simple analytic theory are used to study how the diffusion dynamics affects patterns generated in DPN. For a tip generating a constant flux of ink molecules, circles, lines, and letters are studied by varying the deposition rate of ink molecules and the tip scan speed. Even under the most favorable condition studied here, peripheries of patterns fluctuate from perfect circles or lines, due to the random, diffusional nature of self-assembly. The degree of fluctuation is quantified for circles and lines. Circles generated by fixing the tip position do not depend on the deposition rate if the same amount of ink is deposited. For a moving tip, patterns change drastically depending on tip speed and deposition rate. Overall, fast scan or slow deposition relative to the diffusion time scale makes lines narrower. When the tip deposits ink too slowly or scans too fast, patterns become incoherent, making molecules in patterns separated from each other. Therefore, there seems to be an optimal choice of the deposition rate and tip speed that gives both narrow and coherent patterns. We also explore the consequences of varying the relative rates of diffusion of ink molecules on bare surface and on previously deposited molecules.

Thiol Diffusion and the Role of Humidity in “Dip Pen Nanolithography”

“…A number of qualitatively similar experiments have been recently reported [7,21] but analyzed using a different model [8], where the tip is treated as a source of constant flux (as opposed to concentration), and the concentration is zero outside an island. With these assumptions, the island radius should increase as t 1͞2 , which is inconsistent with our results [see the dashed line in Fig.…”

“…First, diffusion of the thiol beyond the initial contact area causes the pattern to be wider than the stamp (for mCP) or the AFM tip terminus (for DPN). Although there have been a few attempts to measure the diffusion rate of thiols on gold [5][6][7][8], these measurements have been mostly phenomenological and thus have not reported diffusion coefficients. A second, more subtle, effect of diffusion is its role in the phase transition that occurs during SAM deposition: At a critical surface concentration, the adsorbed thiols reorient from a prone to a standing orientation.…”

Random Walk Simulation for the Growth of Monolayer in Dip Pen Nanolithography

“…In this respect, theory and modeling have proven to be useful. 4,[7][8][9][10] Central to modeling DPN is how a nascent droplet (deposited from an AFM tip) spreads out to form a SAM afterward. Given that molecules are designed to chemisorb to a substrate, Jang et al 8 proposed a diffusion model of DPN assuming that the molecules are trapped irreversibly once they have reached the chemisorption sites on the substrate.…”

“…A numerical random number generator was used to obtain . The time step of simulation Δt was set according to Jang et al 8 Δt and l must satisfy…”

Multivalent self-assembly at interfaces : from fundamentals kinetic aspects to applications in nanofabrication

“…Ratner and coworkers introduced a diffusion model where spreading is possible only over SAM-covered regions. 45 Ink molecules coming from the source are immediately trapped and immobilized by available adsorption sites at the surface. When all nearby surface sites are occupied, new ink molecules migrate from the source across the covered region, thus continuously moving the boundary of the SAM-covered area.…”