Simplistic model for the dendritic growth of a monolayer in dip pen nanolithography

This paper presents a simple random-walk (RW) model for monolayer growth in dip pen nanolithography (DPN). The monolayer in the RW model grows via a combination of hopping down and serial pushing of molecules deposited from the tip. The directional coherence in pushing induces branches of a monolayer that grow in preferential directions that are determined by the underlying lattice for the surface. The RW model accurately reproduces a molecular dynamics (MD) simulation for the DPN of nonpolar molecules on goldlike surfaces, indicating that the pushing mechanism accurately describes molecular motions. The molecular deposition in the MD simulation is found to be close to a random Poisson process. The high directional coherence produces self-replicating branches in the monolayer that are characteristic of dendritic growth. With a change in directional coherence, the RW model produces diverse structures such as circles, hexagons, and dendrites.