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 gold-like 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.