Monte Carlo Modeling of the Graphene Moiré Structure on an Ir(111) Substrate

Abstract

The article simulates graphene moiré patterns on the Ir(111) substrate. The difference in substrate and graphene periods leads to the formation of a moiré superstructure, which is periodic vertical deformations with hexagonal symmetry. The interaction between carbon atoms in graphene is significantly stronger than that with substrate atoms. Therefore, graphene is considered not stretchable. Van der Waals forces determine the interaction between carbon atoms and substrate atoms. The Lennard-Jones potential models these forces. The surface potential replaces substrate exposure to carbon atoms. Our model calculates the surface potential in one unit cell and translates it using parallel transfer. The surface potential is the sum of the two-particle potentials for the atomic interaction. Comparison with experimental data and unification rules set Lennard-Jones potential parameters. The minimum energy determines the position of the graphene atoms. The simulation describes different orientations of the graphene crystal lattice relative to the substrate lattice. If the principal directions of the two lattices coincide, then the period of the moiré pattern has a maximum value of 2.54 ± 0.02 nm. This value is in good agreement with the experimental period 2.52 nm. The height of the graphene film above the substrate surface is calculated to be 0.330 ± 0.001 nm. Experimental measurements and ab inito calculations give a value of 0.330 ± 0.005 nm. Rotation of the graphene relative to the principal directions of the substrate lattice results in a shorter moiré period. A study of the dependence of the moiré pattern period on the angle of rotation of the graphene crystal lattice relative to the substrate shows a nonlinear decreasing law.