Atomistic simulations of low energy ion irradiation of 2D materials: From <i>ab-initio</i> molecular dynamics to simple binary collision model

Ion irradiation is a powerful tool to tune the properties of two-dimensional (2D) materials by creating defects and introducing impurities. At the same time, efficient defect production and especially ion implantation into 2D materials require a careful choice of ion energies, as when energies are too low or too high, production of defects and implantation rate will be unsatisfactorily low. As for the bulk systems, various approaches have been employed to predict optimum ion energies for specific tasks, but they cannot always be directly applied to 2D materials. Here, we carry out ab initio molecular dynamics (MD) and analytical potential (AP) MD simulations and compare the results to those obtained with a simple binary collision approximation (BCA) model. We show that when chemical interactions between the ions and target atoms are essential, as in the case of B and N ion implantation into graphene, as compared to inert gas ions, the AP MD and the BCA model are inadequate. We further suggest a modified-BCA approach with the corrected displacement threshold energies, which account for chemical interactions between the ion and target atoms. The threshold energy can be obtained from first-principles calculations, and the modified-BCA model gives qualitatively and, for some ions, even quantitatively correct results for the energies corresponding to the onset of defect production and substitution probabilities, while being at the same time many orders of magnitude computationally less expensive than the first-principles MD. We show that in any case the BCA and modified-BCA calculations provide the upper and lower bounds on the optimum ion energy.