Penetration of the first-two-row elements through mono-layer graphene

Hetero atoms penetrating through defected mono-layer graphene is systematically studied by Density Functional Theory (DFT) and Nudged Elastic Band (NEB) methods. The energy curves of the first-two-row elements (from Li to Ar) through four types of defects are calculated. We find three types of curve shapes, which energetically favor different interplays with graphene: intercalation, doping and bonding. For intercalation type, the energy curve is mountain-like and can be well described with a single characterizing parameter: energy barrier. The other two need to be described with more parameters as called “bonding energy” and “doping energy”. We compute all these characterizing parameters, which can be useful in estimating the reacting rates. In addition, the response of barriers to the extra charges and holes are discussed as an avenue to manipulate the graphene intercalation. We find certain amount of extra charges would decrease the barrier but adding holes would always increase the barrier.