Band Gap Engineering in Two-Dimensional Materials by Functionalization: Methylation of Graphene and Graphene Bilayers.

Graphene is well-known for its unique combination of electrical and mechanical properties. However, its vanishing band gap limits the use of graphene in microelectronics. Covalent functionalization of graphene has been a common approach to address this critical issue and introduce a band gap. In this Article, we systematically analyze the functionalization of single-layer graphene (SLG) and bilayer graphene (BLG) with methyl (CH) using periodic density functional theory (DFT) at the PBE+D3 level of theory. We also include a comparison of methylated single-layer and bilayer graphene, as well as a discussion of different methylation options (radicalic, cationic, and anionic). For SLG, methyl coverages ranging from 1/8 to 1/1, (i.e., the fully methylated analogue of graphane) are considered. We find that up to a coverage θ of 1/2, graphene readily accepts CH, with neighbor CH groups preferring positions. Above θ = 1/2, the tendency to accept further CH weakens and the lattice constant increases. The band gap behaves less regularly, but overall it increases with increasing methyl coverage. Thus, methylated graphene shows potential for developing band gap-tuned microelectronics devices and may offer further functionalization options. To guide in the interpretation of methylation experiments, vibrational signatures of various species are characterized by normal-mode analysis (NMA), their vibrational density of states (VDOS), and infrared (IR) spectra, the latter two are obtained from ab initio molecular dynamics (AIMD) in combination with a velocity-velocity autocorrelation function (VVAF) approach.