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 (CH₃) 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 CH₃, with neighbor CH₃ groups preferring trans positions. Above θ = 1/2, the tendency to accept further CH₃ 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.