Modeling Graphene with Nanoholes: Structure and Characterization by Raman Spectroscopy with Consideration for Electron Transport

Recent advances in controlled synthesis and characterization of single-layer graphene nanostructures with defects provide the basis for gaining an understanding of the complex nanomaterials by theoretical investigation. In this work, we modeled defective single-layer graphene (DSLG), where nanostructures with divacancy, trivacancy, tetravacancy, pentavacancy, hexavacancy, and heptavacancy defects, having pore sizes from 0.1 to 0.5 nm, were considered. Nanostructures with molecular oxygen adsorption to mimic experimental conditions were also investigated. On the basis of calculated formation energies of the optimized nanostructures, a few DSLGs were selected for theoretical characterization of the defect-induced <i>I</i>(<i>D</i>)/<i>I</i>(<i>D</i>′) Raman intensity ratios. We found that the <i>I</i>(<i>D</i>)/<i>I</i>(<i>D</i>′) ratio decreases with an increase in the nanohole size and in the number of adsorbed oxygens, which explains an experimental observation of a decrease in this characterization signature with an increase in exposure time to oxygen plasma. The predicted ratio was also confirmed by Raman spectroscopy measurements for graphene oxide quantum dots. The results were rationalized based on an analytical analysis of the <i>D</i>′ band electron-defect matrix elements. Finally, consideration of patterned graphene nanostructures with vacancies for field effect transistor (FET) application was shown to provide a route to bandgap generation, and potentially improvement of the <i>I</i><sub>on</sub>/<i>I</i><sub>off</sub> ratio in a FET by nanohole passivation, e.g., by hydrogenation. FETs based on patterned graphene with small pores could have a similar high level of performance as graphene nanoribbons, however with the added benefit of no width confinement.