Theoretical investigation of quantum capacitance in armchair-edge graphene nanoribbons

Graphene nanoribbons (GNRs) are considered as a prospective material for the next generation of nanoelectroic devices. One of the important properties of GNRs in determining the performance of such devices is capacitance; in particular, the quantum capacitance when the device size approaches in the scale of nanometer. This work presents a comprehensive investigation of the bandgap structure and the classical and quantum capacitance in armchair-edge GNRs (A-GNRs) using semi-analytical method. The method is simple and more realistic considering edge effects of A-GNRs. The results show that the edge effects have significant influence in defining the bandgap which is a necessary input in the accurate analyses of capacitance. The classical capacitance is completely determined by the device geometry and a dielectric constant of the medium. The quantum capacitance is obtained considering edge effects and discussed for both degenerate (high gate voltage) and nondegenerate (low gate voltage) regime. It is demonstrated that the total capacitance is equivalent to the classical capacitance in nondegenerate regime, whereas in degenerate regime, quantum capacitance dominates over the classical capacitance. Such detail analysis of GNRs considering a realistic model would be useful for the optimized design of GNR based nanoelectronic devices.