Empirical model for bandgaps of armchair graphene nanoribbons

Based on an empirical approach, we present a relation for the bandgaps of armchair graphene nanoribbons (aGNRs) as a function of their widths and number of armchair chains. Experimental bandgaps of a number of atomically well-defined aGNRs are studied here. It is found that experimentally reported bandgaps are underestimated or overestimated by existing theoretical models. Experimental data reveal that the bandgaps of N = 3p and N = 3p + 1 families of aGNR are directly related to the width and number of armchair chains. An empirical model for calculating the bandgaps of aGNRs is devised based on theoretical and experimental observations. Calculated bandgaps offer significant corrections for armchair aGNRs compared with previous tight-binding and density functional theory studies, and the amount of correction is represented by a semi-empirical correction term. The proposed relation indicates that not only the ribbon width but also the number of armchair chains plays a crucial role in determining the values and scaling rule for the bandgaps. Compared with previous models, our estimated bandgaps from the proposed empirical model can track qualitative and quantitative patterns of the experimental bandgaps very precisely, thus helping predict the bandgap of an aGNR for potential electronic and optoelectronic applications. The proposed empirical relation also gives insight into the correlation between the physical structure and electronic properties of a GNR. Furthermore, this model can be taken as a guide for devising a similar empirical model for calculating the bandgaps of other types of GNRs.