The continued miniaturization of Si-integrated devices in CMOS technology is approaching the physical limits. To meet the requirements of the international technology roadmap for semiconductors, the innovation of novel nano-electronic devices are expected. Graphite-related materials such as fullerenes, carbon nanotubes, and graphene have been extensively studied in recent years due to their exceptional electronic, opto-electronic, and mechanical properties. Graphene, a one-atomic carbon sheet with a honeycomb lattice, is a gapless material that has attracted significant attention due to its unique physical properties. This material shows an extraordinarily high carrier mobility and is considered to be a potentially high speed transistor material. To induce a bandgap, graphene sheets can be patterned into ribbons. Depending on the width and the chirality, a Graphene NanoRibbon (GNR) can have semiconducting or metallic properties. The bandgap of a semiconducting GNR is inversely proportional to its width. In order to obtain an energy bandgap larger than 0.1eV, which is essential for electronic applications, the width of the GNR must be scaled below 10nm. In this regime line-edge roughness is the dominant scattering mechanism.
To model carrier transport of carriers in GNRs, the Non-Equilibrium Green's Function (NEGF) formalism and an atomistic tight-binding model have been employed. We model the effect of line-edge roughness using a non-perturbative approach. In this method, many GNR samples with rough edges are generated using a Gaussian or exponential distribution and then an ensemble average is calculated. Line-edge roughness at the two edges can have some degrees of correlation. Cross correlation between two random processes is described by a correlation coefficient which lies between -1 and +1. A correlation coefficient of +1 can be achieved in between the two edges of unzipped carbon nanotube GNRs, whereas the correlation coefficient for GNRs obtained from other methods is nearly zero. Our studies show that this correlation can play a significant role on the electronic properties of GNRs. In GNRs with un-correlated roughness, the electronic bandgap is strongly modulated by line-edge roughness. In GNRs with a correlation factor of +1, the width of the ribbon remains nearly constant and the bandgap is only weakly affected.