The electronic properties of graphene nano-ribbons in the presence of line-edge roughness scattering are studied. The conductance, the mean free path, and the localization length of carriers are analytically derived using an effective mass model for the band structure. The model developed provides a deep insight into the operation of graphene nanoribbon devices in the presence of line-edge roughness. The effects of geometrical parameters on the conductance of graphene nanoribbons are estimated assuming a diffusive transport regime. However, in the presence of disorder, localization of carriers can occur, which can significantly reduce the conductance of the device. The effect of localization on the conductance of rough nanoribbons is studied analytically. Since this regime is not suitable for the operation of electronic devices, one can employ these models to obtain critical geometrical parameters to suppress the localization of carriers in graphene nanoribbon devices.
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