Electrostatic potential barrier for electron emission at graphene edges induced by the nearly free electron states

Abstract

Using the density functional theory, we studied the electronic structures of zigzag graphene nanoribbons with hydroxyl, H, ketone, aldehyde, or carboxyl terminations under a lateral electric field. The critical electric field for electron emission is proportional to the work function of the functionalized edges except the hydroxylated edge, which leads to the anomalous electric field outside the edge, owing to the electrons in the nearly free electron (NFE) state in the vacuum region. The strong electric field also causes a potential barrier for the electron emission from the H-terminated edge owing to the downward shift of the NFE state.