Abstract
The electron work function for graphene fragments with pure edges and those functionalized by hydrogen atoms is calculated using the density functional theory method, and the obtained results are used to evaluate the current–voltage (I-V) characteristics of a vertically aligned rectangular graphene sheet. The calculated results of the electric potential spatial distribution in the vicinity of the graphene layer indicates a highly inhomogeneous distribution of the electric field amplification factor along its external edge, so that the maximum amplification occurs near the vertices of the layer. Such an inhomogeneity promotes a highly inhomogeneous distribution of the emission current along the graphene layer edge. At relatively low voltages, the emission is provided mainly by the region near the vertices of the layer, where the relative contribution of this region decreases with an increase in applied voltage. This effect manifests itself in a deviation of the emission I-V characteristics from the classical Fowler–Nordheim dependence, a deviation that has been observed in recent experiments. This study shows the possibility of decreasing the degree of emission current inhomogeneity along the graphene layer edge by giving it a rounded shape.
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