Analytical calculation of field enhancement factor of 2D structure graphene film

Field emitters are one of the promising electron sources for vacuum electronic devices operating in mm-wave and terahertz frequencies, where emission performance is critically governed by the field enhancement factor. While extensive analytical models exist for one-dimensional emitters like carbon nanotubes and Spindt tip, the corresponding framework for a thin-film (like two-dimensional) emitter remains lacking. In this work, an analytical field enhancement factor is derived using the floating-sphere and image-charge approach, based on a vertically oriented graphene sheet inside a closely spaced diode configuration. The model explicitly incorporates emitter dimensions such as height, width, thickness, and anode–emitter spacing. The proposed expression is validated by comparison with previously reported experimental data on reduced graphene oxide film based emitters. Good agreement between the emission current predicted via the proposed approach, and experimentally obtained data are observed for ultra-thin films, whereas a deviation in predicted and experimentally obtained data for films with higher thickness is observed. This deviation rises with increasing thickness, highlighting the limitations of the two-dimensional approximation. The proposed approach provides a useful analytical tool to estimate the field enhancement of graphene sheet field emitters for miniaturized THz vacuum electron device applications.