Correction factors for field emission from a nanoscopic emitter based on ab initio calculation of the electron eigenstates

We have recently calculated the quantized eigenstates of an electron emitter whose form is that of a paraboloid with nanoscopic radius of curvature $\mathrm{R}$ at the apex. We have used these eigenstates to calculate the emitted current from such a nanoscale emitter. We find that the corresponding Fowler-Nordheim (FN) curves are strongly nonlinear deviating from the well-known behavior predicted by the traditional FN theory. To make our theory easily accessible, we present factors that rectify the original FN equation for the emitted current as a function of known $\mathrm{R}$., compensating for the quantum confinement effects of high apical curvature. These practical-interest correction factors, however, are derived from exact analytical calculations for electron quantum states inside such a nanoscale emitter tip.