Collector dependence of field emission in the Scanning Field Emission Microscopy

We have performed density functional VASP calculations of a carbon covered tungsten surface under the presence of an electric field F directed away from the surface i.e., pushing the electrons into the surface. We have found that under the presence of this field the extrapolated to the surface straight line which represents the increase of the vacuum energy with distance cuts the energy axis on the surface below the value E
vac
at F = 0, by an amount ΔW = 0.1 - 0.15eV when F = 1V/nm. This effectively constitutes an F dependent decrease of the work- function W(F), which at higher F can explain the reported collector dependence of current in Scanning Field Emission Microscopy.