Electronic Processes at the Carbon-Covered (100) Collector Tungsten Surface

We have performed density functional VASP calculations of a pure and of a carbon-covered (100) tungsten surface under the presence of an electric field E directed away from the surface. Our aim is to answer the question of an increased penetrability of electrons at the collector side of a nanometric tunnel diode when covered by carbon atoms, a purely quantum mechanical effect related to the value of the workfunction phi. To obtain phi at a non-zero electric field we have extrapolated back to the electrical surface the straight line representing the linear increase in the potential energy with distance outside the metal-vacuum interface. We have found that under the presence of E the workfunction phi = E-vac - E-F of the (100) pure tungsten surface has a minor dependence on E. However, the carbon-covered tungsten (100) surface workfunction phi(C - W) has a stronger E dependence. phi(C - W) decreases continuously with the electric field. This decrease is Delta phi = 0.08 eV when E = 1 V/nm. This Delta phi is explained by our calculated changes with electric field of the electronic density of both pure and carbon-covered tungsten. The observed phenomena may be relevant to other surfaces of carbon-covered tungsten and may explain the reported collector dependence of current in Scanning Field Emission Microscopy.