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We point out an apparently overlooked consequence of the boundary conditionsobeyed by the electric displacement vector at air-metal interfaces: thecontinuity of the normal component combined with the quantum mechanicalpenetration of the electron gas in the air implies the existence of a surfaceon which the dielectric function vanishes. This, in turn, leads to anenhancement of the normal component of the total electric field. We study thiseffect for a planar metal surface, with the inhomogenous electron densityaccounted for by a Jellium model. We also illustrate the effect for equilateraltriangular nanoislands via numerical solutions of the appropriate Maxwellequations, and show that the field enhancement is several orders of magnitudelarger than what the conventional theory predicts.

Field enhancement at metallic interfaces due to quantum confinement