Exact eigenstates of a nanoscopic paraboloidal emitter: Field emission quantities and spot size of the near field electron microscope

The eigenstates of a paraboloidal nano-tip are obtained by solving exactly Schroedinger's equation. Then the incident current density (ICD) and parallel velocity of such an emitter are obtained and shown to exhibit a non-Fowler-Nordheim behavior. These explain partly the resolution of Near-Field SEM. Competing effects between the ICD and an applied field at constant voltage are found.