Field Emitted Current from a Paraboloidal Nano-Emitter Using its Exact Eigenstates and a Three- Dimensional WKB Expression for the Transmission Coefficient

Following our work on field emission from emitting tips of radius of curvature R, 5<;R<;20 nm[1] (any tip with R above 20 nm can be regarded as planar) we have considered field emission from tips with R<;5nm. Such small values of R are nowadays achievable in practice [2]. We have therefore considered emission from tip with the shape of a paraboloid by revolution. A rotational parabolic curvilinear system of coordinates has been used as shown in figure 1. In a very recent work such a system and have calculated the incidents to the barrier current as a function of R which in no way resembles plane wave current density. In this paper we use a 3-dimensional WKB approximation to calculate the transmission coefficient and finally the emitted current.