3-DIMENSIONAL ELECTROSTATIC POTENTIAL, AND POTENTIAL-ENERGY BARRIER, NEAR A TIP-BASE JUNCTION

The geometry of an atomically sharp or nearly atomically sharp tip in proximity to a planar anode may be closely approximated in the prolate-spheroidal coordinate system. An exact three-dimensional electrostatic-potential solution for a free charge in such a tip/base junction is given in this letter, including calculations for both the symmetrical on-axis case and the asymmetric off-axis case. An exact solution for the potential-energy barrier is also given; this solution has immediate applications in three-dimensional tunneling studies and in calculations of electron trajectories in micron- and submicron-sized field-emitter arrays. (C) 1994 American Institute of Physics.