METHODS FOR CALCULATING ELECTROSTATIC QUANTITIES DUE TO A FREE CHARGEIN A NANOSCALE 3-DIMENSIONAL TIP BASE JUNCTION

The exact solutions for fully three-dimensional electrostatic quantiti es due to a free charge in a nanoscale tip/base junction, such as the scanning-tunneling microscope, are given for the problem as modeled in the prolate-spheroidal coordinate system. These exact solutions consi st of summation series of integrals of conical functions, and methods for calculating these exact solutions with high accuracy are described in detail in this paper. Calculated results for the surface-charge di stribution on the tip and the base due to a free electron in a nanosca le tip/base junction are also presented. This analysis has important i mplications for the ultimate objective of quantifying electron tunneli ng, from first principles, in nonplanar geometries such as sharp vacuu m field emitters. (C) 1995 American Institute of Physics.