Lateral resolution of the scanning tunnelling microscope

Abstract

A theoretical study of the current distribution in a model which extracts the prominent characteristics of a tip‐surface geometry in a scanning tunnelling microscope is presented. The sample is a Sommerfeld metal with a planar surface while the tip, also made of a Sommerfeld metal with a planar surface, presents a hemispherical protrusion. Schrödinger's equation is solved by using a form of the finite element method suitable to treat the three‐dimensional tunnelling problem. We have derived the current distribution for several values of the protrusion radius and for various gaps between the electrodes. From these results, we investigate the ideal resolution of the scanning tunnelling microscope for realistic values of these geometrical parameters. Though applied to a rather simple model, at this stage, our method appears to be a suitable scheme for further, more refined computations, accounting for the detailed atomic structure of the electrodes. 1988 Blackwell Science Ltd