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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. Schriidinger's equation is solved by using a form of the finite element method suitable to treat the three-dimensional tunnelling problem. We have deriveddoi:10.1111/j.1365-2818.1870.tb06328.x fatcat:josmli54erhsneyrtvy52bs3me