Why does tunneling current change so strongly with the distance between the tip and a surface?

In a scanning tunneling microscope, the tunneling current is highly sensitive to the distance between the probe tip and the sample surface because the probability of electrons "tunneling" through the potential barrier decreases exponentially as that distance increases.1

This phenomenon occurs because electrons exhibit wavelike properties, allowing them to penetrate regions that are forbidden under the rules of classical physics. When the tip is positioned within a few angstroms of a surface, these electrons can cross the gap between the two. Because the probability of this transfer drops off so rapidly with even slight changes in spacing, the microscope can detect minute variations in the surface topography, enabling it to resolve individual atoms.12