Role of tip electronic structure in scanning tunneling microscope images

Tunneling to a spherical metal tip is analyzed, going beyond the s-wave approximation for the tip wave functions. For metal surfaces, the scanning tunneling microscope image is found to correspond to a contour of constant surface local density of states, under rather general assumptions. However, for semimetallic or semiconducting surfaces, the image may deviate in a simple but crucial way from the local density of states, as illustrated by the case of graphite.