Tunneling Microscope (STM) allows to probe the local geometric and
electronic structure of surfaces on a mesoscopic scale down to atomic
distances. Binnig and Rohrer  developed the first STM for
which they were awarded the Nobel Prize in 1986.
Figure 1: Principle of scanning tunneling microscopy: Applying a negative sample voltage yields electron tunneling from occupied states at the surface into unoccupied states of the tip. Keeping the tunneling current constant while scanning the tip over the surface, the tip height follows a contour of constant local density of states (pictures from ).
The principle of the STM is based on the strong distance dependence of the quantum mechanical tunneling effect (Fig. 1). A thin metal tip is brought in close proximity of the sample surface. At a distance of only a few Å, the overlap of tip and sample electron wavefunctions is large enough for a tunneling current It to occur which is given by
where d denotes the tip-sample distance and k is a constant depending on the height of the potential barrier . For metals with typical work functions of 4 eV-5 eV, k is of the order of 1 Å-1. Hence, an increase of the tunneling distance of only 1 Å changes the tunneling currents by about an order of magnitude. If the tip is scanned over the sample surface while an electronic feedback loop keeps the tunneling current constant ( constant current mode), the tip height follows a contour of constant local density of states and provides information on the topography of the sample surface.
Figure 2: Scanning tunneling microscope  with eddy current damping developed in our group.