Distance tunneling microscopy

Figure 7.18 Scanning tunneling microscopy is based on the tunneling of electrons between the surface and an atomically sharp tip positioned at a few angstroms above the surface. The tunneling current depends sensitively on the distance s between the tip and the surface. An image of the surface is obtained by scanning the tip horizontally over the surface. A control system keeps the tunneling current and therefore the distance between tip and surface constant the scans are a plot of the vertical position of the piezoelectrically driven tip versus its horizontal position.

More detailed studies of surface structure can be carried out using scanning tunneling microscopy (STM). For the use of this technique, a metal tip is scanned over the surface, and the distance from the tip to the surface is determined by the tunneling current between them. Images of surfaces with subnanometer resolution are often obtained using this method. 

In scanning tunnelling microscopy a typical barrier height (V - E in eqn 3.6) is 2 eV. If the measured current i is proportional to the tunnelling probability for electrons, show that it should vary with distance d from the surface (expressed in nanometres) according to... 

---