Theory of the scanning tunneling microscope.

We present a theory for tunneling between a real surface and a model probe tip, applicable to the recently developed "scanning tunneling microscope". The tunneling current is found to be proportional to the local density of states of the surface, at the position of the tip. The effective lateral resolution is related to the tip radius R and the vacuum gap distance d approximately as [(2angstroms)(R+d)]1/2. The theory is applied to the 2x1 and 3x1 reconstructions of Au(110); results for the respective corrugation amplitudes and for the gap distance are all in excellent agreement with experimental results of Binnig et al. if a 9angstrom tip radius is assumed.