Contact resistance in the scanning tunneling microscope at very small distances

A theoretical analysis of the contact resistance in the scanning tunneling microscope at very small distances is presented. For a single atom, we find that the resistance saturates at close contact, its value being $\frac{h}{{2e}^2}$. Our analysis of the recent experimental results of Gimzewski and Möller shows that the mechanical instability predicted by Pethica and co-workers appears for a distance of 1.5 Å between the tip and the sample.