  We present first-principles total-energy electronic-structure calculations
that provide the microscopic mechanism of the adatom interchange reaction on
the Sn- and Pb-covered Ge(111)-(2x8) and the Sb-covered Si(111)-(7x7) surfaces
with and without the tip of the atomic force microscope (AFM). We find that,
without the presence of the AFM tip on the Ge surface, the adatom interchange
occurs through the migration of the adatom, the spontaneous formation of the
dimer structures of the two adatoms, the dimer-dimer structural transitions
that induce the exchange of the positions of the two adatoms, and then the
backward migration of the adatom. We also find that the dimer structure is
unfeasible at room temperature on the Si surface and the adatom interchange are
hereby unlikely. With the presence of the tip, we find that the reaction
pathways are essentially the same for the Ge surface but that the energy
barriers of the migration and the exchange processes are substantially reduced
by the AFM tip. We further find that the AFM tip induces the spontaneous
formation of the dimer structure even on the Si surface, hereby opening a
channel of the interchange of the adatoms. Our calculations show that the bond
formation between the AFM tip atom and the surface adatom is essential for the
atom manipulation using the AFM tip.
