Theoretical study of short- and long-range forces and atom transfer in scanning force microscopy

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Abstract
We investigate the interaction energy, the short-range force components, and the electron potential between two Al(001) slabs, which mimic a blunt tip close to an atomically corrugated sample in scanning force microscopy. The adhesive energy and perpendicular force calculated using the self-consistent-field pseudopotential method in the local-density approximation are site dependent, but can be accurately represented by a universal function in terms of scaled variables in the attractive range. The lateral force which determines friction variations on an atomic scale is not simply proportional to the perpendicular force and is typically one order of magnitude smaller. At larger separations the effect of the total long-range Van der Waals force and of its gradient are estimated to be small for a sharp conical support tip, but quite appreciable for a rounded support tip with a radius as small as 200 Å. By calculating the interaction energy of an Al atom between two slabs, we also study the possibility of single-atom transfer between tip and sample, and show that the double well in the interaction energy collapses into a single minimum at a slab separation larger than two bulk interlayer spacings. The atom is preferentially located on the side of the deeper minimum, but can hop between the two wells at finite temperatures. Moreover, the position of the deeper minimum relative to the electrodes can vary as the tip is scanned against the sample. Finally we explore possible relations between the short-range perpendicular force and the tunneling conductance through the potential barrier between two semi-infinite jellium slabs as a function of their separation.