The analytical relations between particles and probe trajectories in atomic force microscope nanomanipulation

A new approach to the problem of manipulation of nanoparticles on a surface is proposed. Exploitinganalogies with traditional scattering theory, we show how the geometry of the particles, andtheir interaction with the underlying surface, could be determined from measurable quantities likethe angle of deflection and the spacing between consecutive scan lines in atomic force microscopyexperiments. An analytical formula is derived and applied to spherical gold particles moved on flatand patterned silicon surfaces.