Utilizing the coulomb force on a carbon nanotube to enhance the resolution of electrostatic force microscope

Various sources, which affect the resolution of the electrostatic force microscope, are discussed. In addition to an overall hump due to the finite distribution of charges, we find that the electrostatic force versus lateral position plot shows better resolution in certain scanning directions, and in some others it may even exhibit misleadingly different amplitudes from different positions with the same magnitude of charge. Since the electric field measured experimentally is outside of the sample, we need to solve an integral equation to determine the charge distribution. But due to the finite resolution of the probe, the problem can be much simplified by discretizing the space and ending up with the simple process of inverting a matrix. The influence by the image charges from the conducting substrate is automatically taken care of. We describe analytic/ numerical calculations for the charge distribution on the nanotube and its atomic force with a conducting surface or a charged cluster. Implication caused by the tilt of the nanotube is also discussed.