Effective tip radius in electrostatic force microscopy

A method to determine the effective electrostatic tip radius of arbitrarily shaped conducting tips in atomic force microscopy is presented. The method is based on the finding that for conductive samples, the electrostatic force can be separated into two contributions: one from a constant background that depends only on the macroscopic shape of the tip (cone or pyramid and cantilever), and another that depends only on the radius of curvature of the tip apex. Based on a simple theoretical expression derived from the generalized image charge method, we show that the tip radius can be directly determined from experimental force-distance characteristics. For irregular tip shapes, we show that the measured tip radius is the average of two principal curvatures, in agreement with tip shape images obtained by scanning electron microscopy.