Quantitative Noncontact Electrostatic Force Imaging of Nanocrystal Polarizability

A simple analytical model describing tip-surface interactions in an electrostatic force microscopy (EFM) experiment is proposed. Tip-surface capacitance is modeled as a sum of capacitances of cone, sphere, and plate with the substrate. Individual tips are calibrated according to this model by the choice of tip radius. Differences in EFM signal amplitude between probes are explained by differences in the sphere radii. Three tips with different sphere radii were used to detect EFM force gradients on an array of samples of dispersed Au nanoparticles with diameters ranging from 6 to 18 nm. The spatial distribution of the electric field created by an Au nanoparticle polarized by the inhomogeneous field of the tip is calculated analytically. The particle diameter and tip-surface separation dependence of the measured force gradient due to metal sphere polarization is compared to that predicted by the model. A statistically significant z-offset factor is introduced into the model to correct for the curvature mismatch between the model system and the actual tip