National Institute of Standards and Technology,
Keywords: atomic force microscopy, nanoscale electrostatic interaction
Summary:The nanoscale electrostatic interaction between a conductive atomic force microscopy (AFM) probe and a sample is observed in various AFM modes like Kelvin probe force microscopy, scanning capacitance microscopy, and dielectric AFM to determine local surface potential, dopant profile, charge trapping, and dielectric properties among others. There is no simple analytical description of the electrostatic interaction generated in the confined probe-sample geometry by various static and dynamic variants of these AFM modes. An accurate description of the involved physics is obtained by means of a finite element analysis modeling of the system, However, the alternative of using numerical analysis is not very popular being slower and requiring relatively high computation resources. In this work we revised the contributions from different parts of the AFM probe to the probe-sample capacitance by both analytical and numerical methods. We tried to reconciliate the two approaches and observed the differences as a function of geometry and material parameters. This was investigated in both amplitude and frequency modulations of various force and force gradient electrostatic AFM implementations to extract the measurement sensitivities of the observed deflection and frequency of an AFM probe to parameters of interest like surface potential and dielectric constant. The obtained measurement sensitivities are relevant in selecting the optimal scanning mode and its operational parameters but are also showing the critical role of the numerical analysis to the correct interpretation of the measurements.