Electrostatic forces acting on the tip in atomic force microscopy: Modelization and comparison with analytic expressions

Abstract

With the model of equivalent charge distribution, we calculated the exact electrostatic force acting on the real ͑conical͒ tip of an atomic force microscope. This model applies to a conductive tip in front of a conductive plane. We compared the equivalent charge model with several analytic models used to date to approximate the electrostatic forces and discussed their degree of validity. We estimated the contribution of the cantilever to the total force and showed, on the basis of theoretical calculations and experimental results, that the contribution of cantilever may constitute the essential part of the electrostatic force in the range of distances used in electrostatic force microscopy in the air.

Force measurements with the atomic force microscope: Technique, interpretation and applications

“…Also procedures to calculate the electrostatic force between metals precisely but numerically are described [225,226]. The contribution of the cantilever as a correction in particular at large distances was realized and described by several authors [227,228]. The effect of surface roughness was considered by Boyer et al [229].…”

Piezoresponse force spectroscopy of ferroelectric-semiconductor materials

“…For the spherical part of the tip apex, the solution is rigorous, while for the conical part of the tip an approximate line-charge model can be used. 81,82 Here, we develop the approximate expressions for piezoresponse of the initial and intermediate ͑cylindrical and nested cylindrical͒ domains for the finite Debye length of ferroelectric semiconductor.…”

Carbon nanotubes as a tip calibration standard for electrostatic scanning probe microscopies

“…[2,3,4] For small tip-surface separations tip geometry can be accounted for using the spherical tip approximation and the corresponding geometric parameters can be obtained from electrostatic force-or force gradient distance and bias dependences. [5,6] Such a calibration process is often tedious and tip parameters tend to change with time due to mechanical tip instabilities. [7] Alternatively, the tip contribution to measured surface properties can be quantified directly using an appropriate calibration method.…”