Quantifying electrostatic force contributions in electrically biased nanoscale interactions

A study of the validity of analytical methods for calculating the electrostatic force interaction in alternating current electrostatic force microscopy is presented. Using a simple harmonic oscillator model, two analytical frameworks aimed at relating the electrostatic force between the cantilever tip and the sample with measurable parameters (amplitude and phase of the cantilever) are derived. The validity of the frameworks is examined based on two parameters that define the oscillation amplitude of the cantilever (tip voltage and tip-sample distance). Results are compared with an analytical model of the electrostatic interaction between tip and sample (tip-sample capacitance) and the range of validity of these two frameworks is provided. Our analysis confirms that the commonly used interpretation of the amplitude and the phase as a measure for the electrostatic force and for the derivative of the electrostatic force is only valid for very small oscillation amplitudes and depends on the tip geometry. Furthermore, this study demonstrates that these two techniques suffer from sensitivity limitations at large tip-sample distances. Finally, we compare the two frameworks with an alternative technique for the quantification of the tip-sample electrostatic interaction we have recently proposed and we discuss and experimentally demonstrate its advantages in terms of reliability and sensitivity, providing an example of dielectric constant measurement of a thin insulating film. (C) 2014 AIP Publishing LLC.