Electrostatic force microscopy and potentiometry of realistic nanostructured systems

TL;DR

This paper develops a comprehensive capacitance model for electrostatic force microscopy that accounts for complex nanostructures and larger probe-sample distances, improving data interpretation and clarifying Kelvin potential concepts.

Contribution

It introduces a general capacitance model considering multiple conductors and applied potentials, addressing limitations of previous approximations in EFM and KPM.

Findings

Electrostatic force can switch from repulsive to attractive depending on potentials and distances.

Numerical simulations and experiments validate the model's ability to describe realistic nanostructured systems.

The model enhances understanding of Kelvin potential in local potentiometry applications.

Abstract

We investigate the dependency of electrostatic interaction forces on applied potentials in Electrostatic Force Microscopy (EFM) as well as in related local potentiometry techniques like Kelvin Probe Microscopy (KPM). The approximated expression of electrostatic interaction between two conductors, usually employed in EFM and KPM, may loose its validity when probe-sample distance is not very small, as often realized when realistic nanostructured systems with complex topography are investigated. In such conditions, electrostatic interaction does not depend solely on the potential difference between probe and sample, but instead it may depend on the bias applied to each conductor. For instance, electrostatic force can change from repulsive to attractive for certain ranges of applied potentials and probe-sample distances, and this fact cannot be accounted for by approximated models. We propose a general capacitance model, even applicable to more than two conductors, considering values of potentials applied to each of the conductors to determine the resulting forces and force gradients, being able to account for the above phenomenon as well as to describe interactions at larger distances. Results from numerical simulations and experiments on metal stripe electrodes and semiconductor nanowires supporting such scenario in typical regimes of EFM investigations are presented, evidencing the importance of a more rigorous modelling for EFM data interpretation. Furthermore, physical meaning of Kelvin potential as used in KPM applications can also be clarified by means of the reported formalism.