Influence of the Substrate and Tip Shape on the Characterization of Thin Films by Electrostatic Force Microscopy

Abstract

Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: G. M. SachaAbstract-Electrostatic force microscopy has been shown to be a useful tool to determine the dielectric constant of nanoscaled thin films that play a key role in many electrical, optical and biological phenomena. Previous approaches have made use of simple analytical models to analyze the experimental data for these materials. Here we show that the electrostatic force shows a completely different behavior when the shape of the tip and sample are taken into account. We present a complete study of the interaction between the whole tip and the layers below the thin film. We demonstrate that physical magnitudes such as the surface charge density distribution and the size of the materials have a strong influence on the EFM signal. The EFM sensitivity to the substrate below the thin film decreases with the substrate thickness and saturates for thicknesses above two times the length of the tip, when it is close to that of an infinite medium.

A Model for the Characterization of the Polarizability of Thin Films Independently of the Thickness of the Film

“…Within these limits, previous results have shown that the cantilever part contributes only as a constant value to the force 18 . To analyze the electrostatic interaction we calculate the surface charge density on the tip and sample with the Generalized Image Charge Method (GICM) 19 . Using this technique, the surface charge density is replaced by a set of N point charges and M segments of length L i along the tip axis.…”

“…18 To analyze the electrostatic interaction, we calculate the surface charge density on the tip and sample with the generalized image charge method (GICM). 19 Using this technique, the surface charge density is replaced by a set of N point charges and M segments of length L i along the tip axis. The electrostatic potential can then be calculated by the following expression…”

Unveiling Alternating Current Electronic Properties at Ferroelectric Domain Walls

“…Local parasitic stray capacitances, C stray , exist in addition to the contributions from the tip–sample system, as illustrated in Figure 2b. Stray capacitances, also termed fringe capacitance, [ 127 ] originate from both the upper part of the tip [ 128,129 ] and the cantilever [ 130 ] and can be several orders of magnitude larger than the actual local capacitance of the material, C sample . [ 131 ] Values of C stray = 10 −10 F have been reported, whereas material properties may be as low as 10 −18 F. [ 103,132,133 ] Parasitic stray effects are a common challenge in local probe measurements leading, for example, to a bias in polarization hysteresis loops in switching experiments.…”

Quantitative Theory for Probe-Sample Interaction With Inhomogeneous Perturbation in Near-Field Scanning Microwave Microscopy

“…In (3), the Green's function is calculated as (9) The physical meaning of is the potential at the position of due to a unit point charge at the position . Thus, for the case when there is no analytical solution, we can numerically calculate it by putting a unit charge at the position of and evaluate the potential at .…”

“…The interaction between tip and sample is difficult to analyze numerically due to the complexity of tip geometry, and large computation area for three-dimensional (3-D) samples. Replacing the tip by a small conducting sphere is widely used to approximate tip-sample interaction [7], [8], but the accuracy of this approximation is questionable due to the important contribution from the upper part of the tip [9], [10]. An approximate analytical solution is also used [11], [12], but the tip geometry is limited to very few specific types [13]- [15].…”