Quantifying the dielectric constant of thick insulators by electrostatic force microscopy: effects of the microscopic parts of the probe

Abstract

We present a systematic analysis of the effects that the microscopic parts of electrostatic force microscopy probes (the cone and cantilever) have on the electrostatic interaction between the tip apex and thick insulating substrates (thickness > 100 μm). We discuss how these effects can influence the measurement and quantification of the local dielectric constant of the substrates. We propose and experimentally validate a general methodology that takes into account the influence of the cone and the cantilever, thus enabling us to obtain very accurate values of the dielectric constants of thick insulators.

Nanoscale dielectric microscopy of non-planar samples by lift-mode electrostatic force microscopy

“…The tip is represented as a truncated cone of half-angle θ , and cone height H, terminating in a tangent hemisphere of radius R [35]. In addition, a disc of thickness W, overseeing the cone base by an amount L is located onto the cone base to model eventual local cantilever effects.…”

“…Poisson's equation solution results in the distribution of the static electric potential around the tip and in the sample, from which we derive the Maxwell stress tensor on the tip surface, and, by integration of it on the surface of the tip, we obtain the electrostatic force (see further details elsewhere [35]). The mesh was set to at least 200000 elements.…”

Traceable measurement and imaging of the complex permittivity of a multiphase mineral specimen at micron scales using a microwave microscope

“…In the case of the rock specimen, the measured areas (Table 3 and Figs. [12][13][14] were at least 1 mm away from the edge of the specimen, so the proximity with the boundary with air should have minimal effect. The boundaries of the mineral phases within the rock sample must also have an effect, but this will be smaller because the permittivity of the epoxy matrix (ε' = 2.94) is higher than that of air.…”

“…The resonator must be an integral part of whatever model is used as the relation between complex permittivity and the observed perturbations in frequency and Q-factor must be established. Accurate models that incorporate the tip geometry have been developed for use in Electrostatic Force Microscopy (EFM) experiments for measuring permittivity [14], but these are not directly applicable. It is well established [11] that cavity perturbation theory and an electrostatic model [2] (with modifications that will be summarised in Section III) can be used to obtain accurate measurements of permittivity and loss tangent using spherical tips.…”

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

“…Some experimental results on the analysis of the tip shape over thick films can be found on Refs [22] [23].In figure 4a we have represented the electrostatic force as a function of the thin film thickness for tips with lengths between L tip =3m and L tip =20m, and half-angles between =17.5º and =35º. In this figure we have fixed R=25nm.…”