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by Keyword: Permittivity


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Gomila, G., Gramse, G., Fumagalli, L., (2014). Finite-size effects and analytical modeling of electrostatic force microscopy applied to dielectric films Nanotechnology , 25, (25), 255702 (11)

A numerical analysis of the polarization force between a sharp conducting probe and a dielectric film of finite lateral dimensions on a metallic substrate is presented with the double objective of (i) determining the conditions under which the film can be approximated by a laterally infinite film and (ii) proposing an analytical model valid in this limit. We show that, for a given dielectric film, the critical diameter above which the film can be modeled as laterally infinite depends not only on the probe geometry, as expected, but mainly on the film thickness. In particular, for films with intermediate to large thicknesses (>100 nm), the critical diameter is nearly independent from the probe geometry and essentially depends on the film thickness and dielectric constant following a relatively simple phenomenological expression. For films that can be considered as laterally infinite, we propose a generalized analytical model valid in the thin-ultrathin limit (<20-50 nm) that reproduces the numerical calculations and the experimental data. Present results provide a general framework under which accurate quantification of electrostatic force microscopy measurements on dielectric films on metallic substrates can be achieved.

Keywords: Dielectric constant, Dielectric films, Electrostatic force microscopy, Quantification, Analytical models, Electric force microscopy, Electrostatic force, Film thickness, Permittivity, Probes, Substrates, Ultrathin films, Accurate quantifications, Electrostatic force microscopy, Finite size effect, Lateral dimension, Metallic substrate, Numerical calculation, Polarization forces, Quantification, Dielectric films


Fumagalli, L., Gramse, G., Esteban-Ferrer, D., Edwards, M. A., Gomila, G., (2010). Quantifying the dielectric constant of thick insulators using electrostatic force microscopy Applied Physics Letters , 96, (18), 183107

Quantitative measurement of the low-frequency dielectric constants of thick insulators at the nanoscale is demonstrated utilizing ac electrostatic force microscopy combined with finite-element calculations based on a truncated cone with hemispherical apex probe geometry. The method is validated on muscovite mica, borosilicate glass, poly(ethylene naphthalate), and poly(methyl methacrylate). The dielectric constants obtained are essentially given by a nanometric volume located at the dielectric-air interface below the tip, independently of the substrate thickness, provided this is on the hundred micrometer-length scale, or larger.

Keywords: Borosilicate glasses, Finite element analysis, Insulating thin films, Mica, Nanostructured materials, Permittivity, Polymers, Scanning probe microscopy