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(Color online) Scheme of the method to obtain the effective dielectric constant of a thin film sample. The electrostatic force of a system composed by a thin film over a dielectric substrate (equipotential lines shown at the top) is used as the input of an artificial neural network. The output value is the effective dielectric constant of an equivalent sample composed by a semiinfinite dielectric substrate (equipotential lines shown at the bottom). R = 25 nm, h1 = 5 nm, ɛ1 = 10, ɛ2 = 5, ɛeff = 5.59, V0 = 1 V, and D = 5 nm.
(Color online) Gradient force versus tip sample distance for both a thin film and an equivalent semiinfinite dielectric sample obtained by artificial neural networks for a spherical tip with R = 25 nm (a) and three different macroscopic tips (b). Details about the tip and sample geometries are shown in the figure.
(Color online) (a) Effective dielectric constant for ultrahigh thin film dielectric constants obtained by the analytical approximation and the ANN. Continuous line represents the range where the analytical expression gives better results than the ANN. (b) Gradient force for thin films characterized by ɛ1 = 500 and ɛ1 = 10 000. Inset shows the electrostatic force for ɛeff = 10, 30, 50, ∞ (top to bottom). In all figures, R = 25 nm, θ = 17.5°, L = 14 μm, V0 = 1 V, h1 = 1 nm, and ɛ2 = 5.
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