Study of the electrostatic force between a conducting tip in proximity with a metallic surface: Theory and experiment

Abstract

A formula has been derived for the electrostatic force between the conducting tip and a planer metallic surface by exploiting the fact that the tip–sample geometry can be described by confocal hyperboloids of revolution. The prolate spheroidal coordinate system was found to be most convenient for this purpose. The general behavior of force curves obtained in the attractive regime using a conducting cantilever and an optical beam deflection system is in reasonably good agreement with the theory over a wide range of distances. The results are important in the context of design, development, and understanding of scanning probe microscopes involving voltage bias between the probe and sample.

Electrostatic forces in micromanipulation: Experimental characterization and simulation including roughness

“…An expression for the hyperboloid configuration has been given by Refs. [22,6]. Bonaccurso et al [23] also took into account the tilting angle influence in the electrostatic interaction during AFM measurements.…”

Microworld Modeling in Vacuum and Gaseous Environments

“…The expression is derived by solving the Laplace equation in a prolate spheroidal coordinate system and by treating the tip-sample geometry as two confocal hyperboloids. Please refer to Patil and co-workers [74,75] for calculation details. The boundary conditions are: the tip is at a potential V and the sample is grounded.…”

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

“…The first information we extract from Eq. (43) is that in the absence of Coulomb interactions (i.e. K c = 1), the screening part cancels because of the pre-factor K 2 c − 1 in front of the function f r ′ Sc .…”