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.

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Small amplitude Atomic Force Microscopy (AFM) is a relatively new AFM technique which was specifically developed to perform linear measurements of nanomechanical phenomena. This is achieved by using ultra‐small cantilever amplitudes and very high sensitivity deflection sensors. Recently this technique has been used in ultra‐high vacuum (UHV) and liquid environments to measure atomic and molecular forces and dynamics with high precision. Here we focus on three examples which are interesting from a nanoengineering standpoint: Atomic energy dissipation (atomic friction), atomic‐scale contact mechanics, and nanotribology/molecular ordering in confined liquid films.

The electrostatic force between a gold tip and an atomically flat highly oriented pyrolytic graphite substrate has been measured as a function of tip-sample separation distance for low bias voltages (<1 v). The experiments involve phase-sensitive detection of the reflected laser beam off a stiff oscillating cantilever as it approaches the sample. The results are compared with the theoretical model in which the tip-sample geometry is described by confocal hyperboloids of revolution. The general behaviour of the force curve was found to be in agreement with theoretical expectations only for distances of >600Å. The deviations at smaller distances probably could be due to extraneous material such as graphite nanoflakes or a conducting liquid column present between tip and sample. The results have direct bearing on understanding the interaction forces in scanning probe microscopy techniques in which tip-sample junctions are biased.

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