A promising technique capable of performing localized resistance measurements over a surface is presented using a modified commercial atomic force microscope with a conducting probe. Its overall purpose is to obtain simultaneous cartographies of surface roughness and local resistance within a given microscopic area of a sample with nanometer scale resolution. Although an elaboration of suitable probes remains an ongoing problem, convincing images of some metal surfaces that reveal occasionally surprising features have already been obtained. Calculations performed from measurements have allowed us to clarify the mechanical nature of the tip/surface nanocontact and hence to determine the most probable transport process according to the range of resistance considered.

The problem of capacitance between a rough sphere and a rough plane very close to each other is studied. The problem is simplified by gathering the roughness of both members onto the plane. We begin by considering the case where the sphere and the plane are both ideally smooth. Starting from a known exact formula of the capacitance involving an infinite sum, we derive a simple and easy to use approximate expression. Then we consider the case where the sphere is smooth and the plane rough. The new formula for the capacitance involves an integral in which the weighting function is the height distribution. To validate this formula, the results of two experiments, during which the derivative of the capacitance with respect to the separation has been recorded, are considered. Comparison of the measurements with theoretical calculations indicates the approach is valid.