Effect of contact statistics on electrical contact resistance

The flow of electrical current through a microscopic actual contact spot between two conductors is influenced by the flow through adjacent contact spots. A smoothed version of this interaction effect is developed and used to predict the contact resistance when the statistical size and spatial distribution of contact spots is known. To illustrate the use of the method, an idealized fractal rough surface is defined using the random midpoint displacement algorithm, and the size distribution of contact spots is assumed to be given by the intersection of this surface with a constant height plane. With these assumptions, it is shown that including finer scale detail in the fractal surface, equivalent to reducing the sampling length in the measurement of the surface, causes the predicted resistance to approach the perfect contact limit.