Constriction resistance of a multispot contact: an improved analytical expression

When dealing with a multispot metallic contact two different problems are raised: whether the calculation of the constriction resistance R_c is required from geometrical considerations and whether one calculates the real area of contact from electrical measurements. Attention is focused on the second case, and it is shown that when the total area built up by the elementary spots represents a large fraction of the apparent area of contact, then the usual analytical expressions of the resistance can be imprecise. Considering the case of n elementary spots of radius r regularly spread in a disc of radius R representing the interface of contact of two metals of equal resistivity ρ, they give an improved expression of the resistance. When the total area of the spots is equal to the disc area, this expression gives for any value of n the usual R_c=ρ/2R. Conversely, when n=1, it gives, for any value of R, the correct expression: R_c=ρ/2r. It is shown that this improved expression is quite useful when the number of spots is small and the real area of contact close to the apparent one, i.e. in many practical cases