Single and multi-spot current density distribution

This paper provides an analysis of the current density distribution in a single circular contact spot for cases that represents geometrical configurations that are closer to what occurs in real contacting members. In the past, flat contact spots have been used to estimate current density distributions for single circular spots by assuming that bridge conditions do not exist. However, the bridge condition changes the current density at the edge of the contact spot. With no bridge, the mixed boundary conditions for voltage and electric field lie in a plane and give rise to infinite current densities at the edge of the contact spot. In the present paper, when bridge geometries exist, it was found the mixed boundary conditions do not lie in a plane and give rise to finite current densities at the edges. In this work, electromagnetic theory was used to calculate the current density distribution that occurs for bridge geometries. These results are subsequently compared to the traditional results that are often used in analyses and show as the slope of the bridge increases, the current density at the edge decreases to finite values. In addition, it was seen that as the slope increases the current density tends to even out across the contact spot. Consequently, it is seen that the bridge condition at the contact spot may impact the degradation rate for current density driven mechanisms such as electro-migration. In addition, to complete the picture, the impact on average current density in individual spots is reviewed regarding the effects of spot size and position in the contact region.