The Effects of Bridge Structures on Current Density and Temperature Distributions

In earlier work [1,2] it was shown that bridge structures adjacent to contact spots effect current density distributions. Specifically, it was shown that the current density at the edge of contact spots is finite as compared to infinite results for the ideal co-planar cases which are often used in estimating contact resistance. In the former case, hyperbolic bridge structures were used to demonstrate the finite results. In the present paper, additional structures such as elliptical shapes are used to show more generally that finite results exist for various bridge structures. In addition, the temperature distribution in the contact region is evaluated and compared to the ideal co-planar case. It is asserted that the relation between contact voltage and temperature is preserved in cases where symmetrical bridge structures exist. In the present work, modified solutions to the Laplace equation are used to show that non-co-planar boundary conditions are met to provide valid solutions for bridge structure cases. The results are compared to the ideal case of co-planar conditions. It is seen in single contact spots, significant deviations from co-planar results can occur, depending on the details of the bridge structure. Moreover, in multi-spot contact interfaces it is shown that the effects from parallel current paths mitigate the single spot results.