Theoretical study on contact current density in the boundary of random rough surfaces

Abstract

We theoretically calculate here how random roughness affects the contact current density and equivalently contact resistance by utilizing a perturbative expansion method. Then, By taking into consideration self-affine roughness on the surface of the solids, we find the contact current density. The obtained results illustrate the total contact current exhibits significant dependence on the properties of the self-affine rough surface such as root-mean-square of roughness and Hurst exponent. Assuming a lower value of root-mean-square roughness for a solid in a higher potential compared to another which is connected to a lower potential, results in a decrement of the total contact current compared to the current between solids without roughness. By considering similar rough parameters for both solids, the contribution of the perturbed contact current becomes zero. Moreover, repercussions by considering the conductivity contrast between components are explored.