A theory of contact resistance under AC conditions

Abstract

Electrical contact is an important issue to high power microwave sources, pulsed power systems, field emitters, thin film devices and integrated circuits, interconnects, etc. Contact resistance and the enhanced ohmic heating that results have been treated mostly under steady state (DC) condition. In this paper, we consider the AC contact resistance for a simple geometry, namely, that of two semi-infinite slab conductors of different thicknesses joined at z = 0, with current flowing in the z-direction. The conductivity of the two planar slabs may assume different values. We propose a procedure to accurately calculate the normalized contact resistance under the assumption σ≫ωϵ, where ω is the frequency, σ is the electrical conductivity, and ϵ is the dielectric constant of the material in either channel. We found that in the low frequency limit, the normalized AC contact resistance reduces to the DC case, which was solved exactly by Zhang and Lau. At very high frequency, we found that the normalized contact resistance is proportional to ω, in which case the resistive skin depth becomes the effective channel width, and the physical origin of the contact resistance is identified. The transition between the high and low frequency limits was explored, where, in some cases, the normalized contact resistance may become negative, meaning that the total resistance is less than the total bulk resistance expected from the two current channels. In other cases, the numerical data suggest that the normalized contact resistance is proportional to ω in the transition region. Other issues are addressed.