Effects of Surface Roughness on Electrical Contact, RF Heating and Field Enhancement.

Abstract

Surfaces are never perfectly flat. Because of the surface roughness on a microscopic scale, true contact between two conductors occurs only at the asperities (small protrusions) of the contacting surfaces, leading to contact resistance, an important issue to high power microwave sources, pulsed power systems, tribology, thin film devices, integrated circuits, and interconnects, etc. Another profound effect of surface roughness is the excessive local field enhancement that triggers RF breakdown, and the rapid loss of superconductivity in a superconducting cavity. This thesis models various effects of surface roughness, including electrical contact resistance for both bulk and thin film contacts. Scaling laws are constructed for a large range of resistivity ratios and aspect ratios. Also presented is roughness-induced enhanced RF heating, and the enhanced RF electric and magnetic fields. Presented first is the bulk contact resistance with dissimilar materials. For decades, the basic model for contact resistance remains that of Holm’s a-spot, where current flows through a circular constriction of small radius a and zero thickness at the bulk interface. We vastly extend Holm’s theory to higher dimensions, including dissimilar materials. Both Cartesian and cylindrical channels are analyzed. A scaling law for the contact resistance has been constructed for arbitrary aspect ratios and resistivity ratios. This scaling law has been validated in various tests, simulations, and experiments. This thesis next presents the thin film contact resistance with dissimilar materials. Simple, analytical scaling laws have been developed, for both cylindrical and Cartesian geometries. We have identified the optimal condition for minimization of the thin film contact resistance. The current crowding effect, which may induce excessive ohmic heating, is also studied. Extension to general a-spot geometry is made. This work may offer useful insights for the design and fabrication of thin film devices and components. Presented also is roughness-induced enhanced RF heating, and the enhanced RF electric and magnetic fields. We analytically compute the power absorption due to a hemispherical protrusion with arbitrary permittivity ε, permeability μ and conductivity σ, on a flat surface. The local electric and magnetic field enhancements on the protrusion are calculated analytically. Scaling laws are derived.