Modeling effects of random rough surface on conductor loss at microwave frequencies

The roughness of the interfaces between metal and dielectric layers in high-speed interconnect and microelectronic package often causes significant additional power absorption at microwave frequencies which is detrimental to signal and power integrity. To quantify the roughness effect on power loss, we use a random rough surface model with root-mean-square height, correlation function and spectral density to characterize the roughness. Analytic models based on small perturbation method of second order are developed for two-dimensional and three-dimensional problems. Our formulation takes into account both dielectric and conductive media. The similarities with and differences from Morgan's classical result and the Hammerstad and Bekkadal formula are discussed. Results are compared and verified with numerical method of moments and T-matrix method. We also propose and demonstrate procedures of estimating the roughness-induced absorption enhancement factor by extracting power spectral densities from measured surface profile data. Comparing the measured propagation loss with the roughness-corrected smooth-problem loss yields excellent agreement. Additionally, we apply multiple scattering equations to study the scattering and absorption of electromagnetic waves on a conducting plane surface with a random distribution of hemispherical bosses. We derive multipole solutions up to third order to analyze close range interactions between nearby bosses. Surface current and absorption enhancement factors are further computed for different embossed surfaces.