Random Rough Surface Effects on Wave Propagation in Interconnects

To address the rough surface effects in high-speed interconnects on printed circuit boards (PCBs) and microelectronic packages, we study the electromagnetic wave propagation in a rough surface environment. In our model, the rough surface is characterized by a stochastic random process with correlation function or spectral density. This paper reviews the analytical theory, numerical simulations and experimental results based on such a model. We describe the rough surface characterization and the extraction of roughness parameters from 3D profile measurements. Initially we study the 2D case with the rough surface height function varying in only one horizontal direction and consider the case of plane wave incidence. Analytic second-order small perturbation method (SPM2) was used to obtain simple closed-form expressions for the absorption enhancement factor. The numerical transfer matrix (T-matrix) method and the method of moments (MoM) were also used. We next consider the case of the 3D problem with the rough surface height varying in both horizontal directions. We also used SPM2 to obtain a simple closed form expression for the enhancement factor. In interconnect problems, electromagnetic (EM) waves propagate in a guided wave environment. Thus, we next considered a waveguide model to study the effects of random roughness on wave propagation and compare with results from the plane wave formulation. Analytic SPM2 and numerical finite element method (FEM) with mode matching were used to obtain the enhancement factor. We also describe experimental results and correlation with the theoretical models. Finally, we explain how the enhancement factor concept used throughout lends itself to direct inclusion of rough surface effects in a wide variety of modeling problems.