Off-Chip Rough-Metal-Surface Propagation Loss Modeling and Correlation with Measurements

We discuss a small-perturbation method (SPM) for the prediction of the surface-roughness augmented propagation loss encountered on interconnects on high-speed packages and boards. In this methodology, rough surfaces are characterized by their power spectral density (PSD) that can be obtained from surface height profiles by the application of Fourier methods and averaging. Piecewise uniformly rough interconnect structures can be treated by localization of the SPM and assigning corresponding effective conductivities in an electromagnetic field solver. Quantitative surface imaging techniques for acquiring surface height maps include optical interferometry, scanning probe microscopy and scanning electron microscopy. Reactive ion etching is used to expose copper surfaces on post-lamination samples with organic dielectrics. For demonstration of the SPM through correlation with measurements, de-embedding of the transmission line loss is performed using a two-line method. Atomic force microscopy is employed to image the rough ground plane of the micro-strip interconnect and obtain its PSD. Good agreement between measured and predicted loss is shown.