Accuracy of Physics-Based Via Models for Simulation of Dense Via Arrays

This paper studies the accuracy of the physics-based via model, specifically when applied to dense via arrays. The physics-based model uses Green´s functions for cylindrical waves in radial waveguides to model the via return current paths and the coupling between vias. The effects of approximations made in this model are studied with regard to four types of modes based on an eigenmode expansion for the radial waveguide. It is found that for the mode conversion in the vicinity of the via, an accurate consideration of nonpropagating modes becomes critical with an increasing cavity height. For the interaction between vias in dense arrays, anisotropic modes have an impact for small pitches, whereas the coupling by nonpropagating modes is small for practical printed circuit board dimensions. For a data rate of 20 Gb/s, conclusions with regard to the applicability of the physics-based via model to a multilayer structure are drawn. For 80-mil pitch, a good agreement to full-wave results can be observed. Measurements have been carried out to validate this finding. For 40-mil pitch, the accuracy of the physics-based via model is not sufficient for data rates of 20 Gb/s or higher.