Analysis of wave propagation along coaxial through silicon vias using a matrix method

This paper presents an efficient method for the determination of the dispersion relation of wave propagation along coaxial structures with radially layered dielectric filling based on a matrix method known from the theory of optical waveguides. The method is applied for investigations of coaxial through silicon vias having different dimensions and different conductivities of the silicon semiconductor filling. The fundamental modes are derived, results are correlated to full-wave simulation results, and the physical phenomena of quasi TEM, slow-wave and skin-effect propagation in the fundamental mode are discussed with regard to signal integrity.