Analytical evaluation of scattering parameters for equivalent circuit of through silicon via array

The high level of integration in digital electronic chips based on three-dimensional (3D) technology requires accurate modelling of the vertical interconnects (the through silicon vias – TSVs). An accurate prediction of the signal propagation and crosstalk of the TSVs cannot be based on the single via since the interaction among adjacent TSVs in a high density array cannot be neglected. An algorithm is proposed that extends the approach for modelling a TSV array with a complete analytical evaluation of the final multiport scattering parameter matrix, thus making the electromagnetic modelling of such structures more efficient without relying on commercial circuit solvers. The proposed method requires much less processing time with respect to commercial solvers with a comparable accuracy.