Some results pertaining electromagnetic characterization and model building for passive systems including TSVs, for 3-D IC applications

Electromagnetic (EM) modeling and simulation techniques for passive linear systems as in 3D ICs and SIPs are presented. On TSVs' we present high throughput analytical 2D admittance (CG) and impedance (RL) models, with consideration of MOS effect in silicon. These 2D models are computationally useful for parasitic estimates, while the simulation of critical subsystems requires 3D accurate models. We show results from an emerging 3D field solver solution to the computation of the RL matrices with very low overhead on the matrix elements computation, being analytically tractable for cylindrical TSVs. For extraction and simulation of systems containing a significant number of passive elements, the output from field solver is best expressed as passive dynamical models generated with an efficient semi-definite programming algorithm.