Time domain electromagnetic analysis of a via in a multilayer computer chip package

A methodology for deriving an equivalent circuit of a via in a multilayer computer chip package using a time-domain full-wave solution of Maxwell´s equations is presented. The approach is general and its applicability is limited by the ability of the circuit simulator to model frequency-dependent elements. To accurately model the curved geometry, the nonorthogonal FDTD (finite-difference time-domain) algorithm is employed instead of the conventional FDTD method because it provides a piecewise-linear model of curved surfaces, and, with a variable mesh density, it can represent complicated structures without an excessive number of unknowns. The nonorthogonal FDTD results were validated with measurements, and an equivalent circuit model was developed from the results.<>