Efficient variation-aware EM-semiconductor coupled solver for the TSV structures in 3D IC

In this paper, we present a variational electromagnetic-semiconductor coupled solver to assess the impacts of process variations on the 3D integrated circuit (3D IC) on-chip structures. The solver employs the finite volume method (FVM) to handle a system of equation considering both the full-wave electromagnetic effects and semiconductor effects. With a smart geometrical variation model for the FVM discretization, the solver is able to handle both small-size or large-size variations. Moreover, a weighted principle factor analysis (wPFA) technique is presented to reduce the random variables in both electromagnetic and semiconductor regions, and the spectral stochastic collocation method (SSCM) is used to generate the quadratic statistical model. Numerical results validate the accuracy and efficiency of this solver in dealing with process variations in hybrid material through-silicon via (TSV) structures.