An Efficient Quasi-Transient Electro-Thermal Algorithm for System-in-Package Based on the Unconditionally Stable Finite Difference Method

In this study, we proposed a quasi-transient electro-thermal analysis algorithm based on the finite difference method to comprehensively delineate the coupling phenomena within the highly integrated systems under the transient external electro-magnetic pulse (EMP). The quasi-transient coupling scheme is realized by interpolating a time factor between the two fields, thus harmonizing their time scale discrepancies efficiently. This process resolves transient physical mechanisms adeptly and saves computational cost effectively. To enhance its adaptability in diverse multi-scale targets, especially for those processed by integrated circuit’s advanced packaging techniques, including the redistribution layer (RDL), through-silicon via (TSV), and highly integrated system-in-package (SiP), we employ the subgridding discretization method and adopt the alternating direction implicit (ADI) scheme for both fields facilitating an unconditionally stable computation. On this basis, we conducted several quasi-transient electro-thermal analyses for different advanced packaging components to quantify their electrical and thermal response induced by the EMP incidence, thereby substantiating the efficacy of the method in such complex problems.