Physics-Enhanced BGA-RDL Interconnects Model for Millimeter-Wave 3-D Packaging

This article presents a physics-enhanced equivalent circuit model for high-frequency interconnections integrating ball grid arrays (BGAs) with redistribution layers (RDLs), fabricated using wide-ground coplanar waveguide (CPW) structures. Moving beyond existing models proficient in characterization of basic parameters, the core innovation lies in the establishing an equivalent circuit model that enables quantifiable calculation and early prediction of eddy current inductance. In addition, a refined method for accurately modeling the inductance within BGA interconnects is proposed. Based on this model, the scaling laws governing inductance parameters with respect to BGA pitch and the effects of varying numbers of ground bumps are also discussed. The proposed model demonstrates predictive accuracy above 92% for transmission characteristics across from 0.1 to 40GHz. Systematic validation using 15 distinct physical samples, covering diverse BGA and RDL configurations, confirms an error below 8% empirical fitting with measured data. This modeling tool significantly enhances design efficiency and reliability for millimeter-wave 3-D packaging and integration systems by providing fast and accurate simulation of critical interconnection performance.