Electromigration (EM) in power distribution network (PDN) is a major reliability issue in 3D ICs. While the EM issues of local vias and through-silicon-vias (TSV) have been studied separately, the interplay of TSVs and conventional local vias in 3D ICs has not been well investigated. This co-design is necessary when the die-to-die vertical power delivery is done using both TSVs and local interconnects. In this work, we model EM for PDN of 3D ICs with a focus on multi-scale via structure, i.e., TSVs and local vias used together for vertical power delivery. We study the impact of structure, material, and pre-existing void conditions on EM-related lifetime of our multi-scale via structures. Experimental results demonstrate that our EM modeling can effectively capture the EM reliability of the entire multi-scale via in 3D PDN, which can be hard to achieve by the traditional EM analysis based on the individual local via or TSV.