Electrical modeling of Copper and Mixed Carbon bundles as a composite for 3D Interconnect applications

Generally Copper filled through silicon vias (TSVs) are considered effective for 3D IC applications, however Copper (Cu) filled interconnects are not devoid of electrical and mechanical problems. Carbon nanotubes (CNTs) are considered more robust, with high current carrying capacity, and mechanically tough compared to other materials considered. The fabrication of the Cu/CNTs in the TSVs are investigated thoroughly and a process to consistently grow vertical CNTs with Cu filling post CNT growth in a TSVs is established. The grown CNTs are observed to be mixed bundles comprising of Single Walled Nanotubes (SWNT), and Multiwalled Nanotubes (MWNT) in different proportions. The paper presents the designed closed loop surface current density, bidirectional vertical delay and crosstalk models for Mixed Carbon bundles (MCB) with Copper filled TSV interconnects. The developed models are expressed as a function of Cu filling ratio, SWNT/MWNT proportion in the mixed carbon bundles, TSV geometry including tapered profile of the via, and the diameter of CNTs. The current density, delay and S-parameters are analyzed using the developed models for a standard TSV design. The surface current density model indicates consistent current density along the surface, for higher proportion of SWNT in the MCB, with minimum Copper in the via. The cross talk models suggests similar transmission and reflection properties for MCB/Cu composite when compared to Cu based TSVs. The delay models suggests improvement in the signal propagation for composite consisting of Cu, and MCB with higher proportion of MWNTs. The models are considered a useful tool for 3D IC designers, especially towards placement and routing stage of the chip design.