Compact modeling and optimization of fine-pitch interconnects for silicon interposers

This paper presents the first optimization methodology for silicon interposer interconnect technology. The dimensions of these fine-pitch interconnects are roughly a few microns, because of which they can neither be treated as on-chip RC interconnects, nor as conventional off-chip interconnects. 3D extraction tools can provide an accurate estimate of the circuit parameters, but they prove to be very slow and tedious for design space exploration and optimization. Thus, the novel analytical models developed here for the frequency dependent resistance of fine-pitch interconnects are essential to efficiently optimize these interconnects. The error in the model is shown to be less than 15% for interconnect dimensions and frequency range of interest. The analytical models developed are then used to optimize the data-rate and cross-sectional dimensions to maximize the bandwidth-density and minimize the energy-per-bit, simultaneously.