On the upper bound of total uncorrelated crosstalk in large through silicon via arrays

Large via arrays contribute substantially to the coupling path of crosstalk between channels of interconnects. In principle, in order to design robust interconnects, the crosstalk contributions from all aggressor channels must be quantified and adequately superposed to represent the crosstalk mechanism. If the modeling is based on frequency domain electromagnetic simulations, in general, it is necessary to simulate the complete geometry for a large number of frequencies in order to accurately represent the physical effects. In this paper, an efficient statistical frequency domain superposition of crosstalk is proposed and validated against time domain methods. The proposed approach provides a measure of total crosstalk by assuming uncorrelated signals on different channels. Using this definition, it can be reasoned whether an upper bound of total uncorrelated crosstalk exists and which vias should be included in a meaningful approximation of a large array.