Statistical Distribution of Through-Silicon via Cu Pumping

Cu pumping is defined as the irreversible extrusion of Cu from Cu-filled through-silicon vias (TSVs) exposed to high temperatures. The distribution of Cu pumping values over the TSVs of a single wafer has a large intrinsic spread. In previous publications both a lognormal distribution and a distribution of the maximum of two normal variables were used to fit experimental data. In this paper, these two types of statistical distribution are compared, showing that the maximum of two normal distributions provides a better fit, in particular at the right tail which is more significant for the potential reliability impact of Cu pumping. Also, it is shown how Cu pumping is determined by the network of random high angle grain boundaries in the Cu region near the TSV top, as an extension of a previous analysis which occurred at the TSV top surface only. This relation between Cu pumping and Cu microstructure provides a physical interpretation of the maximum of two normal distributions, based on the deformation mechanisms underlying Cu pumping.