The modeling of DC current crowding for Through-silicon Via in 3-D IC

With increased current density induced by current crowding in Through-silicon Via(TSV), the reliability problem of interconnection of 3-D IC power grid, especially the electromigration (EM), cannot be ignored. To ensure the EM current limit is not exceed and the reliability of power delivery network of 3-D IC is stable, it is essential to accurately analyze the current crowding effect of TSV before manufacturing. So in this paper, a two dimensional analytical method for DC current crowding of 3-D interconnection, which includes TSV and bump, is proposed based on Laplace equation firstly. Then, the proposed method is validated by simulation tool, and a good correlation is obtained between proposed method and simulation result. With the proposed current crowding model, the distribution of voltage and current density can be characterized in two dimensions. Based on the proposed method, some instructive physical design rules of power/ground TSV can be obtained, which is beneficial for the optimization of PDN design and the relief of EM problem induced by current crowding effect.