An Analytical Through Silicon Via (TSV) Surface Roughness Model Applied to a Millimeter Wave 3-D IC

In the millimeter wave (mmW) frequency range, the root mean square height of the through silicon via (TSV) sidewall roughness is comparable to the skin depth, and hence, becomes a critical factor for TSV modeling and analysis. In this paper, the impact of the TSV sidewall roughness on electrical performance, such as the loss and impedance alteration in the mmW frequency range, is examined and analyzed. The second-order small analytical perturbation method is applied to obtain a simple closed-form expression for the power absorption enhancement factor of the TSV. In this study, we propose an electrical model of the TSV, which considers the TSV sidewall roughness effect, the skin effect, and the metal oxide semiconductor effect. The parameters of the proposed circuit model can be determined analytically; the accuracy of the model is validated through a comparison of circuit model behavior for full wave electromagnetic field simulations up to 100 GHz.