Electrical Circuit Modeling and Validation of Through-Silicon Vias Embedded in a Silicon Microfluidic Pin-Fin Heat Sink Filled With Deionized Water

This article presents the electrical circuit model of signal-ground through-silicon vias (TSVs) in a silicon microfluidic pin-fin heat sink in which the pin-fins are surrounded by deionized water. Such TSVs are asymmetric vertically because the TSVs are partially embedded in cylindrical pin-fins as well as in a rectangular silicon base. In this article, we propose a circuit model that segregates the asymmetric geometry into two symmetric segments: one segment for a silicon base and the other segment for cylindrical silicon pin-fins surrounded by deionized water, which we refer to as "a pin-fin segment." Specifically, the pin-fin segment is modeled using two-dielectric coaxial-line formulas to represent the double layers of silicon dioxide and silicon that surround the copper vias. Using the developed circuit model, this article quantitatively analyzes the impact of fluidic designs, such as the diameter and height of pin-fins on the electrical characteristics of TSVs. Following circuit model validation using high-frequency electromagnetic field simulations, the modeling results are compared with measured data.