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.

中文翻译：

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嵌入去离子水的硅微流钉鳍式散热器中嵌入的硅通孔的电路建模和验证

本文介绍了硅微流体针翅式散热器中信号接地硅通孔（TSV）的电路模型，其中针翅被去离子水包围。这样的TSV在垂直方向上是不对称的，因为TSV部分嵌入圆柱销形鳍片以及矩形硅基底中。在本文中，我们提出了一种电路模型，该模型将不对称几何形状分为两个对称段：一个段用于硅基底，另一个段用于被去离子水包围的圆柱形硅针状鳍片，我们称其为“针状鳍片”分割。” 具体而言，使用两电介质同轴线公式对引脚-鳍段进行建模，以表示围绕铜过孔的二氧化硅和硅的双层。使用开发的电路模型，本文定量分析了流体设计的影响，例如针形鳍的直径和高度对TSV的电气特性的影响。在使用高频电磁场仿真验证电路模型之后，将建模结果与测量数据进行比较。