求解複雜結構金屬-介電體電容之新隨機算法

Abstract

在IC製程不斷微型化的今日，金屬導線間寄生電容準確計算的重要性日益顯著。本篇論文目的在於發展一新隨機算法，希望針對複雜金屬-介電體結構之寄生電容計算，能提供更好的解決方案。藉由參考前人提出之隨機步進演算法，發展出一套新隨機算法，逐一對各種模型進行測試，並與理論值及商用軟體比較。 此新隨機算法在單純兩平行極板且單一介質之模型中，與理論電容值之誤差小於百分之一；在兩平行極板含有垂直邊界金屬導體且單一介質上下對稱之模型中，此新隨機算法之上、下極板電容值的對稱性，明顯優於商用軟體之計算結果，且兩者誤差不大，故可相信在簡單模型中，此新隨機算法之對稱性及準確度可優於商用軟體。觀察各模型之計算結果，此新隨機算法亦可達到極高的準確度。 此新隨機算法相較於有限元素法，在複雜結構中反而能縮短運算時間，提升計算速度，此為新隨機算法最大的優勢。此新隨機算法的另一優勢為擴展至三維模型的簡易性，因為步進的機率分布主要根據夾角與介電係數決定，只要多加上一個角度參數即可擴展至三維模型。

In today’s era which the IC manufacturing process continuously miniaturizing, an accurate calculation of the parasitic capacitance between the metal wires has become increasingly important. This paper aims to develop a new stochastic algorithm in order to provide a better solution for the parasitic capacitance calculation of complex metal-dielectric structure. By referring to previous random walk algorithm, we have developed a new stochastic algorithm, through which tested various models, as well as compared with theoretical values and commercial software. In the model of simply two parallel plates and a single medium, the error between this new stochastic algorithm and the theoretical capacitance value is less than one percent; in the model of two parallel plates containing vertical boundary metal conductor and a symmetry single medium, through this new randomized algorithm, the symmetry between the capacitances of the upper and underneath plate is significantly better than the calculation results of commercial software, and the error between these two is not large. It can be concluded that in a simple model, the symmetry and accuracy of this new stochastic algorithm are more outstanding than commercial software. Observing the results of the models, this new stochastic algorithm can also achieve extremely high accuracy. Compared to finite element method, in a complex structure, this new stochastic algorithm can efficiently shorten the calculating time and improve the processing speed. This is the biggest advantage of the new stochastic algorithm. Another advantage of this new stochastic algorithm is the simplicity of extending to three-dimensional model. Since the probability distribution is mainly based on the angle and the dielectric constant, by simply adding one angle parameter, it can be expanded to three-dimensional model.