基于保角变换的片内互连线电容二维解析模型

2D Analytical Model for On-Chip Interconnect Capacitance Extraction Based on Conformal Mapping Method

通过保角变换严格推导了计入交叠电场贡献的有用电容元的解析表达式,在此基础上提出的互连线二维解析模型能够在一定的连线截面几何参数范围内取得精确的提取结果.实验证明,对于双线系统和多线系统,文中推导的解析模型的提取误差的均方值分别小于2%和7%,均优于对比文献的提取精度.作为一种有竞争力的电容提取方法,该解析模型能够应用于互连线分析设计工具软件之中.

Based on the conformal mapping method, we rigorously derive analytical expressions for useful elementary capacitances, including the contributions of superposition electric fields, upon which an accurate 2D analytical model of interconnect capacitance is established within certain parameter ranges of cross section geometries of interconnect lines. It is verified through simulation that the mean square errors of analytical models for double-line system and multi-line system are less than 2 % and 7 % respectively. The proposed expressions excel other referenced expressions in capacitance extraction accuracy, being able to act as a competitive capacitance extraction method embedded in interconnect analysis and design tools.