基于镜像法提取多层介质中3D电容参数的研究

3D capacitance extraction in multi-layered dielectric media based on image method

提出了一种适用于任意多层电介质分层结构中的3D互连电容参数提取的新方法——反射镜像法。该方法无需对格林函数进行推导,而是根据自由电荷反射原理计算反射镜像的位置和镜像电荷系数从而获得各级镜像分布,继而计算任意多层电介质环境下的3D电容,包括底层或顶层介质接地情况下的3D电容。该方法可克服级数形式的格林函数因受限于电介质分层数目而难以适应大规模集成电路中复杂多变电介质环境下的3D电容参数提取问题。通过对导体面元建立层次式数据结构,这一方法可以利用层次式算法(hierarchical method)实现计算加速。实验证明,该方法能在保证可靠精度的情况下达到迅速收敛,与层次式加速算法结合后,计算效率可达到FastCap法的数倍。

An image method for 3D capacitance extraction suitable for multi-layered dielectric media with an arbitrary number of layers is proposed. The approach does not make tedious derivation of the Green＇ s function in infinite series, but calculates the coefficient of image charges and the locations of reflection images based on the principle of free charge reflection to acquire the distribution of different images, and then calculates the 3D capacitances in layered media with an arbitrary number of layers, including top-grounding and bottom-grounding media. The method can extricate the series-form Green＇ s function from the layer number limitation and can be applicable in 3D capacitance extraction of the modern very large scale integrated circuits （VLSI）. By constructing a hierarchical data structure, this approach can be accelerated by using the hierarchical method. Numerical experiments show that this method converges rapidly yet attains high precision. By incorporating with the fast hierarchical method, this method can run several times faster than the FastCap.