A New Stochastic Solver for Multi Metal-Dielectric Interconnect Capacitances Extraction

This study aims at developing a fast and accurate stochastic solver for extracting 2D and 3D multi metal-dielectric interconnect capacitances. The new stochastic solver is fundamentally based on the squared-shaped random walk, combing Stop at Interface method proposed by Chang,C.C. et al. and technique of numerical characterization of Green''s function method proposed by Yu in order to solve the multi-dielectric problems. As for the purpose to enhance accuracy, we use a novel square like integration method to calculate the electric field proposed by Chang,C.C. et al. Factors such as the grid sizes, realizations and the grid points of the finite difference method are three major parameters for the random walk. However, little literature has been published on the issue of evaluating the influence of each parameters. Thus, in this study, it is also illustrated the errors and computation costs by adjusting these three factors. Numerical results show that the grid size has the dominant influence on accuracy, followed by realizations and grid points of finite difference. The smaller the grid size is, the more possibility to capture the potential distribution clearly. Hence, the accuracy have a great improvement. In addition, once the realizations up to a specific value, the computational results converge. It is, therefore indicating the accuracy cannot be improved by more realizations. Further, the grid points of finite difference is proven to have less influence on the accuracy and become even independent with the accuracy when grid size is decreasing of realizations is increasing. In the last part, by comparing the results of 2D and 3D, we discover that it is prone to converge in 3D cases. This is because the 3D simulation has an extra dimension than 2D which implies more realizations superimposing on the model. This is because 2D simulations compute less grid points such that high realizations of each point will lead to accuracy result. In contrast, Therefore, in 3D cases, it is simply using little realizations to achieve high accuracy. To sum up, the proposed new stochastic method can solve more complicated 2D and 3D cases than the commercial software. In addition, the accuracy of the proposed method has been proven to meet up with a specific extent. It is hope to providing an optimized programming with parallel computation.