Parasitic Extraction Of Integrated Circuits Based On Random Walk Method On Grid

At present,the signal frequency of integrated circuits is constantly increasing,and the feature size is also keeping decreasing.Many unattended physical effects in the early days of integrated circuit development gradually affect the improvement of integrated circuit performance.A representative factor is the parasitic effect of interconnection.Some processes need to add suspension conductor to meet the requirements of keeping flatness of the chip.The increase of suspension conductor also leads to the increase of parasitic effect,so the parasitic extraction becomes very important.There are advantages and disadvantages in the existing parasitic parameter extraction methods.Among them,the floating random walk method has the highest theoretical precision,no discrete error,and can be highly parallelized,but the convergence speed is slow,which is difficult to adapt to complex geometric shapes and complicated materials and is not efficient to handle Non-Manhattan structures.Discrete geometry and finite element method are based on volume discretization,which can naturally adapt to complex shapes and complex materials.But the linear equations formed by this type of method are difficult to parallelize calculations.In this paper,the floating random walk method has almost no correlation between each walk,and can be highly parallelized.It can be introduced into the discrete external differential framework which can adapt to the complex multi-coal structure.It starts from the space to be investigated,randomly walking and terminating at the reaching boundary and uses mathematical statistics to calculate the probability of terminating on each boundary,then using it as the weight to calculate the field distribution of the target space point,and finally obtain various physical quantities.Although the accuracy of the method depends on the grid,the solution remains efficient,and it occupies very little storage space,and has significant advantages in solving local field distribution and massively parallel computing.The experimental results in this paper prove that the grid-based random walk method is more efficient as the number of grids increases.In the case of 10,546 nodes,the computational efficiency is 2.3 times that of the finite element method.The method can be used for the treatment of suspended conductors.The floating conductor has the characteristics that the surface potential is unknown and its surface charge is zero.The conventional method is obviously affected when processing a system containing a large number of suspended conductors.The method proposed in this paper can achieve faster extraction speed than the traditional method under the premise of ensuring accuracy.In this paper,we also discuss the random walk method under the discrete external differential framework for the sensitivity analysis.The sensitivity of the potential to the process parameters can be obtained by deriving the partial derivative of the transfer matrix,and then we can get the sensitivity of the parasitic parameters to the process parameters.