Research On Polyhedron Mesh Of IC Parasitic Parameter Extraction

With the continuous development of integrated circuits,the feature size is decrea sing,resulting in more and more significant interconnect parasitic effects.Especially w hen the feature size of the device is reduced to the nanometer level,the interconnect ion parasitic extraction is gradually becoming the development process of the integr ated circuit.primary issue.Among various engineering fields including electromagnetic fields,the finite element method is the most widely used and most important nume rical analysis method.It has mature algorithm theory and has high efficiency and pr ecision.Due to the diversification of applications,relatively complex geometries have emerged.When using triangular elements to deal with such problems,the number of degrees of freedom is large,the calculation becomes complicated,and the cost of nu merical calculation becomes large.Therefore,the polygonal finite element method is p roposed.The polygon finite element method is to establish the linear equations by using the electric scalar bits on the dual grid nodes as the unknowns.By constructing the interpolation function on the polygon and performing numerical analysis based on the Galerkin method,the electric and magnetic fields in space and time are studied.The distribution and variation law,and finally the post-processing calculation of electromagnetic parameters on various devices and systems.This method can effectively avoid the related complexity introduced by using vector finite elements.And the polygonal mesh is conducive to maintaining the original shape of the geometry,and can be flexibly applied to high-order finite element analysis.Its characteristic based on the node scalar potential also facilitates the implementation of post processing.The formed linear matrix has good symmetry and sparse characteristics,and the time loss and computational resource loss required to solve the equation are less.In this paper,the capacitance extraction algorithm on the unstructured grid discrete space is discussed firstly.The polygon finite element method based on mean value coordinates,Sibson coordinates,Laplace coordinates and Wachspress coordinates id discussed.Secondly,the finite element method to establish a stable algebraic system requires a coordinated grid to guarantee.Therefore,the method of polygon mesh generation is discussed.Due to the local mesh refinement and the separation component design,some mismatched grids appear.In this paper,a general method is proposed to deal with uncoordinated grids.This method can connect various meshes to form polygonal elements.These elements are generally degenerated into triangular elements and then segmented by segmentation based on the finite element frame.Get the interpolation function on the cell grid.In order to realize the generation of polygon mesh based on the original triangulated mesh,this paper uses the twelve-conductor electrostatic system and the four-conductor electrostatic system as examples to analyze the generation process of the polygon mesh.In the two-dimensional space,the three-conductor electrostatic system is taken as the analysis object,and the validity and correctness of the polygon finite element method are verified.Then the conventional finite element method and polygon finite element method are used to deal with the discordant mesh.The practicability of the polygon finite element method is verified.In general,the polygon finite element method is to use the electric scalar quantity of each node on the dual grid element as the unknown quantity,and establish the interpolation function on the polygon.The numerical analysis is based on the Galerkin method.The algorithm is combined for the processing of the partial design.Topology optimization calculation and unified calculation of multiple grids have important significance.