Multilayer integrated circuit electromagnetic field calculation method and device based on mixed-order finite element

Abstract

The embodiment of the invention discloses a multilayer integrated circuit electromagnetic field calculation method and device based on a mixed order finite element. The method comprises the steps of obtaining a first triangular grid of a multi-scale layout of a multi-layer super-large-scale integrated circuit according to a Delaunay grid generation algorithm; determining the maximum value of the side length of a grid unit in the grid, and based on the maximum value, performing grid subdivision on the first triangular grid to form a second triangular grid; based on this, establishing a first-order unit and a finite element stiffness matrix thereof, and solving an initial value of an electromagnetic field of the multi-layer super-large-scale integrated circuit according to field-circuit coupling; based on the second triangular grid, establishing a mixed order unit according to the grid units of which the initial value change speed of the electromagnetic field exceeds or does not exceed apreset value and the grid units of the small-scale area of the multilayer integrated circuit layout; and establishing a finite element stiffness matrix according to the mixed order unit, and calculating the electromagnetic field of the multi-layer super-large-scale integrated circuit. The method can improve the calculation precision of the electromagnetic field of the multi-layer super-large-scale integrated circuit, and is high in calculation efficiency.

Description

technical field [0001] The invention relates to the field of finite element analysis of integrated circuit layout, in particular to a multilayer integrated circuit electromagnetic field calculation method and device based on mixed-order finite elements. Background technique [0002] Integrated circuits have played a very important role in all walks of life and are the cornerstone of the modern information society. It is a miniature electronic device or component. It uses a certain process to interconnect the transistors, resistors, capacitors, inductors and other components and wiring required in a circuit, and makes them on a small or several small semiconductor chips or media. on the substrate, and then encapsulated in a package to become a microstructure with the required circuit functions. [0003] For multi-layer VLSI with complex layout of multi-scale structure, it has become more and more important to analyze power integrity and signal integrity. In the early days, ...

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Problems solved by technology

In the early days, when the integrated circuit structure was simple, the transmission line model or equivalent circuit model could be used to analyze the power integrity and signal integrity of the analog integrated circuit, but as the size of the integrated circuit becomes smaller and smaller, the power consumption becomes smaller and smaller, and The number of transistors is increasing, the processing speed is getting faster, the function is getting stronger, and the density of integrated circuit components is increasing. The layout of integrated circuit components, leads connecting components, power layers, etc. It is becoming more and more complex. At present, multi-layer VLSI has a very complex layout structure. The geometric shapes on the layout usually have multi-scale complex structures, and the scale ranges from centimeters to nanometers.

For multi-layer VLSI with such a complex structure, the traditional analysis method of transmission line model or equivalent circuit model is no longer applicable due to too many simplifications and equivalents. Therefore, for this multi-scale structure and Multi-layer VLSI with a scale ranging from centimeters to nanometers requires a more accurate numerical calculation method based on electromagnetic field theory, such as the finite element method, because the finite element method can use flexible unstructured grids for calculations, To adapt to the multi-scale layout of multi-layer VLSI with multi-scale complex structure

[0004] However, the inventor found in the process of implementing the present invention that when using the finite element method to solve the electromagnetic field calculation problem of a multi-layer VLSI with a multi-scale complex structure in the prior art, dense grids are used in order to improve the calculation accuracy, resulting in Even if the first-order finite element is used, the unknowns are on the order of tens of millions, and the calculation efficiency is low; but if the grid used is relatively sparse, the calculation accuracy cannot meet the requirements. At this time, the common method is to increase the finite element calculation order. number, such as increasing the first-order unit to the second-order unit, but if all the units are raised to the second-order unit, it will also lead to a sharp increase in the calculation of unknowns, and the calculation efficiency is still very low

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