Conducting Structure Resistance Determination via Equipotential Partitioning
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Solution Overview
Problem
Existing methods for determining the resistance of conducting structures in integrated circuits, such as BEM and FMM, require significant computational time and resources due to the large size of the matrix equations involved, making them inefficient for accurate and timely analysis.
Innovation Solution
The method partitions the conducting structure into polygons based on equipotential lines and boundaries, representing electric potentials of boundary elements as linear combinations of equipotential lines to construct a smaller matrix equation, which reduces computational resources and time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If BEM or FMM techniques are used to determine resistance by solving large matrix equations, then measurement precision is improved, but computational time and resources increase significantly
Solution Approach 1:
The patent segments the conducting structure into multiple regions based on equipotential lines, creating a simplified geometric representation. This segmentation allows the complex resistance calculation to be broken down into smaller, more manageable computations while maintaining accuracy through the equipotential-based regional division.
Solution Approach 2:
The patent extracts only the essential boundary information and equipotential line characteristics to create a reduced-order model. By taking out only the critical geometric and electrical properties needed for resistance calculation, the method eliminates unnecessary computational complexity while preserving measurement precision.
2Measurement precision
If the entire area of the conducting structure is discretized using FEM, then measurement precision is improved, but device complexity and computational resources increase
Solution Approach 1:
The patent extracts only the boundary information and equipotential line characteristics rather than discretizing the entire area. This extraction approach creates a simplified model that maintains precision by focusing on the critical electrical boundaries and equipotential regions, thereby reducing matrix equation complexity significantly.
Solution Approach 2:
The patent uses equipotential lines as fundamental building blocks to define the conducting structure regions. By organizing the discretization around equipotential boundaries rather than uniform spatial grids, the method achieves both precision and reduced complexity, as equipotential lines naturally capture the electrical characteristics of the structure.
Data Source
AI summary
Systems and techniques are described for determining a resistance of a conducting structure. The conducting structure can be partitioned into a set of polygons based on (1) equipotential lines and (2) boundaries of the conducting structure. Next, a matrix equation can be constructed, wherein for at least one polygon in the set of polygons, electric potentials of boundary elements on the boundaries of the polygon are represented by linear combinations of electric potentials of two or more equipotential lines. The resistance of the conducting structure can then be determined by solving the matrix equation.