Kernel Convolution Method for Semiconductor Design Metrics
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Solution Overview
Problem
Current semiconductor manufacturing processes face high computational costs due to the need for precise modeling and correction of electron scattering, resist diffusion, and other effects, which require complex calculations involving surface integrals and multiple variables, leading to increased workload and inefficiency.
Innovation Solution
A method using a convolution of a kernel function and a deformation function with a shift angle to calculate metrics across the entire semiconductor design, allowing for efficient computation of external and internal densities, and optionally using Fourier series development or projection to reduce calculation complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional surface integral calculations are used to compute metrics for each point of interest, then measurement precision is maintained, but computation time increases significantly
Solution Approach 1:
The patent divides the design into discrete points of interest and uses pre-calculated visibility kernels for each point. Instead of performing full surface integrals for every metric calculation, the method segments the computation into: (1) pre-computing visibility kernels once per point of interest, and (2) reusing these kernels for multiple metric computations. This segmentation reduces redundant calculations while maintaining precision.
Solution Approach 2:
The patent performs preliminary calculation of visibility kernels before the actual metric computations. The visibility kernel K(x,y) is pre-computed based on the point of interest and stored, then reused across multiple metric calculations. This preliminary action eliminates the need to re-calculate integral surfaces for each metric, significantly reducing computation time while preserving accuracy.
2Manufacturing precision
If multiple variables (CD, Space, density) are calculated using full surface integrals, then model accuracy is improved, but device complexity increases
Solution Approach 1:
The patent creates a universal visibility kernel K(x,y) that serves multiple functions simultaneously. The same kernel is used to calculate CD, Space, density, and other metrics for a given point of interest. This multi-functional approach maintains manufacturing precision across all metrics while reducing calculation complexity by avoiding separate surface integral computations for each variable.
Solution Approach 2:
The patent changes the computational parameters from multiple independent surface integrals to a single kernel-based convolution operation. By transforming the calculation paradigm from integral-based to convolution-based using pre-computed kernels, the method maintains accuracy for multiple variables while significantly simplifying the computational structure.
3Manufacturing precision
If high precision models are used for proximity effect correction, then manufacturing precision is improved, but productivity decreases
Solution Approach 1:
The patent creates simplified copies of the complex proximity effect models in the form of visibility kernels. These kernel representations capture the essential correction behavior without requiring full model computations during metric calculation. The kernels act as compressed copies that maintain correction quality while enabling faster processing and higher productivity.
Data Source
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AI summary
The invention discloses a method for calculating the parameters of a resist model of an IC manufacturing process. According to an embodiment of the method of the invention, a function representative of the target design convoluted throughout the whole target design with a kernel function compounded with a deformation function with a shift angle. Advantageously, the deformation function is replaced by its Fourier series development, the order of which is selected so that the product of convolution is invariant through rotations within a tolerance of the corrections to be applied to the target design. Alternatively, the product of convolution may be decomposed into basic kernel functions selected varying by angles determined so that a deformation function for a value of the shift angle can be projected onto a couple of basic kernel functions the angles of which are proximate to the shift angle.