Orthogonal Convolution Kernels for Lithographic Resist Simulation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional lithographic simulation methods fail to accurately and efficiently simulate the image of a mask pattern in a photoresist, as they do not fully represent chemical processes and are time-consuming, with empirical models being unstable and requiring extensive user interaction.
Innovation Solution
A method involving the convolution of an aerial image with orthogonal convolution kernels that form a complete basis, ensuring rotational and mirror symmetry conservation, to quickly and accurately determine the resist image, reducing computation time and user interaction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional physical modeling of chemical processes is used, then accuracy of resist image simulation is improved, but computation time increases significantly
Solution Approach 1:
The patent replaces complex physical/chemical modeling with a mathematical convolution operation. Instead of simulating chemical amplification and diffusion processes physically, the invention uses convolution of the aerial image with a resist kernel to directly compute the resist image, achieving comparable accuracy with significantly reduced computation time.
Solution Approach 2:
The patent transforms the simulation approach by changing from physical parameter-based modeling (chemical reactions, diffusion coefficients) to a mathematical transformation approach. The resist image is obtained through convolution operation with a kernel that encapsulates the resist characteristics, fundamentally changing how the simulation parameters are handled.
2Productivity
If empirical modeling approach is used, then computation speed is improved, but model stability and reliability deteriorate
Solution Approach 1:
The patent introduces a resist kernel as an intermediary mathematical object that mediates between the aerial image and the final resist image. This kernel acts as a stable, pre-characterized filter that provides consistent results across different simulations, improving reliability while maintaining computational efficiency through the convolution operation.
3Ease of operation
If conventional resist modeling is used, then user interaction and model calibration are simplified, but prediction accuracy of resist critical dimension deteriorates
Solution Approach 1:
The patent creates a mathematical copy of the resist response characteristics through the convolution kernel. Instead of requiring users to calibrate complex physical models, the kernel encapsulates the resist behavior as a reusable mathematical object that can be directly applied to aerial images, simplifying operation while improving prediction accuracy through consistent mathematical transformation.
Data Source
AI summary
A method for determining an image of a mask pattern in a resist coated on a substrate, the method including determining an aerial image of the mask pattern at substrate level; and convolving the aerial image with at least two orthogonal convolution kernels to determine a resist image that is representative of the mask pattern in the resist.