Resist Pattern Calculation Using Variable Diffusion Lengths
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Solution Overview
Problem
Existing methods for calculating resist patterns in lithography processes, such as those described in Japanese Patent Laid-Open No. 08-148404, face challenges in accurately representing the diffusion phenomenon of acids in resists due to the optical proximity effect and low k1 conditions, leading to inaccuracies in resist pattern size calculation.
Innovation Solution
A method involving a computer program that calculates a resist pattern by determining a light intensity distribution, convoluting it with a first diffusion length, calculating a representative light intensity, applying a correction function to the convoluted distribution using constants and an exponential term, and then calculating the resist pattern based on the corrected intensity and a slice level.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a mathematical convolution of light intensity distribution is performed using a single diffusion length, then the calculation process is simple, but the accuracy of resist pattern size calculation deteriorates under low k1 conditions
Solution Approach 1:
The patent applies different diffusion lengths to different regions of the resist pattern based on local light intensity characteristics. Bright regions use one diffusion length while dark regions use another, allowing the calculation to account for the different acid diffusion behaviors in high and low intensity areas, thereby improving overall calculation accuracy without excessive complexity
Solution Approach 2:
The patent changes the diffusion length parameter based on the light intensity distribution. By selecting different diffusion length values corresponding to different light intensity regions, the model adapts to the varying acid diffusion conditions across the resist pattern, resolving the contradiction between simple calculation and accurate prediction
2Device complexity
If a single diffusion length is used for convolution, then the calculation model is simple, but it cannot represent the acid diffusion phenomenon with sufficient precision under low k1 conditions
Solution Approach 1:
The patent introduces spatially varying diffusion lengths that reflect the local chemical conditions in different regions of the resist. Bright regions with high acid generation use different diffusion characteristics than dark regions, accurately representing the physical chemistry of the exposure process while maintaining computational feasibility
Solution Approach 2:
The patent makes the diffusion length dynamic by selecting different values based on the local light intensity distribution. This dynamic approach allows the model to adapt to varying chemical conditions across the resist pattern, improving reliability without requiring a completely complex chemical simulation model
3Ease of operation
If the optical image is convoluted in the same mathematical form regardless of light intensity magnitude, then the calculation method is uniform and simple, but it does not account for the different behavior of acid in bright and dark regions
Solution Approach 1:
The patent applies different convolution parameters (diffusion lengths) to different regions based on their light intensity characteristics. This regional differentiation allows the calculation to reflect the actual chemical behavior in bright and dark regions while maintaining a systematic and implementable calculation framework
Solution Approach 2:
The patent changes the convolution parameters based on the light intensity distribution map. By selecting appropriate diffusion lengths for different intensity regions, the method maintains mathematical uniformity in approach while adapting parameters to local conditions, thereby improving accuracy without sacrificing methodological consistency
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach improves the accuracy of resist pattern calculation by accounting for the behavior of acids under varying light intensities, reducing prediction errors and enhancing device characteristics.
Implementation Method 1
the light intensity distribution of the optical image is convoluted using various variance values (to be referred to as diffusion lengths hereinafter)
Data Source
AI summary
A recording medium stores a program for causing a computer to execute a method of calculating a resist pattern. The method includes: a first step of calculating a light intensity distribution of an optical image formed on the resist, based on the reticle pattern and an exposure condition; a second step of convoluting, using a first diffusion length, the calculated light intensity distribution; a third step of calculating a representative light intensity from the calculated light intensity distribution or the convoluted light intensity distribution; a fourth step of correcting the convoluted light intensity distribution by adding, to the convoluted light intensity distribution, a correction function including a first function given by:{∑k=0n(akJk)}exp(-αJ)where J is the distribution of the representative light intensity; and a fifth step of calculating the resist pattern based on the corrected light intensity distribution and a slice level set in advance.