Non-linear Edge Placement Correction in Multi-beam Lithography
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Solution Overview
Problem
Charged-particle multi-beam writing technologies face challenges in maintaining accurate edge placement due to non-linear behavior, particularly when adjusting exposure doses, leading to deviations in feature size and critical dimension uniformity.
Innovation Solution
A method is introduced to correct edge positions by using a predefined non-linear function that inverts the relationship between nominal and actual edge positions, taking into account parameters such as assigned dose, beamlet blur, and proximity effects, allowing for precise adjustment during vector pattern creation or rasterization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If linear edge shift correction is applied, then edge position can be adjusted, but non-linear behavior causes uniformity loss in critical dimensions
Solution Approach 1:
The patent transforms the linear correction parameter into a non-linear correction function. The correction amount is determined by a function of the distance from the pattern edge, creating a non-linear relationship that compensates for the non-linear edge shift behavior. This ensures that edge position accuracy is maintained while critical dimension uniformity is preserved across different feature sizes and doses.
2Manufacturing precision
If dose-dependent correction is applied, then edge placement accuracy improves, but calculation complexity increases due to non-linear functions
Solution Approach 1:
The patent manages calculation complexity by formulating the non-linear correction in a systematic way. The correction function is based on the distance from the pattern edge and the assigned dose, allowing for efficient calculation through a defined mathematical relationship. This approach maintains edge placement precision while keeping the correction process computationally tractable through structured parameter transformation.
Data Source
AI summary
A rasterized exposure method implementing a position correction for edge positions to correct for a non-linear relationship between the position of a feature edge (dCD) of a pattern element boundary and the nominal position of the boundary as expressed through the dose of exposure (d) of the edge pixel is provided. The position correction includes: determining a position value of the edge position, determining a corrected position value based on the position value using a predefined non linear function, and modifying the pattern to effectively shift the pattern element boundary in accordance with the corrected position value. The non linear function describes the inverse of the relationship between a nominal position value (d), which is used as input value during exposure of the pattern, and a resulting position (dCD) of the pattern element boundary generated when exposed with the nominal position value.