Pixel Coverage Polygon Generation for Parametric Beam Patterns
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Solution Overview
Problem
High-precision approximation of polygon vertexes in electron beam writing devices for semiconductor fabrication is time-consuming due to the need for high-precision calculations of coverage areas for multi-beam irradiation, especially when dealing with complex patterns defined by parametric curves like B-spline and Bezier curves.
Innovation Solution
A method that divides parametric curves into segments, calculates the area equivalent to the curve portions, and generates polygons using these segments, allowing for efficient and accurate calculation of pixel coverage by reducing the number of vertexes required for high-precision approximation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If high-precision approximation is used to calculate coverage area of parametric curves, then manufacturing precision is improved, but processing time increases
Solution Approach 1:
The patent divides a parametric curve into multiple line segments by sampling points along the curve. Instead of using complex high-precision approximation methods for the entire curve, it segments the curve into manageable parts and calculates coverage area for each segment separately. This segmentation allows for faster computation while maintaining acceptable precision by using simpler geometric calculations for each segment rather than complex curve approximation.
2Manufacturing precision
If the number of vertexes of approximate polygon is increased, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent segments the parametric curve into multiple line segments with a controlled number of vertexes. By dividing the curve into segments and calculating coverage for each segment separately, it achieves acceptable approximation precision without requiring a single complex polygon with a large number of vertexes. This reduces the overall data structure complexity while maintaining manufacturing precision through systematic segmentation.
Solution Approach 2:
The patent uses partial approximation by sampling a sufficient number of points along the parametric curve to capture its essential shape characteristics. Instead of using excessive vertexes to achieve perfect approximation, it employs partial action by selecting key sampling points that provide adequate precision for coverage calculation, thereby reducing data complexity while maintaining acceptable manufacturing precision.
Data Source
AI summary
In one embodiment, a data generation method is for calculating a coverage of a polygon in each of a plurality of pixels obtained by dividing a target to be irradiated with a charged particle beam into predetermined sizes. The method includes dividing a parametric curve that defines a pattern shape into a plurality of parametric curves, calculating, for each of the plurality of parametric curves, an area of a region surrounded by a segment connecting end points among control points of the parametric curve and the parametric curve, calculating positions of vertexes of a figure having an area equivalent to the calculated area and having, as one side thereof, the segment connecting the end points, and generating the polygon by using the vertexes.