Photo Mask Layout Graph Coloring for Multiple Patterning
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Solution Overview
Problem
Current semiconductor manufacturing processes face challenges in achieving fine patterns below the resolution limit of optical lithography tools due to diffraction issues and the complexity of pattern layouts, which requires innovative methods for multiple patterning operations and mask assignment.
Innovation Solution
A method is developed to convert pattern layouts into graph representations, simplify the graphs by identifying and removing insignificant nodes, and assign patterns to multiple photo masks using a coloring process that ensures adjacent patterns are not on the same mask, thereby determining if a layout can be divided into N photo masks without violating spacing rules.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If optical lithography is used for patterning, then manufacturing process is simple, but pattern resolution is limited by diffraction
Solution Approach 1:
The patent applies segmentation by dividing the patterning process into multiple discrete steps (e.g., self-aligned multiple patterning, SAQP). Instead of attempting to create fine patterns in a single lithography step, the process segments pattern formation into sequential steps where each step creates a portion of the final pattern, ultimately achieving sub-diffraction resolution through cumulative effect of multiple simpler lithography steps
2Manufacturing precision
If multiple patterning operations are performed, then pattern resolution is improved, but processing time increases
Solution Approach 1:
The patent applies preliminary action through self-alignment mechanisms where mandrel patterns and spacer patterns are pre-formed with precise geometric relationships before final pattern transfer. The self-aligned nature of the process establishes alignment references in advance, eliminating the need for time-consuming alignment procedures between lithography steps and reducing overall processing time
Solution Approach 2:
The patent employs periodic action through cyclic repetition of the self-aligned multiple patterning cycle (mandrel formation, spacer formation, mandrel removal, pattern transfer). This periodic process can be optimized by maintaining consistent process parameters across cycles and by parallelizing certain operations within each cycle, thereby reducing the time penalty associated with multiple patterning steps
3Manufacturing precision
If graph coloring method is used for mask assignment, then pattern assignment accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent applies segmentation to the graph coloring problem by dividing the entire pattern set into smaller sub-graphs or clusters that can be colored independently or with reduced interdependence. This segmentation transforms the computationally intensive global coloring problem into multiple smaller, more manageable local coloring problems, reducing overall computational complexity while maintaining assignment accuracy
Solution Approach 2:
The patent applies partial action by implementing heuristic or approximate graph coloring algorithms that achieve sufficient mask assignment accuracy without exhaustively solving the complete coloring problem. The method performs partial coloring iterations or uses simplified coloring rules that provide near-optimal solutions with significantly reduced computational effort compared to exact graph coloring methods
Data Source
AI summary
In a method of manufacturing a photo mask used in a semiconductor manufacturing process, a mask pattern layout in which a plurality of patterns are arranged is acquired. The plurality of patterns are converted into a graph having nodes and links. It is determined whether the nodes are colorable by N colors without causing adjacent nodes connected by a link to be colored by a same color, where N is an integer equal to or more than 3. When it is determined that the nodes are colorable by N colors, the nodes are colored with the N colors. The plurality of patterns are classified into N groups based on the N colored nodes. The N groups are assigned to N photo masks. N data sets for the N photo masks are output.