Cell Placement Constraint Method for Multiple Patterning
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Solution Overview
Problem
In semiconductor manufacturing, maintaining a desired critical dimension (CD) for patterned photoresist layers with high aspect ratios is challenging, especially when using multiple patterning techniques, as not all layer patterns can be resolved into a predefined number of masks due to graph representation k-colorability issues, which are computationally intensive and impractical for large layouts.
Innovation Solution
The method involves determining k-colorability of graph representations for layer patterns by generating subsets of cells and adjusting spacings between them to exceed the minimum coloring spacing (MCS), allowing for decomposition into a specific number of masks for multiple patterning, using algorithms to optimize cell arrangements and outputting subsets for mask manufacturing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If multiple patterning techniques are used to achieve smaller feature sizes, then manufacturing precision is improved, but device complexity increases due to computational intensity of graph representation k-colorability
Solution Approach 1:
The patent divides the layer pattern into multiple subsets, where each subset can be independently processed and assigned to different masks. This segmentation allows the complex k-colorability problem to be broken down into smaller, more manageable sub-problems, reducing overall computational complexity while maintaining the ability to achieve precise critical dimensions through multiple patterning.
Solution Approach 2:
The patent modifies the spacing parameter between features in the layer pattern. By adjusting spacings to exceed the minimum coloring spacing (MCS), the patent transforms the graph representation to make it k-colorable, thereby enabling multiple patterning decomposition while reducing computational complexity through parameter optimization.
2Manufacturing precision
If graph representation k-colorability is used to determine mask decomposition, then manufacturing precision is improved, but loss of time increases due to computational intensity
Solution Approach 1:
The patent performs preliminary actions by pre-calculating and storing spacing thresholds and graph representation templates before the actual mask decomposition process. This allows rapid determination of k-colorability during manufacturing without performing computationally intensive calculations in real-time, thereby reducing loss of time while maintaining manufacturing precision.
Solution Approach 2:
The patent creates simplified copies or representations of the layer pattern as graph representations, which can be quickly processed to determine k-colorability. These graphical models serve as efficient substitutes for direct computational analysis of the actual pattern, reducing computational time while preserving the essential information needed for precise mask decomposition.
3Ease of manufacture
If cell-based chip design is used, then ease of manufacture is improved, but device complexity increases due to placement constraint requirements
Solution Approach 1:
The patent develops a universal placement constraint methodology that can be applied across different cell-based chip designs. By creating a standardized approach to determine k-colorability and assign masks that works for various cell types and configurations, the patent maintains ease of manufacture while managing placement constraint complexity through a single reusable framework.
Data Source
AI summary
A method for outputting a first number of subsets of a layer pattern comprising a plurality of cells arranged in a row includes selecting subsets of cells from the plurality of cells, constructing a graph representation for each subset of cells, identifying graph representations that are not colorable with a first number of labels, identifying subsets of cells that correspond to the identified graph representations, changing a distance between cells in each of the identified subset of cells, wherein the changed distances are greater than the first spacing, labeling the graph representations with the first number of labels, and outputting subsets of the layer pattern to a machine readable storage medium for manufacturing a set of masks that is used to form a single, patterned layer. Each subset of the layer pattern represents a separate mask pattern and includes features of the layer pattern corresponding to a label in the labeled graph representations.