Photoresist Mask Decomposition via Graph Colorability Analysis
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Solution Overview
Problem
The decomposition of a single photoresist mask pattern into three separate mask patterns is a labor-intensive, trial-and-error process, and it is often unclear whether a photoresist mask pattern can be successfully decomposed using current methodologies, leading to wasted effort.
Innovation Solution
A method involving node mapping and colorization to determine the decomposability of a single photoresist mask pattern into three layers, where nodes are assigned colors to ensure no adjacent nodes have the same color, and iterative removal and replacement processes are used to achieve a layout that can be decomposed into three photoresist mask patterns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If trial-and-error decomposition methods are used to decompose a single photoresist mask pattern into three separate mask patterns, then decomposition can be achieved, but the process becomes labor-intensive and time-consuming
Solution Approach 1:
The patent applies preliminary action by performing node mapping and colorability analysis before the actual decomposition process. The method pre-identifies nodes, determines their colorability status, and assesses whether the layout can be decomposed into three colors before committing to the decomposition workflow. This preliminary assessment prevents wasted effort on non-decomposable patterns and guides the subsequent decomposition steps.
Solution Approach 2:
The patent introduces an intermediary computational analysis layer between the original mask pattern and the final decomposition. This intermediary process involves creating a node representation of the layout, performing colorability analysis, and using this intermediate information to guide the decomposition. The intermediary analysis acts as a mediator that translates the geometric mask pattern into a graph-theoretic representation that can be systematically evaluated and decomposed.
2Extent of automation
If trial-and-error decomposition methods are used without knowing decomposability in advance, then decomposition attempts can be made, but significant effort is wasted on non-decomposable patterns
Solution Approach 1:
The patent performs preliminary colorability analysis before decomposition attempts by mapping nodes and evaluating whether each node can be assigned one of three colors such that no adjacent nodes share the same color. This preliminary determination of decomposability allows the system to identify non-decomposable patterns early and avoid wasting computational resources and user effort on patterns that cannot be successfully decomposed.
Solution Approach 2:
The patent implements feedback by using the results of the colorability analysis to inform subsequent decomposition decisions. The system evaluates the colorability status and uses this feedback to determine whether to proceed with decomposition or to modify the layout. This feedback mechanism prevents wasted effort by providing actionable information about the feasibility of decomposition before the actual decomposition process begins.
3Adaptability or versatility
If manual decomposition processes are used for photoresist mask patterns, then flexibility in handling complex patterns is maintained, but productivity and efficiency decrease
Solution Approach 1:
The patent replaces manual mechanical decomposition processes with an automated computational system based on graph theory and colorability analysis. The system automatically maps layout features to nodes, performs colorability evaluation, and determines decomposability without manual intervention. This substitution of automated computational mechanics for manual processes maintains the ability to handle complex patterns while dramatically increasing productivity and reducing the time required for decomposition.
Solution Approach 2:
The patent changes the parameter space by transforming the geometric mask pattern into a graph-theoretic representation with nodes and adjacency relationships. This parameter transformation allows the application of algorithmic colorability analysis and automated decomposition methods. By changing from spatial geometric parameters to graph-theoretic parameters, the system enables automated processing while maintaining the ability to handle complex pattern topologies that would be difficult to manage manually.
Data Source
AI summary
A method of determining whether a layout is colorable includes assigning nodes to polygon features of the layout. The method includes designating nodes as being adjacent nodes for nodes separated by less than a minimum pitch. The method includes iteratively removing nodes having less than three adjacent nodes from consideration to identify a node arrangement, wherein all nodes in the node arrangement have at least three adjacent nodes. The method includes determining whether the layout is colorable based on the node arrangement. Determining whether the layout is colorable includes independently assessing each internal node of node arrangement to determine whether each internal node of the node arrangement is colorable. The method includes generating a colored layout design for fabrication of the semiconductor device if each internal node of the node arrangement is colorable; and modifying the layout if at least one internal node of the node arrangement is not colorable.