SID SADP Mask Layout Determination for Complex 2D Patterns
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Solution Overview
Problem
The semiconductor industry faces challenges in determining effective mask layouts for the spacer-is-dielectric self-aligned double-patterning (SID SADP) process, particularly for complex two-dimensional patterns, which are not adequately addressed by existing technologies.
Innovation Solution
A system determines mandrel and trim mask layouts by analyzing graph colorability, merging shapes to resolve conflicts, and optimizing shape placement to improve manufacturability, using a process that involves identifying core and additional shapes in the mandrel mask layout and utilizing the trim mask to separate merged shapes, thereby enhancing the printing of two-dimensional patterns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing mask layout determination methods are used, then simple patterns can be printed, but complex two-dimensional patterns cannot be adequately addressed
Solution Approach 1:
The patent segments the complex two-dimensional pattern into multiple shapes that can be represented as vertices in a graph. Each shape is analyzed independently and assigned to different masks based on graph coloring, enabling complex patterns to be broken down into manufacturable components that satisfy minimum spacing requirements.
Solution Approach 2:
The patent transforms the two-dimensional spatial pattern problem into a graph theory problem by creating a graph representation where shapes are vertices and spacing violations are edges. This dimensional transformation allows the application of graph coloring algorithms to solve the mask layout determination, adding a mathematical dimension to the physical manufacturing problem.
2Ease of manufacture
If shapes are merged to resolve graph colorability, then manufacturability improves, but shape complexity increases
Solution Approach 1:
The patent merges shapes that are connected in the graph representation when the graph is not two-colorable. By combining adjacent shapes into single vertices, the graph becomes two-colorable, enabling valid mask assignments. This merging resolves coloring conflicts and ensures manufacturability while minimizing the increase in shape complexity.
Solution Approach 2:
The patent changes the topological parameters of the pattern by merging shapes, which modifies the graph structure. This parameter change transforms an unmanufacturable configuration into a manufacturable one by altering the connectivity and spacing relationships, enabling the graph coloring algorithm to produce a valid solution.
3Manufacturing precision
If additional shapes are added to mandrel mask layout, then pattern completeness improves, but mask complexity increases
Solution Approach 1:
The patent performs preliminary graph coloring analysis before final mask layout determination. By pre-identifying which shapes need to be included as additional shapes in the mandrel mask layout, the method ensures pattern completeness is achieved while minimizing unnecessary mask complexity through optimized shape selection and placement.
Data Source
AI summary
Methods and apparatuses are described for determining mask layouts for printing a design intent on a wafer using a spacer-is-dielectric self-aligned double-patterning process. A system can determine whether a graph corresponding to a design intent is two-colorable. If the graph is not two-colorable, the system can merge one or more pairs of shapes in the design intent to obtain a modified design intent, so that a modified graph corresponding to the modified design intent is two-colorable. The system can then determine a two-coloring for the modified graph. Next, the system can place one or more core shapes in a mandrel mask layout which correspond to vertices in the modified graph that are associated with a selected color in the two-coloring. The system can then place one or more shapes in a trim mask layout for separating the shapes in the design intent that were merged.