Mask Shape Vertex Collapsing for Lithography Simulation
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Solution Overview
Problem
Conventional approaches to modifying mask shapes for lithography result in the proliferation of vertices and segments, leading to increased computational load, data storage, and communication bandwidth, as well as jagged, staircase representations of edges that are difficult to simulate accurately.
Innovation Solution
The method involves moving segments and collapsing replicated vertices into a single vertex, reducing the number of vertices and segments, and applying vertex displacements to achieve smoother mask shapes, thereby mitigating the proliferation and improving simulation efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If segments are moved and vertices are replicated to apply corrections to mask shapes, then correction precision is improved, but the number of vertices and segments increases leading to increased computational load
Solution Approach 1:
The patent merges replicated vertices by identifying vertices at the same location and consolidating them into single vertices. This merging process reduces the total number of vertices and segments in the mask shape representation while preserving the correction precision achieved through the segment movement and vertex replication process
Solution Approach 2:
The patent discards redundant replicated vertices that result from segment movements by detecting and removing duplicate vertex locations. This recovery process eliminates unnecessary computational complexity while maintaining the essential geometric corrections to the mask shape
2Manufacturing precision
If vertices are replicated during segment movement, then correction accuracy is improved, but data storage requirements increase
Solution Approach 1:
The patent combines multiple replicated vertices that occupy the same spatial location into a single vertex representation. This merging significantly reduces the quantity of vertex data stored while preserving the geometric accuracy achieved through the correction process
3Adaptability or versatility
If multiple segments and vertices are created to represent mask shapes, then shape correction flexibility is improved, but communication bandwidth requirements increase
Solution Approach 1:
The patent merges adjacent segments that share common vertices into simplified segment representations. This reduces the total number of segments that need to be communicated while maintaining the flexibility to represent complex mask shape corrections
4Measurement precision
If vertices are not collapsed after replication, then correction precision is maintained, but simulation accuracy decreases due to jagged representations
Solution Approach 1:
The patent merges replicated vertices into single vertices at their common location, eliminating the jagged staircase representations that occur when vertices are not collapsed. This produces smooth mask shape boundaries that improve simulation accuracy while preserving the correction precision through proper vertex positioning
Data Source
AI summary
In some aspects, a mask shape is represented by vertices that are connected by segments. A correction to the mask shape is received. The correction may include displacements of the segments and displacements of the vertices. The mask shape is modified by a processor, as follows. The segments are moved according to the segment displacements. As part of this process, vertices that are endpoints of the moved segments are replicated. The replicated vertices are then collapsed. The resulting vertices are then moved according to the vertex displacements. This process of modifying the mask shape may be used as part of a mask synthesis process, to synthesize or correct the mask shapes according to some desired result.