SOCS Kernel Reordering for Photolithography Simulation
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Solution Overview
Problem
Conventional Sum of Coherent Systems (SOCS) approximation in photolithographic processing is not accurate and computationally efficient due to its reliance on a fixed set of kernels derived from the optical system, which does not account for the specific photomask layout, leading to suboptimal feature fabrication in integrated microdevices.
Innovation Solution
The method involves determining a set of kernels from a transmission cross coefficient (TCC) matrix, reordering them based on object-specific geometry information to prioritize relevance, and truncating the SOCS series to include only the most important kernels for the specific object being simulated, thereby improving the accuracy and efficiency of image intensity simulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a fixed set of kernels from TCC matrix is used in SOCS approximation, then the method is computationally efficient, but the accuracy of image intensity simulation deteriorates because it does not account for object-specific geometry information
Solution Approach 1:
The patent pre-calculates and stores the complete set of kernels from the TCC matrix decomposition before actual simulation. This preliminary preparation allows the kernels to be readily available for rapid reordering and selection during object-specific simulations, reducing computational overhead while maintaining accuracy
Solution Approach 2:
The patent dynamically reorders kernels based on object-specific geometry information for each simulation case. Instead of using a static fixed kernel set, the system adapts the kernel ordering and selection to match the specific object being simulated, thereby improving accuracy without requiring complete recalculation of the TCC matrix
2Measurement precision
If more kernels are included in the SOCS series truncation, then the simulation accuracy improves, but the computational time increases
Solution Approach 1:
The patent changes the selection criterion for kernels from a fixed count-based truncation to an object-relevance-based selection. By reordering kernels according to their relevance to the specific object geometry, the system can achieve high accuracy with fewer kernels by selecting only those most relevant to the current simulation object
Solution Approach 2:
The patent uses partial action by selecting only the necessary subset of kernels relevant to each object rather than using all available kernels. This selective approach achieves sufficient simulation accuracy without the computational cost of processing the complete kernel set
3Manufacturing precision
If the same finite set of kernels is used for all masks, then the method is consistent and easy to implement, but the manufacturing precision deteriorates because it does not optimize for specific photomask layouts
Solution Approach 1:
The patent applies local quality by tailoring the kernel selection and ordering to the specific characteristics of each photomask layout and object being simulated. Different objects receive customized kernel sets optimized for their geometry, rather than applying a uniform kernel set to all cases
Solution Approach 2:
The system pre-computes the TCC matrix decomposition and stores the complete kernel set in advance. This preliminary action enables rapid object-specific optimization without requiring complex real-time calculations during the actual simulation process
Data Source
AI summary
A method for determining kernels in a sum of coherent systems (SOCS) approximation is provided. Information for an object to be simulated in a manufacturing process is determined. For example, information based on geometries that are included in a layout or mask is determined. A set of kernels from a transmission cross coefficient (TCC) matrix are also determined. The set of kernels may be weighted by importance values in an order of importance. The kernels may then be re-ordered based on the information for the object. These kernels are then re-ordered in the SOCS series to reflect their order of importance. The SOCS series of kernels is then truncated at the number of kernels desired. Accordingly, by re-ordering the kernels that may be more relevant to the object to include higher weights, when the truncation occurs, the kernels that are most relevant may be included in the SOCS approximation.