Source Mask Optimization for Lithographic Image Fidelity
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Solution Overview
Problem
Current methods for optimizing source and mask in lithographic processes are time-consuming and often result in unsolvable optimization problems, especially when dealing with complex designs, due to the intricate nature of the lithographic process and the need to account for both source illuminator and mask optimization.
Innovation Solution
The implementation of methods that generate a source illumination profile and a continuous tone mask using optimization techniques such as the Lagrange method and homotopy methods, which determine optimum intensity for each pixel of the source and transmission values for the mask based on optimized diffraction orders, to improve image fidelity and throughput.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional optimization methods are used for source and mask in lithographic processes, then image fidelity can be improved, but the optimization time becomes excessively long and the problems become unsolvable for complex designs
Solution Approach 1:
The patent segments the optimization problem into distinct computational stages and components, breaking down the complex source and mask optimization into manageable parts that can be solved more efficiently. This segmentation allows the system to handle complex designs without becoming computationally intractable, thus reducing optimization time while maintaining image fidelity.
Solution Approach 2:
The patent employs parameter changes by transforming the optimization problem into different mathematical representations and using homotopy continuation methods that gradually transition between parameter states. This allows the system to navigate complex optimization landscapes more efficiently, finding solutions faster while maintaining the quality of the optimized source and mask parameters.
2Manufacturing precision
If conventional optimization methods are used for source and mask in lithographic processes, then image fidelity can be improved, but the device complexity increases making the problem unsolvable
Solution Approach 1:
The patent segments the complex optimization problem into distinct computational stages, breaking down the intricate source and mask optimization into manageable sub-problems. This segmentation reduces the apparent complexity by handling the optimization in discrete steps rather than as a single monolithic problem, making complex designs tractable.
Solution Approach 2:
The patent introduces intermediary computational representations and transformation steps that mediate between the input design specifications and the final optimized source and mask. These intermediaries simplify the overall problem structure by providing intermediate targets that are easier to optimize than the final solution directly, thus reducing device complexity in the optimization process.
3Productivity
If faster optimization methods are used, then productivity increases, but the manufacturing precision of the lithographic process may be compromised
Solution Approach 1:
The patent uses parameter changes through homotopy continuation methods that systematically transform the optimization problem through a sequence of parameter variations. This allows the system to maintain solution accuracy throughout the optimization process while moving efficiently toward the final solution, thus achieving both high productivity and manufacturing precision.
Solution Approach 2:
The patent incorporates feedback mechanisms that continuously monitor the quality of the optimization solution and adjust the computational approach accordingly. This feedback ensures that even as optimization speed increases, the image fidelity and manufacturing precision requirements are maintained by adapting the optimization process to preserve solution quality.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces the time required for optimization, enabling faster and more efficient reproduction of complex designs by determining optimal source illuminator profiles and mask designs that enhance image fidelity and manufacturing efficiency.
Implementation Method 1
expose specific portions of each layer to radiation
Implementation Method 2
the optimization derives optimum diffraction orders of the radiation
Data Source
AI summary
A method and apparatus for generating a source illuminator profile and a mask design, subsequently optimizing the source illuminator profile and mask design based upon a set of target intensity profiles. In various implementations, the Lagrange method of optimization is employed to optimize the radiation source, wherein an optimum intensity for each pixel of the source is determined. Subsequently, a continuous tone mask is generated based upon the diffraction orders of the optimized source. With various implementations, the target intensity profile is generated by deriving a set of band limited target frequencies corresponding to the optical lithographic system. Subsequently, homotopy methods may be employed to optimize the source illuminator profile and the continuous tone mask based upon the set of band limited target frequencies.