Lithographic Projection System Configuration Optimization
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Solution Overview
Problem
Current lithographic apparatuses face challenges in quickly and accurately determining the optimal configuration of projection systems with multiple optical elements and manipulators to achieve desired optical properties, which affects the precision and efficiency of the lithographic process.
Innovation Solution
A method is introduced that involves formulating a cost function representing the difference between actual and desired optical properties, scaling it using physical constraints, and using singular value decomposition to find a solution configuration for the manipulators that minimizes the scaled cost function, while satisfying constraints such as physical limits and redundancy checks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional methods are used to determine manipulator configuration, then computational accuracy can be maintained, but computational time increases and productivity decreases
Solution Approach 1:
The patent segments the configuration determination process into distinct phases: a setup phase that computes transformation matrices and cost function parameters (performed once or infrequently), and a rapid evaluation phase that uses these pre-computed elements to quickly evaluate different manipulator configurations. This segmentation allows the computationally intensive work to be done once, enabling rapid subsequent evaluations.
Solution Approach 2:
The patent performs preliminary computations of transformation matrices, Jacobian matrices, and cost function parameters before the actual configuration optimization is needed. These pre-computed elements are stored and reused during rapid configuration evaluation, eliminating the need to recompute them repeatedly and significantly reducing computational time for each evaluation.
2Manufacturing precision
If detailed computational methods are used to ensure accuracy, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent extracts and separates the complex computational elements (transformation matrices, Jacobian matrices, cost function parameters) from the rapid evaluation process. By computing these complex elements once in advance and storing them, the system can perform rapid configuration evaluations using simpler operations that reference the pre-computed data, thus reducing the computational complexity of the main optimization loop while maintaining accuracy.
Solution Approach 2:
The patent transforms the configuration determination problem into a parameter optimization problem where the cost function is expressed in terms of manipulator parameters. By using pre-computed transformation matrices and Jacobians, the system changes the parameters efficiently, allowing rapid evaluation of how different parameter settings affect the optical properties without recomputing the entire system model each time.
Data Source
AI summary
A method of determining a configuration of a projection system for a lithographic apparatus, wherein manipulators of the projection system manipulate optical elements so as to adjust its optical properties, the method comprising: receiving dependencies of the optical properties of the projection system on a configuration of the manipulators, receiving a plurality of constraints of the manipulators, formulating a cost function, wherein the cost function represents a difference between the optical properties of the projection system for a given configuration of the manipulators and desired optical properties, wherein the cost function is formulated using the dependency of the optical properties on the configuration of the manipulators, scaling the cost function into a scaled variable space, wherein the scaling is performed by using the plurality of constraints and finding a solution configuration of the manipulators which substantially minimizes the scaled cost function subject to satisfying the plurality of constraints.