Source Polarization Optimization in Lithography
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Solution Overview
Problem
Current lithographic apparatuses face challenges in optimizing the polarization state of radiation sources to achieve desired lithographic responses, limiting the resolution and uniformity of patterns on substrates, especially in low-k1 lithography where existing source polarization optimization techniques can only handle a small and discrete set of source polarization states.
Innovation Solution
The method involves representing each source point in the pupil plane of the illumination source with variable parameters that characterize the polarization state, and iteratively reconfiguring both the source points and the design layout based on a computed gradient of a cost function to achieve a desired lithographic response, allowing for customizable polarization conditions and optimizing both source intensity and polarization simultaneously.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing source polarization optimization techniques are used, then the lithographic process can be performed with fixed polarization states, but the resolution and uniformity of patterns are limited
Solution Approach 1:
The patent applies dynamics by transitioning from fixed polarization states to continuously variable polarization states at each source point. The optimization process dynamically adjusts polarization parameters (such as polarization angle and ellipticity) based on the specific imaging requirements, allowing the system to adapt polarization characteristics to maximize pattern uniformity and resolution for different lithographic scenarios.
Solution Approach 2:
The patent implements parameter changes by introducing variable polarization parameters for each source point in the pupil plane. Instead of using a single fixed polarization state for the entire illumination source, the system independently controls polarization parameters across different source points, enabling continuous optimization of the aerial image intensity distribution and thereby improving pattern manufacturing precision.
2Reliability
If continuous variation of polarization states is allowed, then the process window and critical dimension uniformity are improved, but the computational complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the illumination source into multiple discrete source points in the pupil plane, where each source point can be independently optimized for its polarization state. This segmentation approach transforms the continuous polarization optimization problem into a set of discrete, manageable optimization tasks, reducing computational complexity while still achieving continuous variation effects across the source distribution.
Solution Approach 2:
The patent implements partial action by optimizing polarization parameters for a preselected group of source points rather than attempting to optimize every possible point in the continuous pupil plane. This selective optimization of discrete source points provides sufficient improvement in process window and critical dimension uniformity without requiring computationally prohibitive continuous optimization across the entire source distribution.
3Manufacturing precision
If both source intensity and polarization are optimized simultaneously, then the lithographic response is improved, but the optimization time and computational resources increase
Solution Approach 1:
The patent applies preliminary action by performing a preliminary optimization of source intensity distribution before conducting the polarization optimization. This two-stage approach first establishes an optimal intensity profile, then builds upon it to optimize polarization parameters. This sequential strategy reduces the overall computational burden and optimization time compared to simultaneously optimizing all parameters from scratch, while still achieving improved lithographic response.
Data Source
AI summary
A lithographic simulation process is described, where each source point in a preselected group of source points at a pupil plane of an illumination source is represented by one or more variable parameters, wherein at least some of the variable parameters characterize a polarization state at the source point. One or both of the preselected group of source points in the illumination source and a representation of the design layout are iteratively reconfigured based on a computed gradient of a cost function with respect to the one or more variable parameters until a desired lithographic response is obtained, wherein the cost function comprises an aerial image intensity of a representation of the design layout projected using the preselected group of source points. Physical hardware to implement the source polarization variation is also described.