Stochastic Variation Modeling for Lithography Pattern Fidelity
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Solution Overview
Problem
Current lithographic processes face challenges in reproducing patterns with dimensions smaller than the classical resolution limit, particularly due to stochastic variations such as line edge roughness (LER) and line width roughness (LWR), which affect the fidelity of pattern transfer and throughput in semiconductor manufacturing.
Innovation Solution
A method is disclosed to determine the relationship between stochastic variations in aerial and resist images and design variables, allowing for the optimization of lithographic processes by adjusting design variables to minimize cost functions and improve throughput, using a computer-implemented approach that includes measuring and fitting parameters to model these variations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Length of moving object
If lithographic processes are used to reproduce patterns with dimensions smaller than the classical resolution limit, then the feature size is reduced, but stochastic variations such as line edge roughness and line width roughness increase
Solution Approach 1:
The patent changes physical and chemical parameters of the resist material and illumination conditions to reduce stochastic variations. Specifically, it modifies resist composition, exposure dose, and illumination wavelength to minimize line edge roughness and line width roughness while maintaining sub-resolution feature printing capability
Solution Approach 2:
The patent implements feedback mechanisms by measuring actual pattern dimensions and roughness parameters, then using this data to adjust subsequent lithographic process parameters. This closed-loop approach continuously optimizes pattern fidelity while printing at reduced feature sizes
2Manufacturing precision
If design variables are adjusted to minimize stochastic variations, then pattern fidelity is improved, but process complexity increases
Solution Approach 1:
The patent performs preliminary optimization of design variables including resist formulation, illumination parameters, and exposure conditions before actual pattern printing. By pre-characterizing and optimizing these parameters, the system reduces stochastic variations without requiring complex real-time adjustments during production
Solution Approach 2:
The patent segments the lithographic process into distinct optimization stages: resist material optimization, illumination parameter optimization, and exposure process optimization. This modular approach allows each parameter set to be independently tuned, reducing overall process complexity while achieving high pattern fidelity
3Manufacturing precision
If exposure dose is increased to reduce stochastic variations, then line edge roughness is reduced, but throughput decreases
Solution Approach 1:
The patent changes the wavelength parameter of illumination and the chemical composition of resist to achieve lower line edge roughness at reduced exposure doses. By operating at optimized wavelengths and using specially formulated resists, the system maintains high pattern fidelity without the throughput penalty associated with high-dose exposure
Data Source
AI summary
A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the design variables, from a distribution of the values of the characteristic for that set of values of the design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the design variables.