3D Stochastic Lithography Modeling for Resist Defect Prediction
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Solution Overview
Problem
Stochastic phenomena in lithographic processes, particularly EUV lithography, lead to defects such as line edge roughness, critical dimension non-uniformity, and unintended feature printing, reducing yield and necessitating computationally expensive Monte Carlo simulations.
Innovation Solution
A stochastic model is used to analyze stochastic randomness in three dimensions, receiving inputs like light exposure and resist parameters to generate probability distributions for success or failure, enabling optimization of illumination and mask design to mitigate these effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If Monte Carlo simulations are used to analyze stochastic phenomena in lithography, then manufacturing precision is improved, but use of energy and loss of time increase
Solution Approach 1:
The patent extracts only the essential stochastic components (photon shot noise, chemical noise, development noise) from the full lithographic process and models them separately using probability density functions. This selective extraction allows precise analysis of stochastic effects without requiring computationally intensive full-process Monte Carlo simulations, thereby improving analysis precision while reducing computational time.
Solution Approach 2:
The patent creates a simplified mathematical model that copies the essential statistical characteristics of stochastic phenomena using probability density functions and moment calculations. This analytical copy replaces the need for repeated full Monte Carlo simulations, providing equivalent precision with significantly reduced computational cost and time.
2Manufacturing precision
If Monte Carlo simulations are used to model stochastic variations, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent segments the stochastic process into distinct independent components: photon shot noise, chemical noise in resist, and development noise. Each component is modeled separately using appropriate probability density functions, allowing the overall process variation to be analyzed through combination of simpler models rather than a single complex Monte Carlo simulation.
Solution Approach 2:
The patent transforms the complex stochastic process into a set of statistical parameters (mean, variance, higher moments) that characterize each noise component. By changing the representation from full process simulation to parameter-based modeling, the patent achieves equivalent precision with reduced model complexity and improved interpretability.
3Manufacturing precision
If three-dimensional modeling is performed, then manufacturing precision is improved, but use of energy increases
Solution Approach 1:
The patent transitions from two-dimensional planar analysis to three-dimensional volumetric analysis by introducing the depth dimension in the resist film. The probability density functions are evaluated at multiple depths, allowing analysis of stochastic effects through the thickness of the resist layer. This dimensional extension provides superior spatial resolution for predicting printability while maintaining computational efficiency through analytical integration.
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 provides a computationally efficient method to predict and reduce stochastic defects, improving yield by optimizing lithographic processes and reducing unintended feature printing.
Implementation Method 1
stochastic phenomena in the resist process (e.g., for a family of photoresists known as Chemically Amplified Photoresists, these phenomena include photo-acid generator's (PAG) activation
Implementation Method 2
The polymer contains certain functional groups which get cleaved due to chemical reactions caused by exposure to light (deprotection)
Implementation Method 3
Lithography is a process used to manufacture electronic circuits in which light is used to transfer a geometric pattern from a photomask, based on the layout design, to a silicon substrate by a photo-sensitive polymer
Implementation Method 4
DUV lithography or EUV lithography may be subject to random stochastic phenomenon based on any one, any combination or all of: (1) photon shot noise
Implementation Method 5
stochastic phenomena in the resist process (e.g., for a family of photoresists known as Chemically Amplified Photoresists, these phenomena include photo-acid generator's (PAG) activation, acids/quencher molecules random walk and reactions
Implementation Method 6
stochastic phenomena in the resist development (e.g., dissolution of entangled partially deprotected polymer chains)
Data Source
AI summary
A method and system for 3D modeling of stochastic variation of a lithographic process. The lithographic process is subject to random stochastic phenomena, with the resulting stochastic randomness potentially becoming a major challenge. The stochastic phenomena are modeled using a stochastic model, such as a random field model, that models stochastic randomness. To extend the application of the stochastic model to predict 3D aspects and increase the accuracy of modeling, the stochastic randomness for each level of a plurality of levels discrete from one another in a resist thickness direction may be modeled and analyzed across the plurality of level to generate a 3-dimentional distribution of the stochastic randomness. In turn, indications of 3-dimentional distribution of the stochastic randomness may be used to modify one or both of the light exposure and resist parameters in order to reduce the effect of stochastic randomness on the lithographic process.