Apodization Model for Optical Lithography CD Error Reduction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing OPC models in semiconductor manufacturing cannot accurately predict pupil apodization effects in high-NA optical lithography systems, leading to significant errors in critical dimension (CD) and instability in the lithography process due to the use of inaccurate ideal Gaussian models.
Innovation Solution
A system that collects and models the spatial transmission profile of the optical lithography system to construct a piece-wise or enhanced Gaussian apodization model, which is then incorporated into the lithography model to accurately predict apodization effects, using techniques such as partitioning transmission profiles into sectional or pixellized models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If an ideal Gaussian model with a single parameter is used to model apodization effect, then the model complexity is low, but the manufacturing precision deteriorates due to significant CD errors
Solution Approach 1:
The patent divides the single-parameter Gaussian model into a multi-parameter model by segmenting the apodization function into multiple independent parameters (amplitude, width, shape parameters). This segmentation allows each parameter to be optimized independently to match different regions of the transmission profile, thereby improving manufacturing precision while maintaining manageable model complexity through modular parameter optimization.
Solution Approach 2:
The patent transforms the single-parameter Gaussian model into a multi-parameter model by introducing additional parameters (amplitude A, width σ, shape parameters α and β). This parameter expansion enables the model to capture the complex frequency-dependent transmission characteristics of the optical system, significantly reducing CD errors by providing sufficient degrees of freedom to fit the measured transmission profile.
2Adaptability or versatility
If multi-dimensional optimization is used to calibrate the apodization parameter simultaneously with other parameters, then the adaptability improves, but the stability deteriorates due to model distortion
Solution Approach 1:
The patent segments the model calibration process into separate stages: first optimizing the apodization parameters independently by fitting to measured transmission data, then optimizing other OPC parameters. This segmentation prevents the apodization parameters from being distorted by simultaneous optimization with other model components, thereby maintaining model stability while still achieving good adaptability through the initial independent calibration.
Solution Approach 2:
The patent performs preliminary optimization of the apodization parameters before conducting the full multi-dimensional optimization of all OPC parameters. This preliminary action establishes accurate baseline values for the apodization parameters, preventing them from being unintentionally distorted during subsequent optimization, thus maintaining model stability while preserving adaptability.
3Ease of operation
If the ideal Gaussian model is used in high-NA lithography systems, then the ease of operation is high, but the manufacturing precision deteriorates due to frequency-dependent attenuation errors
Solution Approach 1:
The patent extends the simple Gaussian model by introducing additional parameters (amplitude A, shape parameters α and β) that specifically address the frequency-dependent transmission characteristics of high-NA optical systems. These parameter changes enable the model to accurately capture the complex attenuation behavior across different spatial frequencies while maintaining a relatively simple functional form that is still easy to implement and operate.
Data Source
AI summary
One embodiment of the present invention provides a system that accurately predicts an apodization effect in an optical lithography system for manufacturing an integrated circuit. During operation, the system starts by collecting an apodization-effect-induced spatial transmission profile from the optical lithography system. The system then constructs an apodization model based on the spatial transmission profile. Next, the system enhances a lithography model for the optical lithography system by incorporating the apodization model into the lithography model, wherein the enhanced lithography model accurately predicts the effects of apodization on the optical lithography system.