Neural Network Modeling Post-Lithography Critical Dimension Variation
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Solution Overview
Problem
Current semiconductor manufacturing simulations fail to accurately model stochastic total edge placement error (SEPE) due to oversimplified assumptions of symmetrical critical dimension distributions and computational inefficiencies, limiting their ability to predict full-chip level deviations and yield.
Innovation Solution
A neural network architecture is employed to model post-lithography critical dimensions, using aerial images as training data to generate asymmetric distributions of critical dimensions, allowing for simultaneous modeling of mean, standard deviation, and skewness, thereby addressing the limitations of conventional simulation models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional simulation models with symmetrical CD distribution assumptions are used, then model simplicity is maintained, but modeling accuracy deteriorates
Solution Approach 1:
The patent applies asymmetry by using neural networks to model asymmetric critical dimension distributions instead of assuming symmetric normal distributions. The neural network outputs asymmetric probability density functions that can capture skewness and higher moments, allowing accurate modeling of real-world CD variations that deviate from symmetry.
Solution Approach 2:
The patent changes parameters by transitioning from fixed distribution assumptions (symmetrical normal distribution with only mean and standard deviation) to data-driven neural network models that can output multiple statistical moments including mean, standard deviation, skewness, and higher moments, enabling flexible adaptation to actual measurement data.
2Reliability
If physical models with conventional software are used, then modeling capability is provided, but computational efficiency deteriorates
Solution Approach 1:
The patent uses copying by training neural networks on simulation data (aerial images) to create surrogate models that replicate the behavior of complex physical lithography processes. Once trained, these neural network models can predict CD distributions much faster than running full physical simulations, providing both accuracy and computational efficiency.
Solution Approach 2:
The patent applies preliminary action by performing computationally intensive physical simulations and neural network training during the model development phase using available simulation data. The resulting trained neural network models can then be applied to new design scenarios much more efficiently, as they only require forward passes through the neural network rather than re-running complex physical simulations.
3Ease of manufacture
If separate empirical models for CD mean and SEPE are used, then ease of implementation is maintained, but modeling accuracy deteriorates
Solution Approach 1:
The patent merges separate empirical models for CD mean and stochastic effects into a unified neural network framework. The neural network simultaneously outputs multiple statistical moments (mean, standard deviation, skewness, and higher moments) from a single input aerial image, capturing the correlations between different statistical parameters that are lost when using separate models.
Solution Approach 2:
The patent implements universality by designing a single neural network architecture that performs multiple functions: predicting CD mean, standard deviation, skewness, and higher moments simultaneously from aerial images. This multi-functional approach replaces multiple separate models and provides a comprehensive description of CD distributions.
Data Source
AI summary
A method of modeling distributions of post-lithography critical dimensions includes the following steps. A plurality of aerial images of respective portions of a physical design layout of a semiconductor wafer are generated, and the plurality of aerial images are employed as training data. In the method, first and second portions of a neural network architecture are generated. The first portion includes a neural network which is shared by a plurality of output channels, and the second portion includes a plurality of neural networks, wherein each of the plurality of neural networks respectively correspond to one of the plurality of output channels. The method further includes training the first and second portions of the neural network architecture with the training data, and outputting the distributions of the post-lithography critical dimensions based on the plurality of output channels.