Background: Thin mask model has been conventionally used in optical lithography simulation. In extreme ultraviolet (EUV) lithography thin mask model is not valid because the absorber thickness is comparable to the mask pattern size. Rigorous electromagnetic (EM) simulations have been used to calculate the thick mask amplitudes. However, these simulations are highly time consuming.
Aim: Proposing a prototype of a convolutional neural network (CNN) which reduces the calculation time of rigorous EM simulations in a small mask area with specific mask patterns.
Approach: We construct a CNN which reproduces the results of the EM simulation. We define mask 3D amplitude as the difference between the thick mask amplitude and the thin mask amplitude. The mask 3D amplitude of each diffraction order is approximated using three parameters which represent the on-axis and the off-axis mask 3D effects. The mask 3D parameters of all diffraction orders are trained by a CNN.
Results: The input and the targets of the CNN are a cut-mask pattern and mask 3D parameters calculated by the EM simulation, respectively. After the training with 199,900 random cut-mask patterns, the CNN successfully predicts the mask 3D parameters of new cut-mask patterns.
Conclusions: We construct a CNN which predicts the diffraction amplitudes from 2D EUV mask patterns. After the training, the CNN successfully reproduces the mask 3D amplitude. CNN prediction is 5000 times faster than the rigorous EM simulation. Next challenge is to construct a practical CNN which covers a large area with general mask patterns.
Thin mask model has been conventionally used in optical lithography simulation. In this model the diffracted waves from the mask are assumed to be Fourier transform of the mask pattern. In EUV (Extreme UltraViolet) lithography thin mask model is not valid because the absorber thickness is comparable to the mask pattern size. Fourier transformation is not suitable for calculating the diffracted waves from thick masks. Rigorous electromagnetic simulations such as finitedifference time-domain method, rigorous coupled wave analysis and 3D waveguide model are used to calculate the diffracted waves from EUV masks. However, these simulations are highly time consuming. We reduce the calculation time by adapting a CNN (Convolutional Neural Network). We calculate the far-field diffraction amplitudes from an EUV mask by using the 3D waveguide model. We divide the diffraction amplitudes into the thin mask amplitudes (Fourier transform of the mask pattern) and the residual mask 3D amplitudes. The incident angle dependence of the mask 3D amplitude for each diffraction order is fitted by using three parameters which represent the on-axis and the off-axis mask 3D effects. We train a CNN where the inputs are 2D mask patterns and the targets are the mask 3D parameters of all diffraction orders. After the training, the CNN successfully predict the mask 3D parameters. The CNN prediction is 5,000 times faster than the electromagnetic simulation. We extend the transmission cross coefficient formula to include the off-axis mask 3D effects. Our formula is applicable to arbitrary source shapes and defocus. We can use the eigen value decomposition method to accelerate the calculation.
Thin mask model has been conventionally used in optical lithography simulation. In this model the diffracted waves from the mask are assumed to be Fourier transform of the mask pattern. This assumption is the basis of Hopkins' method and sum of coherent system model. In EUV (Extreme UltraViolet) lithography thin mask model is not valid because the absorber thickness is comparable to the mask pattern size. Fourier transformation cannot be applied to calculate the diffracted waves from thick masks. Rigorous electromagnetic simulations such as finite-difference time-domain method, rigorous coupled wave analysis and 3D waveguide method are used to calculate the diffracted waves from EUV masks. However, these simulations are highly time consuming. We reduce the calculation time by adapting a convolutional neural network. We construct a convolutional network which can predict the diffracted waves from 1D EUV mask patterns. We extend the TCC method to include the off-axis mask 3D effects. Our model is applicable to arbitrary source shapes and defocus.
KEYWORDS: Feature extraction, Feature selection, Lithography, Simulation of CCA and DLA aggregates, Machine learning, Manufacturing, Computer programming, Semiconducting wafers, Design for manufacturability, Very large scale integration
As VLSI device feature sizes are getting smaller and smaller, lithography hotspot detection and elimination have become more important to avoid yield loss. Although various machine learning based methods have been proposed, it is not easy to find appropriate parameters to achieve high accuracy. This paper proposes a feature selection method by using the probability distributions of layout features. Our method enables automatic feature optimization and classifier construction. It can be adaptive to different layout patterns with various features. In order to evaluate hotspot detection methods in the situation close to actual problem, dataset based on ICCAD2019 dataset is used for evaluation. Experimental results show the effectiveness of our method and limitations.
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