Machine learning aided solution to the inverse problem in optical scatterometry

Liu, Shuo; Chen, Xiuguo; Yang, Tianjuan; Guo, Chunfu; Zhang, Jiahao; Ma, Jianyuan; Chen, Chao; Cai, Wei; Zhang, Chuanwei

doi:10.1016/j.measurement.2022.110811

Cited by 25 publications

(13 citation statements)

References 33 publications

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“…In our proposed method, an artificial neural network (ANN) is chosen as the inverse problem solver for its exceptional capability to handle nonlinear regression and serve as a powerful and comprehensive approximator 13 . Additionally, the utilization of an ANN model offers the advantage of reducing measurement time.…”

Section: Inverse Model and Parameter Retrievalmentioning

confidence: 99%

AI-guided numerical-aperture-controlled scatterometry for measurement of deep HAR and thin-film structures with a large depth variation

Yang

et al. 2023

Optical Measurement Systems for Industrial Inspection XIII

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This research means to solve the challenges in measuring deep high-aspect-ratio (HAR) and thin-film structures in 3D integrated circuits. As the semiconductor industry reaches its physical limitations in device scaling, advanced technologies such as advanced lithography and packaging have become crucial in extending Moore's law. This has led to the use of denser nano-to-sub-micron structures in three-dimensional integrated circuits (3D-IC), resulting in smaller, more functional devices. However, measuring these complex and deep HAR and thin-film structures with a large depth range from a few nanometers to a few hundred micrometers using a single optical system is challenging. To address this need, this article presents an AI-guided scatterometry method using numerical aperture control to achieve a large measurement range. The system uses broadband light to generate multi-wavelength reflection responses from the samples. With the help of an electromagnetic simulation tool and an artificial neural network model, the depth resolution can be improved through inverse modeling. The results demonstrate the ability to measure a wide range of samples with depths ranging from nanometers to micrometers scale, including sub-micron HAR openings and ultra-thin films, as long as the measurement bias is controlled within acceptable limits.

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Section: Inverse Model and Parameter Retrievalmentioning

confidence: 99%

AI-guided numerical-aperture-controlled scatterometry for measurement of deep HAR and thin-film structures with a large depth variation

Yang

et al. 2023

Optical Measurement Systems for Industrial Inspection XIII

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“…The surrogate model offers an efficient solution for tackling such problems, particularly when establishing a complex or computationally expensive forward model is challenging. Some researchers have successfully utilized artificial neural networks in optical scatterometry [20][21][22]. The NN-based surrogate model has the potential for efficient and repeatable calculations, which is employed in this work.…”

Section: Nn-based Surrogate Modelmentioning

confidence: 99%

“…Additionally, the minimum square error is applied as the train loss function. The rectified linear unit activation function is selected for the hidden layers, while the output layer employs a linear function [22].…”

Section: Nn-based Surrogate Modelmentioning

confidence: 99%

Condition-number-based measurement configuration optimization for nanostructure reconstruction by optical scatterometry

Yang

Chen

Liu

et al. 2023

Meas. Sci. Technol.

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The quality of the measured signature is influenced not only by the instrument’s precision but also by the selected measurement configuration. In optical scatterometry, the purpose of measurement configuration optimization (MCO) is to select an optimal or suboptimal combination of measurement conditions, such as the angles of incidence, azimuth, polarization and wavelength, to achieve higher measurement accuracy. This analysis not only requires an effective optimization strategy but is also time-consuming. In this work, we propose a general MCO method that incorporates error propagation theory and condition-number-based error estimation technique, by which the MCO problem can be formulated as an optimization problem for the condition number of the coefficient matrix in the linear estimation of parameter deviations. The method is demonstrated on a multi-wavelength Mueller matrix scatterometry measuring a Si grating. With the help of the neural-network-based surrogate model, the feasibility of the method is verified by making a comparison with Latin Hypercube sampling. Fitting results of the measured and calculated Mueller matrix spectra obtained at the selected optimal measurement configuration show a good agreement. The proposed method is promising to provide an alternate solution to globally evaluate the MCO problem in optical scatterometry and other measurement scenarios.

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“…The latter can retrieve complete structural parameters but requires a complex model and laborious numerical simulations which make the evaluation process difficult and timeconsuming. A possible compromise would be the use of machine learning, which was already successfully applied to the evaluation process in optical scatterometry [4]. Training a machine learning model for image evaluation initially also requires high computational costs, but once the training is finished, results are achieved fast and reliable.…”

Section: Haar-like Feature Examinationsmentioning

confidence: 99%

Nanoform evaluation approach using Mueller matrix microscopy and machine learning concepts

et al. 2022

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We realized an imaging Mueller matrix microscope for nanostructure characterization. For investigations on nanoform characterization via Mueller matrix images, we measured and simulated Mueller matrix images of specially designed nanostructures. As an approach towards machine learning evaluation in imaging ellipsometry, we calculated Haar-like features of the images and observed a higher sensitivity to subwavelength features in off-diagonal matrix elements compared to microscopy.

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Machine learning aided solution to the inverse problem in optical scatterometry

Cited by 25 publications

References 33 publications

AI-guided numerical-aperture-controlled scatterometry for measurement of deep HAR and thin-film structures with a large depth variation

AI-guided numerical-aperture-controlled scatterometry for measurement of deep HAR and thin-film structures with a large depth variation

Condition-number-based measurement configuration optimization for nanostructure reconstruction by optical scatterometry

Nanoform evaluation approach using Mueller matrix microscopy and machine learning concepts

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