Abstract: A method and system for predicting complex electric field images with a parameterized model are described. A latent space representation of a complex electric field image is determined based on dimensional data in a latent space of the parameterized model for a given input to the parameterized model. The given input may be a measured amplitude (e.g., intensity) associated with the complex electric field image. The complex electric field image is predicted based on the latent space representation of the complex electric field image. The predicted complex electric field image includes an amplitude and a phase. The parameterized model comprises encoder-decoder architecture. In some embodiments, determining the latent space representation of the electric field image comprises minimizing a function constrained by a set of electric field images that could be predicted by the parameterized model based on the dimensional data in the latent space and the given input.

Abstract: Disclosed is a method comprising: obtaining measured data relating to at least one measurement by a measurement apparatus configured to irradiate radiation onto each of one or more structures on a substrate: decomposing the measured data using a decomposition method to obtain multiple measured data components: obtaining simulated data relating to at least one simulation based on the one or more structures: decomposing the simulated data using the decomposition method to obtain multiple simulated data components: matching between at least a portion of the simulated data components and at least a portion of the measured data components; and extracting a feature of the substrate based on the matching of at least a portion of the simulated data components and at least a portion of the measured data components.

Abstract: A measurement process is performed for each of a plurality of locations on a product of a fabrication process at which a parameter of interest characterizing the fabrication process is believed to be nominally the same, to derive measured signals for each location including at least one image. A dimensional reduction method is applied to a dataset of the measured signals, to obtain components of the dataset, including components indicative of variation between the images. For at least one of these components, one or more associated ones of the measured signals are identified, comprising at least one set of corresponding pixels in the respective images for the plurality of locations. The contribution of the identified measured signals in the dataset is reduced or eliminated to obtain a processed signal, and the parameter of interest is obtained from the processed signal.

Abstract: A method of designing a target includes obtaining a model of an initial dataset, performing a Bayesian optimization using the model which provides an improved model, and performing an optimization of the target design using the improved model.

Abstract: Disclosed is a method of measuring a target on a substrate using a metrology tool comprising an illumination source operable to emit an illumination beam for illuminating the target and a metrology sensor for collecting the scattered radiation having been scattered by the target. The method comprises calculating a target angle based on cell dimensions of a unit cell of said target in a first direction and a second direction orthogonal to said first direction; and order numbers of a selected pair of complementary diffraction orders in said first direction and second direction. At least one pair of measurement acquisitions is performed at a first target orientation and a second target orientation with respect to the illumination beam, wherein said target angle for at least one of said at least one pair of measurement acquisitions is an oblique angle.

Abstract: A method and system for predicting process information (e.g., phase data) using a given input (e.g., intensity) to a parameterized model are described. A latent space of a given input is determined based on dimensional data in a latent space of the parameterized model for a given input to the parameterized model. Further, an optimum latent space is determined by constraining the latent space with prior information (e.g., wavelength) that enables converging to a solution that causes more accurate predictions of the process information. The optimum latent space is used to predict the process information. The given input may be a measured amplitude (e.g., intensity) associated with the complex electric field image. The predicted process information can be complex electric field image having amplitude data and phase data. The parameterized model comprises variational encoder-decoder architecture.

Abstract: A method and system for predicting complex electric field images with a parameterized model are described. A latent space representation of a complex electric field image is determined based on dimensional data in a latent space of the parameterized model for a given input to the parameterized model. The given input may be a measured amplitude (e.g., intensity) associated with the complex electric field image. The complex electric field image is predicted based on the latent space representation of the complex electric field image. The predicted complex electric field image includes an amplitude and a phase. The parameterized model comprises encoder-decoder architecture. In some embodiments, determining the latent space representation of the electric field image comprises minimizing a function constrained by a set of electric field images that could be predicted by the parameterized model based on the dimensional data in the latent space and the given input.