Abstract: A method, computer program and associated apparatuses for metrology. The method includes determining a reconstruction recipe describing at least nominal values for use in a reconstruction of a parameterization describing a target. The method includes obtaining first measurement data relating to measurements of a plurality of targets on at least one substrate, the measurement data relating to one or more acquisition settings and performing an optimization by minimizing a cost function which minimizes differences between the first measurement data and simulated measurement data based on a reconstructed parameterization for each of the plurality of targets. A constraint on the cost function is imposed based on a hierarchical prior. Also disclosed is a hybrid model method comprising obtaining a coarse model operable to provide simulated coarse data; and training a data driven model to correct the simulated coarse data so as to determine simulated data for use in reconstruction.

Abstract: A modular autoencoder model is described. The modular autoencoder model comprises input models configured to process one or more inputs to a first level of dimensionality suitable for combination with other inputs: a common model configured to: reduce a dimensionality of combined processed inputs to generate low dimensional data in a latent space; and expand the low dimensional data in the latent space into one or more expanded versions of the one or more inputs suitable for generating one or more different outputs; output models configured to use the one or more expanded versions of the one or more inputs to generate the one or more different outputs, the one or more different outputs being approximations of the one or more inputs; and a prediction model configured to estimate one or more parameters based on the low dimensional data in the latent space.

Abstract: A method, computer program and associated apparatuses for metrology. The method includes determining a reconstruction recipe describing at least nominal values for use in a reconstruction of a parameterization describing a target. The method includes obtaining first measurement data relating to measurements of a plurality of targets on at least one substrate, the measurement data relating to one or more acquisition settings and performing an optimization by minimizing a cost function which minimizes differences between the first measurement data and simulated measurement data based on a reconstructed parameterization for each of the plurality of targets. A constraint on the cost function is imposed based on a hierarchical prior. Also disclosed is a hybrid model method comprising obtaining a coarse model operable to provide simulated coarse data; and training a data driven model to correct the simulated coarse data so as to determine simulated data for use in reconstruction.

Abstract: A modular autoencoder model is described. The modular autoencoder model comprises input models configured to process one or more inputs to a first level of dimensionality suitable for combination with other inputs; a common model configured to: reduce a dimensionality of combined processed inputs to generate low dimensional data in a latent space; and expand the low dimensional data in the latent space into one or more expanded versions of the one or more inputs suitable for generating one or more different outputs; output models configured to use the one or more expanded versions of the one or more inputs to generate the one or more different outputs, the one or more different outputs being approximations of the one or more inputs; and a prediction model configured to estimate one or more parameters based on the low dimensional data in the latent space.

Abstract: A modular autoencoder model is described. The modular autoencoder model comprises input models configured to process one or more inputs to a first level of dimensionality suitable for combination with other inputs; a common model configured to: reduce a dimensionality of combined processed inputs to generate low dimensional data in a latent space; and expand the low dimensional data in the latent space into one or more expanded versions of the one or more inputs suitable for generating one or more different outputs; output models configured to use the one or more expanded versions of the one or more inputs to generate the one or more different outputs, the one or more different outputs being approximations of the one or more inputs; and a prediction model configured to estimate one or more parameters based on the low dimensional data in the latent space.

Abstract: Methods for calibrating metrology apparatuses and determining a parameter of interest are disclosed. In one arrangement, training data is provided that comprises detected representations of scattered radiation detected by each of plural metrology apparatuses. An encoder encodes each detected representation to provide an encoded representation, and a decoder generates a synthetic detected representation from the respective encoded representation. A classifier estimates from which metrology apparatus originates each encoded representation or each synthetic detected representation. The training data is used to simultaneously perform, in an adversarial relationship relative to each other, a first machine learning process involving the encoder or decoder and a second machine learning process involving the classifier.

Abstract: A method, computer program and associated apparatuses for metrology. The method includes determining a reconstruction recipe describing at least nominal values for use in a reconstruction of a parameterization describing a target. The method includes obtaining first measurement data relating to measurements of a plurality of targets on at least one substrate, the measurement data relating to one or more acquisition settings and performing an optimization by minimizing a cost function which minimizes differences between the first measurement data and simulated measurement data based on a reconstructed parameterization for each of the plurality of targets. A constraint on the cost function is imposed based on a hierarchical prior. Also disclosed is a hybrid model method comprising obtaining a coarse model operable to provide simulated coarse data; and training a data driven model to correct the simulated coarse data so as to determine simulated data for use in reconstruction.

Abstract: Methods for calibrating metrology apparatuses and determining a parameter of interest are disclosed. In one arrangement, training data is provided that comprises detected representations of scattered radiation detected by each of plural metrology apparatuses. An encoder encodes each detected representation to provide an encoded representation, and a decoder generates a synthetic detected representation from the respective encoded representation. A classifier estimates from which metrology apparatus originates each encoded representation or each synthetic detected representation. The training data is used to simultaneously perform, in an adversarial relationship relative to each other, a first machine learning process involving the encoder or decoder and a second machine learning process involving the classifier.

Abstract: Methods of determining a value of a parameter of interest are disclosed. In one arrangement, a symmetric component and an asymmetric component of a detected pupil representation from illuminating a target are derived. A first metric characterizing the symmetric component and a second metric characterizing the asymmetric component vary non-monotonically as a function of the parameter of interest over a reference range of values of the parameter of interest. A combination of the derived symmetric component and the derived asymmetric component are used to identify a correct value from a plurality of candidate values of the parameter of interest.

Abstract: Methods of determining a value of a parameter of interest are disclosed. In one arrangement, a symmetric component and an asymmetric component of a detected pupil representation from illuminating a target are derived. A first metric characterizing the symmetric component and a second metric characterizing the asymmetric component vary non-monotonically as a function of the parameter of interest over a reference range of values of the parameter of interest. A combination of the derived symmetric component and the derived asymmetric component are used to identify a correct value from a plurality of candidate values of the parameter of interest.

Abstract: Methods and apparatus for estimating an unknown value of at least one of a plurality of sets of data, each set of data including a plurality of values indicative of radiation diffracted and/or reflected and/or scattered by one or more features fabricated in or on a substrate, wherein the plurality of sets of data include at least one known value, and wherein at least one of the plurality of sets of data includes an unknown value, the apparatus including a processor to estimate the unknown value of the at least one set of data based on: the known values of the plurality of sets of data, a first condition between two or more values within a set of data of the plurality of sets of data, and a second condition between two or more values being part of different sets of data of the plurality of the sets of data.

Abstract: Methods and apparatus for estimating an unknown value of at least one of a plurality of sets of data, each set of data including a plurality of values indicative of radiation diffracted and/or reflected and/or scattered by one or more features fabricated in or on a substrate, wherein the plurality of sets of data include at least one known value, and wherein at least one of the plurality of sets of data includes an unknown value, the apparatus including a processor to estimate the unknown value of the at least one set of data based on: the known values of the plurality of sets of data, a first condition between two or more values within a set of data of the plurality of sets of data, and a second condition between two or more values being part of different sets of data of the plurality of the sets of data.