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 of simulating an electromagnetic response of a metrology target comprising first and second gratings, wherein the second grating is below the first grating, the method comprising: receiving a model defining (i) the first grating as having a first number of grating lines within a pitch, each of the first number of grating lines separated by a first pitch; and (ii) the second grating as having a second number of grating lines within the pitch, each of the second number of grating lines separated by a second pitch; using the model and the first pitch to simulate properties of the first grating and generate a first scattering matrix; using the model and the second pitch to simulate properties of the second grating and generate a second scattering matrix; generating a scattering matrix defining properties of the metrology target by combining the first scattering matrix and the second scattering matrix.

Abstract: A method of inspection for defects on a substrate, such as a reflective reticle substrate, and associated apparatuses. The method includes performing the inspection using inspection radiation obtained from a high harmonic generation source and having one or more wavelengths within a wavelength range of between 20 nm and 150 nm. Also, a method including performing a coarse inspection using first inspection radiation having one or more first wavelengths within a first wavelength range; and performing a fine inspection using second inspection radiation having one or more second wavelengths within a second wavelength range, the second wavelength range comprising wavelengths shorter than the first wavelength range.

Abstract: A method and apparatus for selecting patterns from an image such as a design layout. The method includes obtaining an image (e.g., of a target layout) having a plurality of patterns; determining, based on pixel intensities within the image, a metric (e.g., entropy) indicative of an amount of information contained in one or more portions of the image; and selecting, based on the metric, a sub-set of the plurality of patterns from the one or more portions of the image having values of the metric within a specified range. The sub-set of patterns can be provided as training data for training a model associated with a patterning process.

Abstract: A method and apparatus of detection, registration and quantification of an image is described. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A method of inspection for defects on a substrate, such as a reflective reticle substrate, and associated apparatuses. The method includes performing the inspection using inspection radiation obtained from a high harmonic generation source and having one or more wavelengths within a wavelength range of between 20 nm and 150 nm. Also, a method including performing a coarse inspection using first inspection radiation having one or more first wavelengths within a first wavelength range; and performing a fine inspection using second inspection radiation having one or more second wavelengths within a second wavelength range, the second wavelength range comprising wavelengths shorter than the first wavelength range.

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: An apparatus and method to determine a property of a substrate by measuring, in the pupil plane of a high numerical aperture lens, an angle-resolved spectrum as a result of radiation being reflected off the substrate. The property may be angle and wavelength dependent and may include the intensity of TM- and TE-polarized radiation and their relative phase difference.

Abstract: Parameters of a structure (900) are measured by reconstruction from observed diffracted radiation. The method includes the steps: (a) defining a structure model to represent the structure in a two- or three-dimensional model space; (b) using the structure model to simulate interaction of radiation with the structure; and (c) repeating step (b) while varying parameters of the structure model. The structure model is divided into a series of slices (a-f) along at least a first dimension (Z) of the model space. By the division into slices, a sloping face (904, 906) of at least one sub-structure is approximated by a series of steps (904?, 906?) along at least a second dimension of the model space (X). The number of slices may vary dynamically as the parameters vary. The number of steps approximating said sloping face is maintained constant. Additional cuts (1302, 1304) are introduced, without introducing corresponding steps.

Abstract: A patterning device for patterning product structures onto a substrate and an associated substrate patterned using such a patterning device. The patterning device includes target patterning elements for patterning at least one target from which a parameter of interest can be inferred. The patterning device includes product patterning elements for patterning the product structures. The target patterning elements and product patterning elements are configured such that the at least one target has at least one boundary which is neither parallel nor perpendicular with respect to the product structures on the substrate.

Abstract: A method for training a machine learning model configured to predict a substrate image corresponding to a printed pattern of a substrate as measured via a metrology tool. The method involves obtaining a training data set including (i) metrology data of the metrology tool used to measure the printed pattern of the substrate, and (ii) a representation of a mask pattern employed for imaging the printed pattern on the substrate; and training, based on the training data set, a machine learning model to predict the substrate image of the substrate as measured by the metrology tool such that a cost function is improved, wherein the cost function includes a relationship between the predicted substrate image and the metrology data.

Abstract: A method of calculating electromagnetic scattering properties of a structure represented as a nominal structure and a structural perturbation, has the steps: 1008 numerically solving a volume integral equation comprising a nominal linear system 1004 to determine a nominal vector field being independent with respect to the structural perturbation; 1010 using a perturbed linear system 1006 to determine an approximation of a vector field perturbation arising from the structural perturbation, by solving a volume integral equation or an adjoint linear system. Matrix-vector multiplication of a nominal linear system matrix convolution operator may be restricted to sub-matrices; and 1012 calculating electromagnetic scattering properties of the structure using the determined nominal vector field and the determined approximation of the vector field perturbation.

Abstract: A method and apparatus of detection, registration and quantification of an image is described. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A defect prediction method for a device manufacturing process involving production substrates processed by a lithographic apparatus, the method including training a classification model using a training set including measured or determined values of a process parameter associated with the production substrates processed by the device manufacturing process and an indication regarding existence of defects associated with the production substrates processed in the device manufacturing process under the values of the process parameter, and producing an output from the classification model that indicates a prediction of a defect for a substrate.

Abstract: A method and apparatus of detection, registration and quantification of an image is described. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: Described herein is a method for quantifying uncertainty in parameterized (e.g., machine learning) model predictions. The method comprises causing a parameterized model to predict multiple posterior distributions from the parameterized model for a given input. The multiple posterior distributions comprise a distribution of distributions. The method comprises determining a variability of the predicted multiple posterior distributions for the given input by sampling from the distribution of distributions; and using the determined variability in the predicted multiple posterior distributions to quantify uncertainty in the parameterized model predictions. The parameterized model comprises encoder-decoder architecture.

Abstract: A defect prediction method for a device manufacturing process involving production substrates processed by a lithographic apparatus, the method including training a classification model using a training set including measured or determined values of a process parameter associated with the production substrates processed by the device manufacturing process and an indication regarding existence of defects associated with the production substrates processed in the device manufacturing process under the values of the process parameter, and producing an output from the classification model that indicates a prediction of a defect for a substrate.

Abstract: A method including: obtaining a logistic mathematical model predicting the formation of a physical structure created using a patterning process; evaluating the logistic mathematical model to predict formation of a part of the physical structure and generate an output; and adapting, based on the output, an aspect of the patterning process.

Abstract: Disclosed is a method for reconstructing a parameter of a lithographic process. The method comprises the step of designing a preconditioner suitable for an input system comprising the difference of a first matrix and a second matrix, the first matrix being arranged to have a multi-level structure of at least three levels whereby at least two of said levels comprise a Toeplitz structure. One such preconditioner is a block-diagonal matrix comprising a BTTB structure generated from a matrix-valued inverse generating function. A second such preconditioner is determined from an approximate decomposition of said first matrix into one or more Kronecker products.

Abstract: A method for determining the existence of a defect in a printed pattern may include obtaining a) a captured image of a printed pattern from an image capture device, and b) a simulated image of the printed pattern generated by a process model. The method may include generating a combined image as a weighted combination of portions of the captured image and the simulated image. The method may include determining whether a defect exists in the printed pattern based on the combined image.