Methods include generating a scanner aerial image using a neural network, where the scanner aerial image is generated using a mask inspection image that has been generated by a mask inspection machine. Embodiments also include training the neural network with a set of images, such as with a simulated scanner aerial image and another image selected from a simulated mask inspection image, a simulated Critical Dimension Scanning Electron Microscope (CD-SEM) image, a simulated scanner emulator image and a simulated actinic mask inspection image.

A process of characterizing a process window of a patterning process, the process including: obtaining a set of inspection locations for a pattern, the pattern defining features to be applied to a substrate with a patterning process, the set of inspection locations corresponding to a set of the features, the set of features being selected from among the features according to sensitivity of the respective features to variation in one or more process characteristics of the patterning process; patterning one or more substrates under varying process characteristics of the patterning process; and determining, for each of the variations in the process characteristics, whether at least some of the set of features yielded unacceptable patterned structures on the one or more substrates at corresponding inspection locations.

A method to improve a lithographic process of imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method including: computing a multi-variable cost function, the multi-variable cost function being a function of a stochastic variation of a characteristic of an aerial image or a resist image, or a function of a variable that is a function of the stochastic variation or that affects the stochastic variation, the stochastic variation being a function of a plurality of design variables that represent characteristics of the lithographic process; and reconfiguring one or more of the characteristics of the lithographic process by adjusting one or more of the design variables until a certain termination condition is satisfied.

A method of determining electromagnetic scattering properties of a finite periodic structure has the steps: 1002: Calculating a single-cell contrast current density, within a unit-cell supporting domain of a single one of a finite collection of unit cells. 1004: Calculating a scattered electric field outside the finite collection of unit cells, by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density. 1006: The Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells. The Green's function integrated with the determined single-cell contrast current density is obtained for observation points above the supporting domain with respect to a substrate underlying the finite periodic structure. 1008: Determining an electromagnetic scattering property, for example a diffraction pattern, of the finite periodic structure using the calculated scattered electric field.

A method for manufacturing a plurality of mechanical resonators (100) in a manufacturing wafer (10), the resonators being intended to be fitted to an adjusting member of a timepiece, the method comprising the following steps: (a) manufacturing a plurality of resonators in at least one reference wafer according to reference specifications, such manufacture comprising at least one lithography step to form patterns of the resonators on or above the reference wafer and a step of machining in the reference plate using the patterns; (b) for the at least one reference plate, establishing a map indicative of the dispersion of stiffnesses of the resonators relative to an average stiffness value; (c) dividing the map into fields and determining a correction to be made to the dimensions of the resonators for at least one of the fields in order to reduce the dispersion; (d) modifying the reference specifications for the lithography step so as to make the corrections to the dimensions for the at least one field in the lithography step; (e) manufacturing resonators in a manufacturing wafer using the modified specifications.

A method for determining a deformation of a resist in a patterning process. The method involves obtaining a resist deformation model of a resist having a pattern, the resist deformation model configured to simulate a fluid flow of the resist due to capillary forces acting on a contour of at least one feature of the pattern; and determining, via the resist deformation model, a deformation of a resist pattern to be developed based on an input pattern to the resist deformation model.

Disclosed is a method for obtaining a computationally determined interference electric field describing scattering of radiation by a pair of structures comprising a first structure and a second structure on a substrate. The method comprises determining a first electric field relating to first radiation scattered by the first structure; determining a second electric field relating to second radiation scattered by the second structure; and computationally determining the interference of the first electric field and second electric field, to obtain a computationally determined interference electric field.

Methods for training a process model and determining ranking of simulated patterns (e.g., corresponding to hot spots). A method involves obtaining a training data set including: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on the substrate using the mask pattern, and (iii) measured values of a parameter of the patterning process applied during imaging of the mask pattern on the substrate; and training a machine learning model for the patterning process based on the training data set to predict a difference in a characteristic of the simulated pattern and the printed pattern. The trained machine learning model can be used for determining a ranking of hot spots. In another method a model is trained based on measurement data to predict ranking of the hot spots.

A device manufacturing method, the method comprising: obtaining a measurement data time series of a plurality of substrates on which an exposure step and a process step have been performed; obtaining a status data time series relating to conditions prevailing when the process step was performed on at least some of the plurality of substrates; applying a filter to the measurement data time series and the status data time series to obtain filtered data; and determining, using the filtered data, a correction to be applied in an exposure step performed on a subsequent substrate.

Methods and systems are described for generating assessment maps. A method includes receiving a first vector map comprising a first set of vectors each indicating a distortion of a particular location on a substrate and generating a second vector map indicating a change in direction of a magnitude of the distortion of the particular location on the substrate. The method further includes generating a third vector map comprising vectors reflecting reduced noise in distortions across the plurality of locations on the substrate and generating a fourth vector map projecting a direction component of each vector component in the third set of vectors to a radial direction. The method further includes generating a fifth vector map by grouping the vectors of the fourth set of vectors and determining a magnitude associated with each group of vectors.