Abstract: A method for determining a metric of a feature on a substrate obtained by a semiconductor manufacturing process involving a lithographic process, the method including: obtaining an image of at least part of the substrate, wherein the image includes at least the feature; determining a contour of the feature from the image; determining a plurality of segments of the contour; determining respective weights for each of the plurality of segments; determining, for each of the segments, an image-related metric; and determining the metric of the feature in dependence on the weights and the calculated image-related metric of each of the segments.

Abstract: A method including: computing a value of a first variable of a pattern of, or for, a substrate processed by a patterning process by combining a fingerprint of the first variable on the substrate and a certain value of the first variable; and determining a value of a second variable of the pattern based at least in part on the computed value of the first variable.

Abstract: A method for determining a measurement recipe describing one or more measurement settings for measuring a parameter of interest from a substrate subject to an etch induced parameter error, the etch induced parameter error affecting measurement of the parameter of interest in a recipe dependent manner. The method include obtaining parameter of interest set-up data relating to measurements of at least one set-up substrate on which the parameter of interest has various first induced set values and etch induced parameter set-up data relating to measurements of at least one set-up substrate on which the etch induced parameter has various second induced set values. The recipe is determined so as to minimize the effect of the etch induced parameter on measurement of the parameter of interest.

Abstract: A method of determining a field of view setting for an inspection tool having a configurable field of view, the method including: obtaining a process margin distribution of features on at least part of a substrate; obtaining a threshold value; identifying, in dependence on the obtained process margin distribution and the threshold value, one or more regions on at least part of the substrate; and determining the field of view setting in dependence on the identified one or more regions.

Abstract: A method including: computing a value of a first variable of a pattern of, or for, a substrate processed by a patterning process by combining a fingerprint of the first variable on the substrate and a certain value of the first variable; and determining a value of a second variable of the pattern based at least in part on the computed value of the first variable.

Abstract: A method for determining a metric of a feature on a substrate obtained by a semiconductor manufacturing process involving a lithographic process, the method including: obtaining an image of at least part of the substrate, wherein the image includes at least the feature; determining a contour of the feature from the image; determining a plurality of segments of the contour; determining respective weights for each of the plurality of segments; determining, for each of the segments, an image-related metric; and determining the metric of the feature in dependence on the weights and the calculated image-related metric of each of the segments.

Abstract: A method for determining a correction to a patterning process. The method includes obtaining a plurality of qualities of the patterning process (e.g., a plurality of parameter maps, or one or more corrections) derived from metrology data and data of an apparatus used in the patterning process, selecting, by a hardware computer system, a representative quality from the plurality of qualities, and determining, by the hardware computer system, a correction to the patterning process based on the representative quality.

Abstract: Described herein is a method of training a model configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate and determining etch conditions based on the trained model. The method includes obtaining, via a metrology tool, (i) an after development image of the imaged substrate at a given location, the after development image including a plurality of features, and (ii) an after etch image of the imaged substrate at the given location; and training, using the after development image and the after etch image, the model configured to determine defectiveness of a given feature of the plurality of features in the after development image. In an embodiment, the determining of defectiveness is based on comparing the given feature in the after development image with a corresponding etch feature in the after etch image.

Abstract: A method for determining a correction to a patterning process. The method includes obtaining a plurality of qualities of the patterning process (e.g., a plurality of parameter maps, or one or more corrections) derived from metrology data and data of an apparatus used in the patterning process, selecting, by a hardware computer system, a representative quality from the plurality of qualities, and determining, by the hardware computer system, a correction to the patterning process based on the representative quality.

Abstract: A method for monitoring a lithographic process, and associated lithographic apparatus. The method includes obtaining height variation data relating to a substrate supported by a substrate support and fitting a regression through the height variation data, the regression approximating the shape of the substrate; residual data between the height variation data and the regression is determined; and variation of the residual data is monitored over time. The residual data may be deconvolved based on known features of the substrate support.

Abstract: A method, involving determining a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process; determining a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process; and determining a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions. The function may include a correlation.

Abstract: Methods and apparatus for determining a focus of a projection system are disclosed. In one arrangement, a method includes obtaining first data derived from a first measurement of one or more selected properties of a target pattern formed on a substrate by exposing the substrate using the projection system. The first measurement is performed before the substrate is etched based on the target pattern. The method further includes obtaining second data derived from a second measurement of the one or more selected properties of the target pattern. The second measurement is performed after the substrate is etched based on the target pattern. The method further includes determining the focus of the projection system using the first data and the second data.

Abstract: A method, involving determining a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process; determining a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process; and determining a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions. The function may include a correlation.

Abstract: A method of determining a characteristic of one or more processes for manufacturing features on a substrate, the method including: obtaining image data of a plurality of features on a least part of at least one region on a substrate; using the image data to obtain measured data of one or more dimensions of each of at least some of the plurality of features; determining a statistical parameter that is dependent on the variation of the measured data of one or more dimensions of each of at least some of the plurality of features; determining a probability of defective manufacture of features in dependence on a determined number of defective features in the image data; and determining the characteristic of the one or more processes to have the probability of defective manufacture of features and the statistical parameter.

Abstract: A method of determining a sampling control scheme and/or a processing control scheme for substrates processed by a device. The method uses a fingerprint model and an evolution model to generate the control scheme. The fingerprint model is based on fingerprint data for a processing parameter of at least one substrate processed by a device, and the evolution model represents variation of the fingerprint data over time. The fingerprint model and the evolution model are analyzed and a sampling and/or processing control scheme is generated using the analysis. The sampling control scheme provides an indication for where and when to take measurements on substrates processed by the device. The processing control scheme provides an indication for how to control the processing of the substrate. Also, there is provided a method of determining which of multiple devices contributed to a fingerprint of a processing parameter.

Abstract: A lithographic apparatus and associated method of controlling a lithographic process. The lithographic apparatus has a controller configured to define a control grid associated with positioning of a substrate within the lithographic apparatus. The control grid is based on a device layout, associated with a patterning device, defining a device pattern which is to be, and/or has been, applied to the substrate in a lithographic process.

Abstract: A system comprises a topography measurement system configured to determine a respective height for each of a plurality of locations on a substrate; and a processor configured to: determine a height map for the substrate based on the determined heights for the plurality of locations; and determine at least one alignment parameter for the substrate by comparing the height map and a reference height map, wherein the reference height map comprises or represents heights for a plurality of locations on a reference substrate portion.

Abstract: A method for determining an image-metric of features on a substrate, the method including: obtaining a first image of a plurality of features on a substrate; obtaining one or more further images of a corresponding plurality of features on the substrate, wherein at least one of the one or more further images is of a different layer of the substrate than the first image; generating aligned versions of the first and one or more further images by performing an alignment process on the first and one or more further images; and calculating an image-metric in dependence on a comparison of the features in the aligned version of the first image and the corresponding features in the one or more aligned versions of the one or more further images.

Abstract: A method for analyzing a process, the method including obtaining a multi-dimensional probability density function representing an expected distribution of values for a plurality of process parameters; obtaining a performance function relating values of the process parameters to a performance metric of the process; and using the performance function to map the probability density function to a performance probability function having the process parameters as arguments.

Abstract: A method for characterizing post-processing data in terms of individual contributions from processing stations, the post-processing data relating to a manufacturing process for manufacturing integrated circuits on a plurality of substrates using a corresponding processing apparatus for each of a plurality of process steps, at least some of the processing apparatuses each including a plurality of the processing stations, and wherein the combination of processing stations used to process each substrate defines a process thread for the substrate; the method including: obtaining post-processing data associated with processing of the plurality of substrates in a cyclic sequence of processing threads; and determining an individual contribution of a particular processing station by comparing a subset of the post-processing data corresponding to substrates having shared process sub-threads, wherein a process sub-thread describes the process steps of each process thread other than the process step to which the particu