Abstract: A method of image template matching for multiple process layers of, for example, semiconductor substrate with an adaptive weight map is described. An image template is provided with a weight map, which is adaptively updated based during template matching based on the position of the image template on the image. A method of template matching a grouped pattern or artifacts in a composed template is described, wherein the pattern comprises deemphasized areas weighted less than the image templates. A method of generating an image template based on a synthetic image is described. The synthetic image can be generated based on process and image modeling. A method of selecting a grouped pattern or artifacts and generating a composed template is described. A method of per layer image template matching is described.

Abstract: A method for determining values of design variables of a lithographic process based on a predicted failure rate for printing a target pattern on a substrate using a lithographic apparatus. The method includes obtaining an image corresponding to a target pattern to be printed on a substrate using a lithographic apparatus, wherein the image is generated based on a set of values of design variables of the lithographic apparatus or a lithographic process; determining image properties, the image properties representative of a pattern printed on the substrate, the pattern corresponding to the target pattern; predicting a failure rate in printing the pattern on the substrate based on the image properties; and determining a specified value of a specified design variable based on the failure rate, the specified value to be used in the lithographic process to print the target pattern on the substrate.

Abstract: A method for predicting yield relating to a process of manufacturing semiconductor devices on a substrate, the method including: obtaining a trained first model which translates modeled parameters into a yield parameter, the modeled parameters including: a) a geometrical parameter associated with one or more selected from: a geometric characteristic, dimension or position of a device element manufactured by the process and b) a trained free parameter; obtaining process parameter data including data regarding a process parameter characterizing the process; converting the process parameter data into values of the geometrical parameter; and predicting the yield parameter using the trained first model and the values of the geometrical parameter.

Abstract: Substrates to be processed are partitioned based on pre-processing data that is associated with substrates before a process step. The data is partitioned using a partition rule and the substrates are partitioned into subsets in accordance with subsets of the data obtained by the partitioning. Corrections are applied, specific to each subset. The partition rule is obtained using decision tree analysis on a training set of substrates. The decision tree analysis uses pre-processing data associated with the training substrates before they were processed, and post-processing data associated with the training substrates after being subject to the process step. The partition rule that defines the decision tree is selected from a plurality of partition rules based on a characteristic of subsets of the post-processing data. The associated corrections are obtained implicitly at the same time.

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 determining a correction relating to a performance metric of a semiconductor manufacturing process, the method including: obtaining a set of pre-process metrology data; processing the set of pre-process metrology data by decomposing the pre-process metrology data into one or more components which: a) correlate to the performance metric; or b) are at least partially correctable by a control process which is part of the semiconductor manufacturing process; and applying a trained model to the processed set of pre-process metrology data to determine the correction for the semiconductor manufacturing process.

Abstract: A method and apparatus for training a defect location prediction model to predict a defect for a substrate location is disclosed. A number of datasets having data regarding process-related parameters for each location on a set of substrates is received. Some of the locations have partial datasets in which data regarding one or more process-related parameters is absent. The datasets are processed to generate multiple parameter groups having data for different sets of process-related parameters. For each parameter group, a sub-model of the defect location prediction model is created based on the corresponding set of process-related parameters and trained using data from the parameter group. A trained sub-model(s) may be selected based on process-related parameters available in a candidate dataset and a defect prediction may be generated for a location associated with the candidate dataset using the selected sub-model.

Abstract: A method and apparatus for identifying locations to be inspected on a substrate is disclosed. A defect location prediction model is trained using a training dataset associated with other substrates to generate a prediction of defect or non-defect and a confidence score associated with the prediction for each of the locations based on process-related data associated with the substrates. Those of the locations determined by the defect location prediction model as having confidences scores satisfying a confidence threshold are added to a set of locations to be inspected by an inspection system. After the set of locations are inspected, the inspection results data is obtained, and the defect location prediction model is incrementally trained by using the inspection results data and process-related data for the set of locations as training data.

Abstract: A method for determining a root cause affecting yield in a process for manufacturing devices on a substrate, the method including: obtaining yield distribution data including a distribution of a yield parameter across the substrate or part thereof; obtaining sets of metrology data, each set including a spatial variation of a process parameter over the substrate or part thereof corresponding to a different layer of the substrate; comparing the yield distribution data and metrology data based on a similarity metric describing a spatial similarity between the yield distribution data and an individual set out of the sets of the metrology data; and determining a first similar set of metrology data out of the sets of metrology data, being the first set of metrology data in terms of processing order for the corresponding layers, which is determined to be similar to the yield distribution data.

Abstract: A method for determining a correction for an apparatus used in a process of patterning substrates, the method including: obtaining a group structure associated with a processing history and/or similarity in fingerprint of to be processed substrates; obtaining metrology data associated with a plurality of groups within the group structure, wherein the metrology data is correlated between the groups; and determining the correction for a group out of the plurality of groups by applying a model to the metrology data, the model including at least a group-specific correction component and a common correction component.

Abstract: Generating a control output for a patterning process is described. A control input is received. The control input is for controlling the patterning process. The control input includes one or more parameters used in the patterning process. The control output is generated with a trained machine learning mod& based on the control input, The machine learning model is trained with training data generated from simulation of the patterning process and/or actual process data, The training data includes 1) a plurality of training control inputs corresponding to a plurality of operational conditions of the patterning process, where the plurality of operational conditions of the patterning process are associated with operational condition specific behavior of the patterning process over time, and 2) training control outputs generated using a physical model based on the training control inputs.

Abstract: A method and associated computer program for predicting an electrical characteristic of a substrate subject to a process. The method includes determining a sensitivity of the electrical characteristic to a process characteristic, based on analysis of electrical metrology data including electrical characteristic measurements from previously processed substrates and of process metrology data including measurements of at least one parameter related to the process characteristic measured from the previously processed substrates; obtaining process metrology data related to the substrate describing the at least one parameter; and predicting the electrical characteristic of the substrate based on the sensitivity and the process metrology data.

Abstract: Methods of identifying a hot spot from a design layout or of predicting whether a pattern in a design layout is defective, using a machine learning model. An example method disclosed herein includes obtaining sets of one or more characteristics of performance of hot spots, respectively, under a plurality of process conditions, respectively, in a device manufacturing process; determining, for each of the process conditions, for each of the hot spots, based on the one or more characteristics under that process condition, whether that hot spot is defective; obtaining a characteristic of each of the process conditions; obtaining a characteristic of each of the hot spots; and training a machine learning model using a training set including the characteristic of one of the process conditions, the characteristic of one of the hot spots, and whether that hot spot is defective under that process condition.

Abstract: Methods of identifying a hot spot from a design layout or of predicting whether a pattern in a design layout is defective, using a machine learning model. An example method disclosed herein includes obtaining sets of one or more characteristics of performance of hot spots, respectively, under a plurality of process conditions, respectively, in a device manufacturing process; determining, for each of the process conditions, for each of the hot spots, based on the one or more characteristics under that process condition, whether that hot spot is defective; obtaining a characteristic of each of the process conditions; obtaining a characteristic of each of the hot spots; and training a machine learning model using a training set including the characteristic of one of the process conditions, the characteristic of one of the hot spots, and whether that hot spot is defective under that process condition.

Abstract: A method for determining a correction for an apparatus used in a process of patterning substrates, the method including: obtaining a group structure associated with a processing history and/or similarity in fingerprint of to be processed substrates; obtaining metrology data associated with a plurality of groups within the group structure, wherein the metrology data is correlated between the groups; and determining the correction for a group out of the plurality of groups by applying a model to the metrology data, the model including at least a group-specific correction component and a common correction component.

Abstract: A method for determining a correction relating to a performance metric of a semiconductor manufacturing process, the method including: obtaining a set of pre-process metrology data; processing the set of pre-process metrology data by decomposing the pre-process metrology data into one or more components which: a) correlate to the performance metric; or b) are at least partially correctable by a control process which is part of the semiconductor manufacturing process; and applying a trained model to the processed set of pre-process metrology data to determine the correction for the semiconductor manufacturing process.

Abstract: A method for predicting yield relating to a process of manufacturing semiconductor devices on a substrate, the method including: obtaining a trained first model which translates modeled parameters into a yield parameter, the modeled parameters including: a) a geometrical parameter associated with one or more selected from: a geometric characteristic, dimension or position of a device element manufactured by the process and b) a trained free parameter; obtaining process parameter data including data regarding a process parameter characterizing the process; converting the process parameter data into values of the geometrical parameter; and predicting the yield parameter using the trained first model and the values of the geometrical parameter.

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 determining a root cause affecting yield in a process for manufacturing devices on a substrate, the method including: obtaining yield distribution data including a distribution of a yield parameter across the substrate or part thereof; obtaining sets of metrology data, each set including a spatial variation of a process parameter over the substrate or part thereof corresponding to a different layer of the substrate; comparing the yield distribution data and metrology data based on a similarity metric describing a spatial similarity between the yield distribution data and an individual set out of the sets of the metrology data; and determining a first similar set of metrology data out of the sets of metrology data, being the first set of metrology data in terms of processing order for the corresponding layers, which is determined to be similar to the yield distribution data.

Abstract: A method for determining a control parameter for an apparatus used in a semiconductor manufacturing process, the method including: obtaining performance data associated with a substrate subject to the semiconductor manufacturing process; obtaining die specification data including values of an expected yield of one or more dies on the substrate based on the performance data and/or a specification for the performance data; and determining the control parameter in dependence on the performance data and the die specification data. Advantageously, the efficiency and/or accuracy of processes is improved by determining how to perform the processes in dependence on dies within specification.