Abstract: A method for determining a substrate model for describing a first measurement dataset and a second measurement dataset relating to a performance parameter. The method include obtaining candidate basis functions for a plurality of substrate models. Steps 1 to 4 are performed iteratively for the first measurement dataset and the second measurement dataset until at least one stopping criterion is met so as to determine the substrate model, the steps including: 1. selecting a candidate basis function from the candidate basis functions; 2. updating a substrate model by adding the candidate basis function into this substrate model to obtain an updated substrate model; 3. evaluating the updated substrate model based on the first measurement dataset and/or second measurement dataset; and 4. determining whether to include the basis function within the substrate model based on the evaluation.

Abstract: A substrate including a target structure formed in at least two layers. The target structure includes a first region having periodically repeating features in each of the layers measureable using optical metrology; and a second region having repetitions of one or more product features in each of the layers, the repetitions being sufficient for stochastic analysis to determine at least one local variation metric. The method also includes determining a correction for control of a lithographic process based on measurement of such a target structure.

Abstract: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology 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: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology data.

Abstract: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology 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: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology data.

Abstract: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology data.

Abstract: A method of determining a control parameter for a lithographic process is disclosed, the method includes: defining a substrate model for representing a process parameter fingerprint across a substrate, the substrate model being defined as a combination of basis functions including at least one basis function suitable for representing variation of the process parameter fingerprint between substrates and/or batches of substrates; receiving measurements of the process parameter across at least one substrate; calculating substrate model parameters using the measurements and the basis functions; and determining the control parameter based on the substrate model parameters and the similarity of the at least one basis function to a process parameter fingerprint variation between substrates and/or batches of substrates.

Abstract: In a lithographic process in which a series of substrates are processed in different contexts, object data (such as performance data representing overlay measured on a set of substrates that have been processed previously) is received. Context data represents one or more parameters of the lithographic process that vary between substrates within the set. By principal component analysis or other statistical analysis of the performance data, the set of substrates are partitioned into two or more subsets. The first partitioning of the substrates and the context data are used to identify one or more relevant context parameters, being parameters of the lithographic process that are observed to correlate most strongly with the first partitioning. The lithographic apparatus is controlled for new substrates by reference to the identified relevant context parameters. Embodiments with feedback control and feedforward control are described.

Abstract: A method including: obtaining error information indicative of accuracy of positioning a pattern formed on a layer on a substrate relative to a target position, wherein the pattern has been formed by irradiating the layer with a radiation beam patterned by a patterning device; and producing modification information including a map of positional shifts across the patterning device so as to increase the accuracy of positioning the pattern formed using the patterning device modified according to the modification information, the modification information based on the error information, wherein the error information is independent of any other layer on the substrate.

Abstract: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology data.

Abstract: A method including obtaining a measurement and/or simulation result of a pattern after being processed by an etch tool of a patterning system, determining a patterning error due to an etch loading effect based on the measurement and/or simulation result, and creating, by a computer system, modification information for modifying a patterning device and/or for adjusting a modification apparatus upstream in the patterning system from the etch tool based on the patterning error, wherein the patterning error is converted to a correctable error and/or reduced to a certain range, when the patterning device is modified according to the modification information and/or the modification apparatus is adjusted according to the modification information.

Abstract: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology data.

Abstract: A method including: obtaining error information indicative of accuracy of positioning a pattern formed on a layer on a substrate relative to a target position, wherein the pattern has been formed by irradiating the layer with a radiation beam patterned by a patterning device; and producing modification information including a map of positional shifts across the patterning device so as to increase the accuracy of positioning the pattern formed using the patterning device modified according to the modification information, the modification information based on the error information, wherein the error information is independent of any other layer on the substrate.

Abstract: A method of determining a correction for a process parameter related to a lithographic process, wherein the lithographic process includes a plurality of runs during each one of which a pattern is applied to one or more substrates. The method of determining includes obtaining pre-exposure metrology data describing a property of a substrate; obtaining post-exposure metrology data comprising one or more measurements of the process parameter having been performed on one or more previously exposed substrates; assigning, based on the pre-exposure metrology data, a group membership status from one or more groups to the substrate; and determining the correction for the process parameter based on the group membership status and the post-exposure metrology data.

Abstract: A method including: providing a reference substrate with a first mark pattern; providing the reference substrate with a first resist layer on the reference substrate, wherein the first resist layer has a minimal radiation dose needed for development of the first resist; using a reference patterning device to impart a radiation beam with a second mark pattern in its cross-section to form a patterned radiation beam; and exposing a target portion of the first resist layer of the reference substrate n times to said patterned radiation beam to create exposed areas in the target portion of the first resist layer in accordance with the second mark pattern that have been subjected to an accumulated radiation dose above the minimal radiation dose of the first resist layer, wherein n is an integer with a value of at least two.

Abstract: In a lithographic process in which a series of substrates are processed in different contexts, object data (such as performance data representing overlay measured on a set of substrates that have been processed previously) is received. Context data represents one or more parameters of the lithographic process that vary between substrates within the set. By principal component analysis or other statistical analysis of the performance data, the set of substrates are partitioned into two or more subsets. The first partitioning of the substrates and the context data are used to identify one or more relevant context parameters, being parameters of the lithographic process that are observed to correlate most strongly with the first partitioning. The lithographic apparatus is controlled for new substrates by reference to the identified relevant context parameters. Embodiments with feedback control and feedforward control are described.