Abstract: A method of maintaining a set of fingerprints representing variation of one or more process parameters across wafers subjected to a device manufacturing method, the method including: receiving measurement data of one or more parameters measured on wafers; updating the set of fingerprints based on an expected evolution of the one or more process parameters; and evaluation of the updated set of fingerprints based on decomposition of the received measurement data in terms of the updated set of fingerprints. Each fingerprint may have a stored likelihood of occurrence, and the decomposition may involve: estimating, based the received measurement data, likelihoods of occurrence of the set of fingerprints in the received measurement data; and updating the stored likelihoods of occurrence based on the estimated likelihoods.

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: A patterning device cooling system for thermally conditioning a patterning device of a lithographic apparatus, wherein the patterning device in use, is being irradiated by exposure radiation, wherein the patterning device cooling system comprises: a thermal conditioner configured to thermally condition the patterning device; and a controller configured to control the thermal conditioner to thermally condition the patterning device dependent on an amount of the exposure radiation absorbed by the patterning device.

Abstract: A method including: obtaining information regarding a patterning error in a patterning process involving a patterning device; determining a nonlinearity over a period of time introduced by modifying the patterning error by a modification apparatus according to the patterning error information; and determining a patterning error offset for use with the modification apparatus based on the determined nonlinearity.

Abstract: A method for determining one or more optimized values of an operational parameter of a sensor system configured for measuring a property of a substrate. The method includes: determining a quality parameter for a plurality of substrates; determining measurement parameters for the plurality of substrates obtained using the sensor system for a plurality of values of the operational parameter; comparing a substrate to substrate variation of the quality parameter and a substrate to substrate variation of a mapping of the measurement parameters; and determining the one or more optimized values of the operational parameter based on the comparing.

Abstract: A method of maintaining a set of fingerprints representing variation of one or more process parameters across wafers subjected to a device manufacturing method, the method including: receiving measurement data of one or more parameters measured on wafers; updating the set of fingerprints based on an expected evolution of the one or more process parameters; and evaluation of the updated set of fingerprints based on decomposition of the received measurement data in terms of the updated set of fingerprints. Each fingerprint may have a stored likelihood of occurrence, and the decomposition may involve: estimating, based the received measurement data, likelihoods of occurrence of the set of fingerprints in the received measurement data; and updating the stored likelihoods of occurrence based on the estimated likelihoods.

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.

Abstract: A method for determining one or more optimized values of an operational parameter of a sensor system configured for measuring a property of a substrate is disclosed the method including: determining a quality parameter for a plurality of substrates; determining measurement parameters for the plurality of substrates obtained using the sensor system for a plurality of values of the operational parameter; comparing a substrate to substrate variation of the quality parameter and a substrate to substrate variation of a mapping of the measurement parameters; and determining the one or more optimized values of the operational parameter based on the comparing.

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: 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 determining one or more optimized values of an operational parameter of a sensor system configured for measuring a property of a substrate. The method includes: determining a quality parameter for a plurality of substrates; determining measurement parameters for the plurality of substrates obtained using the sensor system for a plurality of values of the operational parameter; comparing a substrate to substrate variation of the quality parameter and a substrate to substrate variation of a mapping of the measurement parameters; and determining the one or more optimized values of the operational parameter based on the comparing.

Abstract: A device manufacturing method, the method including: 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.

Abstract: A method for correcting values of one or more feed-forward parameters used in a process of patterning substrates, the method including: obtaining measured overlay and/or alignment error data of a patterned substrate; and calculating one or more correction values for the one or more feed-forward parameters in dependence on the measured overlay and/or alignment error data.

Abstract: A method, system and program for determining a position of a feature referenced to a substrate. The method includes measuring a position of the feature, receiving an intended placement of the feature and determining an estimate of a placement error based on knowledge of a relative position of a first reference feature referenced to a first layer on a substrate with respect to a second reference feature referenced to a second layer on a substrate. The updated position may be used to position the layer of the substrate having the feature, or another layer of the substrate, or another layer of another substrate.

Abstract: A patterning apparatus for a lithographic apparatus, the patterning apparatus including a patterning device support structure configured to support a patterning device having a planar surface; a patterning device conditioning system including a first gas outlet configured to provide a first gas flow over the planar surface in use and a second gas outlet configured to provide a second gas flow over the planar surface in use, wherein the first gas outlet and the second gas outlet are arranged at different distances perpendicular to the planar surface; and a control system configured to independently control a first momentum of gas exiting the first gas outlet and a second momentum of gas exiting the second gas outlet or to independently vary the first gas flow and/or the second gas flow over the planar surface of the patterning device.

Abstract: A patterning device cooling system for thermally conditioning a patterning device of a lithographic apparatus, wherein the patterning device in use, is being irradiated by exposure radiation, wherein the patterning device cooling system comprises: a thermal conditioner configured to thermally condition the patterning device; and a controller configured to control the thermal conditioner to thermally condition the patterning device dependent on an amount of the exposure radiation absorbed by the patterning device.

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: A method for determining one or more optimized values of an operational parameter of a sensor system configured for measuring a property of a substrate is disclosed the method comprising: determining a quality parameter for a plurality of substrates; determining measurement parameters for the plurality of substrates obtained using the sensor system for a plurality of values of the operational parameter; comparing a substrate to substrate variation of the quality parameter and a substrate to substrate variation of a mapping of the measurement parameters; and determining the one or more optimized values of the operational parameter based on the comparing.

Abstract: A method, system and program for determining a position of a feature referenced to a substrate. The method includes measuring a position of the feature, receiving an intended placement of the feature and determining an estimate of a placement error based on knowledge of a relative position of a first reference feature referenced to a first layer on a substrate with respect to a second reference feature referenced to a second layer on a substrate. The updated position may be used to position the layer of the substrate having the feature, or another layer of the substrate, or another layer of another substrate.