Abstract: A method for controlling a lithographic apparatus configured to pattern an exposure field on a substrate including at least a sub-field, the method including: obtaining an initial spatial profile associated with a spatial variation of a performance parameter associated with a layer on the substrate across at least the sub-field of the exposure field; and decomposing the initial spatial profile into at least a first component spatial profile for controlling a lithographic apparatus at a first spatial scale and a second component spatial profile for controlling the lithographic apparatus at a second spatial scale associated with a size of the sub-field, wherein the decomposing includes co-optimizing the first and second component spatial profiles based on correcting the spatial variation of the performance parameter across the sub-field.

Abstract: A method for controlling a lithographic apparatus configured to pattern an exposure field on a substrate including at least a sub-field, the method including: obtaining an initial spatial profile associated with a spatial variation of a performance parameter associated with a layer on the substrate across at least the sub-field of the exposure field; and decomposing the initial spatial profile into at least a first component spatial profile for controlling a lithographic apparatus at a first spatial scale and a second component spatial profile for controlling the lithographic apparatus at a second spatial scale associated with a size of the sub-field, wherein the decomposing includes co-optimizing the first and second component spatial profiles based on correcting the spatial variation of the performance parameter across the sub-field.

Abstract: A method for determining a sampling scheme, the method including: obtaining a first fingerprint model relating to a first spatial distribution of a performance parameter over a first portion of a semiconductor substrate and a second fingerprint model relating to a second spatial distribution of the performance parameter over a second portion of the semiconductor substrate; and determining a sampling point corresponding to a measuring location on the semiconductor substrate for generating measurement data based on an expected reduction of a first uncertainty metric associated with evaluation of the first fingerprint model over the first portion and an expected reduction of a second uncertainty metric associated with evaluation of the second fingerprint model over the second portion.

Abstract: A method for determining an intra-field correction for control of a lithographic apparatus configured for exposing a pattern on an exposure field of a substrate, the method includes: obtaining metrology data for use in determining the intra-field correction; determining an accuracy metric indicating a lower accuracy where the metrology data is not reliable and/or where the lithographic apparatus is limited in actuating a potential actuation input which is based on the metrology data; and determining the intra-field correction based at least partially on the accuracy metric.

Abstract: A method for controlling a lithographic apparatus configured to pattern an exposure field on a substrate including at least a sub-field, the method including: obtaining an initial spatial profile associated with a spatial variation of a performance parameter associated with a layer on the substrate across at least the sub-field of the exposure field; and decomposing the initial spatial profile into at least a first component spatial profile for controlling a lithographic apparatus at a first spatial scale and a second component spatial profile for controlling the lithographic apparatus at a second spatial scale associated with a size of the sub-field, wherein the decomposing includes co-optimizing the first and second component spatial profiles based on correcting the spatial variation of the performance parameter across the sub-field.

Abstract: Corrections are calculated for use in controlling a lithographic apparatus. Using a metrology apparatus a performance parameter is measured at sampling locations across one or more substrates to which a lithographic process has previously been applied. A process model is fitted to the measured performance parameter, and an up-sampled estimate is provided for process-induced effects across the substrate. Corrections are calculated for use in controlling the lithographic apparatus, using an actuation model and based at least in part on the fitted process model. For locations where measurement data is available, this is added to the estimate to replace the process model values. Thus, calculation of actuation corrections is based on a modified estimate which is a combination of values estimated by the process model and partly on real measurement data.

Abstract: Corrections are calculated for use in controlling a lithographic apparatus. Using a metrology apparatus a performance parameter is measured at sampling locations across one or more substrates to which a lithographic process has previously been applied. A process model is fitted to the measured performance parameter, and an up-sampled estimate is provided for process-induced effects across the substrate. Corrections are calculated for use in controlling the lithographic apparatus, using an actuation model and based at least in part on the fitted process model. For locations where measurement data is available, this is added to the estimate to replace the process model values. Thus, calculation of actuation corrections is based on a modified estimate which is a combination of values estimated by the process model and partly on real measurement data.