Abstract: A method for determining a spatially varying process offset for a lithographic process, the spatially varying process offset (MTD) varying over a substrate subject to the lithographic process to form one or more structures thereon. The method includes obtaining a trained model (MOD), having been trained to predict first metrology data based on second metrology data, wherein the first metrology data (OV) is spatially varying metrology data which relates to a first type of measurement of the one or more structures being a measure of yield and the second metrology data (PB) is spatially varying metrology data which relates to a second type of measurement of the one or more structures and correlates with the first metrology data; and using the model to obtain the spatially varying process offset (MTD).

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: A lithographic apparatus comprising an object table which carries an object. The lithographic apparatus may further comprise at least one sensor as part of a measurement system to measure a characteristic of the object table, the environment surrounding the lithographic apparatus or another component of the lithographic apparatus. The measured characteristic may be used to estimate the deformation of the object due to varying loads during operation of the lithographic apparatus, for example varying loads induced by a two-phase flow in a channel formed within the object table. Additionally, or alternatively, the lithographic apparatus comprises a predictor to estimate the deformation of the object based on a model. The positioning of the object table carrying the object can be controlled based on the estimated deformation.

Abstract: A lithographic apparatus comprising an object table which carries an object. The lithographic apparatus may further comprise at least one sensor as part of a measurement system to measure a characteristic of the object table, the environment surrounding the lithographic apparatus or another component of the lithographic apparatus. The measured characteristic may be used to estimate the deformation of the object due to varying loads during operation of the lithographic apparatus, for example varying loads induced by a two- phase flow in a channel formed within the object table. Additionally, or alternatively, the lithographic apparatus comprises a predictor to estimate the deformation of the object based on a model. The positioning of the object table carrying the object can be controlled based on the estimated deformation.

Abstract: A lithographic apparatus comprising includes an object table which carries an object. The lithographic apparatus may further comprise at least one include a sensor as part of a measurement system to measure a characteristic of the object table, the environment surrounding the lithographic apparatus or another component of the lithographic apparatus. The measured characteristic may be used to estimate the a deformation of the an object due to a varying loads load during operation of the lithographic apparatus, for example a varying loads load induced by a two-phase flow in a channel formed within of the object table. Additionally, or alternatively, the The lithographic apparatus comprises may include a predictor to estimate the deformation of the object based on a model. The positioning of the object table carrying the object can be controlled based on the estimated deformation.