Abstract: Disclosed is a substrate, associated patterning device and a method for measuring a position of the substrate. The method comprises performing an alignment scan of an alignment mark to obtain simultaneously: a first measurement signal detected in a first measurement channel and a second measurement signal detected in a second measurement channel. The first and second measurement signals are processed by subtracting a first direction component of the first measurement signal from a first direction component of the second measurement signal to obtain a first processed signal, the first direction components relating to said first direction. The position of an alignment mark is determined with respect to the first direction from the first processed signal.

Abstract: Disclosed is a method for modeling measurement data over a substrate area and associated apparatus. The method comprises obtaining measurement data relating to a first layout; modeling a second model based on said first layout; evaluating the second model on a second layout, the second layout being more dense than said first layout; and fitting a first model to this second model according to the second layout.

Abstract: A method of, and associated apparatuses for, performing a position measurement on an alignment mark including at least a first periodic structure having a direction of periodicity along a first direction. The method includes obtaining signal data relating to the position measurement and fitting the signal data to determine a position value. The fitting uses one of a modulation fit or a background envelope periodic fit.

Abstract: Disclosed is a substrate, associated patterning device and a method for measuring a position of the substrate. The method comprises performing an alignment scan of an alignment mark to obtain simultaneously: a first measurement signal detected in a first measurement channel and a second measurement signal detected in a second measurement channel. The first and second measurement signals are processed by subtracting a first direction component of the first measurement signal from a first direction component of the second measurement signal to obtain a first processed signal, the first direction components relating to said first direction. The position of an alignment mark is determined with respect to the first direction from the first processed signal.

Abstract: A method for determining substrate deformation includes obtaining first measurement data associated with mark positions, from measurements of a plurality of substrates; obtaining second measurement data associated with mark positions, from measurements of the plurality of substrates; determining a mapping between the first measurement data and the second measurement data; and decomposing the mapping, by calculating an eigenvalue decomposition for the mapping, to separately determine a first deformation (e.g. mark deformation) that scales differently from a second deformation (e.g. substrate deformation) in the mapping between the data. The steps of determining a mapping and decomposing the mapping may be performed together using non-linear optimization.

Abstract: A measurement apparatus and method for determining a substrate grid describing a deformation of a substrate prior to exposure of the substrate in a lithographic apparatus configured to fabricate one or more features on the substrate. Position data for a plurality of first features and/or a plurality of second features on the substrate is obtained. Asymmetry data for at least a feature of the plurality of first features and/or the plurality of second features is obtained. The substrate grid based on the position data and the asymmetry data is determined. The substrate grid and asymmetry data are passed to the lithographic apparatus for controlling at least part of an exposure process to fabricate one or more features on the substrate.

Abstract: A method for configuring a semiconductor manufacturing process, the method including: obtaining a first value of a first parameter based on measurements associated with a first operation of a process step in the semiconductor manufacturing process and a first sampling scheme; using a recurrent neural network to determine a predicted value of the first parameter based on the first value; and using the predicted value of the first parameter in configuring a subsequent operation of the process step in the semiconductor manufacturing process.

Abstract: A method for configuring a semiconductor manufacturing process, the method including: obtaining a first value of a first parameter based on measurements associated with a first operation of a process step in the semiconductor manufacturing process and a first sampling scheme; using a recurrent neural network to determine a predicted value of the first parameter based on the first value; and using the predicted value of the first parameter in configuring a subsequent operation of the process step in the semiconductor manufacturing process.

Abstract: A measurement apparatus and method for determining a substrate grid describing a deformation of a substrate prior to exposure of the substrate in a lithographic apparatus configured to fabricate one or more features on the substrate. Position data for a plurality of first features and/or a plurality of second features on the substrate is obtained. Asymmetry data for at least a feature of the plurality of first features and/or the plurality of second features is obtained. The substrate grid based on the position data and the asymmetry data is determined. The substrate grid and asymmetry data are passed to the lithographic apparatus for controlling at least part of an exposure process to fabricate one or more features on the substrate.

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 for configuring a semiconductor manufacturing process, the method including: obtaining a first value of a first parameter based on measurements associated with a first operation of a process step in the semiconductor manufacturing process and a first sampling scheme; using a recurrent neural network to determine a predicted value of the first parameter based on the first value; and using the predicted value of the first parameter in configuring a subsequent operation of the process step in the semiconductor manufacturing process.

Abstract: A method for determining substrate deformation includes obtaining first measurement data associated with mark positions, from measurements of a plurality of substrates; obtaining second measurement data associated with mark positions, from measurements of the plurality of substrates; determining a mapping between the first measurement data and the second measurement data; and decomposing the mapping, by calculating an eigenvalue decomposition for the mapping, to separately determine a first deformation (e.g. mark deformation) that scales differently from a second deformation (e.g. substrate deformation) in the mapping between the data. The steps of determining a mapping and decomposing the mapping may be performed together using non-linear optimization.

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: In a method of controlling a lithographic apparatus, historical performance measurements are used to calculate a process model relating to a lithographic process. Current positions of a plurality of alignment marks provided on a current substrate are measured and used to calculate a substrate model relating to a current substrate. Additionally, historical position measurements obtained at the time of processing the prior substrates are used with the historical performance measurements to calculate a model mapping. The model mapping is applied to modify the substrate model. The lithographic apparatus is controlled using the process model and the modified substrate model together. Overlay performance is improved by avoiding over- or under-correction of correlated components of the process model and the substrate model. The model mapping may be a subspace mapping, and dimensionality of the model mapping may be reduced, before it is used.

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: In a method of controlling a lithographic apparatus, historical performance measurements are used to calculate a process model relating to a lithographic process. Current positions of a plurality of alignment marks provided on a current substrate are measured and used to calculate a substrate model relating to a current substrate. Additionally, historical position measurements obtained at the time of processing the prior substrates are used with the historical performance measurements to calculate a model mapping. The model mapping is applied to modify the substrate model. The lithographic apparatus is controlled using the process model and the modified substrate model together. Overlay performance is improved by avoiding over- or under-correction of correlated components of the process model and the substrate model. The model mapping may be a subspace mapping, and dimensionality of the model mapping may be reduced, before it is used.

Abstract: A lithographic technique that involves obtaining values of parameters of a substrate deformation model, wherein the values are based on positional data obtained from an alignment system for a lithographic apparatus; modifying the values using a mapping operation, wherein the mapping operation is based on a correlation found between the parameters and overlay data for a previous set of substrates; and generating, based on the modified values, electronic data adapted to configure the lithographic apparatus.

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 lithographic apparatus has a substrate table on which a substrate is positioned, and an alignment sensor used to measure the alignment of the substrate. In an exemplary processing method, the alignment sensor is used to perform one or more edge measurements in a first step. In a second step, one or more edge measurements are performed on the notch of the substrate. The edge measurements are then used to align the substrate in the lithographic apparatus. In a particular example, the substrate is arranged relative to the alignment sensor such that a portion of the edge surface is positioned at the focal length of the lens. When the alignment sensor detects radiation scattered by the edge surface at the focal length of the lens, the presence of the edge of the substrate is detected.

Abstract: A method for determining one or more optimized values of an operational parameter of a sensor system configured to measure a property of a substrate is disclosed. The method includes: determining a quality parameter for a plurality of substrates; determining measurement parameter values for the plurality of substrates 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 parameter values; and determining the one or more optimized values of the operational parameter based on the comparing.