Abstract: A method of determining a parameter of a patterning process, the method including: obtaining a detected representation of radiation redirected by a structure having geometric symmetry at a nominal physical configuration, wherein the detected representation of the radiation was obtained by illuminating a substrate with a radiation beam such that a beam spot on the substrate was filled with the structure; and determining, by a hardware computer system, a value of the patterning process parameter based on optical characteristic values from an asymmetric optical characteristic distribution portion of the detected radiation representation with higher weight than another portion of the detected radiation representation, the asymmetric optical characteristic distribution arising from a different physical configuration of the structure than the nominal physical configuration.

Abstract: A substrate has first and second target structures formed by a lithographic process. Each target structure has a two-dimensional periodic structure formed in a single layer using first and second lithographic steps. The first target structure has features defined in the second lithographic step displaced relative to features defined in the first lithographic step by a first bias amount. The second target structure has features defined in the second lithographic step displaced relative to features defined in the first lithographic step by a second bias amount. An angle-resolved scatter spectrum of the first target structure and an angle-resolved scatter spectrum of the second target structure is obtained. A measurement of a parameter of a lithographic process is derived from the measurements using asymmetry found in the scatter spectra of the first and second target structures.

Abstract: A method of determining a parameter of a patterning process, the method including: obtaining a detected representation of radiation redirected by a structure having geometric symmetry at a nominal physical configuration, wherein the detected representation of the radiation was obtained by illuminating a substrate with a radiation beam such that a beam spot on the substrate was filled with the structure; and determining, by a hardware computer system, a value of the patterning process parameter based on optical characteristic values from an asymmetric optical characteristic distribution portion of the detected radiation representation with higher weight than another portion of the detected radiation representation, the asymmetric optical characteristic distribution arising from a different physical configuration of the structure than the nominal physical configuration.

Abstract: Methods and apparatus for estimating an unknown value of at least one of a plurality of sets of data, each set of data including a plurality of values indicative of radiation diffracted and/or reflected and/or scattered by one or more features fabricated in or on a substrate, wherein the plurality of sets of data include at least one known value, and wherein at least one of the plurality of sets of data includes an unknown value, the apparatus including a processor to estimate the unknown value of the at least one set of data based on: the known values of the plurality of sets of data, a first condition between two or more values within a set of data of the plurality of sets of data, and a second condition between two or more values being part of different sets of data of the plurality of the sets of data.

Abstract: Method of measuring a height profile of one or more substrates is provided comprising measuring a first height profile of one or more fields on a substrate using a first sensor arrangement, the first height profile being the sum of a first interfield part and a first intrafield part, measuring a second height profile of one or more further fields on the substrate or on a further substrate using a second sensor arrangement, the second height profile being the sum of a second interfield part and a second intrafield part, determining from the measurements with the first sensor arrangement an average first intrafield part, and determining the height profile of the further fields from the second interfield part and the average first intrafield part thereby correcting the measurements of the second sensor arrangement.

Abstract: A method, system and program for determining a fingerprint of a parameter. The method includes determining a contribution from a device out of a plurality of devices to a fingerprint of a parameter. The method including: obtaining parameter data and usage data, wherein the parameter data is based on measurements for multiple substrates having been processed by the plurality of devices, and the usage data indicates which of the devices out of the plurality of the devices were used in the processing of each substrate; and determining the contribution using the usage data and parameter data.

Abstract: A method of reconstructing a characteristic of a structure formed on a substrate by a lithographic process, and an associated metrology apparatus. The method includes combining measured values of a first parameter associated with the lithographic process to obtain an estimated value of the first parameter; and reconstructing at least a second parameter associated with the characteristic of the structure using the estimated value of the first parameter and a measurement of the structure. The combining may involve modeling a variation of the first parameter to obtain a parameter model or fingerprint of the first parameter.

Abstract: A method including: obtaining a detected representation of radiation redirected by each of a plurality of structures from a substrate additionally having a device pattern thereon, wherein each structure has an intentional different physical configuration of the respective structure than the respective nominal physical configuration of the respective structure, wherein each structure has geometric symmetry at the respective nominal physical configuration, wherein the intentional different physical configuration of the structure causes an asymmetric optical characteristic distribution and wherein a patterning process parameter measures change in the physical configuration; and determining a value, based on the detected representations and based on the intentional different physical configurations, to setup, monitor or correct a measurement recipe for determining the patterning process parameter.

Abstract: Methods and apparatus for estimating an unknown value of at least one of a plurality of sets of data, each set of data including a plurality of values indicative of radiation diffracted and/or reflected and/or scattered by one or more features fabricated in or on a substrate, wherein the plurality of sets of data include at least one known value, and wherein at least one of the plurality of sets of data includes an unknown value, the apparatus including a processor to estimate the unknown value of the at least one set of data based on: the known values of the plurality of sets of data, a first condition between two or more values within a set of data of the plurality of sets of data, and a second condition between two or more values being part of different sets of data of the plurality of the sets of data.

Abstract: A method including: computing a value of a first variable of a pattern of, or for, a substrate processed by a patterning process by combining a fingerprint of the first variable on the substrate and a certain value of the first variable; and determining a value of a second variable of the pattern based at least in part on the computed value of the first variable.

Abstract: A substrate having a plurality of features for use in measuring a parameter of a device manufacturing process and associated methods and apparatus. The measurement is by illumination of the features with measurement radiation from an optical apparatus and detecting a signal arising from interaction between the measurement radiation and the features. The plurality of features include first features distributed in a periodic fashion at a first pitch, and second features distributed in a periodic fashion at a second pitch, wherein the first pitch and second pitch are such that a combined pitch of the first and second features is constant irrespective of the presence of pitch walk in the plurality of features.

Abstract: A method of correcting an image characteristic of a substrate onto which one or more product features have been formed using a lithographic process, and an associated inspection apparatus method. The method includes measuring an error in the image characteristic of the substrate, and determining a correction for a subsequent formation of the product features based upon the measured error and a characteristic of one or more of the product feature(s).

Abstract: A method of determining overlay of a patterning process, the method including: obtaining a detected representation of radiation redirected by one or more physical instances of a unit cell, wherein the unit cell has geometric symmetry at a nominal value of overlay and wherein the detected representation of the radiation was obtained by illuminating a substrate with a radiation beam such that a beam spot on the substrate was filled with the one or more physical instances of the unit cell; and determining, from optical characteristic values from the detected radiation representation, a value of a first overlay for the unit cell separately from a second overlay for the unit cell that is also obtainable from the same optical characteristic values, wherein the first overlay is in a different direction than the second overlay or between a different combination of parts of the unit cell than the second overlay.

Abstract: A metrology target includes: a first structure arranged to be created by a first patterning process; and a second structure arranged to be created by a second patterning process, wherein the first structure and/or second structure is not used to create a functional aspect of a device pattern, and wherein the first and second structures together form one or more instances of a unit cell, the unit cell having geometric symmetry at a nominal physical configuration and wherein the unit cell has a feature that causes, at a different physical configuration than the nominal physical configuration due to a relative shift in pattern placement in the first patterning process, the second patterning process and/or another patterning process, an asymmetry in the unit cell.

Abstract: A method of determining a parameter of a patterning process, the method including: obtaining a detected representation of radiation redirected by a structure having geometric symmetry at a nominal physical configuration, wherein the detected representation of the radiation was obtained by illuminating a substrate with a radiation beam such that a beam spot on the substrate was filled with the structure; and determining, by a hardware computer system, a value of the patterning process parameter based on optical characteristic values from an asymmetric optical characteristic distribution portion of the detected radiation representation with higher weight than another portion of the detected radiation representation, the asymmetric optical characteristic distribution arising from a different physical configuration of the structure than the nominal physical configuration.

Abstract: A method of determining overlay of a patterning process, the method including: illuminating a substrate with a radiation beam such that a beam spot on the substrate is filled with one or more physical instances of a unit cell, the unit cell having geometric symmetry at a nominal value of overlay; detecting primarily zeroth order radiation redirected by the one or more physical instances of the unit cell using a detector; and determining, by a hardware computer system, a non-nominal value of overlay of the unit cell from values of an optical characteristic of the detected radiation.

Abstract: A method of configuring a parameter determination process, the method including: obtaining a mathematical model of a structure, the mathematical model configured to predict an optical response when illuminating the structure with a radiation beam and the structure having geometric symmetry at a nominal physical configuration; using, by a hardware computer system, the mathematical model to simulate a perturbation in the physical configuration of the structure of a certain amount to determine a corresponding change of the optical response in each of a plurality of pixels to obtain a plurality of pixel sensitivities; and based on the pixel sensitivities, determining a plurality of weights for combination with measured pixel optical characteristic values of the structure on a substrate to yield a value of a parameter associated with change in the physical configuration, each weight corresponding to a pixel.

Abstract: A substrate has first and second target structures formed thereon by a lithographic process. Each target structure has two-dimensional periodic structure formed in a single material layer on a substrate using first and second lithographic steps, wherein, in the first target structure, features defined in the second lithographic step are displaced relative to features defined in the first lithographic step by a first bias amount that is close to one half of a spatial period of the features formed in the first lithographic step, and, in the second target structure, features defined in the second lithographic step are displaced relative to features defined in the first lithographic step by a second bias amount close to one half of said spatial period and different to the first bias amount.

Abstract: A method of correcting an image characteristic of a substrate onto which one or more product features have been formed using a lithographic process, and an associated inspection apparatus method. The method includes measuring an error in the image characteristic of the substrate, and determining a correction for a subsequent formation of the product features based upon the measured error and a characteristic of one or more of the product feature(s).

Abstract: A method of, and associated apparatus for, determining focus corrections for a lithographic projection apparatus. The method comprises exposing a plurality of global correction fields on a test substrate, each comprising a plurality of global correction marks, and each being exposed with a tilted focus offset across it; measuring a focus dependent characteristic for each of the plurality of global correction marks to determine interfield focus variation information; and calculating interfield focus corrections from the interfield focus variation information.