Abstract: Disclosed is method of optimizing bandwidth of measurement illumination for a measurement application, and an associated metrology apparatus. The method comprises performing a reference measurement with reference measurement illumination having a reference bandwidth and performing one or more optimization measurements, each of said one or more optimization measurements being performed with measurement illumination having a varied candidate bandwidth. The one or more optimization measurements are compared with the reference measurement; and an optimal bandwidth for the measurement application is selected based on the comparison.

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: Disclosed is method of optimizing bandwidth of measurement illumination for a measurement application, and an associated metrology apparatus. The method comprises performing a reference measurement with reference measurement illumination having a reference bandwidth and performing one or more optimization measurements, each of said one or more optimization measurements being performed with measurement illumination having a varied candidate bandwidth. The one or more optimization measurements are compared with the reference measurement; and an optimal bandwidth for the measurement application is selected based on the comparison.

Abstract: A method for manufacturing or adjusting a reticle having a predetermined functionality, the method including obtaining a reticle having a first pattern, the first pattern representing a first functionality of structures provided to a substrate using the reticle, and patterning the reticle having the first pattern with a second pattern using a pattern generating tool, the combined first and second patterns having the predetermined functionality.

Abstract: The disclosure relates to measuring a parameter of a lithographic process and a metrology apparatus. In one arrangement, radiation from a radiation source is modified and used to illuminate a target formed on a substrate using the lithographic process. Radiation scattered from a target is detected and analyzing to determine the parameter. The modification of the radiation comprises modifying a wavelength spectrum of the radiation to have a local minimum between a global maximum and a local maximum, wherein the power spectral density of the radiation at the local minimum is less than 20% of the power spectral density of the radiation at the global maximum and the power spectral density of the radiation at the local maximum is at least 50% of the power spectral density of the radiation at the global maximum.

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 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 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 method including obtaining measurement results of a device manufacturing process or a product thereof, obtaining sets of one or more values of one or more parameters of a distribution by fitting the distribution against the measurement results, respectively, and obtaining, using a computer, a set of one or more values of one or more hyperparameters of a hyperdistribution by fitting the hyperdistribution against the sets of values of the parameters.

Abstract: Methods for calibrating metrology apparatuses and determining a parameter of interest are disclosed. In one arrangement, training data is provided that comprises detected representations of scattered radiation detected by each of plural metrology apparatuses. An encoder encodes each detected representation to provide an encoded representation, and a decoder generates a synthetic detected representation from the respective encoded representation. A classifier estimates from which metrology apparatus originates each encoded representation or each synthetic detected representation. The training data is used to simultaneously perform, in an adversarial relationship relative to each other, a first machine learning process involving the encoder or decoder and a second machine learning process involving the classifier.

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: Methods of determining an optimal focus height are disclosed. In one arrangement, measurement data from a plurality of applications of the metrology process to a target are obtained. Each application of the metrology process includes illuminating the target with a radiation spot and detecting radiation redirected by the target. The applications of the metrology process include applications at different nominal focus heights. The measurement data includes, for each application of the metrology process, at least a component of a detected pupil representation of an optical characteristic of the redirected radiation in a pupil plane. The method includes determining an optimal focus height for the metrology process using the obtained measurement data.

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 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 metrology tool for determining a parameter of interest of a structure fabricated on a substrate, the metrology tool comprising: an illumination optical system for illuminating the structure with illumination radiation under a non-zero angle of incidence; a detection optical system comprising a detection optical sensor and at least one lens for capturing a portion of illumination radiation scattered by the structure and transmitting the captured radiation towards the detection optical sensor, wherein the illumination optical system and the detection optical system do not share an optical element.

Abstract: A target formed on a substrate, the target having: an alignment structure; and a metrology structure; wherein the alignment structure comprises structures that are arranged to generate a beat pattern when the alignment structure is illuminated with source radiation. Advantageously, when the target is illuminated, the beat pattern that appears in an image of the target allows the target to be easily identified using a pattern recognition technique.

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: Disclosed is a method and associated apparatus for measuring a characteristic of interest relating to a structure on a substrate. The method comprises calculating a value for the characteristic of interest directly from the effect of the characteristic of interest on at least the phase of illuminating radiation when scattered by the structure, subsequent to illuminating said structure with said illuminating radiation.