Abstract: Systems, apparatuses, and methods are provided for correcting the detected positions of alignment marks disposed on a substrate and aligning the substrate using the corrected data to ensure accurate exposure of one or more patterns on the substrate. An example method can include receiving measurement data indicative of an interference between light diffracted from a plurality of alignment marks disposed on a substrate or reflected from the substrate. The example method can further include determining substrate deformation data based on the measurement data. The example method can further include determining alignment mark deformation data based on the measurement data. The alignment mark deformation data can include alignment mark deformation spectral pattern data, alignment mark deformation amplitude data, and alignment mark deformation offset data.

Abstract: A method for generating an alignment signal that includes detecting local dimensional distortions of an alignment mark and generating the alignment signal based on the alignment mark. The alignment signal is weighted based on the local dimensional distortions of the alignment mark. Detecting the local dimensional distortions can include irradiating the alignment mark with radiation, the alignment mark including a geometric feature, and detecting one or more phase and/or amplitude shifts in reflected radiation from the geometric feature. The one or more phase and/or amplitude shifts correspond to the local dimensional distortions of the geometric feature. A parameter of the radiation, an alignment inspection location within the geometric feature, an alignment inspection location on a layer of a structure, and/or a radiation beam trajectory across the geometric feature may be determined based on the one or more detected phase and/or amplitude shifts.

Abstract: A method of applying a measurement correction includes determining an orthogonal subspace used to characterize a first principal component of the measurement and a second principal component of the measurement, and rotating the orthogonal subspace by a first angle such that the first principle component rotates to become a first factor vector and the second principle component rotates to become a second factor vector. An asymmetry vector is generated by rotating the second factor vector by a second angle, where the asymmetry vector and the first factor vector define a non-orthogonal subspace. An asymmetry contribution is determined in the measurement based on the projection of the measurement onto the first factor vector in the non-orthogonal subspace. The method also includes subtracting the asymmetry contribution from the measurement.

Abstract: A method of applying a measurement correction includes determining an orthogonal subspace used to characterize the measurement as a plot of data. A first axis of the orthogonal subspace corresponds to constructive interference output from an interferometer of the metrology system plus a first error variable and a second axis of the orthogonal subspace corresponds to destructive interference output from the interferometer of the metrology system plus a second error variable. The method also includes determining a slope of the plot of data and determining a fitted line to the plot of data in the orthogonal subspace based on the slope.

Abstract: A method of applying a measurement correction includes determining an orthogonal subspace used to characterize the measurement as a plot of data. A first axis of the orthogonal subspace corresponds to constructive interference output from an interferometer of the metrology system plus a first error variable and a second axis of the orthogonal subspace corresponds to destructive interference output from the interferometer of the metrology system plus a second error variable. The method also includes determining a slope of the plot of data and determining a fitted line to the plot of data in the orthogonal subspace based on the slope.

Abstract: A method of applying a measurement correction includes determining an orthogonal subspace used to characterize a first principal component of the measurement and a second principal component of the measurement, and rotating the orthogonal subspace by a first angle such that the first principle component rotates to become a first factor vector and the second principle component rotates to become a second factor vector. An asymmetry vector is generated by rotating the second factor vector by a second angle, where the asymmetry vector and the first factor vector define a non-orthogonal subspace. An asymmetry contribution is determined in the measurement based on the projection of the measurement onto the first factor vector in the non-orthogonal subspace. The method also includes subtracting the asymmetry contribution from the measurement.