A computer implemented method for simulating an aerial image of a design of a photolithography mask comprises: obtaining an illumination angle distribution in the pupil plane of the light source; selecting a number of illumination angles by solving an optimization problem; for each selected illumination angle, simulating an electromagnetic near field; for at least one further illumination angle of the illumination angle distribution in the pupil plane of the light source approximating an electromagnetic near field; and obtaining the simulated aerial image of the design of the photolithography mask by superimposing the intensities obtained by imaging the electromagnetic near fields into a wafer plane. Systems can detect defects or assess the relevance of defects or for aligning aerial images.

A method for determining parameters of an imaging transfer function (point spread function) is presented. With regard to a model that describes the imaging transfer function including a number of model parameters, a test substrate is exposed and developed using a test pattern which comprises multiple sub-patterns that are based on the same sub-pattern template but with varying control width of a feature in the template, such as the width of a line or a distance between lines. On the test substrate, isofocal dose measurements are performed using the structures thus formed on a test substrate with varying control and imaging parameters. The isofocal dose thus determined are utilized to determine the model parameters of the imaging transfer function.

A method of determining an overlay measurement of a substrate includes: injecting charge into a charge injection element of the substrate; determining a first capacitance of a first pair of elements and a second capacitance of a second pair of elements; and determining a capacitance ratio based on the first capacitance and the second capacitance. The overlay measurement may be determined based on the capacitance ratio, which may indicate an imbalance.

There is provided a system and method for examining a semiconductor specimen. The method includes obtaining a runtime image of a semiconductor specimen acquired by an examination tool; processing the runtime image to create one or more image strips each containing an edge, and for each image strip, extracting a sequence of topo points representative of a contour of the edge therein; providing the sequence of topo points for each image strip to a trained machine learning (ML) model to be processed, and obtaining, as an output of the ML model, a sequence of updated topo points; and obtaining measurement data on the runtime image using the sequence of updated topo points, wherein the measurement data has improved performance with respect to at least one metrology metric.

A method to determine a metrology contribution from statistically independent sources, the method including providing a plurality of contributions from statistically independent sources obtained at a plurality of measurement settings, and determining a metrology contribution from the contributions wherein the metrology contribution is the contribution having least dependence as a function of the measurement settings.

Disclosed is metrology apparatus for measurement of a diffractive structure on a substrate. comprising: a radiation source operable to provide first radiation for excitation of the diffractive structure, said first radiation having a first wavelength; a detection arrangement operable to detect at least diffracted second radiation comprising a second harmonic of said first radiation, said diffracted second radiation being generated from said diffractive structure and/or substrate and diffracted by said diffractive structure; and a processing arrangement operable to determine a parameter of interest relating to said diffractive structure from at least said diffracted second radiation.

A method for a metrology process, the method includes obtaining first measurement data relating to a first set of measurement conditions and determining a first measurement recipe based on the first measurement data. At least one performance indicator is determined from one or more components of the first measurement data obtained from a component analysis or statistical decomposition. Alternatively, at least one performance indicator is determined from a comparison of one or more first measurement values relating to the first measurement recipe and one or more second measurement values relating to a second measurement recipe, where second measurement recipe is different to the first measurement data and relates a second set of measurement conditions, the second set of measurement conditions being different to the first set of measurement conditions.

The current disclosure describes techniques for managing vertical alignment or overlay in semiconductor manufacturing using machine learning. Alignments of interconnection features in a fan-out WLP process are evaluated and managed through the disclosed techniques. Big data and machine learning are used to train a classification that correlates the overlay error source factors with overlay metrology categories. The overlay error source factors include tool signals. The trained classification includes a base classification and a Meta classification.

A method of calibrating a model for inferring a value for a parameter of interest from a measurement signal including obtaining a first set of metrology signals, corresponding known reference values for the parameter of interest; and at least first and second constraining sets of metrology signals relating to the same application as the first set of metrology signals. The first set of metrology signals and corresponding reference data is used to train at least one model to infer a value for the parameter of interest from the first set of metrology signals subject to a constraint that a difference between first inferred values for the parameter of interest using the model on at least the first constraining set of metrology signals and second inferred values for the parameter of interest using the model on the second constraining set of metrology signals is below a threshold value.

A method for improving imaging of a feature on a mask to a substrate during scanning operation of a lithographic apparatus. The method includes obtaining a dynamic pupil representing evolution of an angular distribution of radiation exposing a mask during a scanning operation of a lithographic apparatus and determining a variation of shift of a feature at a substrate during the scanning operation due to interaction of the dynamic pupil with the mask. The method includes configuring a mask parameter and/or or a control parameter of the lithographic apparatus to reduce the variation of shift of the feature.