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 of determining a stochastic metric, the method including: obtaining a trained model having been trained to correlate training optical metrology data to training stochastic metric data, wherein the training optical metrology data includes a plurality of measurement signals relating to distributions of an intensity related parameter across a zero or higher order of diffraction of radiation scattered from a plurality of training structures, and the training stochastic metric data includes stochastic metric values relating to the plurality of training structures, wherein the plurality of training structures have been formed with a variation in one or more dimensions on which the stochastic metric is dependent; obtaining optical metrology data including a distribution of the intensity related parameter across a zero or higher order of diffraction of radiation scattered from a structure; and using the trained model to infer a value of the stochastic metric from the optical metrology data.

Methods, systems, and apparatus for mapping high dimensional data related to a lithographic apparatus, etch tool, metrology tool or inspection tool to a lower dimensional representation of the data. High dimensional data is obtained related to the apparatus. The high dimensional data has first dimensions N greater than two. A nonlinear parametric model is obtained, which has been trained to map a training set of high dimensional data onto a lower dimensional representation. The lower dimensional representation has second dimensions M, wherein Mis less than N. The model has been trained using a cost function configured to make the mapping preserve local similarities in the training set of high dimensional data. Using the model, the obtained high dimensional data is mapped to the corresponding lower dimensional representation.

Machine learning models can be trained to predict imaging characteristics with respect to variation in a pattern on a wafer resulting from a patterning process. However, due to low pattern coverage provided by limited wafer data used for training, machine learning models tend to overfit, and predictions from the machine learning models deviate from physical trends that characterize the pattern on the wafer and/or the patterning process with respect to the pattern variation. To enhance pattern coverage, training data is augmented with pattern data that conforms to a certain expected physical trend, and applies to new patterns not covered by previously measured wafer data.

A metrology module includes an estimation model that is configured to provide an estimation of independent overlay with tool induced shift on received wafers based on only one azimuth angle spectra. The estimation model can use at least one machine learning algorithm. The estimation model can be derived by the machine learning algorithm applied to calculated training data based on a first training sample set from initial metrology measurements and an additional tool induced shift training sample.

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.

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 measurement process is performed for each of a plurality of locations on a product of a fabrication process at which a parameter of interest characterizing the fabrication process is believed to be nominally the same, to derive measured signals for each location including at least one image. A dimensional reduction method is applied to a dataset of the measured signals, to obtain components of the dataset, including components indicative of variation between the images. For at least one of these components, one or more associated ones of the measured signals are identified, comprising at least one set of corresponding pixels in the respective images for the plurality of locations. The contribution of the identified measured signals in the dataset is reduced or eliminated to obtain a processed signal, and the parameter of interest is obtained from the processed signal.

In some embodiments, one or more non-transitory, machine-readable medium has instructions thereon, the instructions when executed by a processor being configured to perform operations comprising obtaining scanning electron microscopy (SEM) metrology data for first areas on a training wafer, obtaining optical metrology data for second areas on the training wafer, and training a model, by using the SEM metrology data and the optical metrology data for the training wafer, to generate parameters for features on a production wafer based on optical metrology data for areas of the production wafer.