Disclosed is a method for obtaining a computationally determined interference electric field describing scattering of radiation by a pair of structures comprising a first structure and a second structure on a substrate. The method comprises determining a first electric field relating to first radiation scattered by the first structure; determining a second electric field relating to second radiation scattered by the second structure; and computationally determining the interference of the first electric field and second electric field, to obtain a computationally determined interference electric field.

A method for determining a process window of a patterning process based on a failure rate. The method includes obtaining a plurality of features printed on a substrate, grouping, based on a metric, the features into a plurality of groups, and generating, based on measurement data associated with a group of features, a base failure rate model for the group of features, wherein the base failure rate model identifies the process window related to the failure rate of the group of features. The method can further include generating, using the base failure rate model, a feature-specific failure rate model for a specific feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that an estimated failure rate of the specific feature is below a specified threshold.

Disclosed is a method for obtaining a computationally determined interference electric field describing scattering of radiation by a pair of structures comprising a first structure and a second structure on a substrate. The method comprises determining a first electric field relating to first radiation scattered by the first structure; determining a second electric field relating to second radiation scattered by the second structure; and computationally determining the interference of the first electric field and second electric field, to obtain a computationally determined interference electric field.

Disclosed is a method for obtaining a computationally determined interference electric field describing scattering of radiation by a pair of structures comprising a first structure and a second structure on a substrate. The method comprises determining a first electric field relating to first radiation scattered by the first structure; determining a second electric field relating to second radiation scattered by the second structure; and computationally determining the interference of the first electric field and second electric field, to obtain a computationally determined interference electric field.

A method for calculating a spatial map associated with a component, the spatial map indicating spatial variations of thermal expansion parameters in the component, the method comprising: providing or determining a temperature distribution in the component as a function of time; calculating the spatial map associated with the component using the provided or determined temperature distribution in the component and optical measurements of a radiation beam that has interacted directly or indirectly with the component, the optical measurements being time synchronized with the provided or determined temperature distribution in the component.

A method to determine a performance indicator indicative of alignment performance of a processed substrate. The method includes obtaining measurement data including a plurality of measured position values of alignment marks on the substrate and calculating a positional deviation between each measured position value and a respective expected position value. These positional deviations are used to determine a directional derivative between the alignment marks, and the directional derivatives are used to determine at least one directional derivative performance indicator.

A method and associated computer program for predicting an electrical characteristic of a substrate subject to a process. The method includes determining a sensitivity of the electrical characteristic to a process characteristic, based on analysis of electrical metrology data including electrical characteristic measurements from previously processed substrates and of process metrology data including measurements of at least one parameter related to the process characteristic measured from the previously processed substrates; obtaining process metrology data related to the substrate describing the at least one parameter; and predicting the electrical characteristic of the substrate based on the sensitivity and the process metrology data.

Methods and systems for determining a mapped intensity metric are described. Determining the mapped intensity metric includes determining an intensity metric for a manufacturing system. The intensity metric is determined based on a reflectivity of a location on a substrate and a manufacturing system characteristic. Determining the mapped intensity metric also includes determining a mapped intensity metric for a reference system. The reference system has a reference system characteristic. The mapped intensity metric is determined based on the intensity metric, the manufacturing system characteristic, and the reference system characteristic, to mimic determination of the intensity metric for the manufacturing system using the reference system. In some embodiments, the reference system is virtual, and the manufacturing system is physical.

A metrology system may receive a model for measuring one or more selected attributes of a target including features distributed in a selected pattern based on regression of spectroscopic scatterometry data from a scatterometry tool for a range of wavelengths. The metrology system may further generate a weighting function for the model to de-emphasize portions of the spectroscopic scatterometry data associated with wavelengths at which light captured by the scatterometry tool when measuring the target is predicted to include undesired diffraction orders. The metrology system may further direct the spectroscopic scatterometry tool to generate scatterometry data of one or more measurement targets including fabricated features distributed in the selected pattern. The metrology system may further measure the selected attributes for the one or more measurement targets based on regression of the scatterometry data of the one or more measurement targets to the model weighted by the weighting function.

A method and associated computer program for predicting an electrical characteristic of a substrate subject to a process. The method includes determining a sensitivity of the electrical characteristic to a process characteristic, based on analysis of electrical metrology data including electrical characteristic measurements from previously processed substrates and of process metrology data including measurements of at least one parameter related to the process characteristic measured from the previously processed substrates; obtaining process metrology data related to the substrate describing the at least one parameter; and predicting the electrical characteristic of the substrate based on the sensitivity and the process metrology data.