A method to improve a lithographic process of imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method including: computing a multi-variable cost function, the multi-variable cost function being a function of a stochastic variation of a characteristic of an aerial image or a resist image, or a function of a variable that is a function of the stochastic variation or that affects the stochastic variation, the stochastic variation being a function of a plurality of design variables that represent characteristics of the lithographic process; and reconfiguring one or more of the characteristics of the lithographic process by adjusting one or more of the design variables until a certain termination condition is satisfied.

Methods for training a process model and determining ranking of simulated patterns (e.g., corresponding to hot spots). A method involves obtaining a training data set including: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on the substrate using the mask pattern, and (iii) measured values of a parameter of the patterning process applied during imaging of the mask pattern on the substrate; and training a machine learning model for the patterning process based on the training data set to predict a difference in a characteristic of the simulated pattern and the printed pattern. The trained machine learning model can be used for determining a ranking of hot spots. In another method a model is trained based on measurement data to predict ranking of the hot spots.

A method and system for predicting complex electric field images with a parameterized model are described. A latent space representation of a complex electric field image is determined based on dimensional data in a latent space of the parameterized model for a given input to the parameterized model. The given input may be a measured amplitude (e.g., intensity) associated with the complex electric field image. The complex electric field image is predicted based on the latent space representation of the complex electric field image. The predicted complex electric field image includes an amplitude and a phase. The parameterized model comprises encoder-decoder architecture. In some embodiments, determining the latent space representation of the electric field image comprises minimizing a function constrained by a set of electric field images that could be predicted by the parameterized model based on the dimensional data in the latent space and the given input.

The present disclosure generally provides for a system and method for measuring one or more characteristics of one or more substrates in a multi-station processing system using one or more metrology modules at a plurality of metrology stations. In one embodiment, a system controller is configured to cause the multi-station processing system to perform a method that includes processing a plurality of substrates at a plurality of processing stations, advancing one or more of the plurality of substrates to a respective metrology station, measuring one or more characteristics of the plurality of substrates at the respective metrology station, determining a processing performance metric based on the one or more characteristics, comparing the processing performance metric to a tolerance limit to determine if an out of tolerance condition has occurred, and adjusting one or more processing parameters when it is determined that an out of tolerance condition has occurred.

Methods for training a process model and determining ranking of simulated patterns (e.g., corresponding to hot spots). A method involves obtaining a training data set including: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on the substrate using the mask pattern, and (iii) measured values of a parameter of the patterning process applied during imaging of the mask pattern on the substrate; and training a machine learning model for the patterning process based on the training data set to predict a difference in a characteristic of the simulated pattern and the printed pattern. The trained machine learning model can be used for determining a ranking of hot spots. In another method a model is trained based on measurement data to predict ranking of the hot spots.

A method for determining a target feature in a model of a patterning process based on local electric fields estimated for the patterning process is described. The method includes obtaining a mask stack region of interest. The mask stack region of interest has one or more characteristics associated with propagation of electromagnetic waves through the mask stack region of interest. The mask stack region of interest includes the target feature. The method includes estimating a local electric field based on the one or more characteristics associated with the propagation of electromagnetic waves through the mask stack region of interest. The local electric field is estimated for a portion of the mask stack region of interest in proximity to the target feature. The method includes determining the target feature based on the estimated local electric field.

The present invention relates to a method for repairing at least one defect of a lithographic mask, the method comprising the step of: ascertaining parameters of at least one repair shape for the at least one defect, wherein ascertaining parameters comprises: allocating at least one numerical value to a parameter, wherein the numerical value deviates from the numerical value predefined by the at least one defect for said parameter.

Lithographic patterning method for creating features on a surface of a substrate, including the steps of: applying a resist material to the surface; performing resist processing steps, including at least: selectively exposing the resist material layer to a surface treatment step, wherein the resist material in the exposed locations is chemically modified; and developing the resist material layer to selectively remove the resist material locally. The method further comprises detecting, during or after the resist processing steps, a chemical modification of the resist material for monitoring or evaluating the processing steps. The step of detecting is performed by scanning the surface using a scanning probe microscopy device, and wherein the scanning includes contacting the surface with the probe tip in a probing area. The probing area coincides with at least one location of the exposed locations and non-exposed locations, for detecting the chemical modification. The document further describes a system.

A method for determining a target feature in a model of a patterning process based on local electric fields estimated for the patterning process is described. The method includes obtaining a mask stack region of interest. The mask stack region of interest has one or more characteristics associated with propagation of electromagnetic waves through the mask stack region of interest. The mask stack region of interest includes the target feature. The method includes estimating a local electric field based on the one or more characteristics associated with the propagation of electromagnetic waves through the mask stack region of interest. The local electric field is estimated for a portion of the mask stack region of interest in proximity to the target feature. The method includes determining the target feature based on the estimated local electric field.

Methods for training a process model and determining ranking of simulated patterns (e.g., corresponding to hot spots). A method involves obtaining a training data set including: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on the substrate using the mask pattern, and (iii) measured values of a parameter of the patterning process applied during imaging of the mask pattern on the substrate; and training a machine learning model for the patterning process based on the training data set to predict a difference in a characteristic of the simulated pattern and the printed pattern. The trained machine learning model can be used for determining a ranking of hot spots. In another method a model is trained based on measurement data to predict ranking of the hot spots.