Abstract: A method for determining a root cause affecting yield in a process for manufacturing devices on a substrate, the method including: obtaining yield distribution data including a distribution of a yield parameter across the substrate or part thereof; obtaining sets of metrology data, each set including a spatial variation of a process parameter over the substrate or part thereof corresponding to a different layer of the substrate; comparing the yield distribution data and metrology data based on a similarity metric describing a spatial similarity between the yield distribution data and an individual set out of the sets of the metrology data; and determining a first similar set of metrology data out of the sets of metrology data, being the first set of metrology data in terms of processing order for the corresponding layers, which is determined to be similar to the yield distribution data.

Abstract: 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.

Abstract: 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.

Abstract: A method including obtaining verified values of a characteristic of a plurality of patterns on a substrate produced by a device manufacturing process; obtaining computed values of the characteristic using a non-probabilistic model; obtaining values of a residue of the non-probabilistic model based on the verified values and the computed values; and obtaining an attribute of a distribution of the residue based on the values of the residue. Also disclosed herein are methods of computing a probability of defects on a substrate produced by the device manufacturing process, and of obtaining an attribute of a distribution of the residue of a non-probabilistic model.

Abstract: 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.

Abstract: A method for predicting yield relating to a process of manufacturing semiconductor devices on a substrate, the method including: obtaining a trained first model which translates modeled parameters into a yield parameter, the modeled parameters including: a) a geometrical parameter associated with one or more selected from: a geometric characteristic, dimension or position of a device element manufactured by the process and b) a trained free parameter; obtaining process parameter data including data regarding a process parameter characterizing the process; converting the process parameter data into values of the geometrical parameter; and predicting the yield parameter using the trained first model and the values of the geometrical parameter.

Abstract: A method for analyzing a process, the method including obtaining a multi-dimensional probability density function representing an expected distribution of values for a plurality of process parameters; obtaining a performance function relating values of the process parameters to a performance metric of the process; and using the performance function to map the probability density function to a performance probability function having the process parameters as arguments.

Abstract: A method for determining a root cause affecting yield in a process for manufacturing devices on a substrate, the method including: obtaining yield distribution data including a distribution of a yield parameter across the substrate or part thereof; obtaining sets of metrology data, each set including a spatial variation of a process parameter over the substrate or part thereof corresponding to a different layer of the substrate; comparing the yield distribution data and metrology data based on a similarity metric describing a spatial similarity between the yield distribution data and an individual set out of the sets of the metrology data; and determining a first similar set of metrology data out of the sets of metrology data, being the first set of metrology data in terms of processing order for the corresponding layers, which is determined to be similar to the yield distribution data.

Abstract: A method including obtaining verified values of a characteristic of a plurality of patterns on a substrate produced by a device manufacturing process; obtaining computed values of the characteristic using a non-probabilistic model; obtaining values of a residue of the non-probabilistic model based on the verified values and the computed values; and obtaining an attribute of a distribution of the residue based on the values of the residue. Also disclosed herein are methods of computing a probability of defects on a substrate produced by the device manufacturing process, and of obtaining an attribute of a distribution of the residue of a non-probabilistic model.