Abstract: Methods and apparatus for classifying semiconductor wafers. The method can include: sorting a set of semiconductor wafers, using a model, into a plurality of sub-sets based on parameter data corresponding to one or more parameters of the set of semiconductor wafers, wherein the parameter data for semiconductor wafers in a sub-set include one or more common characteristics; identifying one or more semiconductor wafers within a sub-set based on a probability of the one or more semiconductor wafers being correctly allocated to the sub-set; comparing the parameter data of the one or more identified semiconductor wafers to reference parameter data; and reconfiguring the model based on the comparison. The comparison is undertaken by a human to provide constraints for the model. The apparatus can be configured to undertake the method.

Abstract: A method for determining an inspection strategy for at least one substrate, the method including: quantifying, using a prediction model, a compliance metric value for a compliance metric relating to a prediction of compliance with a quality requirement based on one or both of pre-processing data associated with the substrate and any available post-processing data associated with the at least one substrate; and deciding on an inspection strategy for the at least one substrate, based on the compliance metric value, an expected cost associated with the inspection strategy and at least one objective value describing an expected value of the inspection strategy in terms of at least one objective relating to the prediction model.

Abstract: Apparatus and methods of configuring an imputer model for imputing a second parameter. The method includes inputting a first data set including values of a first parameter to the imputer model, and evaluating the imputer model to obtain a second data set including imputed values of the second parameter. The method further includes obtaining a third data set including measured values of a third parameter, wherein the third parameter is correlated to the second parameter; obtaining a prediction model configured to infer values of the third parameter based on inputting values of the second parameter; inputting the second data set to the prediction model, and evaluating the prediction model to obtain inferred values of the third parameter; and configuring the imputer model based on a comparison of the inferred values and the measured values of the third parameter.

Abstract: A method for determining an inspection strategy for at least one substrate, the method including: quantifying, using a prediction model, a compliance metric value for a compliance metric relating to a prediction of compliance with a quality requirement based on one or both of pre-processing data associated with the substrate and any available post-processing data associated with the at least one substrate; and deciding on an inspection strategy for the at least one substrate, based on the compliance metric value, an expected cost associated with the inspection strategy and at least one objective value describing an expected value of the inspection strategy in terms of at least one objective relating to the prediction model.

Abstract: A method of extracting a feature from a data set includes iteratively extracting a feature from a data set based on a visualization of a residual pattern within the data set, wherein the feature is distinct from a feature extracted in a previous iteration, and the visualization of the residual pattern uses the feature extracted in the previous iteration. Visualizing the data set using the feature extracted in the previous iteration may include showing residual patterns of attribute data that are relevant to target data. Visualizing the data set using the feature extracted in the previous iteration may involve adding cluster constraints to the data set, based on the feature extracted in the previous iteration. Additionally or alternatively, visualizing the data set using the feature extracted in the previous iteration may involve defining conditional probabilities conditioned on the feature extracted in the previous iteration.

Abstract: A method of optimizing an apparatus for multi-stage processing of product units such as wafers, the method includes: receiving object data representing one or more parameters measured across the product units and associated with different stages of processing of the product units; and determining fingerprints of variation of the object data across the product units, the fingerprints being associated with different respective stages of processing of the product units. The fingerprints may be determined by decomposing the object data into components using principal component analysis for each different respective stage; analyzing commonality of the fingerprints through the different stages to produce commonality results; and optimizing an apparatus for processing product units based on the commonality results.

Abstract: A method of determining a contribution of a process feature to the performance of a process of patterning substrates. The method may include obtaining a first model trained on first process data and first performance data. One or more substrates may be identified based on a quality of prediction of the first model when applied to process data associated with the one or more substrates. A second model may be trained on second process data and second performance data associated with the identified one or more substrates. The second model may be used to determine the contribution of a process feature of the second process data to the second performance data associated with the one or more substrates.

Abstract: A method of extracting a feature from a data set includes iteratively extracting a feature from a data set based on a visualization of a residual pattern within the data set, wherein the feature is distinct from a feature extracted in a previous iteration, and the visualization of the residual pattern uses the feature extracted in the previous iteration. Visualizing the data set using the feature extracted in the previous iteration may include showing residual patterns of attribute data that are relevant to target data. Visualizing the data set using the feature extracted in the previous iteration may involve adding cluster constraints to the data set, based on the feature extracted in the previous iteration. Additionally or alternatively, visualizing the data set using the feature extracted in the previous iteration may involve defining conditional probabilities conditioned on the feature extracted in the previous iteration.

Abstract: A method of optimizing an apparatus for multi-stage processing of product units such as wafers, the method includes: receiving object data representing one or more parameters measured across the product units and associated with different stages of processing of the product units; and determining fingerprints of variation of the object data across the product units, the fingerprints being associated with different respective stages of processing of the product units. The fingerprints may be determined by decomposing the object data into components using principal component analysis for each different respective stage; analyzing commonality of the fingerprints through the different stages to produce commonality results; and optimizing an apparatus for processing product units based on the commonality results.

Abstract: A method of optimizing an apparatus for multi-stage processing of product units such as wafers, the method includes: receiving object data representing one or more parameters measured across the product units and associated with different stages of processing of the product units; and determining fingerprints of variation of the object data across the product units, the fingerprints being associated with different respective stages of processing of the product units. The fingerprints may be determined by decomposing the object data into components using principal component analysis for each different respective stage; analyzing commonality of the fingerprints through the different stages to produce commonality results; and optimizing an apparatus for processing product units based on the commonality results.

Abstract: A technique to generate predicted data for control or monitoring of a production process to improve a parameter of interest. Context data associated with operation of the production process is obtained. Metrology/testing is performed on the product of the production process, thereby obtaining performance data. A context-to-performance model is provided to generate predicted performance data based on labeling of the context data with performance data. This is an instance of semi-supervised learning. The context-to-performance model may include the learner that performs semi-supervised labeling. The context-to-performance model is modified using prediction information related to quality of the context data and/or performance data. Prediction information may include relevance information relating to relevance of the obtained context data and/or obtained performance data to the parameter of interest.

Abstract: A method of optimizing an apparatus for multi-stage processing of product units such as wafers, the method includes: receiving object data representing one or more parameters measured across the product units and associated with different stages of processing of the product units; and determining fingerprints of variation of the object data across the product units, the fingerprints being associated with different respective stages of processing of the product units. The fingerprints may be determined by decomposing the object data into components using principal component analysis for each different respective stage; analyzing commonality of the fingerprints through the different stages to produce commonality results; and optimizing an apparatus for processing product units based on the commonality results.

Abstract: A technique to generate predicted data for control or monitoring of a production process to improve a parameter of interest. Context data associated with operation of the production process is obtained. Metrology/testing is performed on the product of the production process, thereby obtaining performance data. A context-to-performance model is provided to generate predicted performance data based on labeling of the context data with performance data. This is an instance of semi-supervised learning. The context-to-performance model may include the learner that performs semi-supervised labeling. The context-to-performance model is modified using prediction information related to quality of the context data and/or performance data. Prediction information may include relevance information relating to relevance of the obtained context data and/or obtained performance data to the parameter of interest.