Abstract: A method of processing measurement data relating to a substrate processed by a manufacturing process. The method includes obtaining measurement data relating to a performance parameter for at least a portion of the substrate; and fitting the measurement data to a model by minimizing a complexity metric applied to fitting parameters of the model while not allowing the deviation between the measurement data and the fitted model to exceed a threshold value.

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 for characterizing a patterning process, the method including obtaining a plurality of values of stitching errors made along one or more boundaries between at least two patterned adjacent fields or sub-fields on a substrate; and fitting, using a hardware computer system, a distortion model to the plurality of values to obtain a fingerprint representing deformation of a field or sub-field out of the at least two patterned adjacent fields or sub-fields.

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 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.