Abstract: A method for estimating a parameter across a region on a substrate, the region being divided into a plurality of sub-regions, the method including: obtaining values of the parameter for at least two sub-regions out of the plurality of sub-regions; and estimating the parameter for a position on the region by evaluation of a function having said values of the parameter as input values, wherein the function: a) has piecewise defined base functions, wherein a single base function is defined across a sub-region; and b) is continuous between one or more adjacent sub-regions of the at least two sub-regions within the region.

Abstract: A method to change an etch parameter of a substrate etching process, the method including: making a first measurement of a first metric associated with a structure on a substrate before being etched; making a second measurement of a second metric associated with a structure on a substrate after being etched; and changing the etch parameter based on a difference between the first measurement and the second measurement.

Abstract: A method for selecting an optimal set of locations for a measurement or feature on a substrate, the method includes: defining a first candidate solution of locations, defining a second candidate solution with locations based on modification of a coordinate in a solution domain of the first candidate solution, and selecting the first and/or second candidate solution as the optimal solution according to a constraint associated with the substrate.

Abstract: A method including evaluating, with respect to a parameter representing remaining uncertainty of a mathematical model fitting measured data, one or more mathematical models for fitting measured data and one or more measurement sampling schemes for measuring data, against measurement data across a substrate, and identifying one or more mathematical models and/or one or more measurement sampling schemes, for which the parameter crosses a threshold.

Abstract: A method for optimizing a sequence of processes for manufacturing of product units, includes: associating measurement results of performance parameters (e.g., fingerprints) with the recorded process characteristics (e.g., context); obtaining a characteristic (e.g., context) of a previous process (e.g. deposition) in the sequence already performed on a product unit; obtaining a characteristic (e.g., context) of a subsequent process (e.g., exposure) in the sequence to be performed on the product unit; determining a predicted performance parameter (e.g., fingerprint) of the product unit associated with the sequence of previous and subsequent processes by using the obtained characteristics to retrieve measurement results of the performance parameters (e.g., fingerprints) corresponding to the recorded characteristics; and determining corrections to be applied to future processes (e.g. exposure, etch) in the sequence to be performed on the product unit, based on the determined predicted performance parameter.

Abstract: A method including evaluating, with respect to a parameter representing remaining uncertainty of a mathematical model fitting measured data, one or more mathematical models for fitting measured data and one or more measurement sampling schemes for measuring data, against measurement data across a substrate, and identifying one or more mathematical models and/or one or more measurement sampling schemes, for which the parameter crosses a threshold.

Abstract: A method for estimating a parameter across a region on a substrate, the region being divided into a plurality of sub-regions, the method including: obtaining values of the parameter for at least two sub-regions out of the plurality of sub-regions; and estimating the parameter for a position on the region by evaluation of a function having said values of the parameter as input values, wherein the function: a) has piecewise defined base functions, wherein a single base function is defined across a sub-region; and b) is continuous between one or more adjacent sub-regions of the at least two sub-regions within the region.

Abstract: A method for optimizing a sequence of processes for manufacturing of product units, includes: associating measurement results of performance parameters (e.g., fingerprints) with the recorded process characteristics (e.g., context); obtaining a characteristic (e.g., context) of a previous process (e.g. deposition) in the sequence already performed on a product unit; obtaining a characteristic (e.g., context) of a subsequent process (e.g., exposure) in the sequence to be performed on the product unit; determining a predicted performance parameter (e.g., fingerprint) of the product unit associated with the sequence of previous and subsequent processes by using the obtained characteristics to retrieve measurement results of the performance parameters (e.g., fingerprints) corresponding to the recorded characteristics; and determining corrections to be applied to future processes (e.g. exposure, etch) in the sequence to be performed on the product unit, based on the determined predicted performance parameter.

Abstract: A method of characterizing distortions in a lithographic process, and associated apparatuses. The method includes obtaining measurement data corresponding to a plurality of measurement locations on a substrate, the measurement data comprising measurements performed on a plurality of substrates, and comprising one or more measurements performed on one or more of the substrates for each of the measurement locations. For each of the measurement locations, a first quality value representing a quality metric and a noise value representing a noise metric is determined from the measurements performed at that measurement location. A plurality of distortion parameters is determined, each distortion parameter configured to characterize a systematic distortion in the quality metric and a statistical significance of the distortion parameters from the first quality value and from the noise value is determined. Systematic distortion is parameterized from the distortion parameters determined to be statistically significant.

Abstract: A method, system and program for determining a fingerprint of a parameter. The method includes determining a contribution from a device out of a plurality of devices to a fingerprint of a parameter. The method includes obtaining parameter data and usage data, wherein the parameter data is based on measurements for multiple substrates having been processed by the plurality of devices, and the usage data indicates which of the devices out of the plurality of the devices were used in the processing of each substrate; and determining the contribution using the usage data and parameter data.

Abstract: A method for improving the yield of a lithographic process, the method including: determining a parameter fingerprint of a performance parameter across a substrate, the parameter fingerprint including information relating to uncertainty in the performance parameter; determining a process window fingerprint of the performance parameter across the substrate, the process window being associated with an allowable range of the performance parameter; and determining a probability metric associated with the probability of the performance parameter being outside an allowable range. Optionally a correction to the lithographic process is determined based on the probability metric.

Abstract: A method, system and program for determining a fingerprint of a parameter. The method includes determining a contribution from a device out of a plurality of devices to a fingerprint of a parameter. The method including: obtaining parameter data and usage data, wherein the parameter data is based on measurements for multiple substrates having been processed by the plurality of devices, and the usage data indicates which of the devices out of the plurality of the devices were used in the processing of each substrate; and determining the contribution using the usage data and parameter data.

Abstract: A method of monitoring a device manufacturing process, the method including; obtaining an estimated time variation of a process parameter; determining, on the basis of the estimated time variation, a sampling plan for measurements to be performed on a plurality of substrates to obtain information about the process parameter; measuring substrates in accordance with the sampling plan to obtain a plurality of measurements; and determining an actual time variation of the process parameter on the basis of the measurements.

Abstract: A method for improving the yield of a lithographic process, the method including: determining a parameter fingerprint of a performance parameter across a substrate, the parameter fingerprint including information relating to uncertainty in the performance parameter; determining a process window fingerprint of the performance parameter across the substrate, the process window being associated with an allowable range of the performance parameter; and determining a probability metric associated with the probability of the performance parameter being outside an allowable range. Optionally a correction to the lithographic process is determined based on the probability metric.

Abstract: A method for determining a plurality of corrections for control of at least one manufacturing apparatus used in a manufacturing process for providing product structures to a substrate in a plurality of layers, the method including: determining the plurality of corrections including a correction for each layer, based on an actuation potential of the applicable manufacturing apparatus used in the formation of each layer, wherein the determining includes determining corrections for each layer simultaneously in terms of a matching parameter.

Abstract: In a lithographic process, product units such as semiconductor wafers are subjected to lithographic patterning operations and chemical and physical processing operations. Alignment data or other measurements are made at stages during the performance of the process to obtain object data representing positional deviation or other parameters measured at points spatially distributed across each unit. This object data is used to obtain diagnostic information by performing a multivariate analysis to decompose a set of vectors representing the units in the multidimensional space into one or more component vectors. Diagnostic information about the industrial process is extracted using the component vectors. The performance of the industrial process for subsequent product units can be controlled based on the extracted diagnostic information.

Abstract: A method includes determining topographic information of a substrate for use in a lithographic imaging system, determining or estimating, based on the topographic information, imaging error information for a plurality of points in an image field of the lithographic imaging system, adapting a design for a patterning device based on the imaging error information. In an embodiment, a plurality of locations for metrology targets is optimized based on imaging error information for a plurality of points in an image field of a lithographic imaging system, wherein the optimizing involves minimizing a cost function that describes the imaging error information. In an embodiment, locations are weighted based on differences in imaging requirements across the image field.

Abstract: In a lithographic process, product units such as semiconductor wafers are subjected to lithographic patterning operations and chemical and physical processing operations. Alignment data or other measurements are made at stages during the performance of the process to obtain object data representing positional deviation or other parameters measured at points spatially distributed across each unit. This object data is used to obtain diagnostic information by performing a multivariate analysis to decompose a set of vectors representing the units in the multidimensional space into one or more component vectors. Diagnostic information about the industrial process is extracted using the component vectors. The performance of the industrial process for subsequent product units can be controlled based on the extracted diagnostic information.

Abstract: A method for optimizing a sequence of processes for manufacturing of product units, includes: associating measurement results of performance parameters (e.g., fingerprints) with the recorded process characteristics (e.g., context); obtaining a characteristic (e.g., context) of a previous process (e.g. deposition) in the sequence already performed on a product unit; obtaining a characteristic (e.g., context) of a subsequent process (e.g., exposure) in the sequence to be performed on the product unit; determining a predicted performance parameter (e.g., fingerprint) of the product unit associated with the sequence of previous and subsequent processes by using the obtained characteristics to retrieve measurement results of the performance parameters (e.g., fingerprints) corresponding to the recorded characteristics; and determining corrections to be applied to future processes (e.g. exposure, etch) in the sequence to be performed on the product unit, based on the determined predicted performance parameter.

Abstract: A method for improving the yield of a lithographic process, the method including: determining a parameter fingerprint of a performance parameter across a substrate, the parameter fingerprint including information relating to uncertainty in the performance parameter; determining a process window fingerprint of the performance parameter across the substrate, the process window being associated with an allowable range of the performance parameter; and determining a probability metric associated with the probability of the performance parameter being outside an allowable range. Optionally a correction to the lithographic process is determined based on the probability metric.