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, 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, involving determining a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process; determining a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process; and determining a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions. The function may include a correlation.

Abstract: A method of controlling a semiconductor manufacturing process, the method including: obtaining first metrology data based on measurements performed after a first process step; obtaining second metrology data based on measurements performed after the first process step and at least one additional process step; estimating a contribution to the process of: a) a control action which is at least partially based on the second metrology data and/or b) the at least one additional process step by using at least partially the second metrology data; and determining a Key Performance Indicator (KPI) or a correction for the first process step using the first metrology data and the estimated contribution.

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, involving determining a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process; determining a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process; and determining a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions. The function may include a correlation.

Abstract: Offline metrology measurements are performed on substrates that have been subjected to lithographic processing. Model parameters are calculated by fitting the measurements to an extended high-order substrate model defined using a combination of basis functions that include an edge basis function related to a substrate edge. A radial edge basis function may be expressed in terms of distance from a substrate edge. The edge basis function may, for example, be an exponential decay function or a rational function. Lithographic processing of a subsequent substrate is controlled using the calculated high-order substrate model parameters, in combination with low-order substrate model parameters obtained by fitting inline measurements to a low order model.

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 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 includes obtaining, for each particular feature of a plurality of features of a device pattern of a substrate being created using a patterning process, a modelled or simulated relation of a parameter of the patterning process between a measurement target for the substrate and the particular feature; and based on the relation and measured values of the parameter from the metrology target, generating a distribution of the parameter across at least part of the substrate for each of the features, the distribution for use in design, control or modification of the patterning process.

Abstract: A lithographic process is performed on a set of semiconductor substrates consisting of a plurality of substrates. As part of the process, the set of substrates is partitioned into a number of subsets. The partitioning may be based on a set of characteristics associated with a first layer on the substrates. A fingerprint of a performance parameter is then determined for at least one substrate of the set of substrates. Under some circumstances, the fingerprint is determined for one substrate of each subset of substrates. The fingerprint is associated with at least the first layer. A correction for the performance parameter associated with an application of a subsequent layer is then derived, the derivation being based on the determined fingerprint and the partitioning of the set of substrates.

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 lithographic process is performed on a set of semiconductor substrates consisting of a plurality of substrates. As part of the process, the set of substrates is partitioned into a number of subsets. The partitioning may be based on a set of characteristics associated with a first layer on the substrates. A fingerprint of a performance parameter is then determined for at least one substrate of the set of substrates. Under some circumstances, the fingerprint is determined for one substrate of each subset of substrates. The fingerprint is associated with at least the first layer. A correction for the performance parameter associated with an application of a subsequent layer is then derived, the derivation being based on the determined fingerprint and the partitioning of the set of substrates.

Abstract: A method includes obtaining, for each particular feature of a plurality of features of a device pattern of a substrate being created using a patterning process, a modelled or simulated relation of a parameter of the patterning process between a measurement target for the substrate and the particular feature; and based on the relation and measured values of the parameter from the metrology target, generating a distribution of the parameter across at least part of the substrate for each of the features, the distribution for use in design, control or modification of the patterning process.

Abstract: In the measurement of properties of a wafer substrate, such as Critical Dimension or overlay a sampling plan is produced defined for measuring a property of a substrate, wherein the sampling plan comprises a plurality of sub-sampling plans. The sampling plan may be constrained to a predetermined fixed number of measurement points and is used to control an inspection apparatus to perform a plurality of measurements of the property of a plurality of substrates using different sub-sampling plans for respective substrates, optionally, the results are stacked to at least partially recompose the measurement results according to the sample plan.

Abstract: A device manufacturing method includes: exposing a first substrate using a lithographic apparatus to form a patterned layer having first features; processing the first substrate to transfer the first features into the first substrate; determining displacements of the first features from their nominal positions in the first substrate; determining a correction to at least partly compensate for the displacements; and exposing a second substrate using a lithographic apparatus to form a patterned layer having the first features, wherein the correction is applied for or during the exposing the second substrate.

Abstract: Offline metrology measurements are performed on substrates that have been subjected to lithographic processing. Model parameters are calculated by fitting the measurements to an extended high-order substrate model defined using a combination of basis functions that include an edge basis function related to a substrate edge. A radial edge basis function may be expressed in terms of distance from a substrate edge. The edge basis function may, for example, be an exponential decay function or a rational function. Lithographic processing of a subsequent substrate is controlled using the calculated high-order substrate model parameters, in combination with low-order substrate model parameters obtained by fitting inline measurements to a low order model.

Abstract: A method of calculating process corrections for a lithographic tool, and associated apparatuses. The method comprises measuring process defect data on a substrate that has been previously exposed using the lithographic tool; fitting a process signature model to the measured process defect data, so as to obtain a model of the process signature for the lithographic tool; and using the process signature model to calculate the process corrections for the lithographic tool.

Abstract: A method of calculating process corrections for a lithographic tool, and associated apparatuses. The method comprises measuring process defect data on a substrate that has been previously exposed using the lithographic tool; fitting a process signature model to the measured process defect data, so as to obtain a model of the process signature for the lithographic tool; and using the process signature model to calculate the process corrections for the lithographic tool.