Abstract: A method for determining overlay error includes measuring asymmetry of radiation reflected from each of a plurality of targets on a substrate. The plurality of targets include a predetermined overlay offset. The method also includes comparing the measured asymmetry of the radiation reflected from each of the plurality of targets to the corresponding predetermined overlay offset of the respective target. Additionally, the method includes determining the overlay error of a point on the substrate as a function of measured asymmetry reflected from the point. The function is determined by fitting a polynomial or a Fourier series to a comparison of the measured asymmetry of the radiation reflected from each of the plurality of targets to the corresponding predetermined overlay offset of the respective target. The function limits an effect of linearity error.

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 said 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: Disclosed is a method of measuring a parameter of a litho-graphic process, and associated inspection apparatus. The method comprises measuring at least two target structures on a substrate using a plurality of different illumination conditions, the target structures having deliberate overlay biases; to obtain for each target structure an asymmetry measurement representing an overall asymmetry that includes contributions due to (i) the deliberate overlay biases, (ii) an overlay error during forming of the target structure and (iii) any feature asymmetry. A regression analysis is performed on the asymmetry measurement data by fitting a linear regression model to a planar representation of asymmetry measurements for one target structure against asymmetry measurements for another target structure, the linear regression model not necessarily being fitted through an origin of the planar representation. The overlay error can then be determined from a gradient described by the linear regression model.

Abstract: A method controls scanning function of a lithographic apparatus. A monitor wafer is exposed to determine baseline control parameters pertaining to the scanning function. The baseline control parameters are retrieved from the monitor wafer. Parameter drift is determined from the baseline control parameters. Compensation is performed based on the determination. A different parameterization is used for control of the scanning control module than for communication between the scanning control module and the lithographic apparatus.

Abstract: System and methods estimate model parameters of a lithographic apparatus and control lithographic processing by a lithographic apparatus. An exposure is performed using a lithographic apparatus across a wafer. A set of predetermined wafer measurement locations is obtained. Discrete orthonormal polynomials are generated using the predetermined substrate measurement locations. The overlay errors arising from the exposure are measured at the predetermined locations to obtain overlay measurements. The estimated model parameters of the lithographic apparatus are calculated from the overlay measurements by using the discrete orthogonal polynomials as a basis function to model the overlay across the wafer. Finally, the estimated model parameters are used to control the lithographic apparatus in order to provide corrected overlay across the wafer.

Abstract: A method for determining overlay error includes measuring asymmetry of radiation reflected from each of a plurality of targets on a substrate. The plurality of targets include a predetermined overlay offset. The method also includes comparing the measured asymmetry of the radiation reflected from each of the plurality of targets to the corresponding predetermined overlay offset of the respective target. Additionally, the method includes determining the overlay error of a point on the substrate as a function of measured asymmetry reflected from the point. The function is determined by fitting a polynomial or a Fourier series to a comparison of the measured asymmetry of the radiation reflected from each of the plurality of targets to the corresponding predetermined overlay offset of the respective target. The function limits an effect of linearity error.

Abstract: A method and associated apparatus determine an overlay error on a substrate. A beam is projected onto three or more targets. Each target includes first and second overlapping patterns with predetermined overlay offsets on the substrate. The asymmetry of the radiation reflected from each target on the substrate is measured. The overlay error not resultant from the predetermined overlay offsets is determined. The function that enables calculation of overlay from asymmetry for other points on the wafer is determined by limiting the effect of linearity error when determining the overlay error from the function.

Abstract: A scatterometer configured to measure a property of a substrate, includes a radiation source configured to provide a radiation beam; and a detector configured to detect a spectrum of the radiation beam reflected from a target (30) on the surface of the substrate (W) and to produce a measurement signal representative of the spectrum. The apparatus includes a beam shaper (51, 53) interposed in the radiation path between the radiation source and the detector, the beam shaper being configured to adjust the cross section of the beam dependent on the shape and/or size of the target.

Abstract: A lithographic system includes a lithographic apparatus comprising a projection system which projects a patterned radiation beam onto a target portion of a substrate and an alignment system which measures the position of a feature of the pattern on the substrate at a number of locations over the substrate. A controller compares the measured positions with points on a grid of values and extrapolates values for intermediate positions on the substrate based on values of corresponding intermediate points on the grid, so as to provide an indication of the intermediate positions on the substrate and their displacements relative to the grid. The grid is based on at least one orthogonal basis function, the measurement on the substrate being performed at positions corresponding to the root values of the at least one orthogonal basis function.

Abstract: Variables in each step in a double patterning lithographic process are recorded and characteristics of intermediate features in a double patterning process measured. The final feature is then modeled, and the values of the variables optimized.

Abstract: A method for selecting sample positions on a substrate from a set of all available sample positions is provided, in which a representation of a model, which may represent the variation of one or more properties across the substrate, is analyzed in order to identify the sample positions having the greatest effect on the model.

Abstract: A lithographic system includes a lithographic apparatus and a scatterometer. In an embodiment, the lithographic apparatus includes an illumination optical system arranged to illuminate a pattern and a projection optical system arranged to project an image of the pattern on to a substrate. In an embodiment, the scatterometer includes a measurement system arranged to direct a beam of radiation onto a target pattern on said substrate and to obtain an image of a pupil plane representative of radiation scattered from the target pattern. A computational arrangement represents the pupil plane by moment functions calculated from a pair of orthogonal basis function and correlates the moment function to lithographic feature parameters to build a lithographic system identification. A control arrangement uses the system identification to control subsequent lithographic processes performed by the lithographic apparatus.

Abstract: A method controls scanning function of a lithographic apparatus. A monitor wafer is exposed to determine baseline control parameters pertaining to the scanning function. The baseline control parameters are retrieved from the monitor wafer. Parameter drift is determined from the baseline control parameters. Compensation is performed based on the determination. A different parameterization is used for control of the scanning control module than for communication between the scanning control module and the lithographic apparatus.

Abstract: System and methods estimate model parameters of a lithographic apparatus and control lithographic processing by a lithographic apparatus. An exposure is performed using a lithographic apparatus across a wafer. A set of predetermined wafer measurement locations is obtained. Discrete orthonormal polynomials are generated using the predetermined substrate measurement locations. The overlay errors arising from the exposure are measured at the predetermined locations to obtain overlay measurements. The estimated model parameters of the lithographic apparatus are calculated from the overlay measurements by using the discrete orthogonal polynomials as a basis function to model the overlay across the wafer. Finally, the estimated model parameters are used to control the lithographic apparatus in order to provide corrected overlay across the wafer.

Abstract: A lithographic system includes a lithographic apparatus comprising a projection system which projects a patterned radiation beam onto a target portion of a substrate and an alignment system which measures the position of a feature of the pattern on the substrate at a number of locations over the substrate. A controller compares the measured positions with points on a grid of values and extrapolates values for intermediate positions on the substrate based on values of corresponding intermediate points on the grid, so as to provide an indication of the intermediate positions on the substrate and their displacements relative to the grid. The grid is based on at least one orthogonal basis function, the measurement on the substrate being performed at positions corresponding to the root values of the at least one orthogonal basis function.

Abstract: A scatterometer configured to measure a property of a substrate, includes a radiation source configured to provide a radiation beam; and a detector configured to detect a spectrum of the radiation beam reflected from a target (30) on the surface of the substrate (W) and to produce a measurement signal representative of the spectrum. The apparatus includes a beam shaper (51, 53) interposed in the radiation path between the radiation source and the detector, the beam shaper being configured to adjust the cross section of the beam dependent on the shape and/or size of the target.

Abstract: A method and associated apparatus determine an overlay error on a substrate. A beam is projected onto three or more targets. Each target includes first and second overlapping patterns with predetermined overlay offsets on the substrate. The asymmetry of the radiation reflected from each target on the substrate is measured. The overlay error not resultant from the predetermined overlay offsets is determined. The function that enables calculation of overlay from asymmetry for other points on the wafer is determined by limiting the effect of linearity error when determining the overlay error from the function.

Abstract: A method for selecting sample positions on a substrate from a set of all available sample positions is provided, in which a representation of a model, which may represent the variation of one or more properties across the substrate, is analyzed in order to identify the sample positions having the greatest effect on the model.

Abstract: Variables in each step in a double patterning lithographic process are recorded and characteristics of intermediate features in a double patterning process measured. The final feature is then modeled, and the values of the variables optimized.