Abstract: A method for measuring a parameter of interest from a target and associated apparatuses. The method includes obtaining measurement acquisition data relating to measurement of the target and finite-size effect correction data and/or a trained model operable to correct for at least finite-size effects in the measurement acquisition data. At least finite-size effects in the measurement acquisition data is corrected for using the finite-size effect correction data and/or the trained model to obtain corrected measurement data and/or obtain a parameter of interest; and where the correcting does not directly determine the parameter of interest, determining the parameter of interest from the corrected measurement data.

Abstract: A system includes a radiation source and a phased array. The phased array includes optical elements, waveguides and phase modulators. The phased array generates a beam of radiation. The optical elements radiate radiation waves. The waveguides guide radiation from the radiation source to the optical elements. The phase modulators adjust phases of the radiation waves such that the radiation waves accumulate to form the beam. An amount of incoherence of the beam is based on randomization of the phases.

Abstract: A method for determining a characteristic of a feature in an object, the feature being disposed below a surface of the object is disclosed. The surface of the object is irradiated with a pulsed pump radiation beam so as to produce an acoustic wave in the object. The surface of the object is then irradiated with a measurement radiation beam. A portion of the measurement radiation beam scattered from the surface is received and a characteristic of the feature in the object is determined from at least a portion of the measurement radiation beam scattered from the surface within a measurement time period. A temporal intensity distribution of the pulsed pump radiation beam is selected such that in the measurement time period a signal to background ratio is greater than a signal to background ratio achieved using a single pulse of the pulsed pump radiation beam.

Abstract: A method of determining electromagnetic scattering properties of a finite periodic structure has the steps: 1002: Calculating a single-cell contrast current density, within a unit-cell supporting domain of a single one of a finite collection of unit cells. 1004: Calculating a scattered electric field outside the finite collection of unit cells, by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density. 1006: The Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells. The Green's function integrated with the determined single-cell contrast current density is obtained for observation points above the supporting domain with respect to a substrate underlying the finite periodic structure.

Abstract: An apparatus for determining a characteristic of a feature of an object comprises: a measurement radiation source; a measurement radiation delivery system; a measurement system; a pump radiation source; and a pump radiation delivery system. The measurement radiation source is operable to produce measurement radiation and the measurement radiation delivery system is operable to irradiate at least a part of a top surface of the object with the measurement radiation. The measurement system is operable to receive at least a portion of the measurement radiation scattered from the top surface and is further operable to determine a characteristic of the feature of the object from at least a portion of the measurement radiation scattered from the top surface.

Abstract: As increasing numbers of layers, using increasing numbers of specific materials, are deposited on substrates, it becomes increasingly difficult to detect alignment marks accurately for, for example, applying a desired pattern onto a substrate using a lithographic apparatus, in part due to one or more of the materials used in one or more of the layers being wholly or partially opaque to the radiation used to detect alignment marks. In a first step, the substrate is illuminated with excitation radiation. In a second step, at least one effect associated with a reflected material effect scattered by a buried structure is measured. The effect may, for example, include a physical displacement of the surface of the substrate. In a third step, at least one characteristic of the structure based on the measured effect is derived.

Abstract: An apparatus for determining a characteristic of a feature of an object comprises: a measurement radiation source; a measurement radiation delivery system; a measurement system; a pump radiation source; and a pump radiation delivery system. The measurement radiation source is operable to produce measurement radiation and the measurement radiation delivery system is operable to irradiate at least a part of a top surface of the object with the measurement radiation. The measurement system is operable to receive at least a portion of the measurement radiation scattered from the top surface and is further operable to determine a characteristic of the feature of the object from at least a portion of the measurement radiation scattered from the top surface.

Abstract: A method for determining a characteristic of a feature in an object, the feature being disposed below a surface of the object is disclosed. The surface of the object is irradiated with a pulsed pump radiation beam so as to produce an acoustic wave in the object. The surface of the object is then irradiated with a measurement radiation beam. A portion of the measurement radiation beam scattered from the surface is received and a characteristic of the feature in the object is determined from at least a portion of the measurement radiation beam scattered from the surface within a measurement time period. A temporal intensity distribution of the pulsed pump radiation beam is selected such that in the measurement time period a signal to background ratio is greater than a signal to background ratio achieved using a single pulse of the pulsed pump radiation beam.

Abstract: As increasing numbers of layers, using increasing numbers of specific materials, are deposited on substrates, it becomes increasingly difficult to detect alignment marks accurately for, for example, applying a desired pattern onto a substrate using a lithographic apparatus, in part due to one or more of the materials used in one or more of the layers being wholly or partially opaque to the radiation used to detect alignment marks. In a first step, the substrate is illuminated with excitation radiation. In a second step, at least one effect associated with a reflected material effect scattered by a buried structure is measured. The effect may, for example, include a physical displacement of the surface of the substrate. In a third step, at least one characteristic of the structure based on the measured effect is derived.

Abstract: A method for calculating electromagnetic scattering properties of a finite periodic structure having a direction of periodicity is disclosed. The method numerically calculates electromagnetic scattering properties using spatial discretization in the direction of periodicity and numerically calculates electromagnetic scattering properties using spectral discretization in a direction orthogonal to the direction of periodicity.

Abstract: In scatterometry, a merit function including a regularization parameter is used in an iterative process to find values for the scattering properties of the measured target. An optimal value for the regularization parameter is obtained for each measurement target and in each iteration of the iterative process. Various methods can be used to find the value for the regularization parameter, including the Discrepancy Principle, the chi-squared method and novel modifications of the Discrepancy Principle and the chi-squared method including a merit function.

Abstract: A method of determining electromagnetic scattering properties of a finite periodic structure has the steps: 1002: Calculating a single-cell contrast current density, within a unit-cell supporting domain of a single one of a finite collection of unit cells. 1004: Calculating a scattered electric field outside the finite collection of unit cells, by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density. 1006: The Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells. The Green's function integrated with the determined single-cell contrast current density is obtained for observation points above the supporting domain with respect to a substrate underlying the finite periodic structure.

Abstract: A reconstruction process includes measuring structures formed on a substrate by a lithographic process, determining a reconstruction model for generating modeled patterns, computing and minimizing a multi-variable cost function including model errors. Errors induced by nuisance parameters are modeled based on statistical description of the nuisance parameters' behavior, described by probability density functions. From the statistical description model errors are calculated expressed in terms of average model errors and weighing matrices. These are used to modify the cost function so as to reduce the influence of the nuisance parameters in the reconstruction, without increasing the complexity of the reconstruction model. The nuisance parameters may be parameters of the modeled structure, and/or parameters of an inspection apparatus used in the reconstruction.

Abstract: A reconstruction process includes measuring structures formed on a substrate by a lithographic process, determining a reconstruction model for generating modeled patterns, computing and minimizing a multi-variable cost function including model errors. Errors induced by nuisance parameters are modeled based on statistical description of the nuisance parameters' behavior, described by probability density functions. From the statistical description model errors are calculated expressed in terms of average model errors and weighing matrices. These are used to modify the cost function so as to reduce the influence of the nuisance parameters in the reconstruction, without increasing the complexity of the reconstruction model. The nuisance parameters may be parameters of the modeled structure, and/or parameters of an inspection apparatus used in the reconstruction.

Abstract: In scatterometry, a merit function including a regularization parameter is used in an iterative process to find values for the scattering properties of the measured target. An optimal value for the regularization parameter is obtained for each measurement target and in each iteration of the iterative process. Various methods can be used to find the value for the regularization parameter, including the Discrepancy Principle, the chi-squared method and novel modifications of the Discrepancy Principle and the chi-squared method including a merit function.

Abstract: A library of model diffraction patterns is generated where each represents a diffraction pattern expected from a target structure defined by a set of parameters and having a first part and a second part, the first part comprising a scattering object. The target structure is defined. The scattering effect of the first part of the target structure is defined by a set of first part parameters, for a plurality of different sets of first part parameters. The scattering effect of the second part of the target structure defined by a set of second part parameters, for a plurality of different sets of second part parameters. The results of the calculations is used to calculate the model diffraction patterns.

Abstract: An apparatus and method to determine overlay of a target on a substrate (6) by measuring, in the pupil plane (40) of a high numerical aperture len (L1), an angle-resolved spectrum as a result of radiation being reflected off the substrate. The overlay is determined from the anti-symmetric component of the spectrum, which is formed by subtracting the measured spectrum and a mirror image of the measured spectrum. The measured spectrum may contain only zeroth order reflected radiation from the target.

Abstract: A projection operator framework is described to analyze the concept of localized normal-vector fields within field-material interactions in a spectral basis, in isotropic and anisotropic media. Generate a localized normal-vector field n in a region of the structure defined by the material boundary, decomposed into sub-regions with a predefined normal-vector field and possibly corresponding closed-form integrals. Construct a continuous vector field F using the normal-vector field to select continuous components ET and Dn. Localized integration of normal-vector field n over the sub-regions to determine coefficients of, C. Determine components Ex, Ey, Ez of the electromagnetic field by using field-material interaction operator C to operate on vector field F. Calculate electromagnetic scattering properties of the structure using the determined components of the electromagnetic field.

Abstract: Numerical calculation of electromagnetic scattering properties and structural parameters of periodic structures is disclosed. A reflection coefficient has a representation as a bilinear or sesquilinear form. Computations of reflection coefficients and their derivatives for a single outgoing direction can benefit from an adjoint-state variable. Because the linear operator is identical for all angles of incidence that contribute to the same outgoing wave direction, there exists a single adjoint-state variable that generates all reflection coefficients from all incident waves that contribute to the outgoing wave. This adjoint-state variable can be obtained by numerically solving a single linear system, whereas one otherwise would need to solve a number of linear systems equal to the number of angles of incidence.

Abstract: Scatterometry method and apparatus are useful in a lithographic apparatus and device manufacturing. A back focal plane diffraction intensity image of a measurement projection system configured to project a radiation beam onto a target portion of a substrate is measured. A beam of radiation having a first wavelength is directed to the substrate. A diffraction image of a zeroth diffraction order and higher order diffraction from a diffraction structure in the substrate is provided. A first layer (4) of the diffractionstructure provides a diffraction image having only a zeroth diffraction order. A second layer (5) has a periodic structure (6a, 6b) configured such that a lowest spatial frequency of the periodic structure is lower than spatial frequencies of interest of the first structure. From the diffraction image originating from diffraction of the radiation beam in both the first and second layer a critical dimension metrology parameter is determined.