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: 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: A method of measuring a property of a substrate includes generating a patterned mask configured to cause a radiation beam passing through the mask to acquire the pattern, simulating radiating the substrate with a patterned radiation beam that has been patterned using the mask to obtain a simulated pattern, determining at least one location of the simulated pattern that is prone to patterning errors, and irradiating the substrate with the patterned radiation beam using a lithographic process. The method also includes measuring an accuracy of at least one property of the at least one location of the pattern on the substrate that has been determined as being prone to patterning errors, and adjusting the lithographic process according to the measuring.

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.

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: 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: Reconstruction of an object by which radiation is diffracted is disclosed. Specifically, the reconstruction includes: estimating the object shape; deriving a model diffraction pattern from the estimated shape; illuminating the object with radiation; detecting a diffraction pattern of radiation diffracted by the object; comparing the model diffraction pattern and the detected diffraction pattern; and determining the actual object shape from the difference between the model diffraction pattern and the detected diffraction pattern, wherein the model diffraction pattern is determined using Bloch Mode Expansion.

Abstract: A method of measuring a property of a substrate includes generating a patterned mask configured to cause a radiation beam passing through the mask to acquire the pattern, simulating radiating the substrate with a patterned radiation beam that has been patterned using the mask to obtain a simulated pattern, determining at least one location of the simulated pattern that is prone to patterning errors, and irradiating the substrate with the patterned radiation beam using a lithographic process. The method also includes measuring an accuracy of at least one property of the at least one location of the pattern on the substrate that has been determined as being prone to patterning errors, and adjusting the lithographic process according to the measuring.

Abstract: A lithographic apparatus according to one embodiment includes an alignment system for aligning a substrate. The alignment system comprises an illuminator system configured to illuminate an alignment mark on the substrate with an illumination spot, the alignment mark comprising a plurality of lines and spaces. The system also includes a combiner system configured to transfer two images of the illuminated alignment mark without spatial filtering of the images, rotate the images 180° relatively to each other, and combine the two images; and a detection system configured to detect an alignment signal from the combined images and to determine a unique alignment position by selecting a specific one of extreme values in the detected alignment signal.

Abstract: Reconstruction of an object by which radiation is diffracted is disclosed. Specifically, the reconstruction includes: estimating the object shape; deriving a model diffraction pattern from the estimated shape; illuminating the object with radiation; detecting a diffraction pattern of radiation diffracted by the object; comparing the model diffraction pattern and the detected diffraction pattern; and determining the actual object shape from the difference between the model diffraction pattern and the detected diffraction pattern, wherein the model diffraction pattern is determined using Bloch Mode Expansion.

Abstract: A lithographic apparatus according to one embodiment of the invention includes an alignment subsystem configured to align the substrate on the substrate table relative to the patterning structure. The alignment structure comprises a non-periodic feature which may be detectable as e.g. a capture position or a check position using a reference grating in the alignment subsystem. The non-periodic feature may cause a phase effect in the detected signal of the alignment subsystem or an amplitude effect.

Abstract: A lithographic apparatus according to one embodiment of the invention includes an alignment subsystem configured to align the substrate on the substrate table relative to the patterning structure. The alignment structure comprises a non-periodic feature which may be detectable as e.g. a capture position or a check position using a reference grating in the alignment subsystem. The non-periodic feature may cause a phase effect in the detected signal of the alignment subsystem or an amplitude effect.

Abstract: A lithographic apparatus according to one embodiment of the invention includes an alignment subsystem configured to align the substrate on the substrate table relative to the patterning structure. The alignment structure comprises a non-periodic feature which may be detectable as e.g. a capture position or a check position using a reference grating in the alignment subsystem. The non-periodic feature may cause a phase effect in the detected signal of the alignment subsystem or an amplitude effect.