Abstract: A method and apparatus to measure overlay from images of metrology targets, images obtained using acoustic waves, for example images obtained using an acoustic microscope. The images of two targets are obtained, one image using acoustic waves and one image using optical waves, the edges of the images are determined and overlay between the two targets is obtained as the difference between the edges of the two images.

Abstract: Methods and apparatuses for estimation of at least one parameter of interest of a feature fabricated on a substrate, the feature having a plurality of structure parameters, the structure parameters including the at least one parameter of interest and one or more nuisance parameters. A receiver receives radiation scattered from one or more measured features on the substrate. A pupil generator generates an unprocessed pupil representation of the received radiation. A matrix multiplier multiplies a transformation matrix with intensities of each of a plurality of pixels of the unprocessed pupil representation to determine a post-processed pupil representation in which effects of the one or more nuisance parameters are mitigated or removed. A parameter estimator estimates the at least one parameter of interest based on the post-processed pupil representation.

Abstract: A structure of interest is irradiated with radiation for example in the x-ray or EUV waveband, and scattered radiation is detected by a detector (306). A processor (308) calculates a property such as linewidth (CD) by simulating interaction of radiation with a structure and comparing the simulated interaction with the detected radiation. A layered structure model (600, 610) is used to represent the structure in a numerical method. The structure model defines for each layer of the structure a homogeneous background permittivity and for at least one layer a non-homogeneous contrast permittivity. The method uses Maxwell's equation in Born approximation, whereby a product of the contrast permittivity and the total field is approximated by a product of the contrast permittivity and the background field. A computation complexity is reduced by several orders of magnitude compared with known methods.

Abstract: Disclosed is a method for reconstructing a parameter of a lithographic process. The method comprises the step of designing a preconditioner suitable for an input system comprising the difference of a first matrix and a second matrix, the first matrix being arranged to have a multi-level structure of at least three levels whereby at least two of said levels comprise a Toeplitz structure. One such preconditioner is a block-diagonal matrix comprising a BTTB structure generated from a matrix-valued inverse generating function. A second such preconditioner is determined from an approximate decomposition of said first matrix into one or more Kronecker products.

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 and apparatus of detection, registration and quantification of an image. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A structure of interest is irradiated with radiation for example in the x-ray or EUV waveband, and scattered radiation is detected by a detector (306). A processor (308) calculates a property such as linewidth (CD) by simulating interaction of radiation with a structure and comparing the simulated interaction with the detected radiation. A layered structure model (600, 610) is used to represent the structure in a numerical method. The structure model defines for each layer of the structure a homogeneous background permittivity and for at least one layer a non-homogeneous contrast permittivity. The method uses Maxwell's equation in Born approximation, whereby a product of the contrast permittivity and the total field is approximated by a product of the contrast permittivity and the background field. A computation complexity is reduced by several orders of magnitude compared with known methods.

Abstract: Parameters of a structure (900) are measured by reconstruction from observed diffracted radiation. The method includes the steps: (a) defining a structure model to represent the structure in a two- or three-dimensional model space; (b) using the structure model to simulate interaction of radiation with the structure; and (c) repeating step (b) while varying parameters of the structure model. The structure model is divided into a series of slices (a-f) along at least a first dimension (Z) of the model space. By the division into slices, a sloping face (904, 906) of at least one sub-structure is approximated by a series of steps (904?, 906?) along at least a second dimension of the model space (X). The number of slices may vary dynamically as the parameters vary. The number of steps approximating said sloping face is maintained constant. Additional cuts (1302, 1304) are introduced, without introducing corresponding steps.

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: 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.