Abstract: A parameterized geometric model of a structure can be determined based on spectra from a wafer metrology tool. The structure can have geometry-induced anisotropic effects. Dispersion parameters of the structure can be determined from the parameterized geometric model. This can enable metrology techniques to measure nanostructures that have geometries and relative positions with surrounding structures that induce non-negligible anisotropic effects. These techniques can be used to characterize process steps involving metal and semiconductor targets in semiconductor manufacturing of, for example, FinFETs or and gate-all-around field-effect transistors.

Abstract: Automatic determination of Fourier harmonic order for computation of spectral information for diffraction structures described. An embodiment of a method includes automatically determining a Fourier harmonic order for computation of spectral information for periodic structures, wherein the determination of the Fourier harmonic order is based at least in part on the pitches in each of multiple directions of the periodic structures, material properties of the periodic structures, and characteristics of the periodic structures in which the materials are contained; and computing the spectral information for the periodic structures based at least in part on the determined Fourier harmonic order.

Abstract: A parameterized geometric model of a structure can be determined based on spectra from a wafer metrology tool. The structure can have geometry-induced anisotropic effects. Dispersion parameters of the structure can be determined from the parameterized geometric model. This can enable metrology techniques to measure nanostructures that have geometries and relative positions with surrounding structures that induce non-negligible anisotropic effects. These techniques can be used to characterize process steps involving metal and semiconductor targets in semiconductor manufacturing of, for example, FinFETs or and gate-all-around field-effect transistors.

Abstract: Methods and systems for performing broadband spectroscopic metrology with reduced sensitivity to grating anomalies are presented herein. A reduction in sensitivity to grating anomalies is achieved by selecting a subset of available system parameter values for measurement analysis. The reduction in sensitivity to grating anomalies enables an optimization of any combination of precision, sensitivity, accuracy, system matching, and computational effort. These benefits are particularly evident in optical metrology systems having large ranges of available azimuth angle, angle of incidence, illumination wavelength, and illumination polarization. Predictions of grating anomalies are determined based on a measurement model that accurately represents the interaction between the measurement system and the periodic metrology target under measurement. A subset of available system parameter values is selected to reduce the impact of grating anomalies on measurement results.

Abstract: Provided are optimized scatterometry techniques for evaluating a diffracting structure. In one embodiment, a method includes computing a finite-difference derivative of a field matrix with respect to first parameters (including a geometric parameter of the diffracting structure), computing an analytic derivative of the Jones matrix with respect to the field matrix, computing a derivative of the Jones matrix with respect to the first parameters, and computing a finite-difference derivative of the Jones matrix with respect to second parameters (including a non-geometric parameter). In one embodiment, a method includes generating a transfer matrix having Taylor Series approximations for elements, and decomposing the field matrix into two or more smaller matrices based on symmetry between the incident light and the diffracting structure.

Abstract: Automatic determination of Fourier harmonic order for computation of spectral information for diffraction structures described. An embodiment of a method includes automatically determining a Fourier harmonic order for computation of spectral information for periodic structures, wherein the determination of the Fourier harmonic order is based at least in part on the pitches in each of multiple directions of the periodic structures, material properties of the periodic structures, and characteristics of the periodic structures in which the materials are contained; and computing the spectral information for the periodic structures based at least in part on the determined Fourier harmonic order.

Abstract: Provided are optimized scatterometry techniques for evaluating a diffracting structure. In one embodiment, a method includes computing a finite-difference derivative of a field matrix with respect to first parameters (including a geometric parameter of the diffracting structure), computing an analytic derivative of the Jones matrix with respect to the field matrix, computing a derivative of the Jones matrix with respect to the first parameters, and computing a finite-difference derivative of the Jones matrix with respect to second parameters (including a non-geometric parameter). In one embodiment, a method includes generating a transfer matrix having Taylor Series approximations for elements, and decomposing the field matrix into two or more smaller matrices based on symmetry between the incident light and the diffracting structure.

Abstract: The above and other needs are met by a method of determining actual properties of a film stack by directing an incident beam of light towards the film stack, such that the incident beam of light is reflected from the film stack as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the film stack are estimated. A mathematical model of the film stack is solved with the estimated properties of the film stack, to yield theoretical properties of the reflected beam of light. The mathematical model is solved in part using a fast Z-matrix algorithm. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light, to yield a cost function. The estimated properties of the film stack are iteratively adjusted, and the mathematical model is iteratively solved, until the cost function is within a desired tolerance.

Abstract: A method of determining actual properties of layered media. An incident beam of light is directed towards the layered media, such that the incident beam of light is reflected from the layered media as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the layered media are estimated. A mathematical model of the layered media based on a modal function expansion is solved with the estimated properties of the layered media to yield theoretical properties of the reflected beam of light. The eigenvalues of the modal functions are computed recursively by recasting the eigenvalue equation in the following form: ?ni+1=F(?ni) where ?ni=the eigenvalue of the ith recursion and F is a function such that ?n=F(?n) is mathematically identical to the eigenvalue equation.

Abstract: A method of determining actual properties of layered media. An incident beam of light is directed towards the layered media, such that the incident beam of light is reflected from the layered media as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the layered media are estimated. A mathematical model of the layered media is solved with the estimated properties of the layered media to yield theoretical properties of the reflected beam of light. The mathematical model is solved using a diagonal T matrix algorithm. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light to yield a cost function. The estimated properties of the layered media are iteratively adjusted and the mathematical model is iteratively solved until the cost function is within a desired tolerance. The estimated properties of the layered media are reported as the actual properties of the layered media.

Abstract: A method of determining actual properties of layered media. An incident beam of light is directed towards the layered media, such that the incident beam of light is reflected from the layered media as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the layered media are estimated. A mathematical model of the layered media is solved with the estimated properties of the layered media to yield theoretical properties of the reflected beam of light. The mathematical model is solved using at least one of a modified T matrix algorithm and a Z matrix algorithm. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light to yield a cost function. The estimated properties of the layered media are iteratively adjusted and the mathematical model is iteratively solved until the cost function is within a desired tolerance.

Abstract: A method of determining the actual properties of a film stack. An incident beam of light is directed towards the film stack, such that the incident beam of light is reflected from the film stack as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the film stack are estimated. A mathematical model of the film stack is solved with the estimated properties of the film stack to yield theoretical properties of the reflected beam of light. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light to yield a cost function. The estimated properties of the film stack are iteratively adjusted and the mathematical model is iteratively solved until the cost function is within a desired tolerance. The estimated properties of the film stack are reported as the actual properties of the film stack.