Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates

Abstract

Scatterometry as a non-imaging indirect optical method in wafer metrology is also relevant to lithography masks designed for extreme ultraviolet lithography, where light with wavelengths in the range of 13 nm is applied. The solution of the inverse problem, i.e. the determination of periodic surface structures regarding critical dimensions (CD) and other profile properties from light diffraction patterns, is incomplete without knowledge of the uncertainties associated with the reconstructed parameters. The numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution of the two-dimensional Helmholtz equation. The inverse problem can be formulated as a nonlinear operator equation in Euclidean space. The operator maps the sought mask parameters to the efficiencies of diffracted plane wave modes. We employ a Gauß–Newton type iterative method to solve this operator equation and end up minimizing the deviation of the measured efficiency or phase shift values from the calculated ones. We apply our reconstruction algorithm for the measurement of a typical EUV mask composed of TaN absorber lines of about 80 nm height, a period in the range of 420 nm–840 nm, and with an underlying MoSi-multilayer stack of 300 nm thickness. Clearly, the uncertainties of the reconstructed geometric parameters essentially depend on the uncertainties of the input data and can be estimated by various methods. We apply a Monte Carlo procedure and an approximative covariance method to evaluate the reconstruction algorithm. Finally, we analyze the influence of uncertainties in the widths of the multilayer stack by the Monte Carlo method.

Scatterometry sensitivity analysis for conical diffraction versus in-plane diffraction geometry with respect to the side wall angle

“…In recent years we investigated goniometric EUV scatterometry at line-grating test structures with respect to the determination of the line profile parameters like width, height and side wall angle (SWA) . [1][2][3][4] With respect to width and height the attainable uncertainties are well in line with the requirements of the ITRS metrology roadmap. For the SWA, however, the required uncertainty well below 1 • is still challenging for metrology and mask manufacturing.…”

Comparison of CD measurements of an EUV photomask by EUV scatterometry and CD-AFM

“…For H4, an additional solution is shown representing an adjacent local minimum of the Χ 2 -function. It is known that the Χ 2 -function shows periodic local minima with respect to the height at λ/2 period 22 . The height as determined by AFM is systematically higher and the values are not consistent with scatterometry within their respective uncertainties.…”

“…Neglecting the influence of LER and LWR and multilayer variability in our model, the statistical measurement uncertainties as estimated with MLE are about 10% to 20% while the actual measurement uncertainty is only 1% to 3%. Earlier studies addressing the scatterometry uncertainty budget 21,22 have already emphasized the great importance of systematic errors.…”

“…Slight thickness variations in the repeating groups can, however, lead to fluctuations of several percent in the measured efficiencies. The impact of such variations of the MLS on the reconstructed CDs has been investigated with a least squares method 22 . Here, we include the heights of the two capping layers and the overall height of the repeated groups as additional variables that need to be determined additionally in the MLE-based solution of the inverse problem.…”

Atomic force microscope caliper for critical dimension measurements of micro and nanostructures through sidewall scanning

“…Conventional optical microscopy has inherent optical diffraction limitation while scatterometry require priori sample surface information and rigorous modeling for data extraction [9,10]. Electron-based metrology instruments, including CD scanning electron microscopy (CD-SEM) [11] and transmission electron microscopy (CD-TEM) [12], are commonly used methods.…”