Advances in Optical and Magnetooptical Scatterometry of Periodically Ordered Nanostructured Arrays

Abstract

We review recent advances in optical and magnetooptical (MO) scatterometry applied to periodically ordered nanostructures such as periodically patterned lines, wires, dots, or holes. The techniques are based on spectroscopic ellipsometry (SE), either in the basic or generalized modes, Mueller matrix polarimetry, and MO spectroscopy mainly based on MO Kerr effect measurements. We briefly present experimental setups, commonly used theoretical approaches, and experimental results obtained by SE and MO spectroscopic analyses of various samples. The reviewed analyses are mainly related to monitoring optical critical dimensions such as the widths, depths, and periods of the patterned elements, their real shapes, and their line edge or linewidth roughness. We also discuss the advantages and disadvantages of the optical spectroscopic techniques compared to direct monitoring techniques.

Characterization of the Inverse Problem in Critical Dimension Measurement of Diffraction Gratings

“…When working with the inverse problem, we assume that the material parameters (they can be measured easily with a reference flat sample) and grating period (Λ = (Λ x , Λ y , Λ z )) are known (since it is relatively easy to control during manufacturing), and that the sum d 1 + d 2 is fixed (see Fig. 1 for details) [14]. This leaves d 1 and b as independent input variables.…”

“…The error between a measurement and a calculated value can be characterized by angular distance between the measured and simulated points plotted on Poincaré's sphere [7]. This distance is specified by the azimuthal angle 2Ψ and the polar angle ∆, i.e., Using synthetic data corrupted by a Gaussian noise (this is reasonable to assume, given that the measurement setup is a null-zone ellipsometer [14,18], which measures the angles themselves [19]), fits were done for several virtual measurements. The aim was to generate output data with noise and try to find the original input by minimizing the sum of errors squared (so the Euclidean norm) over a certain number of measurements on different wavelengths, then to find the relationship between the error of the fit and the density of states on the output map.…”

“…A certain diffraction grating has been studied extensively using SE and MOSS at the Division of Magnetooptics, Charles University in Prague [14,18]. The geometrical situation can be seen in Fig.…”

“…A similar comparison can be seen in the case of zeroth order (26 nm, 100 nm) and (5 nm, 200 nm) at 60 degrees of incidence. Fits were performed for the dimensions of the grating studied in [14,18] as well.…”

Magneto-optical spectrum analyzer

“…When reflecting off the sample, linearly polarized lights gains both an ellipticity ( K ) and a rotation of the major polarization axis, known as the Kerr angle (θ K ). For out-of-plane saturated Permalloy, the polar Kerr angle is typically 1 mrad 16 . Both the sign and magnitude of this angle depend on the sign and magnitude of the out-of-plane magnetization of the probed area.…”