Metrology of nano-objects with Mueller polarimetry
A) Characterization of metrological targets (1D diffraction gratings, critical dimensions < 100 nm) in conical diffraction with spectroscopic MM polarimeter operating in visible wavelength range.
Reflection of polarized light by 1D diffraction grating in conical diffraction configuration leads to the cross-talk of two polarization eigenstates that, in turn, results in all non-zero elements of Mueller matrix, contrary to planar diffraction configuration. When solving the inverse metrological problem, namely, reconstructing grating geometry from the measured zeroth order Mueller matrix spectra, this additional non-redundant information reduces the correlation of parameters of grating model. The theoretical studies and development of the numerical algorithms for the simulation of polarized light diffraction on periodic structures using spectral rigorous coupled wave analysis (RCWA) in planar and conical diffraction were performed. They resulted in creation of the in-house software for solving both direct and inverse problems of the diffraction of polarized light using Mueller matrix formalism. Extensive simulations for the interpretation of experimental data allowed choosing the most sensitive alignment configurations to perform the measurements. We have demonstrated that using visible wavelength range complete spectral Mueller polarimetry data measured at conical diffraction configuration allows reconstructing the critical dimensions of metrological structures:
• with an accuracy better than that of a conventional ellipsometer;
• with a speed better than that of atomic force microscopy and scanning electron microscopy (SEM)
• non-destructively unlike the SEM.
Left panel: SEM image of the cleaved diffraction grating (photoresist on silicon): pitch 240 nm, CD – 70 nm, height – 220 nm. White bar: 200 nm. Thin black curve: profile is obtained by fitting polarimetric spectra with symmetric trapezoid model. Right panel: Maps of D2 calculated versus A and L with symmetric trapezoid model and all Mueller matrix spectral coefficients (top row) partial (M14, M13 M34, M33 coefficients only) Mueller matrices (middle row) measured at different azimuthal angles. Maps of D2 calculated versus A and B with asymmetric trapezoid model and all Mueller matrix spectral coefficients measured at different azimuth angles
Appl. Opt. 45(16) 3688 (2006) https://doi.org/10.1364/AO.45.003688
Opt. Express, 15 (5), 2033 (2007) https://doi.org/10.1364/OE.15.002033
B) Mueller polarimetry as a tool for evaluation of asymmetry of diffraction structures
Both experimentally and numerically we demonstrated that the break of 1D diffraction grating profile mirror symmetry leads to the loss of transposition invariance of corresponding zeroth order Mueller matrix measured in conical diffraction.
Left panel: nanoimprint master gratings made with e-beam lithography and wet etching in a polymethyl methacrylate layer, spin-coated on a chromium-covered glass substrate (15cmx15cm), 2 insets show asymmetric grating profile from AFM measurements. Right panel: experimental spectral Mueller matrices of asymmetric gratings measured at the angle of incidence 70° and azimth angles 90° (red line) and 270° (blue circles)
We were the first to suggest exploiting this property for the overlay characterization problem in microelectronics. To avoid mechanical rotation of a sample the reflection Fourier Mueller microscope was built for the measurements of angular resolved Mueller matrices by imaging a back focal plane of high NA microscope objective. Linear dependence of scalar estimator calculated from the elements of back focal plane Mueller matrix on small values of overlay error was predicted by numerical simulations and found experimentally. Thus, using Mueller polarimetry in back focal plane for overlay detection does not require the numerical solution of the inverse electromagnetic problem of polarized light scattering on periodic structures provided two calibrated target with known overlay values are available. Another advantage of this approach is the ability to perform the measurements in smaller metrological boxes compared to currently available metrological techniques. This project was funded by French ANR MuellerFourier (2009-2011), partners – CEA/LETI (Grenoble), Horiba Jobin Yvon (Chilly Mazarin).
Left panel: schematic cross-section of overlay metrological target. Middle and right panels: back focal plane simulated and measured images of element |M14 –M41| of overlay target with CDtop=300 nm, CDbot=150 nm, nominal overlay value of 50 nm. Circles of different radius correspond to different incidence angles; red lines show data for different azimuth angles. Measurement wavelength is 633 nm.
J. Vac. Sci. Technol. B, 29(5) 051804-051804-6 (2011) doi: 10.1116/1.3633693
J. Micro/Nanolith. MEMS MOEMS 10, 033017 (2011) doi: 10.1117/1.3626852