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Assessing form-dependent optical scattering at vacuum- and extreme-ultraviolet wavelengths off nanostructures with two-dimensional periodicity



Bryan M. Barnes, Mark Alexander Henn, Martin Y. Sohn, Hui Zhou, Richard M. Silver


Several metamaterials and nanostructures are form birefringent, exhibiting effective refractive index differences for orthogonal polarizations due to the placement of subwavelength features if the periodicity is smaller than the incident wavelength. As the wavelength decreases below the periodic spacing, form birefringence must be replaced due to high spatial-frequency scattering with form-dependent scattering. For the first time, this form-dependent scattering off technologically relevant two-fold periodic patterns is numerically assessed for deep-, vacuum-, and extreme-ultraviolet illumination wavelengths (DUV, VUV, EUV). Simulations are performed for two geometries as found in nanoelectronics, both as ideal periodic arrays and with a bridging feature that breaks the local periodic symmetry. For periodic layouts, form- dependent scattering intensity ratios decrease with wavelength in the DUV and VUV, but dramatically increase for the 47 nm EUV wavelength due to the wavelength-dependent optical properties of the dielectrics modeled. With an added bridging feature, form-dependent scattering is observed at all five modeled wavelengths with the optimal polarization axis aligned with the long axis of these bridges for all wavelengths except 47 nm. This EUV wavelength is the most sensitive to these pattering faults, which is advantageous for defect inspection in nanoelectronics, with its optimal polarization axis aligned to the long axis of the periodic structure. At each wavelength, the available optical hardware is incorporated as a constraint and the impact of known source intensities is addressed. These clearly defined simulation methodologies for this challenging wavelength range should be extensible to future engineered optical materials designed for DUV and shorter wavelengths.
Physical Review Applied


form birefringence, applied classical electromagnetism, image forming and processing, diffraction and scattering, finite-difference methods


Barnes, B. , , M. , Sohn, M. , Zhou, H. and Silver, R. (2019), Assessing form-dependent optical scattering at vacuum- and extreme-ultraviolet wavelengths off nanostructures with two-dimensional periodicity, Physical Review Applied, [online], (Accessed April 14, 2024)
Created June 24, 2019, Updated July 2, 2019