Calculating form-dependent optical scattering at vacuum- and extreme-ultraviolet wavelengths off nanoelectronic structures

Form birefringence, where the orientation of periodic structures yields effective refractive index differences between orthogonal polarizations, is the basis for several applications including the successful detection of aperiodic imperfections (e.g., defects in nanoelectronics) at visible and ultraviolet wavelengths. As shorter wavelengths are employed by industry, the key assumption behind form birefringence - that the wavelength is larger than the periodicity - is challenged even with decreasing device dimensions. Here, the form dependence of high spatial-frequency scattering off periodic structures is numerically assessed among deep-, vacuum-, and extreme-ultraviolet illumination wavelengths (DUV, VUV, EUV). Form-dependent scattering intensity ratios of the scattering off ideal periodic arrays decrease with wavelength into the VUV, but dramatically increase for the 47 nm EUV wavelength due primarily to the wavelength-dependent optical properties of the dielectrics involved. After adding a bridging defect to this array, the 47 nm wavelength remains most sensitive to these patterning faults. These results should be extensible, not only to structures in nanoelectronics, but also to emerging engineered optical materials for DUV and shorter wavelengths.