Effect of sidewall roughness on the diffraction efficiency of EUV high aspect ratio freestanding transmission gratings

Abstract

Manufacturing-induced sidewall roughness has a significant impact on the diffraction efficiency of extreme ultraviolet (EUV) gratings and masks, which could be evaluated by a Debye-Waller damping factor. The rough profile models of line structures are always parallel to the surface for the reflective elements. In this manuscript, a model of rough lines along the thickness direction is established, which cannot be ignored for high aspect ratio transmission gratings. Numerical calculations are carried out using both a rigorous model and a Fraunhofer approximation model. The two models agree with each other on the low-order transmission efficiencies, and the fitted Debye-Waller factor indicates a larger roughness value than that of the model due to the absorption of EUV irradiation for 90° sidewall angle. When the sidewall angle is smaller than 88°, an extra degree of freedom is introduced to the traditional Debye-Waller factor-based formula. The +1-order transmission efficiency and absorptivity with smooth and rough sidewalls are also analyzed, as well as the effect of incidence angle, wavelength and grating thickness.