Blazed silicon gratings for soft X-ray and extreme ultraviolet radiation: the effect of groove profile shape and random roughness on the diffraction efficiency

The effect of the groove profile shape and random roughness of the reflecting facet of five silicon diffraction gratings (1–4$^\circ$ blaze angle, period 0.4, 1.4, 2, and 4 $\mu$m, various coatings) operating in the soft X-ray and extreme ultraviolet radiation ranges on the outflow of the diffraction efficiency from working orders is studied. Diffraction gratings were fabricated by wet etching of Si(111) vicinal wafers and characterized by atomic force microscopy to determine the shape of the groove profile and roughness. The diffraction efficiency of gratings operating in classical and conical diffraction mounts was calculated based on realistic groove profiles by computer simulation using the PCGrate$^{\mathrm{TM}}$ code and taking into account the scattering intensity using Nevot–Croce or Debye–Waller corrections or using the Monte Carlo method (rigorously). The effect of the groove profile shape and roughness on the diffraction efficiency of the fabricated Si gratings is shown.