The microstructure of Mo/Si multilayers grown by magnetron and ion beam sputter deposition has been characterized over a range of Mo layer thicknesses. We observe an abrupt amorphous-to-crystalline transition in the Mo layers at a thickness of ∼2 nm. The transition exhibits several interesting features including a large decrease in the thickness of the Si-on-Mo interlayer and a significant increase in the roughness of the multilayer. We present an explanation for the transition behavior in terms of a critical thickness for the nucleation of Mo crystallites.

We present a rigorous theoretical treatment of nonspecular x-ray scattering in a distributed imaging system consisting of multilayer-coated reflective optics. The scattering from each optical surface is obtained using a vector scattering theory that incorporates a thin film growth model to provide a realistic description of the interfacial roughness of the multilayer coatings. The theory is validated by comparing calculations based on measured roughness to experimental measurements of nonspecular scattering from a Mo–Si multilayer coating. The propagation of the scattered radiation through the optical system is described in the context of transfer function theory. We find that the effect of nonspecular scattering is to convolve the image with a point spread function that is independent of the coherence of the object illumination. For a typical soft x-ray imaging system, the scattering within the image field from the multilayer coatings is expected to be slightly greater than for single surfaces (as normalized to the reflectivity). This is because the roughness of the coatings includes both replication of the substrate roughness and the intrinsic roughness of the multilayer growth process. Our analysis indicates that the current multilayer coating technology is capable of producing soft x-ray imaging systems that have acceptably low levels of scattering, provided that the optical substrates are sufficiently smooth.

A general theory is developed for the scattering of x rays from a single nonideal interface between two dielectric media. It is then extended to describe the scattering of x rays from a multilayer structure composed of many nonideal interfaces. The most unique feature of this theory is that there are no constraints on the physical structure of the interfaces; the interfaces can have any form of roughness or compositional inhomogeneity. A simple analytical expression is derived for both the near and far radiation field to first order, assuming that the scattering is weak. The theory is valid for arbitrary polarization and at all angles of incidence (measured from the normal) less than the critical angle for total external reflection. Finally, the results are applied to study the effect of different interface structures on the performance of multilayer x-ray optics.

Scattering of the multilayer coatings used for our normal incidence soft x-ray telescope at λ=63.5 Å has been measured at λ=1.54 Å and grazing angles of incidence and at soft x rays near normal incidence. Furthermore, the edge of the moon is used as a known test target to estimate the amount of scattering in the arcsec range from images obtained on the date of the solar eclipse on July 11, 1991. The internal surfaces of the coating are inspected by high-resolution electron microscopy. A theoretical model describing the evolution and replication of roughness from layer to layer throughout the structure, which is in agreement with all experimental data is presented. We find that practically all roughness caused by the growth of the multilayer structure occurs at spatial frequencies which are too high to produce scattering. The substrate roughness is replicated at lower spatial frequencies which might produce scattering within the field of view of an instrument. However, roughness in this range is below the 0.5 Å level again resulting in insignificant amounts of scatter.

Articles you may be interested inLevel-set multilayer growth model for predicting printability of buried native extreme ultraviolet mask defects J. Vac. Sci. Technol. B 33, 021602 (2015); 10.1116/1.4913315Effect of electrostatic chucking and substrate thickness uniformity on extreme ultraviolet lithography mask flatness J.An approximate method is proposed to calculate the extreme ultraviolet ͑EUV͒ scattering from a defect within a multilayer coating. In this single surface approximation ͑SSA͒ the defective multilayer structure is replaced by a single reflecting surface with the shape of the top surface of the multilayer. The range of validity of this approximation has been investigated for Gaussian line defects using two-dimensional finite-difference-time-domain simulations. The SSA is found to be valid for sufficiently low aspect ratio defects such as those expected for the critical defects nucleated by particles on the mask substrate. The critical EUVL defect size is calculated by combining the SSA with a multilayer growth model and aerial image simulations. Another approximate method for calculating the aerial image of an unresolved defect is also discussed. Although the critical substrate defects may be larger than the resolution of higher numerical aperture cameras, the point defect approximation provides a useful framework for understanding the printability of a wide range of defects.