Abstract
X-ray reflectometry is a powerful tool for investigations on rough surface and interface structures of multilayered thin film materials. The X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. However, in previous studies, the calculations of the X-ray reflectivity often show a strange effect where interference effects would increase at a rough surface. And estimated surface and interface roughnesses from the X-ray reflectivity measurements did not correspond to the TEM image observation results. The strange result had its origin in a used equation due to a serious mistake in which the Fresnel transmission coefficient in the reflectivity equation is increased at a rough interface because of a lack of consideration of diffuse scattering. In this review, a new accurate formalism that corrects this mistake is presented. The new accurate formalism derives an accurate analysis of the X-ray reflectivity from a multilayer surface of thin film materials, taking into account the effect of roughness-induced diffuse scattering. The calculated reflectivity by this accurate reflectivity equation should enable the structure of buried interfaces to be analyzed more accurately.
Highlights
X-rays scattered from a material surface at a glancing angle of incidence provide a wealth of information on the structure of the surface layer of materials
We show that the strange result has its origin in a currently used equation due to a serious mistake in which the Fresnel transmission coefficient in the reflectivity equation is increased at a rough interface, and the increase in the transmission coefficient completely overpowers any decrease in the value of the reflection coefficient because of Journal of Materials
These coefficients for refraction obviously contain a mistake because the penetration of X-rays should decrease at a rough interface because of diffuse scattering
Summary
X-ray reflectometry is a powerful tool for investigations on rough surface and interface structures of multilayered thin film materials. The X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. In previous studies, the calculations of the X-ray reflectivity often show a strange effect where interference effects would increase at a rough surface. The strange result had its origin in a used equation due to a serious mistake in which the Fresnel transmission coefficient in the reflectivity equation is increased at a rough interface because of a lack of consideration of diffuse scattering. The new accurate formalism derives an accurate analysis of the X-ray reflectivity from a multilayer surface of thin film materials, taking into account the effect of roughness-induced diffuse scattering.
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