Integration method for directly analyzing interface statistics of periodic multilayers from X-ray scattering

Abstract

An integration method is demonstrated for directly determining the average interface statistics of periodic multilayers from the X-ray scattering diagram. By measuring the X-ray scattering diagram in the out-of-plane geometry and integrating the scattered intensity along the vertical momentum transfer qz in an interval, which is decided by the thickness ratio Γ (ratio of sublayer's thickness to periodic thickness), the cross-correlations between different interfaces are canceled and only the autocorrelations are reserved. Then the multilayer can be treated as a `single interface' and the average power spectral density can be obtained without assuming any vertical correlation model. This method has been employed to study the interface morphology of sputter-deposited W/Si multilayers grown at an Ar pressure of 1-7 mTorr. The results show an increase in vertical correlation length and a decrease in lateral correlation length with increased Ar pressure. The static roughness exponent α = 0 and dynamic growth exponent z = 2 indicate the Edwards-Wilkinson growth model at an Ar pressure of 1-5 mTorr. At an Ar pressure of 7 mTorr, α = 0.35 and z = 1.65 indicate the Kardar-Parisi-Zhang growth model.

Effect of Annealing on Stress, Microstructure, and Interfaces of NiV/B4C Multilayers

“…In contrast, perturbation theory treats scattering amplitude as a power series in roughness height and links it to the power spectral density (PSD) function without assuming any prior distribution of roughness height [26]. An integration method based on perturbation theory can be utilized to determine average interface statistics [27].…”