Fe/Au multilayer growth fronts: Comparison of X-ray diffuse scattering results with atomic-force microscopy profiles

Abstract

The interfacial roughness morphology of sputtered Fe/Au multilayers was derived by combining the results from X-ray specular and non-specular (diffuse) scattering. From the non-specular intensity collected by a two-dimensional image plate we determined the in-plane height–height correlation function 〈 H i( R) H i(0)〉 and the growth correlation length as a function of feature size. From these parameters we determined both the static and dynamic roughness exponents α and z, which agree with the Kardar–Parisi–Zhang (KPZ) model of surface growth. The height difference function derived from the diffuse scattering is compared with several model functions that incorporate the asymptotic behavior of 〈 H( R) 2〉 for the cases of R→0 and R→∞. We show that only one particular function is appropriate. The evolution of the interfacial slope is determined from the roughness exponents, and it is shown that it decreases as a function of time. This asymptotic smoothing is analyzed using the noiseless and stochastic KPZ equations. The noiseless KPZ equation predicts that the growth front is composed of paraboloids, which increase in lateral size and coalesce. This result is supported by an Atomic-force Microscopy measurement of the surface of one of the Fe/Au Multilayers.