Influence of roughness distributions and correlations on x-ray diffraction from superlattices

Abstract

Interfacial roughness in superlattices is currently a topic of significant interest as a result of its impact on device applications and its influence on thin-film phenomena. In this work we examine the effects of interfacial roughness on x-ray diffraction from superlattices. By means of a Taylor expansion of the amplitude reflection coefficient of the multilayer, we present general expressions for the specular, diffuse, and total diffracted intensity from a rough multilayer and examine how these quantities are influenced by roughness distributions and correlations among the interfaces. We present analytical solutions for exemplary structures including superlattices with no roughness, correlated roughness, uncorrelated roughness, and partially correlated roughness. We also present a model for cumulative roughening in multilayers and characterize its diffraction signature. We show how specific configurations of interfacial roughness give rise to a variety of additional features in diffraction spectra beyond the customary pseudo-Debye-Waller attenuation. Specifically, we illustrate how roughness distributions induce broadening of the diffraction features, and how modulations in the diffuse scattering result directly from interfacial roughness correlations. We also show that partial correlation of interfacial roughness constitutes a second important source of peak broadening.