The inclusion of refraction effects in kinematic scattering theory pro
vides a powerful tool for describing diffuse scattering by X-ray refle
ctivity. The theory is applied to multilayers with roughened interface
s. Islands and miscut-induced steps as well as randomly oriented rough
ness are included in the theory. The interfacial roughness leads to a
broad, diffuse intensity distribution around the multilayer Bragg refl
ections. From the line shape, the morphology of the interfaces can be
deduced. The calculated profiles are compared with experimental data f
rom a 4x(Si/GexSi1-x) multilayer with vicinal interfaces. Clear side p
eaks are observed from which the mean island size and the average step
height are deduced, which are consistent with AFM images. (C) 1998 El
sevier Science B.V. All rights reserved.