X-ray reflection at nanometer multilayers

The constructive interference of electromagnetic waves is used for the X-ray reflection at periodical multilayer systems. If X-rays hit an interface in the multilayer a certain fraction of the incoming radiation will be reflected according to the reflection coefficients of the materials. Most of the radiation, however, will penetrate to deeper multilayer areas.

Nevertheless, in the case of constructive interference of all the reflected waves from different interfaces and different depths, a significant amount of the total incoming X-ray radiation will be reflected from the multilayer. The requirement for constructive interference is described by the generalized BRAGG equation, which can by derived in analogy to the X-ray reflection at lattice planes of crystals. However, at every interface the X-rays are weekly deflected. This has to be taken into account by the dispersion correction (δ = dispersion correction of the refractive index n = 1 - δ + iβ). Corrections due to absorption – described by β, the imaginary part of the refractive index – are not taken into account because of the assumption that β << δ is valid.