Interface Induced Loss of Coherence in Superlattices
Extending our x-ray diffraction results obtained on amorphous/crystalline multilayers, we model the disorder at the interface of multilayered structures. In an actual x-ray scattering experiment, peak positions are related to atomic and layer periodicities (using Bragg’s equation), while linewidths are related (using Scherrer’s equation) to the number of scatterers whose positions obey these periodicities. The “coherence length”, evaluated for a periodicity, is this number times the periodicity. Assuming a perfect atomic structure of both materials in the multilayer, all loss of range order is induced by fluctuations at the interface. These fluctuations are either continuous variations in the distance between the two materials, and (or) are discrete variations in the number of atoms building up each layer, both giving rise to “roughness”. Obviously the latter will mainly influence the long range periodicities, while the small range periodicities (corresponding to high angle diffraction peaks) conserve their coherence length.