L. Decaro et al., GENERALIZED LAUE DYNAMICAL THEORY FOR X-RAY REFLECTIVITY AT LOW AND HIGH-INCIDENCE ANGLES ON STRAINED MULTILAYERS, Physical review. B, Condensed matter, 56(15), 1997, pp. 9744-9752
In this work, we present a generalized dynamical theory for strained m
ultilayers within the Laue formalism valid for x-ray Bragg diffraction
. In the generalized theory we take into account all the four solution
s of the secular equation, the asymptotic sphericity of the dispersion
surface, the difference between electric and displacement fields, and
the boundary conditions of continuity at the heterointerfaces for the
tangential components of the electric and magnetic fields. Only the f
ollowing approximations are made: to consider a two-beam case, and to
neglect quadratic terms of the dielectric susceptibility. Our general
equations give the correct x-ray reflectivity in the whole angular ran
ge between 0 and pi/2, i.e., also very far from the Bragg peaks. Great
differences between the predictions of the conventional and generaliz
ed theories are obtained in several cases, for important features of t
he rocking curves, like angular position, peak intensity, and full wid
th at half maximum of superlattice satellite or epitaxial layer peaks.
We discuss in detail the following cases for which only the generaliz
ed theory describes correctly the x-ray scattering: coplanar diffracti
on (i) very far from the Bragg condition, (ii) near to the Bra,og cond
ition for strong asymmetric reflections, and (iii) for highly mismatch
ed heterostructures.