Standing waves from a single heterostructure on GaAs – a computer experiment

Abstract

The phase, node position, intensity and integrated intensity of the standing-wave field have been calculated for a deformed layer on a perfect bulk as a function of angle of incidence and depth inside the crystal. The influence of the various parameters of the deformation, in particular the interface steepness, has been studied. It is found that nodes are never hooked to the deformed planes and that it is only for an incidence corresponding to the middle of the substrate peak that they are hooked to the bulk undeformed planes. The calculation has been applied to two particular situations corresponding to a relatively thick overlayer with an interface of about 100 unit cells, and to very thin overlayers with an interface two unit cells thick. In the latter case it is found that for a surface relaxation of 2% with respect to the bulk the minimum number of lattice planes above the interface for which it can no longer be assumed that the nodes remain hooked to the bulk is of the order of ten.

Theory and applications of x-ray standing waves in real crystals

“…18(b) coincidence between the experimental and theoretical curves is not perfect, that can be due to simplified bicrystal model, that does not take into account transition layer between the film and the substrate. In this situation the theoretical model with transition layer proposed in [71] can be useful for the analysis of the angular dependence of the fluorescence yield from the geterostructures.…”

X-ray transmissivity measurements using dynamical diffraction under grazing-incidence conditions

“…The simplest way would be to use specular reflection at the film/substrate interface. Such a reflection has already been used for instance for generating a standing-wave pattern allowing investigation of the deposited film (Bedzyk, Bommarito & Schildkraut, 1989;Authier, Gronkowski & Malgrange, 1989). It is not suitable however for our purpose since its amplitude is of the same order of magnitude as the reflections from other density gradients in the film and its effect is merely a contribution to the overall reflectivity of the system.…”

An exact solution in the dynamical diffraction theory of lamellarly distorted crystals

“…Remembering these flexibilities, as worked out by Authier et al (1989), one interesting topic is the application to the standing wave method, which affords valuable information about the atomic structure on the crystal surface and an interface between two perfect crystals. When the surface and the interface are associated with an intrinsic lattice distortion, the present theory must be useful for calculating the standing wave field.…”

“…Recently, Bensoussan, Malgrange & SauvageSimkin (1987) and Authier, Gronkowski & Malgrange (1989) worked out numerical calculations on a similar problem. Needless to say, the analytical solution gives more physical insight.…”