X-Ray Diffuse Scattering from Self-Organized Mesoscopic by Martin Schmidbauer

By Martin Schmidbauer

This monograph represents a severe survey of the phenomenal services of X-ray
diffuse scattering for the structural characterization of mesoscopic fabric platforms. The mesoscopic regime includes size scales starting from a couple of as much as a few countless numbers of nanometers. it's of specific relevance at semiconductor layer structures the place, for instance, interface roughness or low-dimensional items equivalent to quantum dots and quantum wires have attracted a lot curiosity. an intensive assessment of the current state of the art thought of X-ray diffuse scattering at mesoscopic buildings is given by means of a important description of varied experimental thoughts. chosen updated examples are mentioned. the purpose of the current e-book is to mix points of self-organized development of mesoscopic constructions with corresponding X-ray diffuse scattering experiments.

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52) holds for an arbitrary three-dimensional ensemble of mesoscopic structures. In the case of a single layer, only lateral correlation has to be considered. e. G(q) = G(q ). Consequently, lateral positional correlation leads to a rodlike structure of diffuse intensity perpendicular to the sample surface and a pronounced in-plane intensity modulation. For free-standing structures, the in-plane intensity distribution of diffuse scattering in the vicinity of h = 0 can be directly compared with the in-plane power spectrum P (qx , qy ) of the height profile h(x, y), as measured by atomic force microscopy, for example.

Several analytical models have been developed to describe the statistical electron density fluctuations. Among them are self-affine models with a cutoff length ξ which quantitatively describes the length up to which the self-affine regime is valid. This cutoff length is also referred to as the roughness correlation length and is different from the correlation lengths introduced in Sect. 4. For rather flat semiconductor surfaces, roughness is mostly connected with the step structure, and the evolution of steps is often related to the diffusion lengths on the surface and step–step interactions.

Therefore, the solutions in vacuum depend on the scattering geometry. The dynamical equations can be solved not only for a perfect semi-infinite crystal as sketched above, but also for multilayers. In this case the boundary conditions at each interface can be expressed as a matrix product. By using this matrix formalism, dynamical theory can be applied to laterally homogeneous ( (r) = (z)) layer systems [8, 10, 11, 12, 38]. In that case the wave field depends solely on the vertical z coordinate (growth direction).

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