Structural characterization and optimization of the diffraction properties of Si1-xGex gradient crystals grown by chemical vapor deposition

Klaus-Dieter Liss



Two theoretical models for the description of the diffraction properties of gradient crystals have been developed, one in the framework of the kinematical theory, the other within a transfer matrix formalism based on the dynamical theory of diffraction. The former gives analytical results that are well suited to describe the widths as well as the characteristic oscillations of the diffraction curves, while the second delivers the exact, extinction-limited intensity distributions. A matrix describes the coupling and the propagations of the forward- and Bragg-diffracted wave functions through a plane, parallel crystal lamella. It applies to the description of any crystalline medium with changes in the diffraction properties along the direction of the surface normal.

Experimentally, a crystal growth technique has been set up to produce novel Si1-xGex gradient crystals with 0 < x < 0.4 on a large surface and with growth rates of up to 0.6 µm/min. Layer thicknesses of several 100 µm have been achieved. The structure has been characterized by visual microscopy, electron microscopy, microprobe analysis, and their diffraction properties. The latter delivers both the mosaic distribution and the lattice parameter broadening due to the gradient. In particular, a tetragonal distortion attributed to different thermal expansion coefficients has been discovered. The anisotrope mosaic distribution gives evidence for the existence of misfit dislocations.

The reflection curves calculated by the transfer matrix method fit well with the experimental results. With the application for a neutron monochromator in mind, the diffraction data show an intensity increase of 25 related to the experimental resolution function. Comparing this value with the calculated reflectivity for perfect silicon, this factor increases to 40. For the sake of feasibility, however, the gradients have grown too rapidly, such that the maximal reflectivity of 100 % has not yet been achieved. In the present example, the widening of the lattice parameter is 70 times the natural line width of ideal silicon and has been pushed with Dd/d = 1.4·10-2 to the 700-fold value.

K.-D. Liß, Strukturelle Charakterisierung und Optimierung der Beugungseigenschaften von Si 1-x Ge x Gradientenkristallen, die aus der Gasphase gezogen wurden. Dissertation, Rheinisch Westfälische Technische Hochschule Aachen, (27 October 1994) 

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Last modified: 18. January 2004
Author: Klaus-Dieter Liß