# Strukturelle Charakterisierung und Optimierung der Beugungseigenschaften von Si(1-x)Ge(x) Gradientenkristallen, die aus der Gasphase gezogen wurden

## TL;DR

This paper develops two models to describe the diffraction properties of Si(1-x)Ge(x) gradient crystals and reports on their experimental growth, revealing structural distortions and improved diffraction performance.

## Contribution

It introduces a transfer matrix model for gradient crystal diffraction and demonstrates the successful growth of SiGe crystals with enhanced properties.

## Key findings

- Transfer matrix model accurately predicts diffraction curves.
- Crystals exhibit tetragonal distortion due to thermal effects.
- Diffraction intensity increases by 25-40 times compared to perfect silicon.

## Abstract

Two theoretical models for the description of the diffraction properties of gradient crystals have been developed, one in the framework of the kinematic theory, the other within a transfer matrix formalism based on the dynamical theory of diffraction. A matrix describes the coupling and the propagation of the forward- and the Bragg-diffracted wave functions through a plane, parallel crystal lamella. It applies for the description of any crystalline medium with changes of 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 um/min. Layer thicknesses of several 100 um have been achieved. A tetragonal distortion attributed to different thermal expansion coefficients has been discovered. The anisotrope mosaic distribution gives evidences for the existence of misfit dislocations. The reflection curves calculated by the transfer matrix method fit well the experimental results. 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.

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Source: https://tomesphere.com/paper/1901.00727