The anomalous isotopic effect on the lattice parameter in silicon and germanium. High resolution measurements using Bragg backscattering of synchrotron radiation

The subject of this thesis ist the investigation of the influence of the isotopic mass on the lattice parameter of silicon and germanium. The temperature dependence of the difference of the lattice parameter of differently isotopic enriched crystals is measured using Bragg backscattering of highly monochromatized synchrotron radiation. This method allows a direct determination of the lattice plane distance in crystals with high accuracy. In silicon a so far not verified anomaly of the effect is observed, which is also indicated but not evidently verified in germanium: in contrast to previous studies, the largest difference of the lattice parameters of the differently isotopic enriched crystals is not observed at the lowest achieved temperature, but the lattice parameter difference first increases with temperature before the lattice parameter converge steadily. The anomalous behaviour can be explained by the influence of phonon modes with negative Grueneisen parameters on the thermal expansion. Because of the high accuracy of the measurements, the results proof the validity of different existing theoretical predictions. While calculations on the basis of interatomic model potentials describe the small isotopic effect insufficiently, calculations in the frame work of the density-functional perturbation theory provide predictions of good agreement with the experimental results. (orig.)