Extended x-ray absorption fine structure (EXAFS) spectroscopy was applied to probe the vibrational properties of bulk crystalline Ge $\left(c\text{−}\mathrm{Ge}\right)$ and Ge nanocrystals (Ge NCs) of $4.4\mathrm{nm}$ mean diameter produced by ion implantation in $\mathrm{Si}{\mathrm{O}}_2$ followed by thermal annealing. EXAFS measurements around the Ge $K$ edge were carried out in the temperature range from $8\text{to}300\mathrm{K}$ at beam line 10-2 of the Stanford Synchrotron Radiation Laboratory (SSRL). Original information about thermal and static disorder, thermal expansion, and anharmonicity effects have been obtained for $c\text{−}\mathrm{Ge}$ and Ge NCs from temperature dependent EXAFS measurements using a correlated anharmonic Einstein model and thermodynamic perturbation theory. It was observed that the Ge NCs were stiffer (showed a stronger bond force constant) than both amorphous Ge $\left(a\text{−}\mathrm{Ge}\right)$ and $c\text{−}\mathrm{Ge}$. Also, the values of the linear thermal expansion (thermal evolution of the mean interatomic distance) obtained for the Ge NCs were smaller than the ones obtained for $c\text{−}\mathrm{Ge}$. These results were compared to the ones obtained for other nanocrystalline systems. They suggest that the increased surface to volume ratio of the nanocrystalline form and the presence of the surrounding $\mathrm{Si}{\mathrm{O}}_2$ matrix might be responsible for the different vibrational properties of $c\text{−}\mathrm{Ge}$ and Ge NCs.

• Received 20 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.184102