Determination of the activation energy of the disproportionation reaction of amorphous GeO$_x$ film on quartz substrate using Raman spectroscopy

Amorphous germanium nanoclusters were formed in the GeO$_x$ film on quartz as a result of the disproportionation reaction GeO$_x$ during furnace annealing. To determine the reaction activation energy, annealing was carried out at temperatures from 400 to 500$^\circ$C. The appearance and growth of amorphous germanium nanoclusters were investigated using Raman spectroscopy. It was found that the position of the Raman scattering peak from amorphous germanium varied with the annealing time, which due to the change in the sizes of nanoclusters, i.e., the phonon localization model can be applied not only to germanium nanocrystals, but also to amorphous germanium clusters, in the case of their ultra-small sizes. In addition, it was found that the saturation time for the formation of amorphous germanium nanoclusters depends exponentially on the annealing temperature. The kinetics analysis of the nanocluster’s formation was carried out within the framework of the Johnson-Mehl-Avrami-Kolmogorov model. The activation energy of the disproportionation reaction was obtained for the first time, which amounted to 1.0 $\pm$ 0.1 eV.