Boson peak in the Raman spectra of amorphous gallium arsenide: Generalization to amorphous tetrahedral semiconductors

We report on the observation of the boson peak in amorphous (a) GaAs formed by high-energy ion bombardment of the crystalline lattice. The experimental data are analyzed according to the theory of inelastic light scattering from fractons. The correlation length ξ and the spectral dimension d̃ of the fractal are determined. In comparison to a-Si:H the crossover frequency from the phonon to the fracton scattering regime, ${\mathrm{\omega }}_{\mathrm{co}1\mathrm{}}$, is lower and scales according to mass law, confirming the vibrational character of the boson peak. The origin of the fractals in tetrahedral amorphous semiconductors is discussed in terms of strained nanometer blobs of host atoms whose overcoordination is relaxed through bond percolation. The intensity increase of the boson peak relative to the amorphous component during the process of amorphization of GaAs, and the increase in the carbon content in a-Si:H, shows a composite structure that consists of a strained fractal region in the relaxed network. Some experimentally observed anomalies such as low values of the sound velocity in tetrahedral amorphous semiconductors, and transformation of the vibrational spectrum by quenching in ${\mathrm{As}}_2$${\mathrm{S}}_3$ are qualitatively explained by the fractal model. On the basis of maximum positions of the boson peak and the first sharp diffraction peak observed in the structure factor of inelastic x-ray or neutron scattering of amorphous semiconductors, the correlation lengths of medium-range order (MRO) are determined and compared for different tetrahedral and vitreous amorphous semiconductors. The observed three to four times shorter value of MRO in tetrahedral relative to vitreous amorphous semiconductors is used to explain a number of differences between their properties.