Phonons and phonon localization in $a-\mathrm{Si}$: Computational approaches and results for continuous-random-network-derived structures

Three different models for $a-\mathrm{Si}$ are studied with respect to the vibrational density of states (VDOS) and phonon localization. The degree of disorder is varied for each model in a large range. For all models structural properties are investigated in connection with the VDOS. Phonon localization is examined via scaling approaches and mobility edges are quantified. Two of the models are continuous random networks (CRN’s): the vacancy model and the Wooten-Winer-Weaire (WWW) model both relaxed with the Keating potential. The vacancy model causes the appearance of an artificial high-energy shoulder of the TO peak, which leads to wrong predictions on localization too. This shortcoming of the vacancy model is caused by a second maximum of the bond angle distribution at large angles. The WWW model is here the superior CRN model for $a-\mathrm{Si}.$ It allows a good reproduction of the experimental VDOS and possesses only about 1% localized states at the upper edge of the VDOS. In the third model, the WWW model relaxed with the Stillinger-Weber potential, dangling bonds and floating bonds are introduced. Its only shortcoming is an artificial maximum in the radial distribution function below the second diffraction peak. Due to defects extra modes at low energies are found that are highly dependent on the quality of the relaxation. The VDOS is well reproduced. About 2% of the modes at high energies are localized. The modes at lowest energies look localized, when systems below 2000 atoms are studied. It turns out that large systems up to 8000 atoms and many independent realizations are required to interpret the phonon properties correctly. The amount of localization is found to be independent of the degree of disorder present in the model, but an increase in the number of localized states with decreasing density is observed. The present investigation permits statements about the suitability of models for amorphous solids, relaxation procedures, standard potentials, and procedures to determine the localization character of states.