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We present a first-principles investigation of the localization properties ofvibrational modes in amorphous silicon nitride ($a$-Si$_3$N$_4$). Ourinvestigation further confirms that the vibrational modes underlying the peakat $\sim$471 cm$^{-1}$ in the infrared spectrum of silicon nitride mainlyconsist of nitrogen motion in the direction normal to the plane defined by thethree Si nearest neighbors. In-plane stretching of N--Si bonds becomes largelydominant above $\sim$700 cm$^{-1}$. In particular vibrational modes underlyingthe infrared peak at 825 cm$^{-1}$ arise from the N--Si bond stretchingmotions. If N--N homopolar bonds were present, we show that N--N bondstretching occurs above $\sim$1100 cm$^{-1}$. Furthermore, we investigate thelocalization properties of vibrational modes by calculating their inverseparticipation ratio (IPR) and phase quotient. From this analysis we infer thatmodes above 600 cm$^{-1}$ shows a progressive increase of the localizationdegree and optic-like behavior, especially above 1000 cm$^{-1}$. At about 650cm$^{-1}$, given the considerable IPR value, and on the basis of projectionalanalysis on silicon-breathing-like motions of the NSi$_3$ units, we suggestthat vibrational modes may involve correlated motions of neighboring SiN$_4$tetrahedra.

Localization properties of vibrational modes in $a$-Si3N4