Quantitative analysis of the effect of disorder-induced mode coupling on infrared absorption in silica.

Abstract

The infrared-absorption spectrum of a-${\mathrm{SiO}}_{2}$ is analyzed in terms of its transverse-optic (TO) and longitudinal-optic (LO) vibrational modes. It is shown that the independent-oscillator model for the a-${\mathrm{SiO}}_{2}$ dielectric function fails to yield a consistent value of mode strength for the optically active oxygen asymmetric stretch (${\mathrm{AS}}_{1}$) TO mode at 1076 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (in-phase motion of adjacent oxygen atoms) when different but equivalent methods of measurement and analysis are used. This inconsistency is resolved by introducing disorder-induced mechanical coupling between the ${\mathrm{AS}}_{1}$ mode and the relatively optically inactive oxygen asymmetric stretch (${\mathrm{AS}}_{2}$) mode (out-of-phase motion of adjacent oxygen atoms) into the oscillator model. Coupled ${\mathrm{AS}}_{1}$- and ${\mathrm{AS}}_{2}$-mode LO-TO frequency pairs are experimentally observed as peaks at approximately 1256--1076 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and 1160--1200 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, in oblique-incidence p-polarized absorption spectra of thin a-${\mathrm{SiO}}_{2}$ films grown thermally on c-Si wafers.Additionally, two other LO-TO-mode pairs are observed in these spectra as absorption peaks at approximately 820--810 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and 507--457 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The simplest form of the coupled-mode model consistent with experiment is found to be one in which the ${\mathrm{AS}}_{1}$-mode LO-TO frequency splitting is due to the ${\mathrm{AS}}_{1}$ transverse effective charge and the ${\mathrm{AS}}_{2}$-mode LO-TO splitting is due to the mechanical coupling between these two modes and not to the ${\mathrm{AS}}_{2}$ transverse effective charge, which is negligibly small. The ${\mathrm{AS}}_{2}$ TO and the ${\mathrm{AS}}_{1}$ LO modes found at approximately 1200 and 1256 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, are shown to be consistent with experimental mode strengths and with the analytic requirements that all LO and TO modes be interspersed and that, as a result of lying between the ${\mathrm{AS}}_{1}$-mode LO-TO pair frequencies, the ${\mathrm{AS}}_{2}$-mode LO-TO frequency splitting be inverted. Comparison of these experimental LO-TO-mode pair frequencies with the vibrational density of states (VDOS) spectrum of a-${\mathrm{SiO}}_{2}$ shows that the TO absorption peaks correspond quite well with the VDOS spectral peaks, whereas the LO absorption peaks do not appear to exhibit any such correspondence.