Physical review. B, Condensed matter · 1988 · 668 citations · 24 references
Natural SciencesMaterials SciencePhysicsMaterials PhysicsSolid State PhysicsSpectroscopyInfrared SpectroscopyInorganic SpectroscopyOptical Properties Of MaterialsOptical Properties Of SolidsOptical SpectroscopyVibrational SpectroscopyAbsorption SpectraAbsorption SpectrumDielectric FunctionInfrared Absorption SpectraInfrared Absorption SpectroscopyOptical Absorption SpectraOptical Dielectric FunctionVibrational Modes
The infrared absorption spectrum of amorphous SiO₂ is studied in terms of its transverse‑ and longitudinal‑optic vibrational modes, and a simple coupled‑mode model is identified as the most consistent with experiment. The authors introduce disorder‑induced mechanical coupling between the in‑phase AS₁ and out‑of‑phase AS₂ oxygen‑stretch modes to reconcile inconsistent mode strengths, and compare the resulting LO‑TO frequencies with the vibrational density of states, finding good agreement for TO peaks but not for LO peaks. This coupling yields experimentally observed LO‑TO frequency pairs at 1256–1076 cm⁻¹ and 1160–1200 cm⁻¹, as well as additional pairs at 820–810 cm⁻¹ and 507–457 cm⁻¹, and shows that the AS₂ TO and AS₁ LO modes at ~1200 and 1256 cm⁻¹ satisfy experimental strengths and exhibit an inverted LO‑TO splitting.
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.
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