Unraveling exciton dynamics in amorphous silicon dioxide: Interpretation of the optical features from 8 to 11 eV

We introduce a model comprehensively describing the optical features of amorphous silicon dioxide ($a$-SiO${}_2$) in the spectral range from $~$8 up to $~$11 eV. Our model is grounded on the critical analysis of the temperature dependence of Kramers-Kronig-derived absorption spectra in the range from $~$8 up to $~$17.5 eV, together with the features of the Urbach absorption tail and of self-trapped exciton emission. In a paper we recently published [Phys. Rev. Lett. 105, 116401 (2010)] we showed the 10.4-eV resonance in the absorption spectra to feature a close Lorentzian line shape, thus implying a delocalized nature for excitons in $a$-SiO${}_2$. Here we provide estimations of the main parameters ruling exciton dynamics in SiO${}_2$, such as the energy of the mean lattice vibrational mode coupled to excitons ($\hslash {\omega }_0=0.083$ eV), the half width of the excitonic energy band ($B~2$ eV), the root-mean-square amplitude of site-to-site energy fluctuations of exciton energy ($D~0.7$ eV), and the exciton-phonon coupling constant ($g~2.1$). The quantum yield of excitonic emission ($\eta ~10{}^{-3}$) at $T=10$ K in $a$-SiO${}_2$ is determined as well. Our model suggests that $a$-SiO${}_2$ features an indirect gap near $~$9 eV and a direct one near $~$11 eV, and allows a coherent description of the properties of the intrinsic Urbach absorption tail. The latter results are satisfactorily explained as arising from the momentary self-trapping of the 10.4-eV exciton. As far as near-edge absorption properties are concerned, our model places SiO${}_2$ in the wider context of wide-band-gap solids, such as LiF or NaF, where excitons are weakly scattered, but strongly coupled to phonons. On the whole, the present study shows that exciton dynamics accounts for all optical properties of $a$-SiO${}_2$ from $~$8 up to $~$11 eV.

Figure 1

K-K-derived absorption coefficient of $a$-SiO${}_2$ (solid lines) in the temperature range from 10 to 300 K in steps of 50 K and at 10 K for $c$-SiO${}_2$ (dashed line). Labels represent temperatures (K) of the closest curve.

Figure 2

(a) Enlargement of the absorption peak at $~$10.4 eV from 10 to 300 K in steps of 50 K (full lines). Absorption coefficient of $c$-SiO${}_2$ at 10 K in the same spectral region (dashed line). Spectra are taken from Fig. 2b of Ref. 27. (b) Enlargement of the peak at $~$11.6 eV in $a$-SiO${}_2$ from 300 to 150 K in steps of 50 K. (c) Enlargement of the peak at $~$11.6 eV in $a$-SiO${}_2$ from 150 to 10 K in steps of 50 K. Labels represent temperatures (K) of the closest curve.

Figure 3

Position of the peak at $~$10.4 eV in $a$-SiO${}_2$ as a function of temperature, as determined via a Lorentzian fit of the peak profiles. The full line is discussed in the text. Data are taken from inset (a) of Fig. 3 of Ref. 27.

Figure 4

Photoluminescence emission spectrum detected at $T=10$ K in $c$-SiO${}_2$ (circles) and $a$-SiO${}_2$ (squares) under excitation with synchrotron radiation of 10.2 eV photon energy.