Optical properties and London dispersion interaction of amorphous and crystalline ${\mathrm{SiO}}_2$ determined by vacuum ultraviolet spectroscopy and spectroscopic ellipsometry

The interband optical properties of crystalline (quartz) and amorphous ${\mathrm{SiO}}_2$ in the vacuum ultraviolet (VUV) region have been investigated using combined spectroscopic ellipsometry and VUV spectroscopy. Over the range of 1.5–42 eV the optical properties exhibit similar exciton and interband transitions, with crystalline ${\mathrm{SiO}}_2$ exhibiting larger transition strengths and index of refraction. Crystalline ${\mathrm{SiO}}_2$ has more sharp features in the interband transition strength spectrum than amorphous ${\mathrm{SiO}}_2$, the energy of the absorption edge for crystalline ${\mathrm{SiO}}_2$ is about 1 eV higher than that for amorphous ${\mathrm{SiO}}_2$, and the direct band-gap energies for $X$-cut and $Z$-cut quartz are 8.30 and 8.29 eV within the absorption coefficient range $2\text{–}20{\mathrm{cm}}^{-1}$. In crystalline ${\mathrm{SiO}}_2$ we report different interband transition peaks at 16.2, 20.1, 21, 22.6, and 27.5 eV, which are in addition to those lower energy transitions previously reported at 10.4, 11.6, 14, and 17.1 eV. We find the bulk plasmon energy in $X$- and $Z$-cut crystalline quartz and amorphous ${\mathrm{SiO}}_2$ to be at 24.6, 25.2, and 23.7 eV, respectively. The oscillator strength $\left(f\right)$ sum rules of the interband transitions for crystalline ${\mathrm{SiO}}_2$ is 10–10.8 electrons per formula unit for transition energies up to 45 eV. These differences in the electronic structure and optical properties, and the physical densities of crystalline and amorphous ${\mathrm{SiO}}_2$, can be attributed to differences in the intermediate-range order (IRO) and long-range order (LRO) of the different forms of ${\mathrm{SiO}}_2$. The intimate relationship between the electronic structure and optical properties and the London dispersion interaction has attracted increased interest recently, and the role of amorphous silica and other structural glass formers as a fluid in high-temperature wetting and materials processes means a detailed knowledge of the optical properties and London dispersion interaction in ${\mathrm{SiO}}_2$ is important. Hamaker constants for the London dispersion interaction of the configuration of two layers of $c\text{−}{\mathrm{SiO}}_2$ or $a\text{−}{\mathrm{SiO}}_2$ separated by an interlayer film have been determined, using full spectral methods, from the interband transition strength. The London dispersion interaction is appreciably larger in $c\text{−}{\mathrm{SiO}}_2$ than $a\text{−}{\mathrm{SiO}}_2$ due to the increased physical density, index of refraction, transition strengths, and oscillator strengths in quartz.

Figure 1

Transmission of crystalline and amorphous ${\mathrm{SiO}}_2$: (a) $X$ cut, (b) $Z$ cut, (c) $a\text{−}{\mathrm{SiO}}_2$.

Figure 2

Complex index of refraction, $\widehat{n}=n+ik$, determined from spectroscopic ellipsometry for (a) $X$-cut quartz, (b) $Z$-cut quartz, (c) $a\text{−}{\mathrm{SiO}}_2$. The index of refraction $n$ is the dotted line, while the extinction coefficient $k$ is the solid line.

Figure 3

Reflectance spectrum of VUV spectrum measured from (a) $X$-cut quartz, (b) $Z$-cut quartz, (c) $a\text{−}{\mathrm{SiO}}_2$.

Figure 4

Complex index of refraction, $(\mathbf{n}=n+ik)$ of crystal and amorphous ${\mathrm{SiO}}_2$, where the index of refraction $n$ is shown by the dashed line and the extinction coefficient $k$ by solid lines. (a) and (e) $X$-cut quartz, (b) and (f) $Z$-cut quartz, (c) and (g) $a\text{−}{\mathrm{SiO}}_2$.

Figure 5

Fundamental absorption edge of ${\mathrm{SiO}}_2$ within low-energy range for (a) $X$ cut, (b) $Z$ cut, (c) $a\text{−}{\mathrm{SiO}}_2$, which was determined from spectroscopic ellipsometry and subsequent Kramers-Kronig transformation of the index of refraction.

Figure 6

Fundamental absorption edge of ${\mathrm{SiO}}_2$: (a) $a\text{−}{\mathrm{SiO}}_2$ (b) $X$-cut quartz, (c) $X$ quartz within wider energy range. The absorption coefficient $\left(\alpha \right)$, in units of ${\mathrm{cm}}^{-1}$, is plotted vs energy. The absorption spectra were extracted from VUV measurement.

Figure 7

Real part of the interband transition strength spectrum $\left(\mathrm{Re}\left[J_{cv}\right]\right)$ of quartz and amorphous ${\mathrm{SiO}}_2$ determined from Kramers-Kronig analysis of VUV reflectance data. (a) $X$-cut quartz, (b) $Z$-cut quartz, (c) $a\text{−}{\mathrm{SiO}}_2$.

Figure 8

Bulk electron-energy-loss function, $-\mathrm{Im}(1∕\epsilon )$, of (a) $X$-cut quartz, (b) $Z$-cut quartz, (c) $a\text{−}{\mathrm{SiO}}_2$, showing the bulk plasmon resonance peaks.

Figure 9

Oscillator strength sum rule of crystal and amorphous ${\mathrm{SiO}}_2$. (a) $X$-cut quartz, (b) $Z$-cut quartz, (c) $a\text{−}{\mathrm{SiO}}_2$.

Figure 10

Profile of two layers of $a$- (or $c$-) ${\mathrm{SiO}}_2$ grains being separated by an interlayer film.