Spectroscopy for Materials Characterization. Группа авторов

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alt="icon1"/>Si─O─)₃Si─O^• measured at T = 8 K under pulsed laser excitation at E _exc = ℏω ₀ = 1.997 eV. Panels (b–d): Zooms that show the ZPL profile (b), the first (c) and the second (d) sidebands plotted as a function of distance from the laser line ω ₀.

In agreement with Figure 2.2, they represent the transitions from the lower vibrational level in the excited electronic state to the first and second vibrational levels in the ground electronic state, respectively. The measured values, therefore, identify the fundamental, ω _g , and the overtone, 2ω _g , frequencies of the nearly equally spaced vibrational levels of the surface‐nonbridging oxygen in the electronic ground state. We note that these sidebands are more and more wider than the ZPL, their FWHM being ∼20 and 40 cm⁻¹ for the first and the second line, respectively; this spreading is due to an inhomogeneous distribution of the vibrational frequency of centers having the same ZPL. From these emission spectra, we also measure the ratio between the integrated intensities of ZPL and the first and second vibrational lines: I _0L /I _1L = 13.5 ± 0.5, I _0L /I _2L = 160 ± 30, the error being mainly due to the inaccuracy in the reference line subtraction to account for the overlapping with nonselectively excited luminescence. Based on the linear electron–phonon coupling, subsequently evidenced by the equal values of vibration frequency both in the ground and in the excited state, we compare these values with the Poisson’s distribution, I _kL = exp(−S) ^L × (S ^L ) ^k /k! and extract the partial Huang–Rhys factor S ^L : I _0L /I _1L = 1/S ^L yields S ^L = 0.074 ± 0.003 and I _0L /I _2L = 2/(S ^L )² yields S ^L = 0.11 ± 0.01. We note that the difference between the values of S is larger than the experimental uncertainty; despite this incongruence, these results quantify the low coupling of the electronic transition with the local Si─O^• stretching mode, namely, the nearly absent relaxation of the Si─O^• bond after excitation.

Figure 2.12 Time‐resolved PL spectrum of the surface‐NBOHC (

Si─O─)₃Si─O^• measured at T = 10 K under pulsed laser excitation at E _exc = ℏω ₀ = 2.112 eV and plotted as a function of the distance from the laser line ω ₀. The laser lineshape, acquired by the scattered light, is also shown arbitrarily scaled respect to the emission spectrum.

We now return to the experimental results on the (

Si─O─)₃Si─O^• to complete the description with the vibrational properties of the excited electronic state. Figure 2.12 shows the spectrum obtained under excitation at E _exc = 2.112 eV, where no resonant luminescence appears. In contrast, a sharp line is detected at lower energies, shifted by 920 ± 3 cm⁻¹ from the excitation; the accuracy being determined by the preliminary detection of the scattered laser line shown in the same figure. This sharp line is the off‐resonance ZPL that, in agreement with Figure 2.2, is excited through the vibrational level 1 of the excited electronic state. Then, the value of 920 ± 3 cm⁻¹ is the measure of the frequency ω _e of the surface Si─O^• stretching in the excited electronic state that is almost coincident with that in the ground electronic state. This finding demonstrates the validity of the linear coupling between the optical transition around 2.0 eV and the localized mode. Moreover, on the basis of the reduced mass of the Si─O molecule (m ^* = 1.692 × 10⁻²⁶ kg), it is possible to calculate the force constant of Si─O^• bond at the surface: k = (ω _surf)²⋅m ^*≈ 508 N m⁻¹.

Inhomogeneous broadening measured by ZPL distribution: Finally, we report the study of the inhomogeneous properties of NBOHC at the surface of silica taking advantage of time‐resolved experiments being able to detect ZPL under tunable laser excitation [29]. Figure 2.13a shows a series of time‐resolved emission spectra measured at T = 10 K with the excitation energy stepwise incremented from 1.887 to 2.077 eV (minimum step 0.003 eV); each spectrum is displayed in the vicinity of the excitation energy thus evidencing the ZPL. From these spectra, we plot in Figure 2.13b the distribution of the ZPL intensity. The experimental data are best fitted by a Gaussian curve centered at 1.995 ± 0.003 eV with FWHM of 0.042 ± 0.005 eV (340 ± 40 cm⁻¹) that represents the inhomogeneous distribution w _inh(E ₀₀) of the electronic transitions, due to the different local environment surrounding the (

Si─O─)₃Si─O^• at the silica surface. Indeed, the inhomogeneity is related to the structural disorder of the silica network in the long‐ and local‐range in comparison with the SiO₄ tetrahedron size. The first is intrinsic to the amorphous state, and is mainly accounted for by the statistical distribution of the Si─O─Si bond angle and the size of (Si─O)n ring structure [30, 31]. The second is due to the presence of point defects that introduce a local distortion into the surroundings, such distortion being dependent on the site [11].

Figure 2.13 Panel (a): Time‐resolved PL spectra of surface‐NBOHC (

Si─O─)₃Si─O^•, measured at T = 10 K, in the ZPL region at different excitation energies from 1.89 to 2.08 eV with step 0.01, 0.006 and 0.003 eV. Panel (b): Distribution of the ZPL intensity, obtained by the spectra reported in the panel (a) (symbols), superimposed to its Gaussian best fit curve.

      We observe that the main experimental outcome is the detectability of the ZPL under site‐selective excitation of inhomogeneously distributed centers, thus allowing the inhomogeneous curve to be drawn directly. The detection of the ZPL is therefore a probe of the silica structure near the NBOHC; this potential is precluded for other defects in silica, because of the stronger phonon coupling of their optical transitions. In those cases, the deconvolution between homogeneous and inhomogeneous broadening can be done only indirectly.

References

      1 1 Herzberg, G. (1966). Molecular Spectra and Molecular Structure. New York: Van Nostrand Reinhold.

      2 2 Rebane, K.K. (1970). Impurity Spectra of Solids. New York: Plenum Press.

      3 3 Stoneham, A.M.

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