*4.3. Oxygen-Deficient Centers*

Oxygen-deficient centers (ODCs) are the basic type of neutral oxygen monovacancies in non-stoichiometric silica and generally correspond to a Si–Si dimer configuration [93]. They are naturally present in unirradiated silica but their concentration considerably rises when a glass is irradiated with UV, X-ray, or *γ*-ray beams [80]. The major formation pathway of ODCs is given in Equation (2), where an energetic photon causes the release of an interstitial oxygen atom from the silica network to form a Si–Si bond.

The first spectroscopic studies on ODCs were performed in the mid-1950s by Garino-Canina [94], Mitchell and Paige [95], and Cohen [96], among others. Their results led to the identification of two optical absorption bands called "E-band" (7.6 eV) and "B2-band" (5.0 eV), which were tentatively assigned to interstitial oxygen atoms and divalent silicon atoms, respectively. In addition, three photoluminescence bands (called *α*, *β*, and *γ*) were observed at approximately 4.3 eV, 3.1 eV, and 2.7 eV, and associated with substitutional Ge atoms at oxygen-vacancy sites. In 1983, O'Reilly and Robertson [97] calculated the electronic structure of the main defects in SiO<sup>2</sup> and suggested two different variants for the oxygendeficient center. The so-called ODC(I) was proposed to be a relaxed Si Si oxygen vacancy, while ODC(II) was identified with an unrelaxed Si Si bond of length 3.06 Å. They also calculated the energy levels for both structures and demonstrated that the 7.6 eV

OA band could be associated with the *σ σ* ∗ transition of the relaxed Si–Si bond. This picture was partially confirmed by Hosono et al. [98] and Imagawa et al. [99] who found that, by heating unirradiated SiO<sup>2</sup> glasses in either hydrogen or oxygen gas flow, the intensity of the E-band decreased in accordance with the assumption that H<sup>2</sup> and O<sup>2</sup> neutralize pre-existing ODCs, as shown by

$$\text{\#Si-Si\#} + \text{H}\_2 \longrightarrow \text{\#Si-H} \quad \text{H} - \text{Si\#} \tag{7}$$

and

$$\text{\textbullet Si} \neg \text{Si} \bullet \text{\textbullet} + \frac{1}{2} \text{O}\_2 \longrightarrow \text{\textbullet Si} \neg \text{O} \neg \text{Si} \bullet \text{\textbullet}.\tag{8}$$

These reactions provided the definitive proof of ODC(I)'s structure and optical activity, but did not clarify the nature of the other defect variant. As experimental evidence built up, two alternative structural models were put forward to explain the spectroscopic behavior of ODCs(II). One is the neutral oxygen vacancy (*V* 0 O ) model originally proposed by O'Reilly and Robertson [97] and subsequently adopted by Imai et al. [75,100] to interpret their findings. While irradiating dehydrated oxygen-deficient silica with ArF and KrF excimer laser, they observed a non-linear decrease in both the B2-band and the PL *α*-band, accompanied by a dose-dependent generation of *E* ′ centers. The intensity of the E-band, however, did not show any change during the experiments and remained at the original intensity level. The analysis of the concentration of *E* ′ with irradiation time revealed that the growth curve can be decomposed into an initial, saturating part due to ODC(II) and a larger, linear-growth component attributable to ODC(I). The formation mechanism of *E* ′ centers was thus proposed to proceed via the direct photoionization of ODCs or holetrapping, as given in reactions (3) and (4). The different response of the 7.6 eV and 5.0 eV bands to laser irradiation can be explained by assuming that the formation efficiency of *E* ′ from ODC(II) is much higher than that from ODC(I), probably because of the similarity between the unrelaxed oxygen vacancy and the Si<sup>+</sup> atom accompanying the *E* ′ *γ* center.

The second model, called the twofold-coordinated silicon (Si<sup>0</sup> 2 ) model, was proposed by Skuja to interpret the origin of the OA band at 5.0 eV and the PL bands at 4.3 eV and 2.7 eV [101]. In the Si<sup>0</sup> 2 notation, the "2" stands for the coordination number of the Si atom and the "0" for its net electric charge. The structure proposed for the ODC(II) was that of a divalent silicon bonded to two bridging O atoms and with a lone pair in an *sp*<sup>2</sup> orbital. The transition that gave rise to the B2-band was identified with the S<sup>0</sup> S<sup>1</sup> excitation of the twofold Si atom, while those associated with the *α*- and *γ*-bands were the transitions S<sup>1</sup> S<sup>0</sup> and T<sup>1</sup> S<sup>0</sup> at the same defect site. This model was supported by the studies of Tsai and Griscom on the structure of a hydrogenated variant of the *E* ′ center, called an H(I) center [102]. They demonstrated that the electron paramagnetic resonance (EPR) features of this defect were compatible with an *sp*<sup>3</sup> silicon atom bonded to two oxygens and one H atom, and resumed the pathway described by Radtsig [103] as a formation mechanism:

$$\bullet \text{\textbullet Si} \bullet \text{O'} + \text{H}\_2 \longrightarrow \bullet \text{\textbullet Si} \bullet \text{\textbullet H}^0 \tag{9}$$

$$\mathbf{^0=Si:} \mathbf{+H^0} \longrightarrow \mathbf{=Si:} \mathbf{-H}.\tag{10}$$

The first step corresponds to the annealing of an NBOHC to give a silanol group and a hydrogen atom. The second step is the reaction of latter with an ODC(II) to convert it into an H(I) center. Both reactions have been confirmed in a number of experimental and theoretical studies and represent the cornerstone of the Si<sup>0</sup> <sup>2</sup> model [104–107].

In 1989, the ODC(II) issue got even more complicated when Tohmon et al. reported the existence of two accidentally overlapping bands making up the B2-band [108]. The first contribution (called B2*α*) was centered at 5.02 eV (FWHM = 0.35 eV) and was related to two emission bands at 4.42 and 2.7 eV. The other band (B2*β*) was peaked at 5.15 eV (FWHM = 0.48 eV) and was linked to emission at 4.24 eV and 3.16 eV. By analyzing

the decay lifetime of the photoluminescence, the authors proposed that the B2*α*-band corresponds to the singlet-to-triplet (S<sup>0</sup> T1) transition of the relaxed Si–Si bond while the corresponding luminescence is due to the inverse transition T<sup>1</sup> S0. The origin of the B2*β*-band was not discussed by the authors but it was subsequently attributed by Kohketsu et al. [109] to the Si center, together with the corresponding 4.24 and 3.16 eV PL bands. These assignments were largely criticized mainly because the B2*α*-band lifetime (*τ* ≈ 100 µs) did not match the value of 10 ns reported in many other studies [110–112]. Moreover, Anedda et al. observed that the 4.4 eV emission band was due to an intrinsic defect and that it shifted to 4.2 eV when the defect was perturbed by an unidentified impurity [113]. The two PL bands were thus called *α<sup>I</sup>* and *αE*, where *I* stands for intrinsic and *E* for extrinsic. On the basis of these observations, Skuja re-elaborated the Si<sup>0</sup> <sup>2</sup> model including the possibility for Ge and Sn to form ODC-like defects which could contribute to the optical properties of low-purity and Ge-doped SiO<sup>2</sup> glasses. According to this new *T* 0 <sup>2</sup> model (with *T* standing for Si, Ge, or Sn), the divalent Si center is responsible for the OA band peaked at 5.02 eV (S<sup>0</sup> S<sup>1</sup> transition) [112,114], as well as for the PL *α<sup>I</sup>* (S<sup>1</sup> S0) and *β* (T<sup>1</sup> S0) bands [101,115]. Similarly, the isoelectronic Ge defect gives rise to the 5.15 eV OA band and the two PL bands *α<sup>E</sup>* and *γ* (transitions as before). This model has gained a wide acceptance in recent years and is backed up by both theoretical [116–119] and experimental [120–122] investigations.
