*4.1. E*′ *Centers*

The best-known defect in crystalline SiO<sup>2</sup> and silica is the *E* ′ center, that is, an unpaired electron in a Si dangling bond. In their experimental work, Hosono et al. demonstrated that strained bonds contained in three- and four-membered rings absorb F2-excimer laser light (7.9 eV, 157 nm) and jump to the lowest electronic spin triplet state (*T*1), causing the opening of the ring and the consequent formation of a pair of point defects [53]. The photolytic reaction can be written as

$$\texttt{\bullet Si-O-Si=\bullet} \rightarrow \{\texttt{\bullet Si-\cdots} \rightarrow \texttt{O-Si\bullet}\}^\* \rightarrow \texttt{\bullet Si} \quad \text{\bullet O-Si\bullet} \tag{1}$$

where the three dashes represent three separated Si–O bonds, the asterisk indicates an electronically excited state, and the dot represents an unpaired electron. The first step of the reaction involves the transition of an electron from the valence to the conduction band and the formation of a self-trapped exciton (STE) consisting of an excited electron (*e* – ) located on a silicon atom and a hole (*h* + ) trapped at one or more neighbouring oxygen atoms [61,62]. This structure is kept metastable by the spontaneous creation of a localised distortion in the SiO<sup>2</sup> network, which lowers the total energy of the system and traps the *e* – –*h* <sup>+</sup> pair at the distortion site [63]. Using self-consistent quantum chemical calculations, Shluger proposed a model in which the exciton self-trapping is accompanied by the weakening of a Si–O bond and the displacement (0.3 Å) of the oxygen atom towards an interstitial position [64]. Other calculations showed that, after electronic excitation, the system relaxes to the nearest energy minimum on the excited-state energy surface by breaking a Si–O bond and moving the Si atom into a planar *sp*<sup>2</sup> configuration [62,63]. In either case, the relaxation of the STE to the ground state (and the possible rehybridization of the silicon orbitals to an *sp*<sup>3</sup> configuration) leads to the formation of a silicon and an oxygen dangling bond known, respectively, as *E* ′ *α* center and non-bridging oxygen hole center (NBOHC) [65].

A second pathway for *E* ′ center formation was proved by Tsai and Griscom while studying the effect of highly-focused ArF excimer laser light (6.4 eV, 193 nm) on silica specimens [66]. As in the previous case, the first step of the proposed mechanism consists in the promotion of an electron to the conduction band and the formation of a self-trapped exciton. Here, however, its de-excitation proceeds through the displacement of the oxygen atom and the formation of an interstitial O<sup>0</sup> atom and a Si Si oxygen vacancy (Frenkel defect pair) [67].

$$\text{\texttt{\texttt{\texttt{Si}\rightarrow O}\rightarrow Si\equiv}}\rightarrow\text{\texttt{\texttt{\texttt{\texttt{\langle\texttt{Si}\rightarrow\cdot}}}^{\rightarrow}}\rightarrow\text{\texttt{\texttt{\langle\texttt{Si}\rightarrow}}}\rightarrow\text{\texttt{\texttt{\langle\texttt{Si}\rightarrow\cdot}}}\rightarrow\text{\texttt{\langle\texttt{Si}\rightarrow\cdot\cdot\text{}}\rightarrow\text{O}^{0}\tag{2}$$

The process involves a non-radiative decay of the electronic excited state, and its efficiency is higher in densified silica where the mean Si–O–Si angle is lower and the mean Si–O bond length is higher [68,69]. By further exciting the oxygen vacancy, the system evolves towards the formation of a Si dangling bond and a nearly planar Si<sup>+</sup> unit [70,71]. To distinguish this variant of *E* ′ center from that obtained via the mechanism (1), we label it an *E* ′ *γ* center.

Si Si Si <sup>+</sup> Si + *e* – (3)

Although the major channel for the formation of *E* ′ centers has not yet been identified, it appears that the bond-dissociation mechanism (1) prevails at higher irradiation energies whereas the Frenkel-type mechanism (2) and (3) predominates at lower energies. This view is supported by experimental results showing that the concentration of *E* ′ *<sup>α</sup>* and NBOHC defects linearly increase with the pulse energy of F<sup>2</sup> lasers (7.9 eV) [53], while that of *E* ′ *γ* centers and O<sup>0</sup> quadratically increases with the pulse energy of KrF (5.0 eV) and ArF lasers (6.4 eV) [72,73]. As a consequence, it has been suggested that the rupture of the Si–O bond described by Equation (1) is assisted by the absorption of a single photon [74], whereas the cleavage of the O atom and the successive formation of the *E* ′ *γ* center is induced by a two-photon absorption process [66]. In the latter case, two alternative pathways have also been proposed. If the absorption is not simultaneous, the first photon is responsible for the formation of the STE while the second serves to ionise the oxygen vacancy and produce the Si dangling bond [75]. These two stpdf correspond to reactions (2) and (3) and each of them is activated by the absorption of one photon. Contrarily, if the two photons are absorbed at the same time, the reaction goes through a biexciton process in which one of the two STEs decays as reported in Equation (2), while the other supplies a hole to foster the reaction [76]:

$$\text{\#Si-Si\#} + h^+ \longrightarrow \text{\#Si^\*} \quad \text{\textdegree Si\#} \tag{4}$$

Two additional variants of *E* ′ defects have seldom been observed in irradiated silica. *E* ′ *s* is a hemi-center typically observed on silica surfaces or interfaces, comprising only a threefold coordinated Si atom with the unpaired electron. The *E* ′ *β* center, on the other hand, features a Si moiety coupled with a hydrogen-saturated oxygen vacancy [77,78]. This defect is generally found in hydrogen-rich silica, where the concentration of silanol groups (SiOH) is higher. In fact, the irradiation of these glasses with F<sup>2</sup> lasers or ionizing beams leads to the rupture of the O–H bond and the formation of a NBOHC and a neutral hydrogen atom (H<sup>0</sup> ) as follows:

$$\bullet \text{\#OH} \longrightarrow \bullet \bullet \text{\#O}^{\bullet} + \text{H}^{0}. \tag{5}$$

The free hydrogen may then diffuse in the silica matrix and react with a pre-existing Si Si oxygen vacancy to generate an *E* ′ *β* center [79]:

$$\text{\#Si-Si\#} + \text{H}^{0} \longrightarrow \text{\#Si}^{\*} \quad \text{H-Si\#} \tag{6}$$

Since all the *E* ′ variants have very similar electronic structures, their optical absorption (OA) spectrum is characterized by the same band, peaking at about 5.8 eV (214 nm) with a full width at half maximum (FWHM) of 0.8 eV and an oscillator strength *f* = 0.14 ± 0.1 [80,81]. An experimental OA spectrum obtained after *γ*-ray irradiation of a wet silica sample is reported in Figure 5. The electronic transition corresponding to this band is still debated. One hypothesis is that the OA originates from the charge transfer from valence band states (i.e., a 2*p* orbital of one of the three O atoms bonded to the *E* ′ center) to the empty state of the Si dangling bond [82]. This is supported by density functional theory calculations showing that the lower part of the absorption spectrum of *a*-SiO<sup>2</sup> corresponds to the superposition of the O(2*p*) Si(*sp*<sup>3</sup> ) transition with that from the occupied Si(*sp*<sup>3</sup> ) state to the diffuse states in the lower part of the conduction band [83].

**Figure 5.** Optical absorption spectrum of a synthetic silica sample showing a band assigned to the *E* ′ center (5.8 eV) and another band assigned to NBOHC (4.8 eV). Adapted from Cannas et al. [84].
