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Abstract
As a high-performance optical material, fused silica is widely applied in high-power laser and photoelectric systems. However, laser induced damage (LID) of fused silica severely limits the output power and performance of these systems. Due to the values in strong field physics and improving the load capacity and performance of high power systems at UV laser, LID at 355 nm of fused silica has attracted much attention. It has been found that, even be treated by advanced processing technologies, the actual damage threshold of fused silica at 355 nm is far below the intrinsic threshold. It means that there is an absorption source near 355 nm in fused silica. However, to date, the absorption source is still unknown. In this paper, a absorption source near 355 nm is found by first-principles calculations. We find that the absorption source near 355 nm is neutral oxygen-vacancy defect (NOV, ≡Si-Si≡) and this defect originates from the oxygen deficiency of fused silica. Our results indicate that NOV defect can be taken as a damage precursor for 355 nm UV laser, and this precursor can be obviously reduced by increasing the ratio of oxygen to silicon. Present work is valuable for exploring damage mechanisms and methods to improve the damage threshold of fused silica at UV laser.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a typical optical material, fused silica has been widely used in high-power laser systems such as the National Ignition Facility (NIF) [1,2], the ShenGuang (SG)-III laser facility [3] and the laser megajoule (LMJ) [4] due to its high stability, low ultraviolet (UV) absorption, and high intrinsic damage threshold. However, it has been found that the laser induced damage threshold (LIDT) of fused silica at 355 nm is still far below the intrinsic threshold, which limits the stable operation of laser systems [5–8]. It means that there is a damage precursor in fused silica which has a strong absorption at 355 nm. There are three kinds of damage precursors in fused silica: impurities, fracture and point defects. Impurities and fracture defects which are induced in the manufacturing process [9–15] can be effectively removed through polishing and post-treatment process techniques [16–21].
Although the LIDT of fused silica has been significantly increased by polishing and post-treatment process techniques, it is still far below the intrinsic threshold of fused silica (about 150 J/cm$^{2}$) [22]. Therefore, the point defects in fused silica, such as the peroxy radical (POR) [23], the non-bridging oxygen hole center (NBOHC) [24], and the peroxy linkage (POL) [25], are now attracted much attention [25–30]. However, the absorption peaks of these point defects are far from 355 nm. To date, it is still unknown what is the damage precursor responsible for the low damage threshold of fused silica at 355 nm and its origination.
It has been found that the actual fused silica is usually oxygen-deficient and the deficiency becomes serious with UV laser irradiation [31–34]. The oxygen deficiency causes the decrease of the O : Si ratio in fused silica (R$_{\rm {O-Si}}$) and the formation of a substoichiometric SiO$_{2}$ (R$_{\rm {O-Si}}$ < 2), which showes higher absorption levels and accounted for the continued degradation of optical performance [27,32,33,35,36]. For example, the experiment report from Xu et al. shows that, 355 nm UV laser radiation can cause the increment of LID damage points and decrease the value of R$_{\rm {O-Si}}$ from 1.7 to 1.4 in fused silica surface [32]. The ab initio molecular dynamic simulations are employed by D. Donadio et al. to study the reaction path and activation barrier of interconversions among oxygen deficient centers in amorphous SiO$_{2}$. Their simulations confirm that the UV photon radiation can induce the interconversion among oxygen deficient centers in amorphous SiO$_{2}$ and influence the absorption lines [36]. Hence, the oxygen deficiency can cause the formation of oxygen-deficiency-related point defects in fused silica, resulting in the obvious changes in electronic structure and optical properties of fused silica.
In this paper, the influence of oxygen deficiency (R$_{\rm {O-Si}}$ < 2) on electronic structure and optical properties of fused silica are investigated by the first-principles calculations. A strong absorption peak near 355 nm in fused silica is found as R$_{\rm {O-Si}}$ is lower than 1.75. Moreover, we find that the intensity of the absorption peak increases with the decreasing R$_{\rm {O-Si}}$. By investigating the electronic density of states and network structures at different R$_{\rm {O-Si}}$, we find that neutral oxygen-vacancy defects (NOV, $\equiv$Si-Si$\equiv$) in fused silica lead to the 355 nm UV laser absorption, and the increasing NOV defects result in a stronger absorption peak. Our results indicate that NOV defect can be taken as a damage precursor of fused silica at 355 nm. This finding can explain why LID of fused silica is so low at 355 nm laser. Present work is valuable for exploring the damage mechanism of fused silica at UV laser and find a way to improve the damage threshold of fused silica.
2. Method
A defect-free fused silica model is generated by simulating the quenching process with molecular dynamics simulation. This method is firstly adopted by J. Sarnthein et al. to obtain a perfectly chemically ordered amorphous SiO$_{2}$. It has been found that the obtained network structure is in good agreement with experiments [37]. In our work, a 2x2x1 crystal silica supercell containing 96 atoms is fully relaxed at 5500 K and then annealed to ambient temperature (300 K) at the speed of 10 K/ps. The Langevin thermostat is used to control the system temperature. The mass density of the final fused silica model without defect is 2.2 g/cm$^{3}$ which is in agreement with the result of the experiment [38].
The calculation in our work is presented by the first-principles simulation which is performed in the framework of Density-Functional theory (DFT) by using the plane wave-pseudopotential code VASP (Vienna ab initio simulation package). The electron correlation is described by Perdew–Burke–Ernzerhof (PBE) pseudopotential based on generalized gradient approximation (GGA) [39]. Moreover, the cutoff energy of plane-wave expansion is set to 500 eV, and the first Brillouin zone is sampled by a 1$\times$1$\times$1 Gamma k-point grid. The force convergence criterion in optimization is set to 0.01 eV/Å, and the energy convergence criterion is set to $1{\times }10^{-5}$ eV. To reduce bandgap underestimation of fused silica, Bathe–Salpeter equation (BSE) based upon the quasi-particle G0W0 calculations is adopted to obtain the electronic structure and optical properties of fused silica model with different R$_{\rm {O-Si}}$.
3. Results and discussion
3.1 Network structure of fused silica at different R$_{O-Si}$
Fused silica is a typical amorphous. To construct the fused silica structures at different R$_{\rm {O-Si}}$, the O atoms are randomly removed from the fused silica, and the structures are optimized to achieve a stable state. Figure 1 illustrates the network structures at different R$_{\rm {O-Si}}$ (2.0, 1.90, 1.80, 1.75, 1.70, 1.65, 1.60). In general, the amorphous structure is quantitatively characterized by pair distribution functions and coordination numbers. The pair distribution is usually used to characterize inter-atomic distance and the coordination number is the number of atoms bonded to a specific atom.
Fig. 1. The structures of fused silica at different R$_{\rm {O-Si}}$ (2.0, 1.90, 1.80, 1.75, 1.70, 1.65, 1.60). Si atoms are shown in yellow, and O atoms are shown in red.
The pair distribution functions for perfect fused silica are present in Fig. 2(a). For perfect fused silica (R$_{\rm {O-Si}}$ = 2.0), Si atoms only link O atoms and the Si-O peak is at 1.63 Å which is consistent with the experimental values [40,41]. Moreover, the nearest distances of the O-O and Si-Si pairs shown by the peak positions are 2.60 Å and 3.12 Å, which have been extensively reported for fused silica [42,43]. Because the pair distribution functions for Si-O and O-O are almost unchanged at different R$_{\rm {O-Si}}$, we only show the pair distribution functions of Si-Si. The pair distribution functions for Si-O and O-O are presented in Fig. S1 in Supplement 1. Figure 2(b) shows the pair distribution functions of Si-Si at different R$_{\rm {O-Si}}$. The first Si-Si peak in Fig. 2(b) represents the Si-Si bond length of fused silica. For the case of R$_{\rm {O-Si}}$ = 2.0, there is one Si-Si peak appears at 3.12 Å. This bond length is much longer than the bond length of Si-O, which means that there is no actual Si-Si bond in the Si-O network of perfect fused silica. For the case of R$_{\rm {O-Si}}$ < 1.8, there are two obvious Si-Si peaks. For example, as R$_{\rm {O-Si}}$ = 1.6, the first Si-Si peak appears at 2.34 Å and the second Si-Si peak appears at 3.2 Å. The bond length of first peak is much shorter than the length of second peak and the bond length of Si-Si in perfect fused silica. The appearance of short Si-Si bond lengths indicates that some oxygen atoms in network are missing and oxygen-deficiency-related defects exist. The average coordination numbers of Si atom at different R$_{\rm {O-Si}}$ are shown in Fig. 3. The Si atom coordination number of perfect fused silica lie in the 4, whereas the coordination number are all less than 4 as R$_{\rm {O-Si}}$ < 2. The coordination number decreases with the decreasing of R$_{\rm {O-Si}}$. When R$_{\rm {O-Si}}$ is 1.6, the coordination number is as low as 3.2. This result directly shows that Si atoms connect less than four oxygen atoms, and oxygen-deficiency-related defects exist as R$_{\rm {O-Si}}$ < 2. As shown above, the results from distribution functions and coordination numbers indicate that the network structures at different R$_{\rm {O-Si}}$ are quite different. Since the electronic structure and optical properties are dependent on the network structures, the electronic structure and optical properties will be different under different R$_{\rm {O-Si}}$. The electronic structure and optical properties of fused silica at different R$_{\rm {O-Si}}$ will be discussed in next sections.
Fig. 2. (a) The pair distribution functions for perfect fused silica. (b) The pair distribution functions of Si-Si bonds for different R$_{\rm {O-Si}}$ cases of fused silica.
Fig. 3. The average coordination number distribution of Si atom in fused silica at different R$_{\rm {O-Si}}$.
3.2 Electronic structures at different R$_{O-Si}$
In this section, the influence of the R$_{\rm {O-Si}}$ on the electronic structure of fused silica is discussed. The G0W0 approximation is applied in the calculation to obtain accurate electronic structures of fused silica.
The total density of states (TDOSs) of the fused silica at different R$_{\rm {O-Si}}$ are shown in Fig. 4(a). In Fig. 4(a), the TDOSs of 2.0, 1.8, 1.7, 1.6 R$_{\rm {O-Si}}$ cases are shown. The TDOSs of other R$_{\rm {O-Si}}$ cases are presented in Fig. S2 in Supplement 1. For comparison, the TDOSs of R$_{\rm {O-Si}}$ < 2 structures are aligned with the Fermi energy of perfect silica which is set to zero. As shown in Fig. 4(a), the band gap of perfect fused silica is 9.6 eV, which is consistent with the experimental data (8.0 eV $\sim$ 9.9 eV) [44]. It also can be found that, in the case of R$_{\rm {O-Si}}$ < 2, the band gap is reduced obviously. The band gap as a function of R$_{\rm {O-Si}}$ is plotted in Fig. 4(b). With the decreasing of R$_{\rm {O-Si}}$ (from 2.0 to 1.60), the band gap decreases from 9.6 eV to 5.0 eV.
Fig. 4. (a) TDOSs of fused silica at different R$_{\rm {O-Si}}$ which are calculated by G0W0 method. (b) Band gaps of fused silica at different R$_{\rm {O-Si}}$.
To analyze the reason for band gap shrinkage, the partial density of states (PDOSs) are calculated. The PDOSs at different R$_{\rm {O-Si}}$ cases are plotted in Fig. 5. As shown in Fig. 5(a), for perfect fused silica, the conduction band and the topmost valence band of fused silica are predominately contributed by oxygen atoms. Different from perfect fused silica, as shown in Fig. 5(b), (c), and (d), both Si atoms and O atoms contribute to the conduction band and the topmost valence band as R$_{\rm {O-Si}}$ < 2. To further study the origin of conduction band and the topmost valence band, we calculate the PDOSs of all atoms at different R$_{\rm {O-Si}}$ cases. Here we take the case of R$_{\rm {O-Si}}$ =1.7 as an example. For concise, the PDOS of all Si atoms in the case of R$_{\rm {O-Si}}$ = 1.7 are presented in Fig. S3 in Supplement 1. Through the detailed calculations, we find that the conduction band and topmost valence band in Fig. 5(c) is contributed by specific Si atoms and O atoms. These Si atoms and O atoms are marked as green and purple in Fig. 6(a), respectively. It can be found that, the structures of these marked atoms are NOV defects ($\equiv$Si-Si$\equiv$). The PDOSs of the atoms in NOV defect and normal Si-O network (non-defect location) are shown in Fig. 6(b). The state near −1 eV is ordinated from the mixture of O 2p and Si 3p orbitals in NOV defects, and the state near 4 eV is ordinated from the mixture Si 3s and Si 3p orbitals in NOV defects, which is mainly correlated with interaction of the NOV defects. The atoms in normal network do not contribute to lowest conduction band states and the topmost valence band states. Hence, we have proved that the NOV defects give rise to the obvious shrinkage of fused silica band gap. The effects of band gap shrinkage and the NOV defects on optical properties of fused silica are discussed in the next section.
Fig. 5. (a) The PDOSs of perfect fused silica. (b - d) The PDOSs of fused silica at different R$_{\rm {O-Si}}$ (1.80, 1.70, 1.60).
Fig. 6. (a) The structure of fused silica in the case of R$_{\rm {O-Si}}$ = 1.7. Si is shown in yellow, and O is in red. The atoms marked green and purple are the Si atoms and O atoms that contribute to the conduction band and the topmost valence band. (b) The PDOSs of Si atoms and adjacent O atoms in NOV defects and normal Si-O network.
3.3 Optical properties of fused silica at different R$_{O-Si}$
The average optical absorptions of fused silica at different R$_{\rm {O-Si}}$, which are calculated by BSE method, are presented in Fig. 7(a). The average absorption coefficient is obtained by averaging the absorption coefficients along three axes (X, Y, Z). As illustrated in Fig. 7(a), the main absorption edge for R$_{\rm {O-Si}}$ = 2.0 is about 9.5 eV and the edges are red-shift for the cases of R$_{\rm {O-Si}}$ < 2.0. It can be found that the lower R$_{\rm {O-Si}}$ is, the larger red shift of main absorption edge is. The red shift of main absorption edge may attribute to the shrinkage of band gap which is described in section 3.2. In Fig. 7(a), we also find that, as R$_{\rm {O-Si}}$ < 2.0, many absorption peaks appear in the region where the energy is less than main absorption edge.
Fig. 7. (a) The average optical absorptions of fused silica at different R$_{\rm {O-Si}}$. The locations of main absorption edges are marked by vertical arrows. (b) The intensities of absorption peaks near 355nm at different R$_{\rm {O-Si}}$.
It is important to note that when R$_{\rm {O-Si}}$ is lower than 1.8, an obvious absorption peak near 3.5 eV appears, which is close to the energy of 355 nm UV laser (see Fig. 7(a)). The strong absorption can cause the low LIDT of fused silica at 355 nm UV laser. In Fig. 7(b), the intensities of absorption peaks near 3.5 eV at different R$_{\rm {O-Si}}$ are presented. From Fig. 7(b), it can be found that, as R$_{\rm {O-Si}}$ $\leq$ 1.75, the intensities of absorption peaks increase sharply with the decrease of R$_{\rm {O-Si}}$. The origination of UV laser absorption peak will be discussed in next section.
3.4 Origination of UV laser absorption peak near 355 nm
The absorption peaks near 3.5 eV (close the photon energy of 355 nm laser) in Fig. 7(a) correspond to the band gaps of R$_{\rm {O-Si}}$ $\leq$ 1.75 (near 5.5 eV) in Fig. 4(b), which are the peaks with lowest energy among all peaks in each absorption spectrum of Fig. 7(a). Excitonic effect can be employed to explain the difference in energies between absorption peaks and band gaps. Due to the Coulomb attraction interaction between electron and hole, the excitonic effect can reduce energy gap in transition process and lead to the energy of absorption peak lower than the band gap. To prove the point, the optical absorption spectrums at R$_{\rm {O-Si}}$ = 1.75 are calculated by G0W0 method and BSE method, respectively (see Fig. 8). The difference between these two methods is that BSE method includes excitonic effect, while G0W0 method does not. In Fig. 8, the first absorption peak at absorption spectrum from the G0W0 method is about 5.5 eV, consistent with the band gap in Fig. 4(b). By comparing the results of the two methods, we find that the excitonic effect causes the shift of first absorption peak (peak with lowest energy ) from 5.5 eV (without excitonic effect) to 3.5 eV (with excitonic effect). Our results show that the excitonic effect plays an important role in the appearance of absorption peaks near 355 nm in fused silica. As shown in section 3.3, the DOSs at band gap edges are from NOV defects. Therefore, it can be concluded that the UV laser absorption peak near 355 nm originates from NOV defect in fused silica and the excitonic effect plays an important role.
Fig. 8. The average optical absorptions of fused silica at R$_{\rm {O-Si}}$ = 1.75. Here, the blue curve is the result from BSE method. The red curve is the result from G0W0 method.
To demonstrate quantitative relationship between the concentration of NOV defects (C$_{\rm {NOV}}$), the intensity of absorption peak near 355 nm and R$_{\rm {O-Si}}$, R$_{\rm {O-Si}}$ versus C$_{\rm {NOV}}$ and R$_{\rm {O-Si}}$ versus intensity of absorption peak near 355nm are presented in Table 1 and Fig. 9. Table 1 shows that the concentration of NOV defects increases with the decreasing of R$_{\rm {O-Si}}$. From Fig. 9, it can be found that the changing trends in Fig. 9(a) and Fig. 9(b) are almost same. It means that the intensity of absorption peak near 355 nm is proportional to the concentration of NOV defects. The results from Fig. 9 confirm that absorption peaks near 355 nm in fused silica originate from NOV defects. Our results indicate that NOV defect can be taken as a damage precursor of fused silica at 355 nm and it gives an explanation for the low damage threshold of adequately preprocessed fused silica at 355 nm. Since the intensity of absorption peak near 355 nm decreases with the increase of R$_{\rm {O-Si}}$, increasing R$_{\rm {O-Si}}$ may be a promising way to increase the damage threshold of fused silica at 355 nm UV laser.
Fig. 9. (a) R$_{\rm {O-Si}}$ versus intensity of absorption peak near 355nm. (b) R$_{\rm {O-Si}}$ versus concentration of NOV defects.
Table 1. The concentrations of NOV defects in fused silica at different R$_{\rm {O-Si}}$.
4. Conclusion
In conclusion, a strong absorption source near 355 nm in fused silica is found by first-principles approach. We find that, as the ratio of oxygen to silicon R$_{\rm {O-Si}}$ lower than 1.75, an obvious absorption peak near 3.5 eV appears in absorption spectrum, which is close to the photon energy of 355 nm UV laser. By investigating the network structure, electronic structure and optical properties of fused silica at different R$_{\rm {O-Si}}$ ($\leq$ 2), we find that absorption peak near 355 nm originates from NOV defect and the excitonic effect plays an important role. We also find that the intensity of absorption peak near 355 nm is proportional to the concentration of NOV defects. Our results indicate that NOV defect can be taken as a damage precursor of fused silica at 355 nm. Present work can be help for exploring the damage mechanism of fused silica and find a way to improve fused silica damage threshold at UV laser.
Funding
Key Project of National Natural Science Foundation of China-China Academy of Engineering Physics joint Foundation (NSAF) (U1830204); Key Laboratory Opening Topic Fund (JCKY20121210C003); National Natural Science Foundation of China (11804046, 12105037, 61505023); Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201800623).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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