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Abstract
The radiation resistance of rare-earth doped optical fibers is critical to applications in space-based environments such as laser radars, optical communications, and laser altimeters. Usually, doping various elements, such as aluminum (Al), phosphorus (P), and boron (B), is necessary to fine-tune the structural, electronic, and optical properties, but often results in degraded radiation resistance. Thus, achieving both excellent optical and radiation properties remain a challenge. Here, we theoretically investigate and compare the electronic, structural, and optical properties of [BPO4]° and [AlPO4]° units in silica glass. We prove that both [BPO4]° and [AlPO4]° units are stable in the SiO2 matrix. As the radiation resistance of [SiO4/2]° is excellent, inferring from the material's structure, the SiO2-BPO4 and SiO2-AlPO4 should have good radiation resistance. From the calculation, the SiO2-BPO4 is structurally and electronically similar to the SiO2-AlPO4. Importantly, the refractive index of SiO2-BPO4 is lower than SiO2-AlPO4, achieving refractive index tuning while maintaining its radiation resistance. Our results provide some guidance for the design of BPO4-based radiation-resistant active fibers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
5 April 2023: Minor corrections were made to the paper.
23 May 2023: A typographical correction was made to the title.
1. Introduction
Rare earth-doped fiber lasers and fiber amplifiers have excellent optical properties and have been widely used in space, nuclear power, and high-energy physics facilities [1–3]. In active fibers cores, it is often necessary to dope Al3+, P5+, and Ge4+ in the core to increase the solubility of rare earth ions and to adjust the refractive index. Previously, many experimental [4–9] and theoretical studies [10–12] focused on doping various ions in silica glass. However, numerous radiation sources in the space environment, such as gamma rays, high-energy electrons beam, and high-energy neutrons beam, affect the doping effect. Active fibers are very sensitive to radiation, mainly resulting in increased optical absorption and degraded laser performance [13,14]. For instance, electronegative [AlO4/2]- groups around Ytterbium ion (Yb3+) can release an electron, becoming an Al-related oxygen hole color center (Al-OHC) in Yb3+/Al3+ double-doped silica glass during the radiation process [15]. And a large amount of Yb3+ can be reduced to Yb2+ due to the released electrons from Al-OHC, significantly decreasing the radiation resistance of active fiber. The O = P double bond would break when electronegative [O = PO3/2]° groups around Yb3+ absorb the ray's energy in Yb3+/P5+ double-doped silica glass under radiation process [16].
However, the silica glass has good radiation resistance in the Al/P co-doped silica glass when the Al/P co-doping ratio equals 1 [17]. Because Al and P preferentially form the electrically neutral [AlPO4]° unit, similar to the [SiO4/2]° structure, which is not easy to gain or lose electrons in the radiation process [18–20]. In the study of Yb3+/Al3+/P5+ co-doped fiber performance, it was found that the concentration of Al-OHC decreased with the increase of P/Al co-doped ratio [17]. And Deschamps et al. speculated that [AlPO4]° played an important role in inhibiting the formation of Al-OHC [21].
Furthermore, B has similar chemical properties to Al, and it has also been widely studied in the doping of silicon dioxide [22–24]. The P, B silicate glass has been characterized by the wide line, magic angle spinning (MAS), and triple quantum MAS NMR spectroscopic techniques to study their chemical composition and properties [25,26]. Guo et al. studied the effect of the B content in Yb/Al/B co-doped silica glass on the spectral properties of Yb3+ ions and found that both the absorption and emission cross-sections decrease with the increase of B content when the B2O3 mole fraction is less than 2% [27]. Research shows that the Al and P will preferentially form electrically neutral [AlPO4]° during the fiber preparation process. Notably, the chemically and thermally stable [BPO4]° building blocks are formed in some studies on composites, graphite, and oxide minerals [28–31]. However, no related research has been seen in the reports on the optical fiber preparation process. Therefore, whether B can replace Al in fused silica is worth exploring.
In this paper, we first construct the SiO2-AlPO4 and SiO2-BPO4 models through molecular dynamic (MD) simulations. And then, we use density functional theory (DFT) to study the possibility of the existence of SiO2-BPO4 by characterizing the structural properties, electron features, electronic structure, and the crystal orbital Hamilton population. The results show that similar to SiO2-AlPO4, SiO2-BPO4 has good structural and energetic stability. Our research provides theoretical support for the existence of [BPO4]° and offers the tunable refractive index of the SiO2 system.
2. Computational methods
The initial perfect molten silicon structure was generated by a 96-atom 2 × 2 × 1 supercell. The quenching process of the supercell was simulated using Ab initio MD (AIMD) [32] simulations under DFT implemented in the Vienna Ab initio Simulation Package (VASP) [33]. The heat quenching process was divided into three steps. First, the 96-atoms supercell was heated from 300 K to 3000 K at 5 ps to achieve equilibrium. The melt was then well equilibrated at this elevated temperature for 10 ps to reach the steady liquid state independent of the initial random distribution of atoms. Then, the supercell was gradually quenched to 300 K through three quenching equilibrium steps, i.e. 3000 K → 2000K (cooling rate ∼100 K/ps), 2000K→1000 K (cooling rate ∼100 K/ps), and 1000 K → 300 K (cooling rate ∼100 K/ps). Finally, the system was cooled to and maintained at 300 K at 10 ps. And the total simulation time for each model to be 55 ps. During the quenching process, the Langevin thermostat was employed to control the temperature of the system [34]. The final mass density of the amorphous SiO2 was 2.2 g/cm3, which agrees well with the experimental result [35].
The electron exchange correction function was described by the generalized gradient approximation (GGA) parameterized by Perdew–Burke–Ernzerhof (PBE) [36,37]. A 1 × 1 × 1 Monkhorst-Pack k-point grid sampled the Brillouin zone for AIMD simulations, and a 4 × 4 × 4 Monkhorst-Pack k-point grid for geometry optimizations and static calculations. The cut-off energy of the plane wave was set to 450 eV. The convergence criteria for the energy and force were set to 10−5 eV and 0.01 eV/ Å, respectively.
3. Results and discussion
Following the procedure in COMPUTATIONAL METHODS, we carried out a 10 ps thermal bath on the amorphous SiO2 structure at a constant temperature of 300 K, and the amorphous SiO2 model is shown in Fig. 1(a). Unless otherwise specified, the SiO2 mentioned below is all amorphous. It contains 96 atoms at a density of 2.2 g/cm-1. The calculated SiO2 total energy by AIMD simulation is shown in Figure S1, and it changed within a small range, showing good thermodynamic stability. In addition, we have shown the structure of the three models, SiO2, SiO2-AlPO4, and SiO2-BPO4, from three angles in Figure S2. Their lattice constants are 9.98417 Å (a), 9.98417 Å (b), and 14.56060 Å (c), and the cell volume is 1451.45378 Å3.
Fig. 1. Simulation model of SiO2, SiO2-AlPO4, and SiO2-BPO4. (a) The SiO2 structure contains 96 atoms with a density of 2.2 g/cm-1. (b) The schematic diagram of the structure of SiO2-AlPO4 and (c) SiO2-BPO4.
Two adjacent SiO2 tetrahedra were replaced by the [AlPO4]° and [BPO4]° units, and the obtained SiO2-AlPO4 and SiO2-BPO4 models are shown in Figs. 1(b) and 1(c), respectively. The formation of the [AlPO4]° unit undergoes the following chemical reactions:
After doping [AlPO4]° and [BPO4]° units in SiO2, we re-optimized the SiO2-AlPO4 and SiO2-BPO4 structures. The statistical results illustrate that the bond length and angle varied due to the ligand field difference for the O atoms, as demonstrated in Figure S3.
Usually, the crystal orbital Hamilton population (COHP) is used from a micro perspective to measure the bonding strength and contribution. In the illustration of Fig. 2(a), we numbered two SiO2 tetrahedra for the doping of [AlPO4]° and [BPO4]° units, including seven oxygen atoms (numbers 1-7) and two doping atoms (numbers 8-9). In Fig. 2, the ordinate is -COHP value. Positive COHP (bonding) reduces the total energy of the system, while the negative value (anti-bonding) increases the total energy.
Fig. 2. The crystal orbital Hamilton population analysis of SiO2-AlPO4 and SiO2-BPO4. (a) The COHP analysis of the No.1(O)-No.8(Al), the inserted graph is two tetrahedra incorporating [AlPO4]° and [BPO4]° units, including seven O atoms (numbers 1-7) and two Si atoms (numbers 8-9). (b) The COHP analysis of the No.1(O)-No.8(B). (c) The COHP of No.4(O)-No.8(Al) for SiO2-AlPO4 and (d) SiO2-BPO4, respectively.
In Figs. 2(a) and 2(b), the calculated results show that the COHPs of No.1(O)-8(Al) and No.1(O)-8(B) have anti-bonding contributions for SiO2-AlPO4 (0 ∼ -0.5 eV) and SiO2-AlPO4 (0 ∼ -1 eV) under the Fermi level. The intensity of COHPs contributions of SiO2-BPO4 is lower than SiO2-AlPO4 (0 ∼ -1 eV), and both of the COHPs of O(2s)-Al(3p) and O(2s)-B(2p) (green line) are anti-bonding contributions. In Fig. 2(c) and Fig. 2(d), a similar situation occurred to the COHPs of No.4(O)-8(Al) and No.4(O)-8(B). It should point out that the anti-bonding peak of No.4(O)-8(B) (-0.85 eV) is lower below the Fermi level compared with No.4(O)-8(Al) (-1.25 eV).
Figures 2(c) and 2(d) show that the O-B bonding contributions are similar to the O-Al bond, having anti-bonding contributions at the top of the valence band (VB). In Figs. 3(a) and 3(b), there are many bonding contributions for SiO2-AlPO4 (No.4(O)-9(P)) and SiO2-BPO4 (No.4(O)-9(P)) in the range of 0 ∼ -4 eV. But the intensity is different. For example, the peaks of the binding energy of SiO2-BPO4 are 0.58 and 0.97, while the values of SiO2-AlPO4 are 0.26 and 0.25. Figure 3(c) shows the total energy of the COHP, that is, the sum of No.4(O)-8(Al or B) and No.4(O)-9(P). Obviously, the great B-O-P bonding contributions affect the total COHP. The anti-bonding and bonding contributions for SiO2-AlPO4 and SiO2-BPO4 are in the blue dashed box (Fig. 3(c)), respectively. In addition, the statistical results illustrate that the bond length and angle significantly vary due to the ligand field difference for the O atoms, as demonstrated in Figure S2.
Fig. 3. The crystal orbital Hamilton population analysis. The COHP of No.4(O)-No.9(P) for (a) SiO2-AlPO4 and (b) SiO2-BPO4, respectively. (c) The COHP's sum of No.4(O)-8(Al or B) and No.4(O)-9(P) for SiO2-AlPO4 and SiO2-BPO4.
The bonding and anti-bonding contributions of COHP reflect two different orbital overlapping modes, which directly affect electron distribution and charge transfer. So, we analyzed the Electron Localization Function (ELF) and electron density difference for SiO2, SiO2-AlPO4, and SiO2-BPO4. Because the Si-O, P-O, Al-O, and B-O bonds shown in Fig. 1 are hypothetical, the actual situation is the interaction of electrons between atoms. The ELF can be obtained by the follow's formula [38]:
The 2D ELF charts of SiO2, SiO2-AlPO4, and SiO2-BPO4 are obtained by slicing the 3D ELF (as shown in Fig. 4(a), SiO2-AlPO4) with a plane in Fig. 4(b) (consists of Al, O, and P atoms). The ELF's value around the Si and O atoms is about 0.75, which displays strong electron localization ability, as demonstrated in Fig. 4(c). The electron distribution of the SiO2-AlPO4 and SiO2-BPO4 are similar in Al-O-P and B-O-P plane, especially in the red dotted line box, as shown in Figs. 4(d) and 4(e). Noteworthy, the SiO2-AlPO4 and SiO2-BPO4 have similar electron distributions. It should point out that the ELF distribution in Al-O-P and B-O-P planes are different from the Si-O-Si plane because the re-optimization of SiO2-AlPO4 and SiO2-BPO4 changed the atom's location.
Fig. 4. The characterization of the Electron Localization Function and the electron density difference. (a) The 3D ELF chart of SiO2-AlPO4. (b) A plane (consisting of Al, O, and P atoms) is used to slice the 3D ELF chart. (c) The 2D ELF charts of SiO2, (d) SiO2-AlPO4, and (e) SiO2-BPO4. The two-dimensional electron density difference is drawn for (f) SiO2, (g) SiO2-AlPO4, and (h) SiO2-BPO4.
In Fig. 4(f-g), we used the same method (in Figure S4) to obtain the 2D differential charge density drawings. The red and blue areas represent the charge captured and released, respectively. We focus on the effect of doping Al and B atoms on to charge density of SiO2-AlPO4 and SiO2-BPO4, so we pay attention to the charge transfer in the red dotted box. Figure 4(f) shows that the charge is symmetrically distributed about dotted lines. In Figs. 4(g) and (h), the Al, B, and P atoms all lose electrons to a certain extent, similar to the Si atom, while the O atom gains electrons. Many charges are distributed around the O-P bond in the Al-O-P bond and B-O-P bond. In other words, the symmetry of charge distribution is broken in SiO2-AlPO4 and SiO2-BPO4, which display different bonding methods and electronic structures. Noteworthy, the charge distribution of SiO2-AlPO4 and SiO2-BPO4 showed a big similarity.
Next, we analyze the density of states of SiO2, SiO2-AlPO4, and SiO2-BPO4. Figure 5(a) shows the partial density of states (PDOS) of SiO2. The top of the VB is mainly contributed by O-2p orbitals, while the bottom of the conduction band (CB) has a mixed effect from O-2p, O-2s, and Si-3s orbitals. More importantly, the calculated forbidden bandwidth of SiO2, SiO2-AlPO4, and SiO2-BPO4 are 5.690 eV, 4.659 eV, and 4.674 eV, respectively, as shown in Fig. 5(b). Doping [AlPO4]° and [BPO4]° units reduced the forbidden band width of SiO2-AlPO4 and SiO2-BPO4 by 1.031 eV and 1.016 eV, respectively. The bandgaps of the SiO2-AlPO4 and SiO2-BPO4 are near equal, with only a marginal difference of 0.015 eV. The reason is that the bottom of the CB is mainly contributed by the P-2p, O-2s, and Si-3s orbitals, and the contribution of 3s and 3p of B and Al atoms is very small, as demonstrated in Figs. 5(c) and 5(d). The similarity of the bandgap provides good support for the partial or total replacement of [AlPO4]° unit by [BPO4]°.
Fig. 5. The density of states of SiO2, SiO2-AlPO4, and SiO2-BPO4. (a) The PDOS of SiO2. (b) The TDOS of SiO2, SiO2-AlPO4, and SiO2-BPO4. (c) The PDOS of SiO2-AlPO4 and (d) SiO2-BPO4, including the contribution of Al, B, P, O, and Si atoms.
In summary, the SiO2-BPO4 has a lower energy and great similarity with the SiO2-AlPO4 in the lattice structure, charge transport, electronic structure, and bonding contributions. Thus, the following process probably occurs:
It is found that adding B atoms can reduce the refractive index of SiO2 [27], which will further affect the numerical aperture (i.e., NA), a critical performance parameter for optical fiber. The NA is calculated with the refractive indices of the core and cladding, and it can be expressed as:
Where n1 is the refractive index of the core, and n2 is the refractive index of the inner cladding. The refractive index, n, can be obtained by the dielectric function:The complex dielectric function usually expresses the refractive index, i.e., ɛ(ω) = ɛ1(ω) + iɛ2(ω), where ω is the frequency of the incident light, ɛ1(ω) and ɛ2(ω) are the real and imaginary parts of the complex dielectric function. Generally, the ɛ2(ω) is used to describe the light absorption behavior, and it is given by the following equation [39]:
Here, the P is the principal value of the integral. The calculated ɛ1 and ɛ2 are shown in Figure S5.
From the literature, adding B continuously decreases the refractive index in Al2O3/B2O3/Yb2O3 glasses [41], which agrees with our theoretical result. In Fig. 6(a), the refractive index does not change dramatically in the range of 0 ∼ 40 eV. The initial refractive indices of SiO2, SiO2-AlPO4, and SiO2-BPO4 are 1.4677, 1.4775, and 1.4688, respectively. Guo et al. measured the change in the refractive index of YbAB glasses at 633 nm with increasing B content and found that the refractive index decreased from 1.4632 to 1.4618 in the range of 0-6.84 mol%. We calculated the refractive index of SiO2 to be 1.4786 at 636 nm, as shown in Fig. 6(b). The theoretical value agrees with the experimental value, which supports the reliability of the calculation.
Fig. 6. The calculated refractive indices of SiO2, SiO2-AlPO4, and SiO2-BPO4. (a) The change of refractive index of SiO2, SiO2-AlPO4, and SiO2-BPO4 in the range of 0 ∼ 40 eV. (b) The refractive index change is in the range of 0 ∼ 6 eV. The position marked by the dotted line is 636 nm (1.95 eV).
In Fig. 6(b), we focus on the change of the refractive index in the visible light band (380-760 nm). The refractive index of the SiO2, SiO2-AlPO4, and SiO2-BPO4 are 1.4752, 1.4856, and 1.4766 at 760 nm. The calculated result shows that the refractive index of SiO2-BPO4 is decreased by 0.61% compared with SiO2-AlPO4 at 760 nm. And the refractive index of SiO2-BPO4 decreased by 0.71% at 380 nm. Obviously, doping the [BPO4]° unit decreased the refractive index effectively compared with [AlPO4]°. By fitting, it is found that SiO2 has the smallest refractive index at different doping concentrations when the ratio Al/P = 1 [20]. Replacing [AlPO4]° unit with [BPO4]° is a possible way to adjust the refractive index in amorphous silica. In order to obtain reliable calculation results, we calculated the refractive index of the SiO2-AlPO4 and SiO2-BPO4 (192 atoms) in Figure S6 and two different doping site models in Figure S7. It can be found that the refractive index of the SiO2-BPO4 is lower than that of the SiO2-AlPO4, as shown in Figures S8 and S9, which is consistent with the above calculation results (96 atoms). Furthermore, the core's refractive index and NA can be tuned by doping [BPO4]° unit to a certain extent without reducing the active fiber's radiation resistance properties [42]. Additionally, in some cases, such as co-doping irradiation-resistant Ce3+/4+ ion in active fibers, the doping concentration of Ce3+/4+ is restricted as it will increase the core refractive index and NA [17]. With the introduction of BPO4, it might be possible to fine-tune the refractive index by co-doping B and Ce while the radiation resistance can be maintained.
4. Conclusions
In summary, our calculations show that the [BPO4]° unit is a stable structure. It can be used to replace [AlPO4]° to reduce the refractive index in fused silica. The calculated results show that the SiO2-BPO4 (-768.2 eV) has a lower energy than SiO2-AlPO4 (-767.3 eV). The DOS's calculation results show that SiO2-AlPO4 and SiO2-BPO4 have similar electronic structures and almost equal bandgap. The crystal orbital Hamilton population of both the O-Al and O-B bonds are anti-bonding contributions and have similar charge distribution and electron density differences. In addition, the refractive index of the SiO2-BPO4 is close to the pure silica, thus not altering the refractive index profile of the silica-based fiber core. In the future, we will further examine the optical and electronic properties of SiO2-BPO4 from the experimental perspective.
Funding
The Science and Technology Innovation Program of Hunan Province (2021RC3083); National Natural Science Foundation of China (12004432).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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