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Abstract
We present an investigation of the optical properties of diamagnetic P centers in P-doped silica by means of first-principles calculations, including many-body perturbation theory (GW and Bethe-Salpeter Equation) techniques. The calculated absorption spectra indicate that the 6.9 eV band is originated from the presence of a large number of [(O–)3P(=O)]0 tetrahedra, while only a negligible number of [(O–)2P(=O)2]− tetrahedra could occur. Furthermore we show that positively charged substitutional P atoms can affect the silica absorption spectrum only above ∼8 eV, while three-fold P defects are not likely to occur as they should give rise to strong features, not observed, below ∼6.5 eV.
© 2018 Optical Society of America
1. Introduction
Phosphorus-doped silica is a material of paramount importance in microelectronics, optoelectronics and in fiber optics technology [1, 2]. In particular, the core of a P-doped optical fiber is typically formed through chemical vapor deposition techniques by adding vapors of POCl3 to the standard vapors of SiCl4 and O2. These vapors react with oxygen to form the SiO2 glass including the P2O5 dopant through the following chemical reactions [2]:
P-doping is employed in the production of fiber amplifiers since it prevents the clustering of typical rare-earth dopants such as erbium, ytterbium and cerium [3–7]. Moreover P-doped optical fibers (OFs) are among the best candidate for the development of distributed radiation detectors and dosimeters [8–11]. In fact OFs doped with phosphorus show higher radiation sensitivity than those doped with other basic dopants [8, 12]. In particular, several types of paramagnetic P-related centers, the so called P1,P2,P4 and the phosphorus-oxygen-hole center (POHC) [13] are induced under irradiation (UV, VUV, x-ray and γ-ray) and give rise to signal attenuation in the visible and infrared part of the spectrum [13–15]. The radiation induced attenuation (RIA) spectrum of P-doped fibers at telecom wavelengths (∼ 1500 nm) is dominated by P1 defects [8, 16]. For dosimetry applications, the most favorable wavelengths in terms of radiation sensitivity fall in the range 500 nm to 600 nm (2–2.5 eV) where the fibers show an enhanced sensitivity due to the formation of POHC centers [9, 13]. Thanks to experimental [13, 17–19] and theoretical investigations [20, 21] the atomic and electronic structure of the P1, P2, POHC, P4 centers is nowadays rather well understood. By contrast very little is known about diamagnetic P-related centers, as far as concerns their optical signature and their role as precursors of the above mentioned paramagnetic defects.
Indirect signature of the presence of some diamagnetic precursors, such as the [(O–)3P=O]0, [], [(O–)2P(=O)2]− or [(O–)3P:], where : indicates a lone pair of valence electrons, has been proposed in few experimental investigations [13, 22]. Refs. [13, 23–25] show that, as a dominant process, a pair of a phosphorus electron center (an electron trapped at a four-fold coordinated P-atom i.e. a P2), and a POHC center is created by excimer laser irradiation [15,25], and also by x-ray irradiation [13, 23], suggesting that the following pair generation mechanism may occur:
from which one can further infer the presence of ultraphosphate (i.e. [(O–)3P=O]0) units, already supported by previous investigations [20, 22, 26], as well as of nearby substitutional P atoms in the pristine sample. Moreover by x-irradiation two variants of the POHC centers could be detected at room temperature [24]. These variants are ascribed to i) a P atom bonded to three bridging O atoms with a fourth non-bridging oxygen carrying an unpaired electron, and ii) a P atom bonded to two non-bridging oxygens which share an unpaired electron [20, 24]. These two variants of the POHC center (the so called l-POHC and r-POHC) would respectively result from a hole trapping process at the precursors [(O–)3P=O]0 and [(O–)2P(=O)2]− sites [13].Furthermore the P1 center or P-E′, has been observed, under irradiation, in P-doped silica as well as in several phosphate glasses [13, 17, 27, 28]. As analogue of Si-E′ centers, it has been speculated [13] to arise from the ionization of a three-fold coordinated P atom ([(O–)3P:]), also known as phosphorous oxygen deficient [PODC(I)] center [30]. However, the EPR signature of P1 centers in Refs. [13, 28] became observable only through a pre- or post-thermal treatment. By contrast EPR spectra collected for thin PTEOS films by using VUV illumination show a remarkable presence of P1 centers with no need of thermal treatments [19]. Furthermore conversion of POHC centers to P1 has been invoked to explain the radiation induced loss spectra of optical fibers in the range 350 to 1600 nm as well as to explain the post-irradiation recovery processes observed in P-doped optical fibers [9, 13, 29]. Such an observation is supported, for example, by the recent studies of Ref. [16] which reports of an irradiation temperature promoted conversion of the l-POHC in P1. The complicate phenomenology [9, 13, 19, 28] mentioned here above suggests that several mechanisms or several diamagnetic precursors might underlie the P1 centers generation.
The optical absorption of pristine P-doped silica is featureless until the UV. In 2007 Rybaltovsky et al. found a band at 6.9 eV in the UV absorption spectrum of a phosphosilicate glass preform doped with 12% molar concentration of P2O5 in the core [30]. Such a band was also observed independently by Origlio et al. using a preform doped with a P content in the core region of ∼ 7 wt% [23]. The band was tentatively supposed to originate from an oxygen deficient center involving a twofold Si and a three-fold P atom [so called PODC(II) center] on the basis of quantum chemical calculations of the excitation energies for a very small cluster [30]. Yet the PODC(II) corresponds locally to a site with a double oxygen deficiency, rather difficult to form in (P2O5)x-(SiO2)1−x glasses, where by contrast one expect an oxygen excess with respect to pure silica. Second, the PODC(II) model is not so consistent with the abundant generation of POHC and P2 paramagnetic centers [13, 15, 23] as it would chiefly imply the detection of other paramagnetic centers, possibly of the E′-like kind. Furthermore in addition to the 6.9 eV band, we also mention that a new absorption band at about 7.4 eV, of unknown origin, has been very recently discovered in P-doped (1 wt%) preforms [31].
The scope of the present paper is to investigate which ones among the precursors mentioned here above (i.e. three-coordinated P atoms, substitutional P atoms, [(O–)3P=O]0 and [(O–)2P(=O)2]−) are responsible or contribute to some extent to the measured optical absorption bands around 6.9 [23, 30] and 7.4 eV [31]. Such an investigation is based on the calculation of optical absorption spectra via GW-BSE approach for a series of configurations of diamagnetic P-defects. According to our results, substitutional diamagnetic P atoms () are optically silent, and the 6.9 eV band is likely to be originated from the presence of a considerable number of [(O–)3P=O]0 units. We also suggest that the presence of PO4 tetrahedral units featuring non-bridging oxygens could lead to an enhanced optical absorption around 7.4 eV. Moreover, concerning the [(O–)2P(=O)2]− tetrahedra, if present, their concentration should be sufficiently small (as compared to [(O–)3P=O]0) not to have a significant impact on the experimentally measured spectra. On the other hand, we provide evidence in favor of another precursor of the r-POHC: a [(O–)3P=O]0 unit sharing a bridging oxygen with a penta-coordinated silicon atom. Finally, as the three-coordinated P atom exhibits optically active bands, never observed experimentally, at 6.1 and 6.4 eV both with large oscillator strengths, its contribution as precursor of the P1 center, should be rather negligible. At variance, as Eq. 2 suggests a likely occurrence of P nearest neighbors as ≡P–O–P≡ units [26], we point out that alternative generation mechanisms for P1 could involve thermally induced bond breaking in ≡P–O–P≡ bridges, eventually observable as P2 to P1 conversion processes.
2. Methods
The calculations carried out in this work are based on density functional theory (DFT). In particular, the LDA exchange-correlation functional has been adopted for the DFT calculations [32] included in this work. Norm-conserving Trouiller-Martins pseudopotentials are used and Kohn-Sham wavefunctions are expanded in a basis of plane waves up to a kinetic cutoff of 70 Ry. The wavefunctions were expanded at the sole Γ point of the Brillouin zone, as justified by the large size and the large band gap of our system. Geometry optimizations have been obtained by means of non-spin-polarized calculations, though spin-polarized calculations (occupations of states are fixed to be either 1 or 0) were performed to test a few hypothesis as reported in the discussion section. The codes used for the present structural calculations are freely available with the Quantum-Espresso (QE) package v6.0 [33].
Calculations of the quasi-particle energies and of optical absorption spectra have been performed by employing many-body perturbation theory techniques as implemented in the SaX package [34]. GW calculations are carried out prior to the absorption spectra calculation through a non self-consistent G0W0 scheme, in which both the electronic Green’s function and the screened Coulomb potential are built up from eigenfunctions and eigenvalues computed at the DFT level. Wave functions and Fock operator have been expanded with a plane wave cutoff of 70 Ry. The irreducible polarizability has been calculated including 1216 states and 6 Ry cutoff. Godby-Needs plasmon pole model has been used for the energy dependence of the screened potential. A Bethe-Salpeter equation (BSE) is then solved to obtain the optical excitation energies of singlet excitations. The energy cutoff for the transitions included in the construction of the BSE Hamiltonian is 0.95 Ry. Convergence tests of the optical absorption spectrum (i.e. by monitoring peaks position and oscillator strengths) vs the BSE parameters reported here above have been carried out [for structure (iii) described in the next section] supporting an overall precision of the full GW-BSE calculations in the present silica-based systems within ∼0.1 eV [35]. The degree of localization of electronic states is evaluated through their normalized self-interaction (SI) [35].
3. Results
3.1. Structures generation
The original v-SiO2 models adopted for the present investigation consist in a periodic supercell containing 108 atoms and 576 electrons in a volume of ∼1600 Å3 [36]. The mobility gap, calculated via GW approach, is 9.4 eV, as typically found in “well-quenched” glasses, resulting in a good agreement with experiments [37]. For the purpose of calculating the optical spectrum of the diamagnetic P related defects thought to exist in P-doped silica [13, 20] we generated six P-doped configurations (shown in Fig. 1) by taking advantage of silica model structures previously generated in Refs. [36, 38–41]. P-doped configurations of (i) a positively charged substitutional , (ii) a neutral three-coordinated P defect [Fig. 1(ii)], and (iii) a [(O–)3P=O]0 tetrahedral unit structure were generated by replacing a silicon with a phosphorus atom in our previously generated silica model [36] and unpuckered configurations [38] [structures (i) and (ii)] and in the so called valence alternation pair (VAP) model [40] [structure (iii)]. Moreover in structure (ii) the second three-coordinated silicon atom of the unpuckered configuration has been passivated with hydrogen so that each silicon atom retains the ideal tetrahedral coordination and no oxygen atom is three-fold coordinated as in the puckered configuration [38]. Similarly also the three-coordinated silicon atom of the VAP model [40] has been passivated with hydrogen so that in structure (iii) the structural unit deviating from the pure silica glass picture is the [(O–)3P=O]0 tetrahedral unit [Fig. 1(iii)]. Successively the three-fold coordinated silicon, hydrogen passivated in Fig. 1(iii), was replaced with phophorus and passivated with an oxygen atom leading to a configuration containing two [(O–)3P=O]0 tetrahedral units [structure (iv)]. We note that hydrogen is introduced in the structures shown in Figs. 1(ii) and 1(iii) only as a passivation trick in order to avoid the disturbing presence of coordination defects such as three-coordinated Si defects [20, 21, 30]. A silica configuration [structure (v)] containing a [(O–)2P(=O)2]− tetrahedron was obtained by adding two terminal oxygens to a twofold P defect configuration which was obtained after replacing a silicon with a phosphorus atom in a twofold Si configurations [39, 41].
Fig. 1 Ball and stick models of the six structures used in the present work: (i) a substitutional P atom, (ii) a three-fold coordinated P atom, (iii) a single [(O–)3P=O]0 tetrahedral unit embedded in silica, (iv) two [(O–)3P=O]0 units embedded in silica, (v) a single [(O–)2P(=O)2]− unit embedded in silica, (vi) four [(O–)3P=O]0 units embedded in silica. Sticks represent bond between atoms. P atoms and their oxygen nearest neighbors are shown with yellow and red balls respectively. The H atom in (b) and (c) is shown with a cyan ball.
The last P-doped silica configuration [structure (vi)] investigated in the present work contains four [(O–)3P=O]0 tetrahedral unit structures and was obtained from the structure (iv) by replacing a ≡Si–O–Si≡ bridge with a ≡P–O–P≡ which is broken during the first-principles relaxation [42] with the concomitant formation of the pair [(O–)3P:] and [(O–)3P=O]0. The threefold P is then passivated with an oxygen atom and the structure further relaxed leading to the formation of the fourth [(O–)3P=O]0 tetrahedral unit in this configuration.
All the structures were subsequently optimized by relaxing the atomic structure using the Broyden-Fletcher-Goldfarb-Shanno (bfgs) algorithm as implemented in the pw.x code [33]. The relaxation criterion was defined by means of a force threshold of 0.02 eV Å−1. As the fully relaxed (FR) configuration of structure (v) actually contained a [(O–)3P=O] tetrahedron with a bridging oxygen shared by a penta-coordinated silicon and by the P tetrahedron [see end of the discussion section], the “ideal” configuration of structure (v) used for the optical absorption calculation in the next section is chosen with the criteria that the two P=O bonds show the least possible length difference using a force threshold for the convergence not more than ten times larger than usual. With such a choice the FR structure (v) is lower in energy by 0.7 eV with respect to the ideal one containing a [(O–)2P(=O)2]− unit discussed in the next section. It is also worth to remark that, despite the present DFT calculations could not stabilize one single [(O–)2P(=O)2]− tetrahedral structure embedded in pure silica, we carried out a test relaxation (not included in the manuscript) for a configuration with a high P-doping level as in Fig. 1(vi), initially containing four neighboring phosphate groups. In the optimized configuration we could observe the spontaneous formation of a [(O–)2P(=O)2]− unit, but with the concomitant presence of other defects such as three-coordinated P atoms.
Structural parameters (e.g. P–O and P=O bond lengths) of the investigated configurations are reported in Table 1 and compared with Refs. [20,21]. The calculated P=O bond length is also in good agreement with the average bond P=O lengths for P2O5 polymorphs reported by [43, 44].
3.2. Optical absorption spectra
Optical absorption spectra of the diamagnetic P-configurations [namely Figs. 1(i),(ii),(iii) and (v)] have been carried out by means of the GW-BSE approach and are shown in Fig. 2. The main exciton peaks positions below ∼7.5 eV together with their corresponding oscillator strengths are summarized in Table 2 for a typical doping concentration of ∼1 wt% P-doping [31]. We note that the oscillator strengths of single excitons are reported in Table 2 as an indication. What matters for the comparison between the theoretical and experimental oscillator strengths is the integral over an energy range of the absorption as expressed in the Smakula’s formula [45].
Fig. 2 Optical absorption spectra of P-doped configurations containing a [(O–)3P=O] unit (black/solid), a [(O–)2P(=O)2]− unit (green/dot-dashed), a three-coordinated P atom (orange/double-dot dashed) and a substitutional unit (blue/dotted) together with the spectrum of the undefected a-SiO2 (red/dashed line). Artificial broadenings of 0.014 eV have been used.
Table 2. Calculated energy position (eV) together with oscillator strengths (f) for the first (brightest) excitons below ∼7.5 eV in silica models containing [(O–)3P:]0, [(O–)3P=O]0 and [(O–)2P(= O)2]− unit structures (∼1 wt% P-doping [31]). The main single-particle transitions underlying the exciton are shown in Figs. 4, 6 and 7.
As far as concerns the [(O–)3P=O]0 tetrahedral unit, no optically active bands are observed below 6.9 eV (Fig. 1). The first absorption peak is located at 6.9 eV with a rather low oscillator strength (f) of 0.004. The decomposition in terms of single-particle transitions shows that the first exciton is composed by a transition (94% of the spectral weight) mainly involving the doubly occupied O 2p lone pair and the bottom of the conduction band (BCB) [Figs. 3(a),(b) and (c)]. The charge density of the first two highest occupied states [Figs. 3(a),(b)], which are localized on the non-bridging oxygen of the PO4 tetrahedron, is consistent with results found for phosphate groups in Ref. [46] where the HOMO in phosphate such as (MeO)3P-O is shown to be degenerate. We note also that the nature of the P–O bond for the non-bridging oxygens is still rather debated and alternative notations might be used i.e. double bond P=O or dative bond P→O [46,47]. Right above 7 eV the spectrum exhibits a series of narrow peaks originated from the transitions between rather localized top of the valence band (TVB) and the BCB states which leads to an enhancement (with respect to pure a-SiO2) of the absorption intensity around 7.4 eV. In fact the disorder [48, 49] due to the presence of P atoms and the subsequent local rearrangements [35] can lead to the localization of states at the valence band edge which in turn may correspond to minor features in the absorption spectrum.
Fig. 3 Charge density (shadowed) of [(a) and (b)] the first two highest occupied states a1, a2 and (c) of the the bottom of conduction band state as calculated for structure (iii) shown in Fig. 1. Isolevels are set to 10% of the grid maximum.
The optical absorption (OA) spectrum calculated for a [(O–)2P(=O)2]− shows intensity also below ∼ 7 eV, in particular with a pair of optical absorption peaks at about 6.1 and 6.5 eV, corresponding to excitons whose oscillator strengths are 0.009 and 0.006, and other two minor peaks at 5.1 and 5.4 eV both with f ∼ 0.001. The decomposition in terms of single particle transitions shows that the latter four excitons are given (more than 90% of spectral weight) by transitions between one of the four highest occupied states [localized on the O 2p of the oxygen nearest neighbors of the P atom as shown in Figs. 5(a),(b),(c) and (d)] and the bottom of conduction band state [Figs. 6(b) and Fig. 5(f)]. Moreover, a third bright exciton peak is found at 7.2 eV which, analogously to the first four exciton peaks, shows a rather large spectral weight (74%) for the transition between a state [Fig. 5(e)], mainly localized on the oxygen nearest neighbors of the P atom although clearly mixed with TVB, and the bottom of conduction band state [Fig. 6(b)].
Fig. 4 (a) Optical absorption spectra and (b) density of states (DOS) of the [(O–)3P=O]0 defect configuration (solid line) and of the undefected a-SiO2 (red dotted line). Artificial broadenings of 0.15 eV and 0.014 eV have been chosen to represent the DOS and the absorption spectra respectively. Vertical dotted lines are used to indicate the defect states a1,a2 (O 2p of the terminal oxygen) and the bottom of the conduction band (bcb). The localization of states in P-doped (squares) and pure silica (discs) models is shown in (b) by means of the normalized |SI|.
Fig. 5 Charge density (shadowed) of [(a) to (e)] the first five highest occupied states a1–a5 and (f) of the bcb state as calculated for structure (v) shown in Fig. 1. Isolevels are set to 10% of the grid maximum.
Fig. 6 (a) Optical absorption spectra and (b) density of states (DOS) of the [(O-)2P(=O)2]− defect configuration (solid line) and of the undefected a-SiO2 (red dotted line). Artificial broadenings of 0.15 eV and 0.014 eV have been chosen to represent the DOS and the absorption spectra respectively. Vertical dotted lines are used to indicate the single-particle transitions A,B,C,D,E between defect states and the bottom of the conduction band (bcb). The localization of states in P-doped (squares) and pure silica (discs) models is shown in (b) by means of the normalized |SI|.
Concerning the calculated optical absorption spectrum of a single positively charged substitutional P [50], i.e. a , no feature is found below ∼7.5 eV [Fig. 2], resulting in a spectrum almost undistinguishable from the one of the pure undefected v-SiO2. In fact diamagnetic substitutional P atoms are isoelectronic with respect to Si atoms. The occupied orbitals of the two species do hybridize, and the top of the valence band consists, as in pure silica, of O 2p nonbonding states [51], so that no defects states appear within the band gap, and thus the optical absorption is similar to the one of pure silica.
We note that by using an UV source with energies of about 10 eV one can ionize the localized electrons of the a levels shown in Figs. 4,6,7. The subsequent relaxation of the electronic structure then leads to the formation of a l-POHC, r-POHC, and a P1 center respectively.
Fig. 7 (a) Optical absorption spectra and (b) density of states (DOS) of the three-coordinated P defect configuration (solid line) and of the undefected a-SiO2 (red dotted line). The localization of states in P-doped (squares) and pure silica (discs) models is shown in (b) by means of the normalized |SI|. Artificial broadenings of 0.15 eV and 0.014 eV have been chosen to represent the DOS and the absorption spectra respectively. Vertical dotted lines are used to indicate the defect states a, b and the bottom of the conduction band (bcb). Bottom panel (c) charge density of the highest occupied state a and (d) a localized state of the conduction band (at ∼11.6 eV).
In Fig. 7(a) we show the OA of a silica model containing a three-coordinated P atom configuration. The calculated optical absorption spectrum shows a rather weak peak [i.e. exciton peak A] at about 5.9 eV and two strong absorption peaks (B and C) at about 6.1 and 6.4 eV with f equals to 0.05 and 0.04 respectively, comparable to the f ∼ 0.1 observed and calculated for twofold Si defects [41]. The electronic density of states [Fig. 7(b)] calculated for the configurations containing a threefold P typically features as highest occupied level a, at ∼ 2 eV above the top of the valence band, a strongly localized state on the threefold P [Fig. 7(c)], and a series of partially localized states b, at ∼ 2 eV above the bottom of the conduction band, given by the mixing of p states of the three-fold P, p non bonding orbitals of the oxygen atoms, and sp states of the silicon atoms [43,51]. The transitions between a and bcb and between a and b levels are responsible for the rather (with respect to B and C) dark exciton A at 5.9 eV [52], and for the optical absorption in the range ∼6.1 to 7.5 eV [Figs. 7]. In particular, the first exciton A results almost entirely (98%) from the a to bcb transition, while the bright excitons (e.g. B and C) in the range ∼6.1 to ∼7.5 eV involve transitions between the a state and a couple of b states with a lower weight (∼70%) not so allowing for an interpretation in terms of single-particle transitions. Above ∼7.5 eV the dominant contribution to the optical absorption spectrum comes from excitons involving multiple transitions between the valence band and the conduction band.
In Fig. 8 we show the OA spectrum of three P-doped silica configurations for a P content of up to 6 wt%. The configurations contain one, two and four [(O–)3P(=O)]0 tetrahedral unit structures. By considering multiple phosphate groups in the simulation cell we could check that, despite the short separation between these groups, the localized states on the non-bridging oxygens are not spoiled by spurious interactions with the environment, which could lead to an excessive broadening of the optical absorption arising from transitions like A of Fig. 4, which would thus contribute to the optical absorption spectrum only as background. By contrast from Fig. 8 it is apparent that the intensity at ∼7 eV can be further enhanced for configurations containing several [(O–)3P(=O)]0 tetrahedral units, suggesting that the intensity of the experimental 6.9 eV peak could be related to the concentration of [(O–)3P(=O)]0 units. In particular by integrating (prior the application of the gaussian broadening) the intensity of the three models plotted in Fig. 8 between 6.5 and 7 eV and by fitting the resulting values vs number of [(O–)3P(=O)]0 units, we obtain an effective oscillator strength for the 6.9 eV peak of 0.006 (with a fit error of 0.001) to be compared with the 0.004 value given in Table 2.
Fig. 8 OA spectrum (solid) of a P-doped silica model with 1 to ∼6 wt% P content (four P atoms): additivity of the peak at ∼7 eV in configurations containing one (solid) and two (red/dotted) and four [(O–)3P(=O)]0 (blue/dashed) units [structures (iii), (iv), (vi) of Fig. 1]. A 0.1 eV broadening is applied. In the inset the experimental optical absorption [taken from Refs. [23] (solid) and [31] (dotted)] of P-doped silica preforms (7 wt% and 1 wt% P content) in the UV-VUV range are shown.
4. Discussion
According to the generally accepted structural model, based on previous investigations by Raman, infared spectroscopies etc, the phosphosilicate glass consists of a network, lacking long-range order, mainly composed of [(O–)2Si(–O)2]0 and to a lesser extent of [(O–)3P=O]0 corner sharing tetrahedra, together with a minor fraction of [(O–)2P(=O)2]− tetrahedra and eventually of substitutional atoms [20,53]. Although it is quite tempting to assume that the 6.9 eV band is related to such basic building blocks or of defects that could easily be derived there from, in the present work we demonstrate that substitutional P atoms do not contribute to the 6.9 eV band leading to a spectrum very similar to the one of pure v-SiO2. Furthermore [(O–)2P(=O)2]− also are not so likely to contribute to the 6.9 eV band as, if present in sufficient amount, they would be responsible for strong peaks at a lower energy (∼ 6 eV). Yet, the explanation of the 6.9 eV band in terms of a major building block is strengthened by our results (Figs. 4 and 8) which strongly indicate that the 6.9 eV peak can originate from a transition between a localized state on the non-bridging oxygen of the [(O–)3P=O]0 unit structure and the bottom of the conduction band. Hence, the present investigation indicates that it is not necessary to assume an oxygen deficiency to explain the 6.9 eV band which is likely to arise simply as consequence of P-doping in silica, in contrast to the assignment of a previous investigation [30].
The rather small (as compared e.g. to those of twofold Si defect [41]) oscillator strengths found in this work for OA peaks in the range 6.5–7.5 eV in the spectra of the [(O–)3P=O]0 and [(O–)2P(=O)2]− structures could lead to think that important contributions to the 6.9 eV band could come also from other defect structures e.g. from three-coordinated P defects. However the neutral three-fold P atom is considered as the precursor of the P1 center but the latter center is sometimes not observed in irradiated P-doped silica samples [15, 23]. Furthermore it could be observed in a discernable manner only after annealing up to 673 K [13] or using more sensitive techniques like second harmonic EPR measurements [16, 54] allowing to detect defects present in low concentrations. Hence the concentration of three-coordinated P atoms in the as manufactured P-doped preforms is likely to be rather small as compared with those typical of the P2 and POHC precursors.
It is also worth to note that, considering the relative position of a levels in Figs. 4, 6 and 7, an UV irradiation of a sample containing a large amount of three-coordinated P defects would most likely lead to a concomitant formation of a large amount of P1 and r-POHC centers, on one hand, and of P2 centers on the other hand (a which captures a free electron). By contrast, experimental observations [13, 15, 23], support clearly a concomitant formation of POHC and of a P2 centers, while a P1 signal can be detected only using dedicated techniques [16]. Hence the generation of P1 center via ionization of an isolated three-coordinated P defect is likely to be limited by the small amount of available precursor sites. By contrast, the annealing at high temperatures lead to the efficient formation of P1 center by allowing to overcome an energy barrier of a conversion process. For instance, provided that P atoms are nearest neighbors as in ≡P–O–P≡ linkages [26, 55], a P–O bond of a P2 center could break up with the concomitant formation of a P1 center together with a nearby [(O–)3P=O]0 tetrahedron. Concerning the origin of the 7.4 eV peak appearing in the experimental absorption spectrum of Ref. [31] the results shown in Fig. 8 suggest that it might also be related to the presence of [(O–)3P=O]0 tetrahedra [solid and dotted lines in Fig. 8]. In particular the origin of the 7.4 eV band could be related to the P-doping induced presence of localized states on the top of the valence band [Fig. 4(b)]. Such an hypothesis is supported by the fact that several excitons in the range 7.2-7.6 eV calculated for the silica models containing [(O–)3P=O]0 units, involve transitions between TVB localized states and bcb and show oscillator strengths (0.002) comparable to the f (0.004) of the first one at 6.9 eV [Table 2]. We also note that the optical absorption intensity above 7.0 eV could also be enhanced by the presence of [(O–)2P(=O)2]− units as signaled by the rather bright exciton (0.009) at 7.2 eV due to such a structural unit [Table 2].
The optical absorption spectrum of the [(O–)2P(=O)2]− contains rather strong peaks in the range ∼6 to 7eV with an f about double of the 6.9 eV exciton peak calculated for [(O–)3P=O]0 [Table 2], so that one could expect to observe them even for a rather low concentration of [(O–)2P(=O)2]− units. Since there is no clear feature or shoulder visible in the experimental spectrum in the range ∼6 to ∼6.5 two scenario are possible: either the concentration of [(O–)2P(=O)2]− units is not sufficient to make them observable as side bands of the 6.9 eV peak [20, 26], or in alternative one should rule out the idea of a precursor of the POHC center showing two non-bridging oxygen atoms as originally proposed by Griscom [13] and look for other possible precursors. In particular, we note that the fully relaxed [(O-)2P(=O)2]− (see also Sec. 3.1) only shows the presence of one single non-bridging oxygen, while the other actually binds to a silicon atom which becomes penta-coordinated [Fig. 9(a)]. Such a configuration, once it is positively charged, becomes the POHC paramagnetic defect with two non-bridging oxygen [13, 20] i.e. the r-POHCS, as shown by the spin-density of our first-principles relaxed structure in Fig. 9(b). Furthermore, the optical absorption spectrum (not shown) calculated for the configuration in Fig. 9(a) has a couple of rather weak peaks at 5.7 and 5.9 eV (f of 0.001 and 0.003) and no absorption peak in the range 6 to 7 eV and a broad peak at ∼7.7 eV orginated from a numerous series of excitons sharing a similar origin of those in found at about ∼7.4 eV for the silica model containing a [(O–)3P=O]0 unit [Fig. 4].
Fig. 9 (a) Charge density of the highest occupied state for the fully relaxed [(O-)2P(=O)2]− configuration: the charge density is localized on the non-bridging oxygen and on the oxygen shared between the four-coordinated P-atom and the penta-coordinated Si atom. (b) Spin-density of the configuration obtained by first-principles relaxation of the neutralized [i.e. by removing one electron] configuration (a) and corresponding to a r-POHC center [20, 24].
The difference (∼ 1.5–2 eV) between the positions (with respect to the top of the valence band) of the localized states in [(O–)2P(=O)2]− and [(O–)3P=O]0 is consistent with a larger hole-trapping efficiency of the former center with respect to the latter [20]. Furthermore, such an energy level difference suggests that, especially by using ArF laser irradiation (6.4 eV), the former PO4 tetrahedra are ionized and give rise to the paramagnetic r-POHC centers much more efficiently than l-POHC, despite [(O–)3P=O]0 are likely to be considerably more abundant than [(O–)2P(=O)2]− as indicated by our calculation of their optical absorption spectra (Figs. 6 and 4). Finally, the present investigation supports the occurrence in P-doped silica, at any P-doping concentration, of connected PO4 units forming ≡P+–O–P+ ≡ bridges (P+ stands for ). In particular the first-principles relaxation of our structures strongly suggests that the ≡P+–O–P+≡ bridge can break apart as soon as one or two electrons are trapped by P atoms of the bridge leading to the formation of a pair of three-coordinated P and [(O-)3P=O]0 units. Such a double phosphorus center (i.e. the ≡P+–O–P+≡ bridge) is likely to be involved in the radiation induced generation of P1 centers as well as in the conversions of P2 and POHC to P1 centers observed in several experimental investigations [9, 13, 16, 29, 42], the study of which is beyond the scope of the present work.
5. Conclusions
In this paper we have shown the results of a first-principles investigation on P-doped silica mainly aiming at understanding the absorption spectrum of the non-irradiated P-doped samples which features an optical absorption band at 6.9 eV. The latter absorption band is likely to be originated from the large number (as expected on the basis of previous structural investigations) of [(O–)3P(=O)]0 tetrahedral units, which, on the basis of the present calculations, give rise to a peak at ∼ 7 eV clearly depending on the concentration of such structural units. As far as concerns the [(O–)2P(=O)2]− tetrahedral structural units the present calculations suggest that they could contribute to the absorption spectrum in the range ∼ 7–7.5 eV. However, the lack of observation of features below 6.5 eV suggest a remarkably low concentration of [(O–)2P(=O)2]− with respect to [(O–)3P(=O)]0 tetrahedral units. Furthermore we show that r-POHC centers might be derived starting from an alternative precursor model which is represented by a [(O–)3P(=O)]0 unit showing a bridging oxygen shared with a pentacoordinated silicon. Despite the fact that substitutional P atoms could be rather abundant, as one may infer from the occurrence of P2 centers in irradiated samples, their contribution to the absorption intensity is shown to be negligible below ∼8 eV. Other defect structures like neutral three-coordinated P atoms are much less likely to occur in as manufactured non irradiated samples. In fact three-coordinated P atoms exhibit two strong optically active bands at 6.1 and 6.4 eV which were never observed experimentally, suggesting its contribution as direct precursor of the P1 center should be rather negligible, and other precursors as the ≡P+–O–P+≡ bridge might be envisaged.
Funding
ARRS-CEA Bilater Project CADHARD (BI-FR/CEA/15-17-001); Area Science Park of Trieste within the Operative Regional Programme of the European Social Fund 2014-2020 of the Autonomous Region of Friuli Venezia Giulia (TALENTS3 Fellowship Programme, code FP1718349005, RaDIOF project).
Acknowledgements
The calculations in this work were performed using the HPC resources of CINECA (IscraB project: OXYRIS-HP10B5K2GU) and of GENCI-CCRT (Grant No. 2016096137). We also acknowledge the CNR-IOM DEMOCRITOS Simulation Center for providing high-performance computing resources.
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