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Correlations Between Structural and Optical Properties of Peroxy Bridges from First-Principles Blaž Winkler, Layla Martin-Samos, Nicolas Richard, Luigi Giacomazzi, Antonino Alessi, Sylvain Girard, Aziz Boukenter, Youcef Ouerdane, and Matjaz Valant J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b11291 • Publication Date (Web): 18 Jan 2017 Downloaded from http://pubs.acs.org on January 19, 2017

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The Journal of Physical Chemistry

Correlations Between Structural and Optical Properties of Peroxy Bridges from First-Principles Blaˇz Winkler,∗,†,‡ Layla Martin-Samos,∗,†,¶ Nicolas Richard,§ Luigi Giacomazzi,¶ Antonino Alessi,‡ Sylvain Girard,‡ Aziz Boukenter,‡ Youcef Ouerdane,‡ and Matjaˇz Valant† †University of Nova Gorica, Materials Research Laboratory, Vipavska 11c, SI-5270 Ajdovˇsˇcina, Slovenia ´ ‡Laboratoire Hubert Curien, UMR-CNRS 5516, F-42000 Saint-Etienne, France ¶CNR-IOM/Democritos National Simulation Center, Istituto Officina dei Materiali, c/o SISSA, via Bonomea 265, IT-34136 Trieste, Italy §CEA, DAM, DIF, Bruyéres-le-Chˆ atel, F-91297 Arpajon, France E-mail: [email protected]; [email protected]

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Abstract This work aims at addressing the issue of the optical signature of peroxy bridges by using first-principles methods that combine Density Functional Theory (DFT), GW (where G and W stand for one particle Green function and screened Coulomb potential, respectively) and the solution of a Bethe-Salpeter Equation (BSE) on a bulk amorphous SiO2 model. We demonstrate that the presence of bridges induces broad and weak absorption bands between 3.2 and 7.5 eV. By analyzing the Si-O-O-Si dihedral angle distributions and the corresponding electronic structure, we show that the low overlap between O−2p states involved in the optical transitions together with the dihedral angle site-to-site disorder are at the origin of this weak and broad absorption. Moreover, the energy difference between the two first optical transitions depends linearly on the energy difference between the two first occupied defect-induced electronic states, i.e. depends on the dihedral angle of the bridge. This behavior may explain the longstanding controversy regarding the optical signature of peroxy bridges in amorphous SiO2 . As the correlation is independent on the specific hosting hard material, the results apply whenever the dihedral angle of the bridge has some degree of freedom.

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Introduction

In oxides, interstitial oxygen atoms are expected to play a fundamental role in many chemical reactions. Among others, they may act as diamagnetic precursors of peroxy-radicals 1–8 , or as intermediate species in oxidation of metallic (or semi-conducting) surfaces 9,10 . They may be involved in oxygen exchange 11 between oxide network and molecular oxygen and in oxygen diffusion through solids 12–20 . Furthermore, beside their fundamental relevance, the interest in absorbed interstitial oxygen atoms and related defects, has been renewed by increasing needs for improved sensors in radiation environments, for which oxygen excess may improve their radiation resistance 21 , by current developments in the field of oxide-based resistive random access memories (OxRRAM) that exploits the reversible process of oxide reduction 2


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under intense electric fields 22,23 and by recent advances in bio-physics, where silica nanoparticles and mesoporous silica are foreseen for various applications like drug delivery or bio-sensoring 24–26 . For the particular case of nanoparticles, due to the small size of the their wall, the oxygen of air can play a role on their properties through the formation of oxygen-related defects at the interface 27,28 . In the case of the most studied prototypical oxide, i.e. silica, the neutral interstitial oxygen atoms are absorbed by the network through formation of PerOxy Links (POL, also called peroxy bridges). Despite a remarkable amount of research work done along the years, POL have never been clearly and directly observed through optical measurements 8,11,29 . In particular, their optical signature is still a source of controversy. One of the first experimental detection of the POL defect in silica glass was described in 1989 by Nishikawa et al. 30 . The authors detected a weak optical absorption around 3.8 eV in oxygen-surplus samples. After a treatment of the samples in hydrogen-rich atmosphere this peak decreased while the known absorption peak, originated from the hydroxyl group (OH), increased significantly. The lack of an electronic paramagnetic resonance (EPR) signal (within the detection limit) from the initial samples, which excluded the presence of other precursory charged defects, allowed the authors to conclude, that the observed peaks were originated from the precursory presence of POLs. The idea behind was that POL defects may be transformed into -OH groups during hydrogen annealing following the reaction: SiO-O-Si + H2 → Si-OH HO-Si . However, in later studies by Awazu et al. 31,32 the 3.8 eV band has been re-assigned to the presence of Cl2 impurities . As the Cl2 model alone could not explain the -OH signal increase, the authors concluded that POL should also be present but with an optical signature hidden by the presence of other defects (including Cl2 itself). Imai et al. 33,34 have attributed a broad and weak absorption feature between 6.5 and 7.8 eV to the presence of POL by analyzing UV absorption of various synthetic silica glasses. This assignment was done on the same basis as Nishikawa et al. 30 . Indeed, the intensity of this broad band was decreasing while the -OH Infrared (IR) absorption was increasing

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after hydrogen treatment. At that time, there were no studies available on the contribution of -OH groups in the UV region 35 . In 2000 Y. Sakurai 36 studied the correlation between a photoluminescence band at 1.5 eV and the optical band at 3.8 eV. Because of their correlated behavior the author concluded that their origin was more likely to arise from the presence of POL than Cl2 . Skuja et al. 37 found a weak band at 7.1 eV (FWHM of 0.7eV, oscillator strength f ≈ 0.01) by comparing the absorption spectra of oxygen-rich silica samples before and after F2 laser treatment. As the attempts to directly and clearly observe POL were quite unsuccessful, leaving too much space for speculation, Kajihara et al. proposed a different approach 11 . The authors tracked 18 O isotope labeled O2 molecules to measure the amount of oxygen that was inserted or exchanged with the silica network during thermal and F2 laser treatments. After irradiation, authors could only detect 65 % of the initial O2 concentration in the sample, indicating that the remaining 35% should have been incorporated into the network under some kind of defect. As none of the measured absorption bands could fully explain the missing 35% of initial O2 , authors concluded that POL should be the main defect for the incorporation O2 , following the reaction Si-O-Si+ 12 O2 → Si-O-O-Si. More recently Mehonic et al. 22 have shown application of silicon oxide as a media for non-volatile data storage with very high capacity and stability. While the material used in this research is silicon rich, the authors have shown that change of resistivity, which is the main mechanism behind data storage, is actually achieved by the migration of oxygen and formation of peroxy groups. Peroxy groups have been detected using a X-ray photo-emission spectroscopy (XPS) and this could be considered as a first direct observation of POLs in silicon oxide. On the theoretical side, the first calculation of POL absorption band was proposed by O’Reily and Robertson in 1983 38 . By solving a tight-binding model Hamiltonian on an αquartz cluster, they found the lowest σ to empty σ ∗ transition with an excitation energy of 8.6 eV. Pacchioni et al. 39 studied the POL defect on a Si2 O8 H6 cluster at different Configuration Interaction (CI) levels, finding the lowest transition at 6.5 ± 0.3 eV with a very low oscillator strength (approximately 10−4 ). The lowest excitation was found to come from a transition

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between an occupied π∗ to the conduction band. Stefanov et al. 40 used bigger clusters than Ref. 39 and combination of double excitations and coupled cluster (CC) methods to find a weak singlet-to-singlet transitions at 5.5 eV (valence to empty σ ∗ band, f=10−4 ). Szymanski et al. 41 studied a role of structural disorder in incorporation of POL on 48 different positions within 72 atoms amorphous-silica model. They reported a strong site-to-site dependence that effects not only local but also medium range geometry of the model. In Ref. 42 the authors calculated the optical absorption spectra of 7 different POL configurations in a 72atom bulk-silica model using TD-DFT. According to their results, no correlation between geometrical parameters such as O-O, Si-Si and Si-O-O-Si angles and excitation energies, coming from electronic transitions localized in the POL, was found. Because the defect is strongly localized the authors concluded that the disorder would play a minor role in such transitions. The lowest excitation was found at 4.45±0.1 eV with an oscillator strength of about 10−3 . This excitation was found to come mainly from transitions between an occupied σ and an empty anti-bonding σ. Very recently a study performed on cluster silica model at the simplest DFT level predict a marked absorption at 7.35 eV 43 . As it is well known, standard DFT is a ground-state theory and therefore do not provide with accurate quasiparticle and optical excitation energies, see for instance 44 . In 2016 Wang et al. 45 performed some GW-BSE calculations in a bulk fused silica model finding three occupied defect states coming from hybridization of oxygen 2p orbitals and an unoccupied defect state coming from O 2p, Si 3s and Si 3p, with a Fermi energy drawn below the first two occupied defect states (see Figure 4 of Ref. 45 ). The authors identified two distinct weak peaks at 4.3 and 6.6 eV to be associated with the presence of POL based on a single POL configuration. It is quite surprising that authors found three occupied defect states above the silica Top of the Valence Band (TVB), as -O-O- hybridized orbitals should give a σ bonding orbital (that energetically stand well below the O 2 p* that control the TVB), two π ∗ and an empty σ ∗ . The quite misleading position of the Fermi level, together with the number of occupied defect states and the lack of a statistical study lead to some doubts on the representativity

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of their results. Table 1: Summary of previous theoretical works. Only lowest excitation energies, oscillator strengths and corresponding main single-particle transitions are reported. TVB and BCB stand for Top of the Valence Band and Bottom of the Conduction Band, respectively. Ref 38 39 40 42

Lowest trans. pσ →pσ ∗ π ∗ →BCB TVB → σ ∗ σ → π ∗ and/or σ ∗ 46

Energy 8.6 eV 6.5(0.3)eV 5.5 eV 4.4(0.1)

f / ≈10−4 10−4 ≈ 10−3

It is interesting to note (see Table 1 for a summary) that different approaches predict transition energies with quite different values (ranging from 4.3 to 8.6 eV) and even different single-particle states to be involved in the lowest peroxy-bridge-induced absorption band. The disagreement between approaches is not only quantitative, which is something that may be understood by the use of different levels of theory (in particular how long range correlation effects are taken into account or not), but also qualitative. In the following, we will demonstrate how the site-to-site disorder, that has only been marginally addressed and never fully explained, directly impacts on the electronic structure and first excitation energies of peroxy bridges, thus providing an additional origin for the qualitative disagreement in previous theoretical studies. Moreover, the analysis of the full electron-hole excitation spectrum to be associated with the presence of POL will provide a basis to understand the experimental ambiguity in determining their optical signature.

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Computational approach

A 108 atom silica model with no coordination defects was used as an ideal reference (undefective silica model). The model was extensively described in Ref. 47 and compared to larger models. POL configurations were created by inserting by hand an oxygen atom into each of the site-dependent 72 Si-O-Si bonds of the undefective silica. 6


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Equilibrium atomic structures, cell parameters, and mean-field ground-state electronic structures were obtained by a full relaxation (atoms and cell parameters) within Density Functional Theory using the Quantum ESPRESSO distribution 48 . The N-1 and N+1 excitations (with N being the ground-state number of electrons) were calculated using perturbative G0 W0 as implemented in SaX 49 . The GW approximation (where G and W stand for one particle Green function and screened Coulomb potential, respectively) provides quasi-particle energies including exchange and long-range correlation effects by solving Dyson-like Equations based on the irreducible polarizability calculated within the Random Phase Approximation (RPA). Subsequently, the neutral excitation energies and wave-functions were found by direct diagonalization of an effective two-particle Hamiltonian, namely the Bethe Salpeter Equation (BSE), that takes into account electronhole (e-h) interactions screened by the effective screening potential, W, calculated in the previous GW step. Eigenvalues and Eigenvectors of the BSE provide with the electron-hole excitation energies and the single-particle decomposition of each excitation, respectively . For energies below the free-electron-hole gap, the electron-hole pair is bound and it is called exciton 50 . GW and BSE have been successfully applied to the calculation of electronic and optical properties of many materials inorganic as well as organic, among many others Refs. 44,51–54 (for a introductory review see 50 ). In the particular case of silica, such approaches have already proven their high accuracy 55–58 . All calculations are based on plane-waves, pseudo potentials and periodic boundary conditions. Perdew-Zunger norm conserving pseudo-potentials 59 for both O and Si have been chosen, following the conclusions of Ref. 60 . For what concerns the DFT relaxations, a planewave cutoff of 80 Ry (≈1100 eV) together with convergence thresholds of 10−6 Ry (10−5 eV) for electrons, 10−4 Ry (10−3 eV) for the total energy and 10−3 Ry/a.u. (10−2 eV/a.u.) for the forces were used. GW-BSE calculations were performed with the following grids: 70 Ry (≈ 950 eV) cutoff for the wave-functions, 70 Ry (≈ 950 eV) cutoff for the Fock operator, 6 Ry (≈ 82 eV) cut-off for irreducible polarizability and screened Coulomb interaction, 800 bands

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(which corresponds to a transition energy cutoff of about 45 eV) for the Green functions in both the polarizability and the self energy. A transition energy cut-off of 1 Ry (13.6 eV) was chosen for the BSE matrix, which grants a precision below 0.01 Ry (0.13 eV) for strongly localized excitons (below the free electron-hole gap). Special Γ-point techniques were used for treatment of the long wave length limit at the GW and BSE levels, see 49,61,62 . Because of the extremely high computational cost of GW-BSE, from the 72 POL configurations that had been relaxed within DFT, we selected 11 configurations for the calculation of optical properties. These 11 configurations, were chosen in such a way that the formation energy distribution is sampled consistently, i. e. few configurations around the tails and more within the standard deviation (see Figure 1). As it will be clear from section 4, these sample configurations are used to understand the optical and electronic properties of POL in terms of general concepts and key quantities.

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Results

3.1

Formation energy and geometry parameters

From the DFT full-relaxation of the 72 POL configurations we have calculated their respective formation energies as total energy differences, assuming an equilibrium with an O2 gas reservoir: 1 Ef = EPOL − ESiO2 − EO2 , 2

(1)

where EPOL is total energy of a given POL configuration, ESiO2 is total energy of the undefective silica model and EO2 is the energy of an isolated oxygen molecule in its triplet ground state. Due to the site-to-site disorder, each Si-O-Si insertion site is slightly different thus each final Si-O-O-Si POL configuration leads to a slightly different formation energy and geometrical equilibrium parameters. Subsequently, formation energies are distributed (see Figure

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1a), with values ranging from 0.56 eV to 2.30 eV and a mean of 1.36(0.32) eV. The geometrical parameters are also distributed (see Table 2 and Figure 1b ): -O-O- distance varies between 1.47 ˚ A and 1.52 ˚ A with a mean value of 1.49(0.01) ˚ A, while the Si-O-O-Si dihedral angle takes values ranging from 90

◦

to 180

◦

with a mean value of 134.5(23.1)◦ . Our results

are in a very good agreement with previous works 13–15,20,39–41,47 .

Figure 1: Subfigure a - Formation energy (Ef ) and subfigure b - dihedral angle (α[Si-O-O-Si]) distributions. Numbered vertical lines indicate the Ef and α[Si-O-O-Si])of the 11 selected configurations for the calculation of electronic and optical properties at the GW-BSE level.

Table 2: O-O distance (d(O-O)) and dihedral angle (α(Si-O-O-Si)) averaged over all 72 POL configurations. For comparison, the d(O-O) and α(Si-O-O-Si) of the lowest formation energy configuration is also shown.

Mean lowest Ef

d(O-O) 1.49(0.01)˚ A 1.495˚ A

α(Si-O-O-Si) 134.5(23.1)◦ 106.9◦

At thermodynamic equilibrium, the formation energy probability distribution has to be Boltzmann weighted. Thus, only the lowest formation energy sites will have a significant probability to host a POL. But, as experiments are usually performed in out-of-equilibrium conditions (non-stoichiometric, strain, high temperature, high pressure and/or irradiation) all insertion sites are in principle accessible. 9



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3.2

Electronic structure

As two oxygen atoms are involved in the POL, one would expect to find, in the band gap neighborhood, two occupied π∗-like orbitals and one unoccupied σ ∗ bond. Indeed, this is mainly what can be observed from the plots of the electronic states on Figure 2) 63 . In the following, these defect-related localized orbitals will be addressed as HOMO-1 (Figure 2a), HOMO (Figure 2b) and LUMO (Figure 2c) to underline their localized (molecular) nature. Figure 2d shows the BCB that mainly comes from oxygen 3s states. It is interesting to note that not all POL configurations behave in a strict way. Two main situations can be identified, through the use of projected DOS (PDOS), with respect to the POL-induced occupied electronic defect levels. In the first situation (case 1), two occupied defect states can be easily distinguished, while in the second one (case 2), one of the occupied defect states is entangled with Top of the Valence Band (TVB) 64 . Figure 3 illustrates the DFT PDOS on the atomic Oxygen 2p orbitals for two POL configurations that exhibit the two different behaviors announced before (Figure 3 case 1 and case 2, respectively). At the GW level, from the 11 calculated configurations, we found a mean mobility gap, also called free electron-hole gap, of 9.4(0.06) eV to be in a very good agreement with the measured photo conductivity threshold 65 in silica. This agreement validates the theoretical approach and our 108-atom model that appears to be large enough to properly describe the POL low-concentration limit (negligible defect-defect interaction). The insertion of a POL defect did not change dielectric properties of the matrix. Table 3 summarizes the defect level energy positions with respect to the TVB for two prototypical situations. In the case when both occupied defect states are distinguishable (case 1), the lower defect state (HOMO-1) is, on average, at 0.16(0.07) eV above TVB while the highest occupied state (HOMO) is at 0.41(0.18) eV. The lowest unoccupied defect state (LUMO) is on average found at 10.58(0.23) eV. When HOMO-1 cannot be easily distinguished from the TBV (case 2), the energy of the HOMO seems to be on average slightly higher, at 0.73(0.20) eV. LUMO is found on average at 10.40(0.18) eV. In all cases, the LUMO is around 1 eV above the BCB, similarly to what 10


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Figure 2: Defect electronic states for the prototypical situation where two occupied defect states can be seen (case 1), HOMO-1 (a), HOMO (b), LUMO (c) and BCB (d). Si and O atoms are represented in blue and red, respectively.

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Figure 3: DOS (at the DFT level) projected on orthogonalized atomic 2p-orbitals for two prototypical behaviors (case 1 and case 2). Green line shows average PDOS on non-defective atoms while black line is the PDOS on the two Oxygens involved in the POL. Artificial broadening of 0.07 eV has been used.

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was found in Ref. 39 , despite the differences in the level of theory and in the use of a 10-atoms SiO2 cluster model passivated with hydrogen instead of a bulk model. Table 3: Average GW energy positions, with respect to the TVB, of defect levels induced by the presence of POL. The two situations, where HOMO-1 is disentangled (case 1) or entangled (case 2) with TVB states, are given separately. All units are in eV.

case 1 case 2

3.3

HOMO-1 0.16(0.07) -

HOMO 0.41(0.18) 0.73(0.20)

LUMO 10.58(0.23) 10.40(0.18)

Optical properties

When analyzing the excitonic structure, we kept the distinction between the two prototypical cases (see Table 4 and Figure 4). In general, the oscillator strengths are very low (between 10−3 and 10−4 ) which is a direct effect of the small overlap between π ∗ (Figures 2a and 2b) and σ ∗ (Figure 2c) orbitals . Considering that the free electron-hole gap is of about 9.4 eV (see subsection 3.2 ), electron-hole interactions are extremely strong leading to exciton binding energies as high as 5.6 eV (see for instance exciton A of Table 4 ). This result highlight the importance of an accurate treatment of the electron-hole interaction for these kind of systems (low dielectric constant materials and defects). Simple band-to-band models, i.e., single particle approximations, would lead to overestimated excitation energies. We can separate the analysis in two spectral regions: low excitations that go from 3.0 to 5.6 eV and high excitations that lie in the UV region between 7.1 and 8.0 eV. The high excitations seem to exhibit a smaller energy broadening than the low excitations. The single-particle decomposition of each high energy excitation contains a long series of singleparticle transitions involving not only the defect states but also 2p and 3s states from TVB and BCB neighborhood. Since the probability of a given single-particle to single-particle transition (weight) is very low, the contribution of few transitions involving defect states 13



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will only marginally affect the overall exciton energy and wave-function. These excitations are, subsequently, not strongly influenced by POL site-to-site disorder. On the other hand, the low energy excitations that are mainly due to transitions between occupied (also TVB in case 2) and unoccupied defect states exhibit larger energy dispersion due to differences in the POL geometries. Table 4: Excitation energies and oscillator strengths of optical excitations ascribed to the presence of POL, when the two occupied defect states (HOMO-1 and HOMO) are distinguishable (case 1) and when the lower state (HOMO-1) is hybridized with TVB (case 2). The columns ”From/To” and ”Weight” provide the main single-particle states involved in a given excitation and their corresponding weight (weight of a given single-particle to single-particle transition contributing to the two-particle excitonic wave function), respectively. Numbers in parenthesis are standard deviations. Same notation as in Figure 4 is used. Energy(eV) A B C D E

3.8 4.2 7.3 7.5 7.6

(0.2) (0.6) (0.2) (0.1) (0.0)

A’ B’ C’ D’

3.2 5.2 7.0 7.6

(0.1) (0.4) (0.2) (0.6)

Osc. Str. (10−3 ) From Case 1 1.9 (1.4) HOMO 3.0 (1.6) HOMO-1 0.7 (0.7) HOMO 0.5 (0.4) HOMO-1 0.5 (0.3) TVB Case 2 0.5 (0.4) HOMO 1.4 (1.0) HOMO-1/TVB 2.8 (2.1) HOMO 5.1 (6.7) HOMO-1/TVB

To

Weight

LUMO LUMO BCB BCB BCB

0.74 0.65 0.92 0.92 0.79

(0.19) (0.14) (0.01) (0.01) (0.17)

LUMO LUMO BCB BCB

0.93(0.01) 0.14 (0.05) 0.93 (0.01) 0.90 (0.04)

The mean optical absorption spectrum has been calculated by taking an average over all 11 individual excitation energies and oscillator strengths, and is shown in Figure 5. The overall low oscillator strength together with the high energy dispersion, spanning an energy range between 3.0 and 8.0 eV, make the POL optical contribution very easily hidden by those of other defects and, in general, very difficult to identify. These are the main reasons why the optical signature of POL has never been clearly assigned. At normal conditions and at thermodynamical equilibrium only the lowest formation en14


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Figure 4: DOS (at the GW level) and optical absorption spectra (OA) of two prototypical situations (case 1 and case 2), black lines, and DOS (at the GW level) and optical absorption spectra of the reference undefective silica (aSiO2 ), green dashed lines. Vertical red dashed line at 0 eV marks TVB. Uppercase letters label excitation peaks (A, B, C, D, E for case 1, A’,B’,C’,D’ for case 2) while lowercase letters label single-particle electronic state energies (a-HOMO-1, b-HOMO, c-BCB, d-LUMO). 15 Red arrows underline the main single-particle ACSexcitation Paragon Plus Environment transition contributing to a given in the OA. An artificial broadening of 0.07 eV has been used for both DOS and OA.


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ergy POL would significantly contribute to the optical absorption. In Table 5, as additional, information we provide the excitation energies to be associated with the lowest formation energy POL. Table 5: Optical excitations of POL configuration with the lowest formation energy. Same notation as in Figure 4 is used. From/To describes which states/bands are mainly involved in the transition together with its corresponding weight. Ind. A B C D E

Energy 3.95 eV 4.65 eV 7.00 eV 7.45 eV 7.67 eV

f (10−3 ) 0.9 5.0 0.9 0.7 0.2

From HOMO HOMO-1 HOMO HOMO-1 TVB

To LUMO LUMO BCB BCB. BCB

Weight 0.935 0.845 0.922 0.918 0.922

Figure 5: Mean optical absorption spectra (OA) of all calculated defective configurations (black line) and reference undefective silica (green dashed line). Inset shows a zoom of the spectrum between 2.5 and 7 eV.

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4

Discussion

The presence of POL induces small distortions to the silica matrix and gives rise to strongly localized electronic defect states (no additional Anderson localization is induced at the silica network level). Within these premises, it would be expected that POL exhibits wellidentifiable absorption peaks. However, contrary to the case of other point defects like oxygen vacancies 58 , the energy dispersion of the low-lying excitations is very broad. Two questions arise from the results: why does the site-to-site disorder impact OA so strongly and would it be possible to find a rational that unravels this influence. Inspired by already known similarities between POLs and the peroxide molecule (H2 O2 ) 39,40 , we use H2 O2 to investigate the variation of HOMO-1 and HOMO with respect to the H-OO-H dihedral angle. The strong influence of the dihedral angle on many electronic properties of H2 O2 is known since many decades (see for instance 66 ) but, to our knowledge, it has never been exploited in the context of POL. We performed a series of ground-state calculations at fixed geometry varying by hand the H-O-O-H dihedral angle. Figure 6 reports the variation of the energy position of HOMO1 and HOMO with respect to the dihedral angle (σ ∗ -like LUMO is barely affected by the dihedral angle variations) for the H2 O2 molecule (black-dashed line and black line in Figure 6, respectively). The relative minimum energy difference between HOMO-1 and HOMO occurs at 90◦ ; both states are degenerate in energy and spatially orthogonal to each other. By increasing the angle the energy difference increases too, up to a value of 3 eV, that corresponds to a dihedral angle of 180◦ . When plotting for each POL configuration its HOMO and HOMO-1 energy level as a function of its corresponding dihedral angle, see Figure 6, it is clear that the key quantity that governs the electronic properties of POL is the Si-O-O-Si dihedral angle distribution (see also Figure 1) that comes from the site-to-site disorder. In Si-O-O-Si the energy difference between HOMO and HOMO-1 is shrank (pink and yellow dashed lines of Figure 6 ) with respect to the H2 O2 molecule in vacuum (Dashed and continuous black lines of Figure 6) 17



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due to the interaction with the silica matrix. It is interesting to note that GW and DFT give very similar relative energy positions of the occupied defect levels, validating the DFT total energy calculations. To be able to plot the HOMO-1 energy position for the cases in which HOMO-1 was entangled with the TVB, we exploit PDOSes, as in Figure 3. At 95◦ the two states are practically degenerated. When the angle increased to around 107◦ , the two states become clearly distinguishable - 107◦ corresponds to the geometry of the lowest formation energy that is very close to the H2 O2 gas phase equilibrium dihedral angle. At even higher angles (from approximately 140◦ ) HOMO-1 becomes strongly entangled with the TVB states.

Figure 6: Energy variation of HOMO and HOMO-1 as a function of the dihedral angle α. Dashed and continuous black lines represent the Kohn-Sham energies of HOMO-1 and HOMO of H2 O2 molecule in vacuum. Blue squares represent HOMO-1 (filled squares) and HOMO (empty squares) Kohn-Sham energies of the two occupied POL defect states (for readability, we used only 20 different POL configurations from the calculated 72). Triangles indicate GW quansi-particle energies of HOMO-1 (filled) and HOMO (empty) of the two occupied POL defect states. Vertical dashed line shows the dihedral angle of the H2 O2 molecule in gas phase. Dashed green and red lines are fits of the GW quasi-particle energies of the two occupied POL defects states. The knowledge of how the electronic structure is affected by the site-to-site dihedral angle disorder could be used to understand the energy dispersion of the low-lying optical 18


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Figure 7: Correlation between the α[Si-O-O-Si] dihedral angle (lower x-axis), energy difference of HOMO-HOMO-1 occupied defect states (upper x-axis) and difference between the two lowest excitation energies (E(B)-E(A)). Black lines are guides to the eyes based on linear fits.

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excitations. In Figure 7 we plot the energy difference between the two lowest lying optical transitions (B-A or B’-A’, see Table 4 and Figure 4) as a function of the dihedral angle and of the energy separation between HOMO-1 and HOMO for the eleven POL configurations. The black lines in Figure 7 are used as guides to the eyes, slightly smoother functions for the region comprised between 130 to 140 degrees may fit the same set of data. For the dihedral angles, in which HOMO-1 is disentangled from TVB, energy differences between the excitons increase linearly with the HOMO and HOMO-1 energy separation. When the energy separation of two states reaches approximately 1 eV, which corresponds to dihedral angles of about 140◦ , the energy difference of the lowest lying excitons reaches a mean value of 2.1 eV and stays constant even at higher energies (higher dihedral angles). In other words, the excitation energy becomes independent of the HOMO and HOMO-1 energy difference (independent of the dihedral angle). This can be understood by examining in detail the single-particle state decomposition of the corresponding exciton B’ in Table 4. The contribution of HOMO-1 on B’ is only of about 14% of the total single-particle decomposition, indicating that the exciton B’ is mainly (86%) made up from different transitions involving TVB states. Consequently, the specific energy position of HOMO-1 is no longer relevant.

5

Conclusions

By the state-of-the-art first principles calculations within the framework of DFT and GWBSE on an amorphous silica model, we have shown that the key quantity governing the electronic and optical properties of peroxy bridges is the -O-O- dihedral angle. As a function of this angle the energy position of the two occupied π ∗ states localized on the bridge changes, similarly to what has been already shown for the H2 O2 molecule. Due to this variation in the energy, the two first optical excitation energies have a different relative position. In silica, due to its amorphous nature, the disorder induces a dihedral angle distribution, i.e. depending on the POL insertion site the equilibrium dihedral angle of the bridge is different.

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At the dihedral angles of about 90◦ both π ∗ orbitals are clearly above the TVB. An increase in the angle causes a shift of the lower energy π ∗ orbital towards lower energies and an increase in its hybridization with states at and below TVB. For dihedral angles above 140 ◦ , the entanglement with TVB is so strong that it becomes fully hybridized with the states of TVB. The optical spectra, including different bridge creation sites, show multiple peaks with excitations energies ranging from 3.2 to 7.5 eV. The oscillator strengths are very low (f=10−3 − 10−4 ) due to the small overlap between the states involved in the transitions (π ∗ and σ ∗ ). The behavior of the π ∗ orbitals with respect to the dihedral angle changes the relative position of the first two optical excitations from around 0.3 eV to 2.1 eV. The saturation regime, reached for an excitation energy of 2.1 eV corresponds to dihedral angles larger than 140 ◦

(180 ◦ corresponds to the maximal repulsion between the two π ∗ orbitals of the bridge).

This excitation energy becomes independent of the HOMO and HOMO-1 energy difference (independent of the dihedral angle) as the single-particle state decomposition of the corresponding exciton (B’ in Table 4) contains 14% of a transition involving HOMO-1 but 86% of transitions made up from different TVB states. Consequently, the specific energy position of HOMO-1 is no longer relevant. Going back to the summary of previous works (Table 1), our results shows that calculations done with different dihedral angles for the POL will lead to different results, even comparing calculations done at the same level of theory (correlation effects and/or electronhole interactions) and model (cluster or bulk). Under the experimental point if view, due to the broad and weak absorption of POL, measurements may detect only some parts of the spectral region for which the POL is absorbing (depending on the concentration of more active defects), such leading to a large spread on the assigned optical absorption bands. The correlation between dihedral angles and opto-electronic properties is completely general and will hold for any hard material (bulk, interface or nano-structure) containing peroxy bridges and allowing for some dihedral angle variability.

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6

Acknowledgements

The research was suported by ”Young Researcher” grant of the Slovenian Research Agency (ARRS), 5100-12/2014-5, CEA/ARRS grant and Research Program P2-0377. Computational part was performed using GENCI-CCRT High performance computing resources (DARI Grant numbers 2014096137 and 2015096137) and CINECA (project OMEGAFIBHP10BMKWVL and OXYRIS-HP10B5K2GU).

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