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The study of oxygen-deficient centers in Al-doped amorphous germanium oxides
Journal of Non-Crystalline Solids 525 (2019) 119694
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The study of oxygen-deficient centers in Al-doped amorphous germanium oxides ⁎
⁎
Xiaoning Guana,b,c, Ru Zhangb, , Baonan Jiaa, Yuwen Duana,c, Xianchun Chend, , Pengfei Lua,
T
⁎
a
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China c Beijing Key Laboratory of Space-ground Interconnectionand Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China d College of Materials Science and Engineering, Sichuan University, Chengdu 610065, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: First-principles GeODC Al-GeODC Optical properties Refractive index
Electronic and optical properties of Germanium oxygen-deficient center (GeODC) defect and Al-doped GeODC defect in 96 atoms amorphous GeO2 (a-GeO2) supercells have been investigated. All the 64 oxygen sites in the aGeO2 configuration have been orchestrated as possible candidates for the construction of 64 different GeODCs. A Ge atom has been substituted by an Al atom in GeODCs to form the Al-GeODCs. It is discovered that the refractive index of a-GeO2 is reduced by GeODC defect, contrary to the situation when Al is doped in GeODC defect. The absorption peak at 5.15 eV is related to GeODC defect. After Al-doping, a new defect state is generated near the top of valence band (TVB), resulting in an absorption peak at 4 eV. The variations of refractive index and optical properties exhibited offer a significant and profound guidance of Al and Ge co-doping in silica optical fiber.
1. Introduction The studies of doped silica optical fiber have been attached extensive importance due to its high sensitivity, easy preparation and potential technological applications [1]. The impurities in silica optical fiber can have an impact on the sensitivity to ionizing radiation and ultraviolet radiation, which is key to the performance of many optical fiber devices [2–4]. Doping of silica optical fibers is a basic characteristic of optical fibers in applications, as well as one of the most commonly used ways to improve the properties of silica optical fibers in many investigations [5],[6]. Germanium-doped (Ge-doped) silica optical fiber is a material of essential importance in the optical fiber technology [7–9]. Photosensitivity in Ge-doped amorphous silica material has been observed due to the refractive index change which is induced by doping of Ge [10]. The photosensitivity and photorefractive effect of Ge-doped silica optical fiber are much higher than that of pure silica optical fiber. The performance of optical fiber is closely related to the transformation of point defects of all kinds during the process of laser irradiation [11–13]. Radiation can bring about point defects which can change the optical properties of the optical fiber through optical absorption [14–17]. The oxygen-deficiency-related point defects in silica and Ge-related ODCs in Ge-doped silica were comprehensively discussed in many experimental and theoretical studies [18–21]. The
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structural and spectroscopic properties of optically active oxygen-deficiency-related point defects are discussed in vitreous silica [18]. The local configurations and vibrations of oxygen vacancies in different charged states in α-quartz GeO2 were considered to study the structural and vibrational properties [19]. Moreover, the point defects can reduce the transmission efficiency and have an influence on the refractive index. The studies found that the optical absorption band at around 5 eV may be caused by the GeODC defect [20]. It is also reported that the irradiation energy at around 5.1 eV of the GeODC defect can cause a variation of refractive index in Ge-doped optical fiber [21]. Therefore, GeODC defect is proven to play a crucial role in manipulating the refractive index and affecting the optical properties in Ge-doped silica optical fiber. Doping aluminum in the silica optical fiber can change the refractive index, improve the radiation sensitivity, and affect the thermoluminescence response of the silica optical fiber [1],[22],[23]. It has been indicated that changing dopant concentrations for doping of Ge and Al can give rise to additional sensitivity in optical fiber lead to optical fiber of additional sensitivity [24]. For silica optical fiber, the influences of photon irradiation on the thermoluminescence response and fading characteristics of doped Ge and Al have been investigated in Ref [2,25–28]. The SBS threshold is altered by adjusting the relative doping level of Al and Ge in the optical fiber while maintaining the step
Corresponding authors. E-mail addresses: [email protected] (R. Zhang), [email protected] (X. Chen), [email protected] (P. Lu).
https://doi.org/10.1016/j.jnoncrysol.2019.119694 Received 2 August 2019; Received in revised form 12 September 2019; Accepted 14 September 2019 0022-3093/ © 2019 Published by Elsevier B.V.
Journal of Non-Crystalline Solids 525 (2019) 119694
X. Guan, et al.
is twice the occupied energy levels of the system. The test calculations show that the quasi-particle band gap change of the system converges to within 0.1 eV after the number of unoccupied energy levels is further increased by three times the occupied energy levels. The iteration step of GW is limited to 6 steps, and the quasi-particle band gap calculated in this step also converges to within 0.1 eV. Then the precision of GW-BSE calculation is set up within 0.1 eV.
index structure in Ref [29]. The Brillouin gain sensing characteristics is analyzed in theory with a W-shaped acoustic waveguide formed by doping Al and Ge in the optical fiber in Ref [30]. The photoluminescence properties were studied by preparing Ge and Al co-doped SiO2 films in Ref [31]. Also, the silica optical fiber highly doped with GeO2 (~30 mol%) had been elaborated in Ref [32,33]. This indicates that Ge atoms may exist as GeO2 clusters instead of being the isolated substitutional atoms in the silica optical fiber, perhaps exist as GeO2 clusters [10]. Therefore, in order to give an all-around understanding of the Ge-doped silica optical fiber, it is necessary to dive deeper into the structure and properties of defects and doped a-GeO2. In this work, we focus on the structural, electronic and optical properties of the ODC defect in a-GeO2 by employing first-principles calculation based on Density-Functional theory (DFT). The GeODC defect structures were constructed to expatiate the impact of local structure on the formation energies. The calculated results show that there is a linear relationship between formation energy and GeeGe bond of GeODC defect structures. In the low energy area, the refractive index is reduced by GeODC defect, while in contrast to the increasement after doping Al in GeODC defect. The optical absorption peak at ~5.1 eV is brought by GeODC defect, which is associated to the unoccupied defect state at 7.35 eV in conduction band. In Al-doped GeODC defect, the optical absorption peak at 4 eV is relevant to the defect level near the bottom of the conduction band (BCB). Based on these results, the properties of these point defects in a-GeO2 are discussed.
The physical structural characteristics is related to the bond length and bond angle of the corner-sharing GeO4 tetrahedral units. Fig. 1(a) shows a typical GeODC defect of a-GeO2 configuration. All the 64 O sites in the a-GeO2 supercell were considered as possible candidates to form 64 different GeODCs by removing 64 different sites of O atoms. Thus we obtained 64 supercells, and every model contains one different GeODC defect. The calculated average values of the GeODC defect model parameters are summarized in Table 1. And the parameters of other references are also listed, our results are similar to those theoretical calculation results listed in Table 1. The formation energy calculations have been performed with all GeODC defect structures to compare the relative stability. The expression of formation energy for the GeODC defect models is defined as follow:
2. Computational methods
Ef (GeODC ) = EGeODC + EO − EGeO2
3. Results and discussion 3.1. GeODCs configurations
(1)
where EGeODC is the total energy of the GeODC defect configurations. EO is the energy of an oxygen molecule in the triplet ground state. EGeO2 is the energy of the non-defective a-GeO2 model. The formation energy calculation results distribution of 64 different GeODC defect models are shown in Fig. 2(a). The range of formation energies in different models are from 4.7 eV to 6.1 eV, which are close to the results in Ref [10,41]. And the values show that the statistical distribution of formation energies mainly concentrated in 5.1–5.5 eV. Fig. 2(b) shows the correlation between formation energy and GeeGe bond length of GeODC defect structures. Due to the change of the local defect structure, the model formation energy changes, and the overall trend shows a linear relationship [42]. The lower formation energy of the structure means that the GeODC defect is relatively easier to form [49].
The initial model of a 2 × 2 × 2 crystal silica supercell is chosen to generate the amorphous silica model containing 96 atoms, Which is large enough to neglect the interaction with its periodic images [10,34–35]. No defects exist in the structure, which is produced by classical molecular dynamics (MD) method with a force convergence of 0.1 eV/Å [36,37], where a three heating-cooling classes is performed. At first, the supercell was heated from 300 K to 5000 K for 50 ps to achieve equilibrium; Then, the system is quenched to 500 K using 9 chained quenching-equilibrating steps; In every step, the system temperature is decreased by 500 K in 35 ps and equilibrated at the intermediate temperature for another 25 ps; Finally, the system is cooled to 300 K and equilibrated for 50 ps. The Tersoff potential is employed to describe the interactions between atoms and the Langevin thermostat to control the temperature of system [38]. The calculated density of the fused silica supercell, 2.2 g/cm3, is the same as the experimental value [39,40]. The atomic positions and lattice structure are fully relaxed of the supercell which is well connected with rings of different sizes. All the Si atoms are substituted by Ge atoms to construct the a-GeO2 structure with 32 Ge atoms and 64 O atoms [41,42]. The oxygen vacancy configurations are generated by removing an O atom from the GeeOeGe structures of the non-defective a-GeO2 model which is shown in Fig. 1(a). The Al-GeODC defect structure are generated by the substitution of a Ge atom with an Al atom which is shown in Fig. 1(b). All the lattice structures are fully relaxed by first-principles calculations after the removal. The resulting supercell by adjusting all of the atomic positions and lattice structures through relaxation. Geometry optimization of these structures have been performed using plane-wave pseudopotential code Vienna ab initio simulation package (VASP) that based on DFT [43–48]. General gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) are applied to describe the electronic exchange and correlation interaction. The optical absorption spectra and geometry energies are calculated by Manybody perturbation theory techniques. The cutoff energy of plane wave basis is 450 eV. GW (where G represents dressed Green's function and W stands for screened Coulomb interaction) and Bathe-Salpeter equation (BSE) equation is used to calculate the electronic and optical properties, respectively. The number of unoccupied energy levels in the calculation
3.2. Al-doped in GeODC configurations Eight sites (Mn, n = 1–8) of Al-doped in GeODC models were selected to compare the relative stability. The sites of 1 to 6 represent the case in which an O atom around GeeGe bond of GeODC defect is substituted by an Al atom. The sites 7 and 8 is the case in which a Ge atom of GeODC defect is substituted by an Al atom. The formation energies of Mn (n = 1–8) were calculated by the following equation.
Ef (Mn) = EAl − ODC + EO − EGeODC − EAl, n = 1 − 6
(2)
Ef (Mn) = EAl − ODC + EGe − EGeODC − EAl, n = 7 − 8
(3)
where EAl−ODC and EGeODC is the total energy of the Al-doped GeODC defect model and GeODC defect of a-GeO2 model, respectively. EGe and EAlis the energy of an isolated Ge and Al atom in the ground state, respectively. EO is the energy of an oxygen molecule in the triplet ground state. The calculated results of Mn (n = 1–8) are shown in Fig. 3. The calculations illustrate that the formation energy is lowest when Ge atom is substituted by Al atom. It indicates that the Al-GeODC defect is more likely to form in Al-doped in GeODC configurations. Al-GeODC defect is more stable than other replacement positions, and we conduct the further calculations. 2
Journal of Non-Crystalline Solids 525 (2019) 119694
X. Guan, et al.
Fig. 1. ODC defect in a-GeO2 Structure. (a) GeODC defect and (b) Al-GeODC defect. Ge atom is shown in green, Al atom is shown in purple and O atom is shown in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 1 Average value of bond lengths and bond angles for GeODC defect model parameters.
This work Reference
Average bond length (Å)
Average bond angle (°)
GeeGe
GeeO
GeeOeGe
OeGeeO
GeeGeeO
2.48 2.46 [50] 2.49 [51]
1.78 1.78 [41] 1.75 [51]
126.3 130 [52] 130.6 [10]
109.2 ∽109 [52] 109.4 [10]
112.8 ∽110 [52] –
3.3. Al-GeODC configurations Four GeODC defect models were selected in orders of ascending formation energy to analyze the effect of Al-GeODC defect configuration. The formation energies is 4.88, 4.96, 5.12 and 5.37 eV with the GeeGe bond lengths around 2.50, 2.49, 2.48 and 2.46 Å, respectively. Then the Al-doped GeODC defect model which in a case that a Ge atom of GeeGe bond in GeODC defect is substituted by an Al atom (Al-model A to Al-model D) is shown in Fig. 1(b). The structure of two tetrahedral units of GeODC defect are affected by bond length and bond angle, so it's important to analyze the parameters of Al-doped GeODC defect model. The parameters of Al-doped GeODC defect model are shown in Table 2. The average value of GeeAl bond lengths in Al-doped GeODC defect model is 2.76 Å, which is longer than the GeeGe bond length. The average GeeO bond length is 1.78 Å the same as that of GeODC defect model. Compared with GeeO bond length with 1.78 Å, the mean value of AleO bond length is much shorter at about 1.73 Å. The average
Fig. 3. The formation energies of Al-doped in GeODC configurations.
bond angles of Ge-O-Ge is 125.9°, which is close to that in GeODC defect model. The OeGeeO bond length has no changed after Al atom replaces Ge atom. The parameter of XeGeeO (X = Al, Ge) angle constant before and after replacement. To further understand the changes in the model after Al doping in ODC a-GeO2 models, the stable properties of Al-doped amorphous model are calculated. EGeODC and EAl−ODC is the total energy of the aGeO2 model with GeODC defect and the Al-doped GeODC defect model,
Fig. 2. (a) Statistical distribution of formation energy (b) Diagram of formation energy and GeeGe bond distance of GeODC defect structures. 3
Journal of Non-Crystalline Solids 525 (2019) 119694
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Table 2 Average value of bond length and bond angle for Al-doped GeODC defect model parameters. Average bond length (Å)
Average bond angle (°)
GeeAl
GeeO
AleO
2.76
1.78
1.73
GeeOeGe 125.9 AleOeGe 129.3
OeGeeO 109.3 OeAleO 115.9
AleGeeO 113.1 GeeAleO 102.8
Table 3 The parameters of Al-doped GeODC defect model samples.
Formation Energy /eV Ge-Al bond length (Å) O-Al-O bond angle (°)
Al-model A
Al-model B
Al-model C
Al-model D
−0.95 2.74 115.7
−1.25 2.79 116.2
−0.87 2.62 113.9
−1.27 2.89 117.8
respectively. EGe is the energy of an isolated Ge atom and EAl is the energy of an isolated Al atom. The formation energy Ef(Al−Ge) is defined as follows:
Ef (Al − Ge = EAl − ODC + EGe − EGeODC − EAl
(4)
The formation energy of Al-doped GeODC defect samples are around −1 eV, which are shown in Table 3. Oxygen vacancy center after Al substitution in GeODC defect has a smaller formation energy, and the negative values indicate that Al-GeODC defect is more likely to form in a-GeO2 structure. The calculation results show that the formation energy can be reduced as the GeeAl bond length increases. It can be seen from the table that the formation energy of the model decrease as the O-Al-O bond angle increases. The reason may be considered that the longer the bond length, the smaller the energy needed to form this local structure, so the lower the formation energy of the overall model. When the Al atom in the tetrahedron is closer to the plane of the three O atoms directly connected to it, the larger bond angle centered on Al, the lower the formation energy required.
Fig. 4. (a) Caclulated optical absorption spectra of Al-doped GeODC defect in red dashed line, GeODC defect in blue line and pure GeO2 structure in black line. (b) Caclulated total density of states of Al-doped GeODC defect in red dashed line, GeODC defect in blue line and pure GeO2 structure in black line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
1.32 eV near TVB and one unoccupied defect state at 7.35 eV in conduction band shown in red dashed line. On the basis of GW, the exciton binding energy of the Bethe-Salpete equation using multi-body perturbation theory is about 1.26 eV. A series of absorption peaks in the optical absorption spectrum are caused by transitions between the occupied states and different unoccupied states. The optical absorption peak of Al-GeODC defect configuration might be due to the transition from the occupied defect state of 1.32 eV to the BCB. For GeODC defect configuration, the optical absorption peak at 5.15 eV might be caused by the transition between the occupied defect state and the unoccupied defect state of 7.35 eV. After doping an Al atom in GeODC defect configuration, a defect state is generated in the band gap and the optical absorption peak at 5.15 eV disappears. It is obvious that red shift phenomenon in total density of states curve occur regardless of the defects before and after doping which compared with the pure a-GeO2 structure.
3.4. Optical and electronic properties The complex dielectric function describes the optical properties of the material, which is related to the action of photons and electrons and used to describe the linear response of the system to electromagnetic radiation [44]. The complex dielectric function expression is given by
ε (ω) = εr (ω) + iεi (ω)
(5)
where εr(ω) is the real part, and εi(ω) is the imaginary part which is obtained from the momentum matrix element of the occupied and unoccupied wave functions. The imaginary part of the relative dielectric function εi(ω) is proportional to the optical absorption coefficient α(ω) and can describe the optical absorption characteristics. To better comprehend the optical properties after doping with Al, the optical absorption spectra (OA) and total density of states (DOS) of the GeODC defect and Al-doped GeODC defect compared with the pure aGeO2 configuration are shown in Fig. 4. The calculation results of the optical band gap is shown at 4.8 eV, which is close to the experimental value [53]. There are no obvious optical absorption peak in band gap of pure a-GeO2 in OA which is shown in Fig. 4(a) with black line. The GeODC defect causes an optical absorption peak around 5.15 eV which is compatible with the experimental results [20]. After doping with an Al atom, the optical absorption peak at 5.15 eV is absent, and an optical absorption peak appears at 4 eV in the band gap. For comparison, TVB of the DOS curve is moved to 0 eV which is shown in Fig. 4(b). It is observed one unoccupied defect state at 7 eV in conduction band of GeODC defect configuration shown in blue line. For AlGeODC defect configuration, there are one occupied defect state at
3.5. Refractive index The complex dielectric function can characterize the physical properties of the material, and reflect the information between the electronic structures and the optical properties, and it is superior compared to some macroscopic optical constants. Complex refractive index of the medium is as follow
n˜ (ω) = n (ω) + iκ (ω)
(6)
where the real part n(ω) is the refractive index and the imaginary part is the extinction coefficient. The optical properties of the medium can be described by n(ω). The extinction coefficient κ(ω) directly describes the attenuation of light waves in the material [54]. The relational expression between them is as follows
4
n2 (ω) − κ 2 (ω) = εr (ω)
(7)
2n (ω) κ (ω) = εi (ω)
(8)
Journal of Non-Crystalline Solids 525 (2019) 119694
X. Guan, et al.
Fig. 5. (a) Refractive index and Extinction coefficient in GeODC defect model. (b) Refractive index and Extinction coefficient in Al-doped GeODC defect model.
The refractive index and extinction coefficient expressions can be obtained by the change between the above relational expressions as follows
⎡ εr 2 (ω) + εi 2 (ω) + εr (ω) n (ω) = ⎢ 2 ⎢ ⎣
⎡ εr 2 (ω) + εi 2 (ω) − εr (ω) κ (ω) = ⎢ 2 ⎢ ⎣
1 2⎤
⎥ ⎥ ⎦
(9)
1 2⎤
⎥ ⎥ ⎦
(10)
We obtained εr(ω) and εi(ω) by the electronic ground state calculations at GW0 + BSE level. The calculated energy dependence of the refractive index and the extinction coefficient is shown in Fig. 5. The trend of refractive index and extinction coefficient curve after doping Al in GeODC defect model is the same as that of the undoped GeODC defect model. The static refractive index n(0) of Al-doped GeODC defect and undoped GeODC defect is 2.68 and 2.61 respectively. As the energy increases, the refractive index increases and reaches a maximum at 5.45 eV and 5.29 eV in the ultraviolet region of Al-doped GeODC defect and GeODC defect respectively. The energy of the last peak corresponds to 9.34 eV of GeODC defect, then the refractive index gradually decreases with increasing energy. And when it reaches a minimum at 24.4 eV, the extinction coefficient reaches a maximum value of 1.79 which showing a strong band edge absorption. When the energy reaches 9.37 eV in Al-doped GeODC defect, the refractive index decreases with increasing energy and reaches a minimum of 24.4 eV, which corresponds to the maximum extinction coefficient. The difference in refractive index can show the magnitude of the change in refractive index. Fig. 6 shows the difference in refractive index between GeODC defects and pure a-GeO2 and between GeODC defects and Al-doped GeODC defects. It was observed that at low energies area, the GeODC defect lowered the refractive index of a-GeO2 model. The refractive index difference between the two becomes positive when the energy is 5.98 eV, then the refractive index of GeODC begins to increase. And their refractive index tends to be the same as the energy increases. When GeODC defect model is doped with Al, the refractive index increases in the low energy range. At an energy of 5.98 eV, the refractive index begins to decrease and gradually tends to the refractive index undoped GeODC defect model. It can be seen that the peak value of the refractive index n(ω) is at the rising edge of the extinction coefficient κ(ω), the valley of n(ω) is at the falling edge of κ(ω), and the minimum value of n(ω) corresponds to the peak of κ(ω).
Fig. 6. (a) Refractive index difference between GeODC defect model and fused a-GeO2 model. (b) Refractive index difference between Al-doped GeODC defect model and GeODC defect model.
4. Conclusion In summary, we have investigated the atomic structures, electronic structures and optical properties of the GeODC defect and Al-GeODC defect in a-GeO2. And the calculated results show that the GeODC defect can give birth to an unoccupied defect state at the conduction band, which is associated with the optical absorption peak at 5.15 eV. In addition, Al-GeODC defect model introduces a new occupied defect state at the TVB and brings about an absorption peak at 4 eV in the optical band gap. Moreover, the optical absorption peak at 5.15 eV disappears by Al-doping in GeODC defect model. Our calculations show that the GeODC defect can bring about the decrease of the refractive index of pure a-GeO2, and the similar performance on the change of the refractive index can also be observed in GeODC defect of Ge-doped optical fiber [21]. It can be shown that Al-doping can increase the 5
Journal of Non-Crystalline Solids 525 (2019) 119694
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refractive index of GeODC defect in a-GeO2, which is consistent with the trend of the refractive index change of Al-doped in silica [29]. Our calculations can offer insightful instructions and new perspectives to further understand the nature of the ODC defect in Al and Ge co-doped silica optical fiber materials.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 61671085 and 61675032), the National Key Research and Development Program of China (No.2017YFB0405100) and the Open Program of State Key Laboratory of Functional Materials for Informatics. We thank for the computational support from the Beijing Computational Science Research Center (CSRC). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jnoncrysol.2019.119694. References [1] I. Hossain, H. Wagiran, N.H. Yaakob, J. Appl. Spectrosc. 80 (2013) 620. [2] N.H. Yaakob, H. Wagiran, M.I. Hossain, A.T. Ramli, D.A. Bradley, S. Hashim, H. Ali, J. Nucl. Sci. Technol. 48 (2011) 1115. [3] S. Lin, H.Y. Wang, X.N. Zhang, D. Wang, D. Zu, J.N. Song, Z.L. Liu, Y. Huang, K. Huang, N. Tao, Z.W. Li, X.P. Bai, B. Li, M. Lei, Z.F. Yu, Hui Wu, Nano Energy 62 (2019) 111. [4] K. Bi, D.Q. Yang, J. Chen, Q.M. Wang, H.Y. Wu, C.W. Lan, Y.P. Yang, Photonics Res. 7 (2019) 457. [5] S. Girard, A. Alessi, N. Richard, L. Martin-Samos, V. De Michele, L. Giacomazzi, S. Agnello, D. Di Francesca, A. Morana, B. Winkler, I. Reghioua, P. Paillet, M. Cannas, T. Robin, A. Boukenter, Y. Ouerdane, Rev. Phys. 4 (2019) 100032. [6] J. Zhang, L. Han, Z. Guan, B. Jia, Z. Peng, X. Guan, B. Yan, G. Peng, P. Lu, J. Lumin. 207 (2019) 346. [7] G. Pacchioni, C. Mazzeo, Phys. Rev. B 62 (2000) 5452. [8] A. Alessi, S. Agnello, Y. Ouerdane, F.M. Gelardi, J. Phys.Condens. Matter 23 (2011) 015903. [9] M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, Y. Ohki, J. Phys.Condens. Matter 11 (1999) 2589. [10] T. Tamura, G. Lu, R. Yamamoto, M. Kohyama, Phys. Rev. B 69 (2004) 195204. [11] F.L. Galeener, D.L. Griscom, M.J. Weber, Mater. Res. Soc. Proc. 61 (1986) 319. [12] A. Othonos, K. Kalli, G.E. Kohnke, Phys. Today 53 (2000) 61. [13] N. Richard, L. Martin-Samos, S. Girard, A. Ruini, A. Boukenter, Y. Ouerdane, J.P. Meunier, J. Phys.Condens. Matter 25 (2013) 335502. [14] I. Reghioua, S. Girard, A. Alessi, D. Di Francesca, L. Martin-Samos, M. Fanetti, N. Richard, M. Raine, M. Valant, A. Boukenter, Y. Ouerdane, J. Lumin. 179 (1) (2016). [15] S. Lin, X.P. Bai, H.Y. Wang, H.L. Wang, J.N. Song, K. Huang, C. Wang, N. Wang, B. Li, M. Lei, H. Wu, Adv. Mater. 29 (2017) 1703238.
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
The study of oxygen-deficient centers in Al-doped amorphous germanium oxides ⁎
⁎
Xiaoning Guana,b,c, Ru Zhangb, , Baonan Jiaa, Yuwen Duana,c, Xianchun Chend, , Pengfei Lua,
T
⁎
a
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China c Beijing Key Laboratory of Space-ground Interconnectionand Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China d College of Materials Science and Engineering, Sichuan University, Chengdu 610065, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: First-principles GeODC Al-GeODC Optical properties Refractive index
Electronic and optical properties of Germanium oxygen-deficient center (GeODC) defect and Al-doped GeODC defect in 96 atoms amorphous GeO2 (a-GeO2) supercells have been investigated. All the 64 oxygen sites in the aGeO2 configuration have been orchestrated as possible candidates for the construction of 64 different GeODCs. A Ge atom has been substituted by an Al atom in GeODCs to form the Al-GeODCs. It is discovered that the refractive index of a-GeO2 is reduced by GeODC defect, contrary to the situation when Al is doped in GeODC defect. The absorption peak at 5.15 eV is related to GeODC defect. After Al-doping, a new defect state is generated near the top of valence band (TVB), resulting in an absorption peak at 4 eV. The variations of refractive index and optical properties exhibited offer a significant and profound guidance of Al and Ge co-doping in silica optical fiber.
1. Introduction The studies of doped silica optical fiber have been attached extensive importance due to its high sensitivity, easy preparation and potential technological applications [1]. The impurities in silica optical fiber can have an impact on the sensitivity to ionizing radiation and ultraviolet radiation, which is key to the performance of many optical fiber devices [2–4]. Doping of silica optical fibers is a basic characteristic of optical fibers in applications, as well as one of the most commonly used ways to improve the properties of silica optical fibers in many investigations [5],[6]. Germanium-doped (Ge-doped) silica optical fiber is a material of essential importance in the optical fiber technology [7–9]. Photosensitivity in Ge-doped amorphous silica material has been observed due to the refractive index change which is induced by doping of Ge [10]. The photosensitivity and photorefractive effect of Ge-doped silica optical fiber are much higher than that of pure silica optical fiber. The performance of optical fiber is closely related to the transformation of point defects of all kinds during the process of laser irradiation [11–13]. Radiation can bring about point defects which can change the optical properties of the optical fiber through optical absorption [14–17]. The oxygen-deficiency-related point defects in silica and Ge-related ODCs in Ge-doped silica were comprehensively discussed in many experimental and theoretical studies [18–21]. The
⁎
structural and spectroscopic properties of optically active oxygen-deficiency-related point defects are discussed in vitreous silica [18]. The local configurations and vibrations of oxygen vacancies in different charged states in α-quartz GeO2 were considered to study the structural and vibrational properties [19]. Moreover, the point defects can reduce the transmission efficiency and have an influence on the refractive index. The studies found that the optical absorption band at around 5 eV may be caused by the GeODC defect [20]. It is also reported that the irradiation energy at around 5.1 eV of the GeODC defect can cause a variation of refractive index in Ge-doped optical fiber [21]. Therefore, GeODC defect is proven to play a crucial role in manipulating the refractive index and affecting the optical properties in Ge-doped silica optical fiber. Doping aluminum in the silica optical fiber can change the refractive index, improve the radiation sensitivity, and affect the thermoluminescence response of the silica optical fiber [1],[22],[23]. It has been indicated that changing dopant concentrations for doping of Ge and Al can give rise to additional sensitivity in optical fiber lead to optical fiber of additional sensitivity [24]. For silica optical fiber, the influences of photon irradiation on the thermoluminescence response and fading characteristics of doped Ge and Al have been investigated in Ref [2,25–28]. The SBS threshold is altered by adjusting the relative doping level of Al and Ge in the optical fiber while maintaining the step
Corresponding authors. E-mail addresses: [email protected] (R. Zhang), [email protected] (X. Chen), [email protected] (P. Lu).
https://doi.org/10.1016/j.jnoncrysol.2019.119694 Received 2 August 2019; Received in revised form 12 September 2019; Accepted 14 September 2019 0022-3093/ © 2019 Published by Elsevier B.V.
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is twice the occupied energy levels of the system. The test calculations show that the quasi-particle band gap change of the system converges to within 0.1 eV after the number of unoccupied energy levels is further increased by three times the occupied energy levels. The iteration step of GW is limited to 6 steps, and the quasi-particle band gap calculated in this step also converges to within 0.1 eV. Then the precision of GW-BSE calculation is set up within 0.1 eV.
index structure in Ref [29]. The Brillouin gain sensing characteristics is analyzed in theory with a W-shaped acoustic waveguide formed by doping Al and Ge in the optical fiber in Ref [30]. The photoluminescence properties were studied by preparing Ge and Al co-doped SiO2 films in Ref [31]. Also, the silica optical fiber highly doped with GeO2 (~30 mol%) had been elaborated in Ref [32,33]. This indicates that Ge atoms may exist as GeO2 clusters instead of being the isolated substitutional atoms in the silica optical fiber, perhaps exist as GeO2 clusters [10]. Therefore, in order to give an all-around understanding of the Ge-doped silica optical fiber, it is necessary to dive deeper into the structure and properties of defects and doped a-GeO2. In this work, we focus on the structural, electronic and optical properties of the ODC defect in a-GeO2 by employing first-principles calculation based on Density-Functional theory (DFT). The GeODC defect structures were constructed to expatiate the impact of local structure on the formation energies. The calculated results show that there is a linear relationship between formation energy and GeeGe bond of GeODC defect structures. In the low energy area, the refractive index is reduced by GeODC defect, while in contrast to the increasement after doping Al in GeODC defect. The optical absorption peak at ~5.1 eV is brought by GeODC defect, which is associated to the unoccupied defect state at 7.35 eV in conduction band. In Al-doped GeODC defect, the optical absorption peak at 4 eV is relevant to the defect level near the bottom of the conduction band (BCB). Based on these results, the properties of these point defects in a-GeO2 are discussed.
The physical structural characteristics is related to the bond length and bond angle of the corner-sharing GeO4 tetrahedral units. Fig. 1(a) shows a typical GeODC defect of a-GeO2 configuration. All the 64 O sites in the a-GeO2 supercell were considered as possible candidates to form 64 different GeODCs by removing 64 different sites of O atoms. Thus we obtained 64 supercells, and every model contains one different GeODC defect. The calculated average values of the GeODC defect model parameters are summarized in Table 1. And the parameters of other references are also listed, our results are similar to those theoretical calculation results listed in Table 1. The formation energy calculations have been performed with all GeODC defect structures to compare the relative stability. The expression of formation energy for the GeODC defect models is defined as follow:
2. Computational methods
Ef (GeODC ) = EGeODC + EO − EGeO2
3. Results and discussion 3.1. GeODCs configurations
(1)
where EGeODC is the total energy of the GeODC defect configurations. EO is the energy of an oxygen molecule in the triplet ground state. EGeO2 is the energy of the non-defective a-GeO2 model. The formation energy calculation results distribution of 64 different GeODC defect models are shown in Fig. 2(a). The range of formation energies in different models are from 4.7 eV to 6.1 eV, which are close to the results in Ref [10,41]. And the values show that the statistical distribution of formation energies mainly concentrated in 5.1–5.5 eV. Fig. 2(b) shows the correlation between formation energy and GeeGe bond length of GeODC defect structures. Due to the change of the local defect structure, the model formation energy changes, and the overall trend shows a linear relationship [42]. The lower formation energy of the structure means that the GeODC defect is relatively easier to form [49].
The initial model of a 2 × 2 × 2 crystal silica supercell is chosen to generate the amorphous silica model containing 96 atoms, Which is large enough to neglect the interaction with its periodic images [10,34–35]. No defects exist in the structure, which is produced by classical molecular dynamics (MD) method with a force convergence of 0.1 eV/Å [36,37], where a three heating-cooling classes is performed. At first, the supercell was heated from 300 K to 5000 K for 50 ps to achieve equilibrium; Then, the system is quenched to 500 K using 9 chained quenching-equilibrating steps; In every step, the system temperature is decreased by 500 K in 35 ps and equilibrated at the intermediate temperature for another 25 ps; Finally, the system is cooled to 300 K and equilibrated for 50 ps. The Tersoff potential is employed to describe the interactions between atoms and the Langevin thermostat to control the temperature of system [38]. The calculated density of the fused silica supercell, 2.2 g/cm3, is the same as the experimental value [39,40]. The atomic positions and lattice structure are fully relaxed of the supercell which is well connected with rings of different sizes. All the Si atoms are substituted by Ge atoms to construct the a-GeO2 structure with 32 Ge atoms and 64 O atoms [41,42]. The oxygen vacancy configurations are generated by removing an O atom from the GeeOeGe structures of the non-defective a-GeO2 model which is shown in Fig. 1(a). The Al-GeODC defect structure are generated by the substitution of a Ge atom with an Al atom which is shown in Fig. 1(b). All the lattice structures are fully relaxed by first-principles calculations after the removal. The resulting supercell by adjusting all of the atomic positions and lattice structures through relaxation. Geometry optimization of these structures have been performed using plane-wave pseudopotential code Vienna ab initio simulation package (VASP) that based on DFT [43–48]. General gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) are applied to describe the electronic exchange and correlation interaction. The optical absorption spectra and geometry energies are calculated by Manybody perturbation theory techniques. The cutoff energy of plane wave basis is 450 eV. GW (where G represents dressed Green's function and W stands for screened Coulomb interaction) and Bathe-Salpeter equation (BSE) equation is used to calculate the electronic and optical properties, respectively. The number of unoccupied energy levels in the calculation
3.2. Al-doped in GeODC configurations Eight sites (Mn, n = 1–8) of Al-doped in GeODC models were selected to compare the relative stability. The sites of 1 to 6 represent the case in which an O atom around GeeGe bond of GeODC defect is substituted by an Al atom. The sites 7 and 8 is the case in which a Ge atom of GeODC defect is substituted by an Al atom. The formation energies of Mn (n = 1–8) were calculated by the following equation.
Ef (Mn) = EAl − ODC + EO − EGeODC − EAl, n = 1 − 6
(2)
Ef (Mn) = EAl − ODC + EGe − EGeODC − EAl, n = 7 − 8
(3)
where EAl−ODC and EGeODC is the total energy of the Al-doped GeODC defect model and GeODC defect of a-GeO2 model, respectively. EGe and EAlis the energy of an isolated Ge and Al atom in the ground state, respectively. EO is the energy of an oxygen molecule in the triplet ground state. The calculated results of Mn (n = 1–8) are shown in Fig. 3. The calculations illustrate that the formation energy is lowest when Ge atom is substituted by Al atom. It indicates that the Al-GeODC defect is more likely to form in Al-doped in GeODC configurations. Al-GeODC defect is more stable than other replacement positions, and we conduct the further calculations. 2
Journal of Non-Crystalline Solids 525 (2019) 119694
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Fig. 1. ODC defect in a-GeO2 Structure. (a) GeODC defect and (b) Al-GeODC defect. Ge atom is shown in green, Al atom is shown in purple and O atom is shown in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 1 Average value of bond lengths and bond angles for GeODC defect model parameters.
This work Reference
Average bond length (Å)
Average bond angle (°)
GeeGe
GeeO
GeeOeGe
OeGeeO
GeeGeeO
2.48 2.46 [50] 2.49 [51]
1.78 1.78 [41] 1.75 [51]
126.3 130 [52] 130.6 [10]
109.2 ∽109 [52] 109.4 [10]
112.8 ∽110 [52] –
3.3. Al-GeODC configurations Four GeODC defect models were selected in orders of ascending formation energy to analyze the effect of Al-GeODC defect configuration. The formation energies is 4.88, 4.96, 5.12 and 5.37 eV with the GeeGe bond lengths around 2.50, 2.49, 2.48 and 2.46 Å, respectively. Then the Al-doped GeODC defect model which in a case that a Ge atom of GeeGe bond in GeODC defect is substituted by an Al atom (Al-model A to Al-model D) is shown in Fig. 1(b). The structure of two tetrahedral units of GeODC defect are affected by bond length and bond angle, so it's important to analyze the parameters of Al-doped GeODC defect model. The parameters of Al-doped GeODC defect model are shown in Table 2. The average value of GeeAl bond lengths in Al-doped GeODC defect model is 2.76 Å, which is longer than the GeeGe bond length. The average GeeO bond length is 1.78 Å the same as that of GeODC defect model. Compared with GeeO bond length with 1.78 Å, the mean value of AleO bond length is much shorter at about 1.73 Å. The average
Fig. 3. The formation energies of Al-doped in GeODC configurations.
bond angles of Ge-O-Ge is 125.9°, which is close to that in GeODC defect model. The OeGeeO bond length has no changed after Al atom replaces Ge atom. The parameter of XeGeeO (X = Al, Ge) angle constant before and after replacement. To further understand the changes in the model after Al doping in ODC a-GeO2 models, the stable properties of Al-doped amorphous model are calculated. EGeODC and EAl−ODC is the total energy of the aGeO2 model with GeODC defect and the Al-doped GeODC defect model,
Fig. 2. (a) Statistical distribution of formation energy (b) Diagram of formation energy and GeeGe bond distance of GeODC defect structures. 3
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Table 2 Average value of bond length and bond angle for Al-doped GeODC defect model parameters. Average bond length (Å)
Average bond angle (°)
GeeAl
GeeO
AleO
2.76
1.78
1.73
GeeOeGe 125.9 AleOeGe 129.3
OeGeeO 109.3 OeAleO 115.9
AleGeeO 113.1 GeeAleO 102.8
Table 3 The parameters of Al-doped GeODC defect model samples.
Formation Energy /eV Ge-Al bond length (Å) O-Al-O bond angle (°)
Al-model A
Al-model B
Al-model C
Al-model D
−0.95 2.74 115.7
−1.25 2.79 116.2
−0.87 2.62 113.9
−1.27 2.89 117.8
respectively. EGe is the energy of an isolated Ge atom and EAl is the energy of an isolated Al atom. The formation energy Ef(Al−Ge) is defined as follows:
Ef (Al − Ge = EAl − ODC + EGe − EGeODC − EAl
(4)
The formation energy of Al-doped GeODC defect samples are around −1 eV, which are shown in Table 3. Oxygen vacancy center after Al substitution in GeODC defect has a smaller formation energy, and the negative values indicate that Al-GeODC defect is more likely to form in a-GeO2 structure. The calculation results show that the formation energy can be reduced as the GeeAl bond length increases. It can be seen from the table that the formation energy of the model decrease as the O-Al-O bond angle increases. The reason may be considered that the longer the bond length, the smaller the energy needed to form this local structure, so the lower the formation energy of the overall model. When the Al atom in the tetrahedron is closer to the plane of the three O atoms directly connected to it, the larger bond angle centered on Al, the lower the formation energy required.
Fig. 4. (a) Caclulated optical absorption spectra of Al-doped GeODC defect in red dashed line, GeODC defect in blue line and pure GeO2 structure in black line. (b) Caclulated total density of states of Al-doped GeODC defect in red dashed line, GeODC defect in blue line and pure GeO2 structure in black line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
1.32 eV near TVB and one unoccupied defect state at 7.35 eV in conduction band shown in red dashed line. On the basis of GW, the exciton binding energy of the Bethe-Salpete equation using multi-body perturbation theory is about 1.26 eV. A series of absorption peaks in the optical absorption spectrum are caused by transitions between the occupied states and different unoccupied states. The optical absorption peak of Al-GeODC defect configuration might be due to the transition from the occupied defect state of 1.32 eV to the BCB. For GeODC defect configuration, the optical absorption peak at 5.15 eV might be caused by the transition between the occupied defect state and the unoccupied defect state of 7.35 eV. After doping an Al atom in GeODC defect configuration, a defect state is generated in the band gap and the optical absorption peak at 5.15 eV disappears. It is obvious that red shift phenomenon in total density of states curve occur regardless of the defects before and after doping which compared with the pure a-GeO2 structure.
3.4. Optical and electronic properties The complex dielectric function describes the optical properties of the material, which is related to the action of photons and electrons and used to describe the linear response of the system to electromagnetic radiation [44]. The complex dielectric function expression is given by
ε (ω) = εr (ω) + iεi (ω)
(5)
where εr(ω) is the real part, and εi(ω) is the imaginary part which is obtained from the momentum matrix element of the occupied and unoccupied wave functions. The imaginary part of the relative dielectric function εi(ω) is proportional to the optical absorption coefficient α(ω) and can describe the optical absorption characteristics. To better comprehend the optical properties after doping with Al, the optical absorption spectra (OA) and total density of states (DOS) of the GeODC defect and Al-doped GeODC defect compared with the pure aGeO2 configuration are shown in Fig. 4. The calculation results of the optical band gap is shown at 4.8 eV, which is close to the experimental value [53]. There are no obvious optical absorption peak in band gap of pure a-GeO2 in OA which is shown in Fig. 4(a) with black line. The GeODC defect causes an optical absorption peak around 5.15 eV which is compatible with the experimental results [20]. After doping with an Al atom, the optical absorption peak at 5.15 eV is absent, and an optical absorption peak appears at 4 eV in the band gap. For comparison, TVB of the DOS curve is moved to 0 eV which is shown in Fig. 4(b). It is observed one unoccupied defect state at 7 eV in conduction band of GeODC defect configuration shown in blue line. For AlGeODC defect configuration, there are one occupied defect state at
3.5. Refractive index The complex dielectric function can characterize the physical properties of the material, and reflect the information between the electronic structures and the optical properties, and it is superior compared to some macroscopic optical constants. Complex refractive index of the medium is as follow
n˜ (ω) = n (ω) + iκ (ω)
(6)
where the real part n(ω) is the refractive index and the imaginary part is the extinction coefficient. The optical properties of the medium can be described by n(ω). The extinction coefficient κ(ω) directly describes the attenuation of light waves in the material [54]. The relational expression between them is as follows
4
n2 (ω) − κ 2 (ω) = εr (ω)
(7)
2n (ω) κ (ω) = εi (ω)
(8)
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Fig. 5. (a) Refractive index and Extinction coefficient in GeODC defect model. (b) Refractive index and Extinction coefficient in Al-doped GeODC defect model.
The refractive index and extinction coefficient expressions can be obtained by the change between the above relational expressions as follows
⎡ εr 2 (ω) + εi 2 (ω) + εr (ω) n (ω) = ⎢ 2 ⎢ ⎣
⎡ εr 2 (ω) + εi 2 (ω) − εr (ω) κ (ω) = ⎢ 2 ⎢ ⎣
1 2⎤
⎥ ⎥ ⎦
(9)
1 2⎤
⎥ ⎥ ⎦
(10)
We obtained εr(ω) and εi(ω) by the electronic ground state calculations at GW0 + BSE level. The calculated energy dependence of the refractive index and the extinction coefficient is shown in Fig. 5. The trend of refractive index and extinction coefficient curve after doping Al in GeODC defect model is the same as that of the undoped GeODC defect model. The static refractive index n(0) of Al-doped GeODC defect and undoped GeODC defect is 2.68 and 2.61 respectively. As the energy increases, the refractive index increases and reaches a maximum at 5.45 eV and 5.29 eV in the ultraviolet region of Al-doped GeODC defect and GeODC defect respectively. The energy of the last peak corresponds to 9.34 eV of GeODC defect, then the refractive index gradually decreases with increasing energy. And when it reaches a minimum at 24.4 eV, the extinction coefficient reaches a maximum value of 1.79 which showing a strong band edge absorption. When the energy reaches 9.37 eV in Al-doped GeODC defect, the refractive index decreases with increasing energy and reaches a minimum of 24.4 eV, which corresponds to the maximum extinction coefficient. The difference in refractive index can show the magnitude of the change in refractive index. Fig. 6 shows the difference in refractive index between GeODC defects and pure a-GeO2 and between GeODC defects and Al-doped GeODC defects. It was observed that at low energies area, the GeODC defect lowered the refractive index of a-GeO2 model. The refractive index difference between the two becomes positive when the energy is 5.98 eV, then the refractive index of GeODC begins to increase. And their refractive index tends to be the same as the energy increases. When GeODC defect model is doped with Al, the refractive index increases in the low energy range. At an energy of 5.98 eV, the refractive index begins to decrease and gradually tends to the refractive index undoped GeODC defect model. It can be seen that the peak value of the refractive index n(ω) is at the rising edge of the extinction coefficient κ(ω), the valley of n(ω) is at the falling edge of κ(ω), and the minimum value of n(ω) corresponds to the peak of κ(ω).
Fig. 6. (a) Refractive index difference between GeODC defect model and fused a-GeO2 model. (b) Refractive index difference between Al-doped GeODC defect model and GeODC defect model.
4. Conclusion In summary, we have investigated the atomic structures, electronic structures and optical properties of the GeODC defect and Al-GeODC defect in a-GeO2. And the calculated results show that the GeODC defect can give birth to an unoccupied defect state at the conduction band, which is associated with the optical absorption peak at 5.15 eV. In addition, Al-GeODC defect model introduces a new occupied defect state at the TVB and brings about an absorption peak at 4 eV in the optical band gap. Moreover, the optical absorption peak at 5.15 eV disappears by Al-doping in GeODC defect model. Our calculations show that the GeODC defect can bring about the decrease of the refractive index of pure a-GeO2, and the similar performance on the change of the refractive index can also be observed in GeODC defect of Ge-doped optical fiber [21]. It can be shown that Al-doping can increase the 5
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refractive index of GeODC defect in a-GeO2, which is consistent with the trend of the refractive index change of Al-doped in silica [29]. Our calculations can offer insightful instructions and new perspectives to further understand the nature of the ODC defect in Al and Ge co-doped silica optical fiber materials.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 61671085 and 61675032), the National Key Research and Development Program of China (No.2017YFB0405100) and the Open Program of State Key Laboratory of Functional Materials for Informatics. We thank for the computational support from the Beijing Computational Science Research Center (CSRC). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jnoncrysol.2019.119694. References [1] I. Hossain, H. Wagiran, N.H. Yaakob, J. Appl. Spectrosc. 80 (2013) 620. [2] N.H. Yaakob, H. Wagiran, M.I. Hossain, A.T. Ramli, D.A. Bradley, S. Hashim, H. Ali, J. Nucl. Sci. Technol. 48 (2011) 1115. [3] S. Lin, H.Y. Wang, X.N. Zhang, D. Wang, D. Zu, J.N. Song, Z.L. Liu, Y. Huang, K. Huang, N. Tao, Z.W. Li, X.P. Bai, B. Li, M. Lei, Z.F. Yu, Hui Wu, Nano Energy 62 (2019) 111. [4] K. Bi, D.Q. Yang, J. Chen, Q.M. Wang, H.Y. Wu, C.W. Lan, Y.P. Yang, Photonics Res. 7 (2019) 457. [5] S. Girard, A. Alessi, N. Richard, L. Martin-Samos, V. De Michele, L. Giacomazzi, S. Agnello, D. Di Francesca, A. Morana, B. Winkler, I. Reghioua, P. Paillet, M. Cannas, T. Robin, A. Boukenter, Y. Ouerdane, Rev. Phys. 4 (2019) 100032. [6] J. Zhang, L. Han, Z. Guan, B. Jia, Z. Peng, X. Guan, B. Yan, G. Peng, P. Lu, J. Lumin. 207 (2019) 346. [7] G. Pacchioni, C. Mazzeo, Phys. Rev. B 62 (2000) 5452. [8] A. Alessi, S. Agnello, Y. Ouerdane, F.M. Gelardi, J. Phys.Condens. Matter 23 (2011) 015903. [9] M. Fujimaki, T. Katoh, T. Kasahara, N. Miyazaki, Y. Ohki, J. Phys.Condens. Matter 11 (1999) 2589. [10] T. Tamura, G. Lu, R. Yamamoto, M. Kohyama, Phys. Rev. B 69 (2004) 195204. [11] F.L. Galeener, D.L. Griscom, M.J. Weber, Mater. Res. Soc. Proc. 61 (1986) 319. [12] A. Othonos, K. Kalli, G.E. Kohnke, Phys. Today 53 (2000) 61. [13] N. Richard, L. Martin-Samos, S. Girard, A. Ruini, A. Boukenter, Y. Ouerdane, J.P. Meunier, J. Phys.Condens. Matter 25 (2013) 335502. [14] I. Reghioua, S. Girard, A. Alessi, D. Di Francesca, L. Martin-Samos, M. Fanetti, N. Richard, M. Raine, M. Valant, A. Boukenter, Y. Ouerdane, J. Lumin. 179 (1) (2016). [15] S. Lin, X.P. Bai, H.Y. Wang, H.L. Wang, J.N. Song, K. Huang, C. Wang, N. Wang, B. Li, M. Lei, H. Wu, Adv. Mater. 29 (2017) 1703238.
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