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First-principle study of the structural, electronic and optical properties of defected amorphous silica
Journal of Non-Crystalline Solids 416 (2015) 36–43
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
First-principle study of the structural, electronic and optical properties of defected amorphous silica Yang Cheng a, Dahua Ren a, Hong Zhang b,c,⁎, Xinlu Cheng a,c a b c
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China College of Physical Science and Technology, Sichuan University, Chengdu 610065, China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, China
a r t i c l e
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Article history: Received 19 October 2014 Received in revised form 28 January 2015 Accepted 11 February 2015 Available online 6 March 2015 Keywords: Density functional theory; Optical properties; Amorphous silica; Oxygen defects
a b s t r a c t The oxygen-excess structures include oxygen dangling bond, peroxy linkage (POL), peroxy radical (POR) and interstitial oxygen molecule or ozone molecule defects, while the oxygen-deficient structures include neutral oxygen vacancy, E′ center and oxygen double-bond. For both the undefected and the various defected structures, the electronic and optical properties are calculated by plane-wave pseudo potential density functional theory. The oxygen-deficient defected structures lead to the remarkable increases in the density of states (DOS) at the top of valence band and near the bottom of the conduction band. The oxygen-excess defected structures change the distribution of defect levels and there appear new levels between the valence band and conduction band. All the defects lead to the increase of static dielectric constants and the enhancing absorption in the low energy range. Absorption peaks can be observed below 2 eV for NBOHC defected structures. Though the energy loss is generated at the lower energy region, the loss strength below 2 eV for oxygen-excess defected structures is stronger than oxygen-deficient defected structures. During the calculation the dangling bond in the structures are neutralized by hydrogen atoms. This work may give insights into the laser induced damage towards to vitreous silica. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Amorphous silica is one of the most important technological materials, as a gate dielectric in metal-oxide-semiconductor transistors which is widely used in many electronic and optoelectronic devices. Amorphous silica is also the main composition of optical fibers. With the development of optical fiber materials during the last decades, the amorphous silicon dioxide structures have attracted many researches' interests in both experiment and theory [1,2]. The studies have shown that defects and impurities constitute an intrinsic part of material [3]. The defects and impurities play an important role in affecting the optical transmission and can cause an attenuation of the optical signal and a decrease of the bandwidth. Though the low impurities have some influences on the transmittance, the main origin of discrepancy for optical transmission owe to the structures defects formed in the manufacturing process [3]. The point defects in solid SiO2 can be considered as the origin of the degradation of its properties. The electronic excitation during ionizing radiation will produce primary electrons, holes, and excitons, and the defect formation will be closely related to the self-trapping or decay processes of these radiation-induced particles [4,8]. The laser ⁎ Corresponding author at: College of Physical Science and Technology, Sichuan University, Chengdu 610065, China. E-mail address: [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.jnoncrysol.2015.02.006 0022-3093/© 2015 Elsevier B.V. All rights reserved.
damaged flaw structures are common in the silica glass structures exposed to the DUV–VUV light [5–7]. Therefore, a detailed understanding and a controlling at atomistic level to the nature of point defects is fundamentally important to synthesize new materials with well defined properties [4]. In recent years, the perfect structures and properties of silicon dioxide have attracted a lot of researchers' attention. However, the perfect structures are ideal and do not exist in nature. So it is necessary to conduct an accurate theoretical research on point defects. The oxygendefects in silicon dioxide can be classified into two categories, oxygenexcess and oxygen-deficient. Oxygen deficient contains the following kinds: neutral oxygen vacancy (≡ Si − Si ≡, ODC), E′ center (≡ Si••Si ≡) and non-bridging oxygen double-bond (_Si_O). The dangling bond of silicon defect (≡ Si•) belongs to E′ center defects. The oxygen-excess is consisted of the following [4,9,10]: (1) oxygen dangling bond (nonbridging oxygen hole center, NBOHC, ≡ Si − O•), (2) peroxy linkage (≡ Si − O − O − Si ≡, POL) and peroxy radical (≡ Si − O − O•, POR), and (3) interstitial oxygen molecule or ozone molecule. Experimentally and theoretically, various spectroscopic techniques have been used to identify these defects. Half a century ago, the existing E′ center defects have been reported with electron paramagnetic resonance by Weeks [46] in irradiated quartz. Then the oxygen-associated hole comprises non-bridging-oxygen hole centers and peroxy radicals are known with confidence from investigation of 29Si and 17O hyperfine spectra
Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
by Griscom [11,12]. With the development of science and technology, the entire spectra of optical absorption and emission are used to identify the defected structures and provide useful information to the defected properties in silicon dioxide. H. Hosono [13] has found an abnormal ≡ Si − Si ≡ bond optical absorption around at 7.6 eV in SiO2 glass network. The optical absorption band of Si dangling bond occurred at 5.8 eV reported by R. A. Weeks and D. L. Griscom [14,15]. Enormous experimental and theoretical calculations have proved that in high-purity silica the optical absorption (OA) of point defects is often the main factor, limiting the practically achievable UV transmittance [14]. For the defected structures there are three major UV optical absorption bands at 4.8, 5.8 and 7.6 eV [13,14,16,17]. Furthermore, at 4.8 eV the major optical transition occurred at the non-bridging oxygen hole center defected structures (NBOHC) and interstitial O3 defected structures according to the H. Hosono et al. [13,14,17]. However, these assignments are still being questioned and it is controversial about the fundamental absorption edge. The ab initio calculation plays a crucial role for evaluating basic properties of point defects. The density functional theory (DFT) or Hartree–Fock (HK) theory has contributed to a better understanding of the nature and generation mechanisms at the atomic scale of several point defects in crystalline and amorphous silica [4,18–21]. The clusters and embedded clusters have been adopted to model silica in order to obtain the optical properties of defected structures [22]. In this paper, the computational methods are depicted in Section 2. The density of states, dielectric function and absorption spectrum of defected silicon dioxide are presented in Section 3. Furthermore, the optical and electronic properties for different kinds of defected amorphous silicon dioxide are compared with the undefected structure, while the energy loss function is given for the different defected structures. Finally, the conclusions are given in Section 4. 2. Computational methods A non-defective molecule cluster of 32 Si and 64 O atoms was built from vitreous silica structure [23,24] as shown in Fig. 1. Defected structures of oxygen-excess and oxygen-deficient (neutral oxygen vacancy, E ′ center, dangling bond of silicon, oxygen dangling bond, oxygen double-bond, peroxy linkage, peroxy radical and interstitial oxygen or ozone molecule) were built with non-defective structure as a precursor. The geometry optimization of these cluster structures were adopted using Amsterdam Density Functional (ADF) [25]. The calculation of properties was performed within the framework of the density functional theory (DFT) [26] using the plane-wave pseudo potential scheme [27] with the generalized gradient approximation (GGA). The electronic exchange and correlation interaction are the Perdew–
Fig. 1. The cluster structure of 32 Si and 64 O atoms. Red is O atom and yellow is silicon, white is H atom.
37
Burke–Enzerhof functional (PBE) [28]. The valence electrons were labeled as Si 3s2 3p2, O 2s2 2p4. The plane-wave basis set with an energy cut-off of 500 eV was applied and Brillouin zone integration was performed over 1 × 1 × 1 grid points using the Monkorst–Pack method [29]. The self-consistent convergence of the total energy was about 1.0 × 10− 6 eV per atom. The maximum atom force was less than 0.05 eV/Å. All the calculations were performed with the Cambridge serial total energy package (CASTEP) code [30]. The cluster structures (32 molecules) were placed in a periodic box and the real size of clusters is about 20 × 21 × 14. In order to eliminate the local effects, the lattice parameter was chosen for 30 × 30 × 20. That is to say, the impact of calculation box on absorption strength can be ignored and the influence of local structure on the absorption spectra from ultraviolet (UV) and vacuum-ultraviolet (VUV) leads to the weaker absorption strength in Fig. 2. Due to the 2:1 ratio of silicon and oxygen atoms, there is a great amount of dangling bonds which exist in our model. So the extra dangling bonds are saturated with hydrogen atoms. 3. Results and discussion The distribution of bond length and bond angle of non-defective amorphous silica is depicted in Fig. 3(a–c). The average bond length and bond angle accord with the experiment [31,32]. In our calculation the average Si\O bond length is 1.653 Å, the average O\Si\O bond angle is 109.51° and that for Si\O\Si is 145.92°. The experimental value according to R. L. Mozzi [32] is as follows: Si\O average bond length is 1.639 Å, O\Si\O average bond angle is 109.47° and Si\O\Si average bond angle is 145.00°. 3.1. The electronic properties The total electronic density of states (TDOS) of defected and perfect models is shown in Figs. 4–5. The DOS of undefected amorphous silica are labeled with black dotted lines. For the DOS of undefected structures in the upper valence band region there is a strong peak at around − 0.7 eV which is caused by the oxygen lone-pair pπ orbitals, while another strong peak occurs at around − 3.0 eV which arises from Si\O\Si weak-bonding states. From −5.0 eV to −10.0 eV (hybridized by O and Si) there is a peak at − 7.2 eV and a small peak at − 5.6 eV which is due to strong Si\O\Si bonding states. From − 20.0 eV to − 17.0 eV (contributed by O 2s) there is only one sharp peak at −18.0 eV. The DOS of oxygen-deficient defected structures are shown in Fig. 4. The E′ center and silicon dangling defected structures also embrace the similar tendency. The distribution of defect levels prefers to
Fig. 2. The absorption spectrum of SiO2 structure with the different sizes of calculation box. The red line is real size of cluster 20 × 21 × 14.
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Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
Fig. 3. Distributions of a-SiO2: (a) Si\O bond lengths, (b) O\Si\O bond angles, and (c) Si\O\Si bond angles.
the lower energies, and remarkable increases appear at the top of valence band and near the bottom of the conduction band in Fig. 4(a,c). The reason is that the E′ center and silicon dangling defected structures introduce one occupied and one unoccupied defect states accompanied by the removal of bulk like Si\O states and O 2p non-bonding states [20]. For the neutral oxygen vacancy (ODC) defected structure there is a new defect state to be discovered at −0.6 eV and the distribution of oxygen s and p states is much more focus on − 20 eV and − 3.3 eV. The hybrid state of Si and oxygen is changed due to the formation of Si\Si bond. The oxygen double-band defects induce two new level states at −0.3 eV and 3.3 eV, the level state at −0.3 eV is caused by oxygen p state and at 3.3 eV is caused by Si s sate in Fig. 4(d). All the deficient oxygen introduces a new defect level appearing in the conduction band and valence band in Fig. 4. Fig. 5 describes the DOS of oxygen-excess defected structures. NBOHC defected structures due to the isolated Si\O bonding state are weaker than the strong Si\O\Si bonding and the band between −10 and − 5 eV is replaced by a Si\O bonding peak at − 4.4 eV and the oxygen s state lies at −16.2 eV in Fig. 5(a). For the POL defected structures the O\O bond gives rise to a bonding pσ resonance at − 3.9 eV and a distinct empty pσ* gap state appears at 2.2 eV, the oxygen 2s band splits into a pair of states at − 20.4 and − 15.3 eV in Fig. 5(c). The distribution strength of levels is significantly enhanced at −6.2 eV due to the form of bond. The POR defected structures have similar effect on the DOS with the POL defected structures. The oxygen 2s band splits into a pair of states at −21.0 eV and −15.3 eV and a distinct state appears at 4.1 eV. The interstitial O2 and O3 molecule defects are similar with the oxygen-deficient defected structures in Fig. 5(d–e). Remarkable increases appear at the top of valence band and two new unoccupied defect levels are found in low valence band. For the interstitial
ozone molecule defected structure, an unoccupied defect levels are found in the lower valence band of −25.2 eV. Another occupied defect level appears in the bottom of the conduction band. The above study for the oxygen-deficient defected structures and oxygen-excess defected structures reveals that the different defects have different influences on the DOS. The oxygen-excess defected structures have less impact on the distribution of the DOS at 0 eV except for the interstitial O2 and O3 molecule. The oxygen-deficient defected structures cause the remarkable increases on defect level at the top of the valence band and in the bottom of the conduction band. 3.2. Optical properties of amorphous silica The optical properties of materials have been described using the complex dielectric function ε(ω) = ε1(ω) + iε2(ω), where the ε1(ω) is a real part and the ε2(ω) is an imaginary part. The imaginary part of complex dielectric function is calculated by summing of all possible transitions from occupied to unoccupied states. It is related to the electronic band structure and can describe the absorption behavior of material [33,34]. The imaginary is given by the following equation: 2 2
ε 2 ðℏωÞ ¼
4π e mω2
!
XZ D i; j
i 2 3 ijMjji f i 1−f i Þ δ E j;k −Ei;k −ω d k ð1Þ
k
where e is the charge of free electrons, m is the mass of free electrons and ω is the frequency of incident photons. M is the dipole matrix, i and j are the initial and final states, respectively, fi is the Fermi distribution function for i-th state with crystal wave vector k. The real
Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
39
Fig. 4. The density of states of oxygen-deficient defected structures: black line is the perfect structure, (a) dangling silicon defect, (b) neutral oxygen vacancy defect (ODC), (c) E′ center defect and (d) oxygen double bond defect.
part ε1(ω) is obtained from the imaginary by the Kramers–Kronig relationship [33,34]: 2 ε1 ðωÞ ¼ 1 þ P π
Z∞ 0
ω0 ε2 ω0 dω0 02 ω −ω2
ð2Þ
where P denotes the principal value of the integral. The other optical constants such as absorption coefficient and energy loss spectrum of electron are also discussed, and the relationships are expressed as follows [35]: Absorption coefficient: IðωÞ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 pffiffiffi 2ðωÞ ε1 ðωÞ2 þ ε2 ðωÞ2 −ε1 ðωÞ
ð3Þ
Energy loss spectrum of electron: LðωÞ ¼
ε2 ðωÞ : ε1 ðωÞ2 þ ε2 ðωÞ2
over here are located in the internal or center defects of structure. The influences on the defected structures are apparent and the defects lead to a peak at 3.2 eV.
ð4Þ
3.2.1. The dielectric function of defected structures The real part of dielectric function for the defected structures is shown in Fig. 6(a–b). As shown, the defects lead to the enhancement of the static dielectric constant with the zero frequency limit. The real part changes of dielectric function for neutral oxygen vacancy defected structure (ODC) and peroxy linkage defected structure are more distinct than others due to the defects of ≡ Si − Si ≡ bond and ≡ Si − O − O − Si ≡ bond. The defected structures of NBOHC and peroxy radical (POR) presented
3.2.2. The absorption spectra of defected structures The absorption spectra of defected structures are shown in Figs. 7–8. For the perfect silicon dioxide structure, the sharpest absorption peak is at around 8.7 eV in Figs. 7–8 (black dotted lines). It is close to the typical absorption peak of ≡ Si − O − Si ≡ bond [4,36–38]. The rest of the absorption peaks occurs at 10.6 eV and 13.2 eV, respectively. According to Laughlin's report [45], the peak at about 10.4 eV is due to an excitonic resonance [46], and the other peaks are due to interband transition in a-SiO2. The absorption spectra of oxygen-deficient defected structures are depicted in Fig. 7(a). The deficient defected structures give rise to optical transitions in the low energy region. The E′ center defected structure results in an optical transition at around 4 eV. For dangling of silicon defected structures the three rather weak absorption peaks are found in the absorption spectra, one at 5.26 eV, and the others at 3.21 eV and 7.1 eV. The optical transition at 5.26 eV is caused by the oxygen 2p lone-pair states to the empty state of Si dangling bond. There is better absorption among 4–6 eV for oxygen double bond defected structure (= Si = O) which occurred at 5.30 eV and 4.52 eV in Fig. 7(a). L. Skuja et al. [4,9] have found the major optical transition oxygen double bond defected structure at 5.65 eV. In Fig. 7(b), the absorption spectra of neutral oxygen vacancy (ODC) are compared with the non-defective. Because of the Si\Si bond introducing highly localized bonding and antibonding, defect levels give rise to a strong characteristic absorption band at 7.5 eV and a weak absorption find at 4.3 eV. Several theoretical and experimental researches have demonstrated the electronic transitions of ≡ Si − Si ≡ bond appearing at 7.6 eV [4,8,39,40] and R Tohmon et al. [41] have also found an excitation near 5.0 eV.
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Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
Fig. 5. The density of states of oxygen-excess defected structures: black line is the perfect structure, (a) NBOHC defect, (b) peroxy radical (POR) defect, (c) peroxy linkage (POL) defect, (d) interstitial O2 defect and (e) interstitial O3 defect.
The absorption spectra for oxygen-excess defected structures are shown in Fig. 8. The absorption spectra of peroxy linkage (POL) defected structure in Fig. 8(a) are similar with that of the neutral oxygen vacancy (ODC) defected structure in Fig. 7(b). Note that the POL defected structures give rise to the marked absorption at 7.35 eV due to the contribution of ≡ Si − O − O − Si ≡ bond. For the POL defected structure a broad absorption bumps in the region of 6.5–7.8 eV have been reported in some theoretical researches [4,8,42]. In Fig. 8(c) the optical transitions of NBOHC defected structures are shown. For NBOHC defected structures a large number of experiments have proven the optical absorption band at 0.86 eV, 2.45 eV and 6.8 eV in visible (VIS) to vacuum-uv (vuv). The absorption of peroxy radical (POR) defected structure is similar with the absorption of NBOHC defected structure in Fig. 8(b). The POR defects give rise to the weak peak at 3.8 eV and two relatively weaker peaks at around 1.08 eV and 1.9 eV. Interestingly, it is found that a weak optical transition in our calculation occurs at 1.90 eV in good
agreement with 1.97 eV found by H. Hosono and R. A. Weeks [43]. The absorption spectra of interstitial oxygen (O2) and ozone (O3) defected structures are shown in Fig. 8(d–e). For the defected structure of interstitial O3 in Fig. 8(e), the most intense peak is at 4.83 eV, and the relative weak absorption peaks are at 5.85 eV and 3.83 eV. Most theories and experiments have confirmed the optical transition at 4.8 eV [17,18] for interstitial O3 defected structure. And L. Skuja et al. [17] have also found the absorption peak at 2.0 eV for this defected structure. The defected structure of interstitial O2 gives rise to the absorption peaks at around 1.63 eV, 2.8 eV, 4.03 eV and 5.48 eV in Fig. 8(e). Experimentally, in the VIS–UV range absorption spectrum induces several bands with maxima at 4.73 eV and around 5.8 eV. And other theoretical studies have also confirmed the absorption peak at 1.62 eV. Taken together, the defects induce lower energy excitation from visible (VIS) to vacuum-uv (vuv) for the amorphous silica. The absorption spectra present various shapes even it is far from well-known
Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
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Fig. 6. The dielectric function of defected structure: (a) oxygen-deficient defects and (b) oxygen-excess defects.
experimental spectra. That is maybe caused by the content of different defects, as R.H. Magruder [47] have obtained the different spectra using oxygen implanted silica. The effect of content of different defects on spectra focus on our research in the future. The introduction of H atoms will induce the excitation in vuv, but we are neglected the impact.
the E′ center defected structure has the largest energy loss at 3.8 eV in uv regions. The energy loss function is rarely studied in theory and experiment in the area of low photon energies. This work can give insight into more understanding about energy loss. 4. Conclusion
3.2.3. The phonon energy loss spectra The phonon energy loss spectrum L(ω) is an important factor describing the energy loss of a fast photon traversing in material. The prominent peak of the L(ω) spectrum represents the characteristics associated with the plasma oscillations [44]. The energy loss spectra of defected and perfect structures are shown in Fig. 9. The main and strong loss peaks at around 8 eV for the silicon dioxide structures. The loss spectra of above 6 eV are almost overlapped with the perfect structure for most defected structures. But the intensity of energy loss spectrum for the peroxy oxygen linkage (POL) and neutral oxygen vacancy (ODC) defected structures have big changes due to the new bond formation in Fig. 9(a–b). In the area of low photon energies the oxygenexcess defected structures have more obvious loss which embraces the loss peaks from 0 eV to 2 eV in Fig. 9(b). The NBOHC and interstitial ozone molecule defected structures catch the largest energy loss at 0.9 eV and 1.6 eV. For the energy loss caused by the oxygen-deficient defected structures the loss peaks appear above 2 eV in Fig. 9(a), and
In summary, the electronic and optical properties of defected amorphous silica structures with all kinds of defects are systematically calculated by plane-wave pseudo potential DFT in the frame of GGA/PBE method. The influence of defects on the distribution of the DOS is described. The defects lead to new defect levels appearing between the valence band and conduction band. The oxygen-deficient defects make defect levels transfer to the lower energy. As the oxygen defects lead to the significant absorption in low photon energy range, the absorption coefficients of POR, interstitial O2 and O3, and NBOHC defected structures become relative small. The absorption of ODC and POL defected structure is stronger than the other defects at 6–8 eV as the form of ≡ Si − Si ≡ and ≡ Si − O − O − Si ≡ bonds. Meanwhile, all defected structures give rise to the increases of the static real dielectric constants. At low energy the strength of the energy loss peak of the oxygen-excess defected structures is much stronger than that of oxygen-deficient defected structures.
Fig. 7. The absorption spectra of oxygen-deficient defected structures, the black line is for un-defected structure. (a) Oxygen double, Si dangling, E′ center defects. (b) Neutral oxygen vacancy defect (ODC).
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Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
Fig. 8. The absorption spectra of oxygen-excess defected structures: black line is un-defected structure. (a) Peroxy linkage defects, (b) non-bridging oxygen hole center (NBOHC) defect, (c) peroxy radical (POR) defect, (d) interstitial O2 defect and (e) interstitial O3 defect.
Fig. 9. The energy loss spectra of oxygen-deficient defected and oxygen-excess defected structures. (a) Oxygen-deficient defects, (b) oxygen-excess defects.
Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
First-principle study of the structural, electronic and optical properties of defected amorphous silica Yang Cheng a, Dahua Ren a, Hong Zhang b,c,⁎, Xinlu Cheng a,c a b c
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, PR China College of Physical Science and Technology, Sichuan University, Chengdu 610065, China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, China
a r t i c l e
i n f o
Article history: Received 19 October 2014 Received in revised form 28 January 2015 Accepted 11 February 2015 Available online 6 March 2015 Keywords: Density functional theory; Optical properties; Amorphous silica; Oxygen defects
a b s t r a c t The oxygen-excess structures include oxygen dangling bond, peroxy linkage (POL), peroxy radical (POR) and interstitial oxygen molecule or ozone molecule defects, while the oxygen-deficient structures include neutral oxygen vacancy, E′ center and oxygen double-bond. For both the undefected and the various defected structures, the electronic and optical properties are calculated by plane-wave pseudo potential density functional theory. The oxygen-deficient defected structures lead to the remarkable increases in the density of states (DOS) at the top of valence band and near the bottom of the conduction band. The oxygen-excess defected structures change the distribution of defect levels and there appear new levels between the valence band and conduction band. All the defects lead to the increase of static dielectric constants and the enhancing absorption in the low energy range. Absorption peaks can be observed below 2 eV for NBOHC defected structures. Though the energy loss is generated at the lower energy region, the loss strength below 2 eV for oxygen-excess defected structures is stronger than oxygen-deficient defected structures. During the calculation the dangling bond in the structures are neutralized by hydrogen atoms. This work may give insights into the laser induced damage towards to vitreous silica. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Amorphous silica is one of the most important technological materials, as a gate dielectric in metal-oxide-semiconductor transistors which is widely used in many electronic and optoelectronic devices. Amorphous silica is also the main composition of optical fibers. With the development of optical fiber materials during the last decades, the amorphous silicon dioxide structures have attracted many researches' interests in both experiment and theory [1,2]. The studies have shown that defects and impurities constitute an intrinsic part of material [3]. The defects and impurities play an important role in affecting the optical transmission and can cause an attenuation of the optical signal and a decrease of the bandwidth. Though the low impurities have some influences on the transmittance, the main origin of discrepancy for optical transmission owe to the structures defects formed in the manufacturing process [3]. The point defects in solid SiO2 can be considered as the origin of the degradation of its properties. The electronic excitation during ionizing radiation will produce primary electrons, holes, and excitons, and the defect formation will be closely related to the self-trapping or decay processes of these radiation-induced particles [4,8]. The laser ⁎ Corresponding author at: College of Physical Science and Technology, Sichuan University, Chengdu 610065, China. E-mail address: [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.jnoncrysol.2015.02.006 0022-3093/© 2015 Elsevier B.V. All rights reserved.
damaged flaw structures are common in the silica glass structures exposed to the DUV–VUV light [5–7]. Therefore, a detailed understanding and a controlling at atomistic level to the nature of point defects is fundamentally important to synthesize new materials with well defined properties [4]. In recent years, the perfect structures and properties of silicon dioxide have attracted a lot of researchers' attention. However, the perfect structures are ideal and do not exist in nature. So it is necessary to conduct an accurate theoretical research on point defects. The oxygendefects in silicon dioxide can be classified into two categories, oxygenexcess and oxygen-deficient. Oxygen deficient contains the following kinds: neutral oxygen vacancy (≡ Si − Si ≡, ODC), E′ center (≡ Si••Si ≡) and non-bridging oxygen double-bond (_Si_O). The dangling bond of silicon defect (≡ Si•) belongs to E′ center defects. The oxygen-excess is consisted of the following [4,9,10]: (1) oxygen dangling bond (nonbridging oxygen hole center, NBOHC, ≡ Si − O•), (2) peroxy linkage (≡ Si − O − O − Si ≡, POL) and peroxy radical (≡ Si − O − O•, POR), and (3) interstitial oxygen molecule or ozone molecule. Experimentally and theoretically, various spectroscopic techniques have been used to identify these defects. Half a century ago, the existing E′ center defects have been reported with electron paramagnetic resonance by Weeks [46] in irradiated quartz. Then the oxygen-associated hole comprises non-bridging-oxygen hole centers and peroxy radicals are known with confidence from investigation of 29Si and 17O hyperfine spectra
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by Griscom [11,12]. With the development of science and technology, the entire spectra of optical absorption and emission are used to identify the defected structures and provide useful information to the defected properties in silicon dioxide. H. Hosono [13] has found an abnormal ≡ Si − Si ≡ bond optical absorption around at 7.6 eV in SiO2 glass network. The optical absorption band of Si dangling bond occurred at 5.8 eV reported by R. A. Weeks and D. L. Griscom [14,15]. Enormous experimental and theoretical calculations have proved that in high-purity silica the optical absorption (OA) of point defects is often the main factor, limiting the practically achievable UV transmittance [14]. For the defected structures there are three major UV optical absorption bands at 4.8, 5.8 and 7.6 eV [13,14,16,17]. Furthermore, at 4.8 eV the major optical transition occurred at the non-bridging oxygen hole center defected structures (NBOHC) and interstitial O3 defected structures according to the H. Hosono et al. [13,14,17]. However, these assignments are still being questioned and it is controversial about the fundamental absorption edge. The ab initio calculation plays a crucial role for evaluating basic properties of point defects. The density functional theory (DFT) or Hartree–Fock (HK) theory has contributed to a better understanding of the nature and generation mechanisms at the atomic scale of several point defects in crystalline and amorphous silica [4,18–21]. The clusters and embedded clusters have been adopted to model silica in order to obtain the optical properties of defected structures [22]. In this paper, the computational methods are depicted in Section 2. The density of states, dielectric function and absorption spectrum of defected silicon dioxide are presented in Section 3. Furthermore, the optical and electronic properties for different kinds of defected amorphous silicon dioxide are compared with the undefected structure, while the energy loss function is given for the different defected structures. Finally, the conclusions are given in Section 4. 2. Computational methods A non-defective molecule cluster of 32 Si and 64 O atoms was built from vitreous silica structure [23,24] as shown in Fig. 1. Defected structures of oxygen-excess and oxygen-deficient (neutral oxygen vacancy, E ′ center, dangling bond of silicon, oxygen dangling bond, oxygen double-bond, peroxy linkage, peroxy radical and interstitial oxygen or ozone molecule) were built with non-defective structure as a precursor. The geometry optimization of these cluster structures were adopted using Amsterdam Density Functional (ADF) [25]. The calculation of properties was performed within the framework of the density functional theory (DFT) [26] using the plane-wave pseudo potential scheme [27] with the generalized gradient approximation (GGA). The electronic exchange and correlation interaction are the Perdew–
Fig. 1. The cluster structure of 32 Si and 64 O atoms. Red is O atom and yellow is silicon, white is H atom.
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Burke–Enzerhof functional (PBE) [28]. The valence electrons were labeled as Si 3s2 3p2, O 2s2 2p4. The plane-wave basis set with an energy cut-off of 500 eV was applied and Brillouin zone integration was performed over 1 × 1 × 1 grid points using the Monkorst–Pack method [29]. The self-consistent convergence of the total energy was about 1.0 × 10− 6 eV per atom. The maximum atom force was less than 0.05 eV/Å. All the calculations were performed with the Cambridge serial total energy package (CASTEP) code [30]. The cluster structures (32 molecules) were placed in a periodic box and the real size of clusters is about 20 × 21 × 14. In order to eliminate the local effects, the lattice parameter was chosen for 30 × 30 × 20. That is to say, the impact of calculation box on absorption strength can be ignored and the influence of local structure on the absorption spectra from ultraviolet (UV) and vacuum-ultraviolet (VUV) leads to the weaker absorption strength in Fig. 2. Due to the 2:1 ratio of silicon and oxygen atoms, there is a great amount of dangling bonds which exist in our model. So the extra dangling bonds are saturated with hydrogen atoms. 3. Results and discussion The distribution of bond length and bond angle of non-defective amorphous silica is depicted in Fig. 3(a–c). The average bond length and bond angle accord with the experiment [31,32]. In our calculation the average Si\O bond length is 1.653 Å, the average O\Si\O bond angle is 109.51° and that for Si\O\Si is 145.92°. The experimental value according to R. L. Mozzi [32] is as follows: Si\O average bond length is 1.639 Å, O\Si\O average bond angle is 109.47° and Si\O\Si average bond angle is 145.00°. 3.1. The electronic properties The total electronic density of states (TDOS) of defected and perfect models is shown in Figs. 4–5. The DOS of undefected amorphous silica are labeled with black dotted lines. For the DOS of undefected structures in the upper valence band region there is a strong peak at around − 0.7 eV which is caused by the oxygen lone-pair pπ orbitals, while another strong peak occurs at around − 3.0 eV which arises from Si\O\Si weak-bonding states. From −5.0 eV to −10.0 eV (hybridized by O and Si) there is a peak at − 7.2 eV and a small peak at − 5.6 eV which is due to strong Si\O\Si bonding states. From − 20.0 eV to − 17.0 eV (contributed by O 2s) there is only one sharp peak at −18.0 eV. The DOS of oxygen-deficient defected structures are shown in Fig. 4. The E′ center and silicon dangling defected structures also embrace the similar tendency. The distribution of defect levels prefers to
Fig. 2. The absorption spectrum of SiO2 structure with the different sizes of calculation box. The red line is real size of cluster 20 × 21 × 14.
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Fig. 3. Distributions of a-SiO2: (a) Si\O bond lengths, (b) O\Si\O bond angles, and (c) Si\O\Si bond angles.
the lower energies, and remarkable increases appear at the top of valence band and near the bottom of the conduction band in Fig. 4(a,c). The reason is that the E′ center and silicon dangling defected structures introduce one occupied and one unoccupied defect states accompanied by the removal of bulk like Si\O states and O 2p non-bonding states [20]. For the neutral oxygen vacancy (ODC) defected structure there is a new defect state to be discovered at −0.6 eV and the distribution of oxygen s and p states is much more focus on − 20 eV and − 3.3 eV. The hybrid state of Si and oxygen is changed due to the formation of Si\Si bond. The oxygen double-band defects induce two new level states at −0.3 eV and 3.3 eV, the level state at −0.3 eV is caused by oxygen p state and at 3.3 eV is caused by Si s sate in Fig. 4(d). All the deficient oxygen introduces a new defect level appearing in the conduction band and valence band in Fig. 4. Fig. 5 describes the DOS of oxygen-excess defected structures. NBOHC defected structures due to the isolated Si\O bonding state are weaker than the strong Si\O\Si bonding and the band between −10 and − 5 eV is replaced by a Si\O bonding peak at − 4.4 eV and the oxygen s state lies at −16.2 eV in Fig. 5(a). For the POL defected structures the O\O bond gives rise to a bonding pσ resonance at − 3.9 eV and a distinct empty pσ* gap state appears at 2.2 eV, the oxygen 2s band splits into a pair of states at − 20.4 and − 15.3 eV in Fig. 5(c). The distribution strength of levels is significantly enhanced at −6.2 eV due to the form of bond. The POR defected structures have similar effect on the DOS with the POL defected structures. The oxygen 2s band splits into a pair of states at −21.0 eV and −15.3 eV and a distinct state appears at 4.1 eV. The interstitial O2 and O3 molecule defects are similar with the oxygen-deficient defected structures in Fig. 5(d–e). Remarkable increases appear at the top of valence band and two new unoccupied defect levels are found in low valence band. For the interstitial
ozone molecule defected structure, an unoccupied defect levels are found in the lower valence band of −25.2 eV. Another occupied defect level appears in the bottom of the conduction band. The above study for the oxygen-deficient defected structures and oxygen-excess defected structures reveals that the different defects have different influences on the DOS. The oxygen-excess defected structures have less impact on the distribution of the DOS at 0 eV except for the interstitial O2 and O3 molecule. The oxygen-deficient defected structures cause the remarkable increases on defect level at the top of the valence band and in the bottom of the conduction band. 3.2. Optical properties of amorphous silica The optical properties of materials have been described using the complex dielectric function ε(ω) = ε1(ω) + iε2(ω), where the ε1(ω) is a real part and the ε2(ω) is an imaginary part. The imaginary part of complex dielectric function is calculated by summing of all possible transitions from occupied to unoccupied states. It is related to the electronic band structure and can describe the absorption behavior of material [33,34]. The imaginary is given by the following equation: 2 2
ε 2 ðℏωÞ ¼
4π e mω2
!
XZ D i; j
i 2 3 ijMjji f i 1−f i Þ δ E j;k −Ei;k −ω d k ð1Þ
k
where e is the charge of free electrons, m is the mass of free electrons and ω is the frequency of incident photons. M is the dipole matrix, i and j are the initial and final states, respectively, fi is the Fermi distribution function for i-th state with crystal wave vector k. The real
Y. Cheng et al. / Journal of Non-Crystalline Solids 416 (2015) 36–43
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Fig. 4. The density of states of oxygen-deficient defected structures: black line is the perfect structure, (a) dangling silicon defect, (b) neutral oxygen vacancy defect (ODC), (c) E′ center defect and (d) oxygen double bond defect.
part ε1(ω) is obtained from the imaginary by the Kramers–Kronig relationship [33,34]: 2 ε1 ðωÞ ¼ 1 þ P π
Z∞ 0
ω0 ε2 ω0 dω0 02 ω −ω2
ð2Þ
where P denotes the principal value of the integral. The other optical constants such as absorption coefficient and energy loss spectrum of electron are also discussed, and the relationships are expressed as follows [35]: Absorption coefficient: IðωÞ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 pffiffiffi 2ðωÞ ε1 ðωÞ2 þ ε2 ðωÞ2 −ε1 ðωÞ
ð3Þ
Energy loss spectrum of electron: LðωÞ ¼
ε2 ðωÞ : ε1 ðωÞ2 þ ε2 ðωÞ2
over here are located in the internal or center defects of structure. The influences on the defected structures are apparent and the defects lead to a peak at 3.2 eV.
ð4Þ
3.2.1. The dielectric function of defected structures The real part of dielectric function for the defected structures is shown in Fig. 6(a–b). As shown, the defects lead to the enhancement of the static dielectric constant with the zero frequency limit. The real part changes of dielectric function for neutral oxygen vacancy defected structure (ODC) and peroxy linkage defected structure are more distinct than others due to the defects of ≡ Si − Si ≡ bond and ≡ Si − O − O − Si ≡ bond. The defected structures of NBOHC and peroxy radical (POR) presented
3.2.2. The absorption spectra of defected structures The absorption spectra of defected structures are shown in Figs. 7–8. For the perfect silicon dioxide structure, the sharpest absorption peak is at around 8.7 eV in Figs. 7–8 (black dotted lines). It is close to the typical absorption peak of ≡ Si − O − Si ≡ bond [4,36–38]. The rest of the absorption peaks occurs at 10.6 eV and 13.2 eV, respectively. According to Laughlin's report [45], the peak at about 10.4 eV is due to an excitonic resonance [46], and the other peaks are due to interband transition in a-SiO2. The absorption spectra of oxygen-deficient defected structures are depicted in Fig. 7(a). The deficient defected structures give rise to optical transitions in the low energy region. The E′ center defected structure results in an optical transition at around 4 eV. For dangling of silicon defected structures the three rather weak absorption peaks are found in the absorption spectra, one at 5.26 eV, and the others at 3.21 eV and 7.1 eV. The optical transition at 5.26 eV is caused by the oxygen 2p lone-pair states to the empty state of Si dangling bond. There is better absorption among 4–6 eV for oxygen double bond defected structure (= Si = O) which occurred at 5.30 eV and 4.52 eV in Fig. 7(a). L. Skuja et al. [4,9] have found the major optical transition oxygen double bond defected structure at 5.65 eV. In Fig. 7(b), the absorption spectra of neutral oxygen vacancy (ODC) are compared with the non-defective. Because of the Si\Si bond introducing highly localized bonding and antibonding, defect levels give rise to a strong characteristic absorption band at 7.5 eV and a weak absorption find at 4.3 eV. Several theoretical and experimental researches have demonstrated the electronic transitions of ≡ Si − Si ≡ bond appearing at 7.6 eV [4,8,39,40] and R Tohmon et al. [41] have also found an excitation near 5.0 eV.
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Fig. 5. The density of states of oxygen-excess defected structures: black line is the perfect structure, (a) NBOHC defect, (b) peroxy radical (POR) defect, (c) peroxy linkage (POL) defect, (d) interstitial O2 defect and (e) interstitial O3 defect.
The absorption spectra for oxygen-excess defected structures are shown in Fig. 8. The absorption spectra of peroxy linkage (POL) defected structure in Fig. 8(a) are similar with that of the neutral oxygen vacancy (ODC) defected structure in Fig. 7(b). Note that the POL defected structures give rise to the marked absorption at 7.35 eV due to the contribution of ≡ Si − O − O − Si ≡ bond. For the POL defected structure a broad absorption bumps in the region of 6.5–7.8 eV have been reported in some theoretical researches [4,8,42]. In Fig. 8(c) the optical transitions of NBOHC defected structures are shown. For NBOHC defected structures a large number of experiments have proven the optical absorption band at 0.86 eV, 2.45 eV and 6.8 eV in visible (VIS) to vacuum-uv (vuv). The absorption of peroxy radical (POR) defected structure is similar with the absorption of NBOHC defected structure in Fig. 8(b). The POR defects give rise to the weak peak at 3.8 eV and two relatively weaker peaks at around 1.08 eV and 1.9 eV. Interestingly, it is found that a weak optical transition in our calculation occurs at 1.90 eV in good
agreement with 1.97 eV found by H. Hosono and R. A. Weeks [43]. The absorption spectra of interstitial oxygen (O2) and ozone (O3) defected structures are shown in Fig. 8(d–e). For the defected structure of interstitial O3 in Fig. 8(e), the most intense peak is at 4.83 eV, and the relative weak absorption peaks are at 5.85 eV and 3.83 eV. Most theories and experiments have confirmed the optical transition at 4.8 eV [17,18] for interstitial O3 defected structure. And L. Skuja et al. [17] have also found the absorption peak at 2.0 eV for this defected structure. The defected structure of interstitial O2 gives rise to the absorption peaks at around 1.63 eV, 2.8 eV, 4.03 eV and 5.48 eV in Fig. 8(e). Experimentally, in the VIS–UV range absorption spectrum induces several bands with maxima at 4.73 eV and around 5.8 eV. And other theoretical studies have also confirmed the absorption peak at 1.62 eV. Taken together, the defects induce lower energy excitation from visible (VIS) to vacuum-uv (vuv) for the amorphous silica. The absorption spectra present various shapes even it is far from well-known
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Fig. 6. The dielectric function of defected structure: (a) oxygen-deficient defects and (b) oxygen-excess defects.
experimental spectra. That is maybe caused by the content of different defects, as R.H. Magruder [47] have obtained the different spectra using oxygen implanted silica. The effect of content of different defects on spectra focus on our research in the future. The introduction of H atoms will induce the excitation in vuv, but we are neglected the impact.
the E′ center defected structure has the largest energy loss at 3.8 eV in uv regions. The energy loss function is rarely studied in theory and experiment in the area of low photon energies. This work can give insight into more understanding about energy loss. 4. Conclusion
3.2.3. The phonon energy loss spectra The phonon energy loss spectrum L(ω) is an important factor describing the energy loss of a fast photon traversing in material. The prominent peak of the L(ω) spectrum represents the characteristics associated with the plasma oscillations [44]. The energy loss spectra of defected and perfect structures are shown in Fig. 9. The main and strong loss peaks at around 8 eV for the silicon dioxide structures. The loss spectra of above 6 eV are almost overlapped with the perfect structure for most defected structures. But the intensity of energy loss spectrum for the peroxy oxygen linkage (POL) and neutral oxygen vacancy (ODC) defected structures have big changes due to the new bond formation in Fig. 9(a–b). In the area of low photon energies the oxygenexcess defected structures have more obvious loss which embraces the loss peaks from 0 eV to 2 eV in Fig. 9(b). The NBOHC and interstitial ozone molecule defected structures catch the largest energy loss at 0.9 eV and 1.6 eV. For the energy loss caused by the oxygen-deficient defected structures the loss peaks appear above 2 eV in Fig. 9(a), and
In summary, the electronic and optical properties of defected amorphous silica structures with all kinds of defects are systematically calculated by plane-wave pseudo potential DFT in the frame of GGA/PBE method. The influence of defects on the distribution of the DOS is described. The defects lead to new defect levels appearing between the valence band and conduction band. The oxygen-deficient defects make defect levels transfer to the lower energy. As the oxygen defects lead to the significant absorption in low photon energy range, the absorption coefficients of POR, interstitial O2 and O3, and NBOHC defected structures become relative small. The absorption of ODC and POL defected structure is stronger than the other defects at 6–8 eV as the form of ≡ Si − Si ≡ and ≡ Si − O − O − Si ≡ bonds. Meanwhile, all defected structures give rise to the increases of the static real dielectric constants. At low energy the strength of the energy loss peak of the oxygen-excess defected structures is much stronger than that of oxygen-deficient defected structures.
Fig. 7. The absorption spectra of oxygen-deficient defected structures, the black line is for un-defected structure. (a) Oxygen double, Si dangling, E′ center defects. (b) Neutral oxygen vacancy defect (ODC).
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Fig. 8. The absorption spectra of oxygen-excess defected structures: black line is un-defected structure. (a) Peroxy linkage defects, (b) non-bridging oxygen hole center (NBOHC) defect, (c) peroxy radical (POR) defect, (d) interstitial O2 defect and (e) interstitial O3 defect.
Fig. 9. The energy loss spectra of oxygen-deficient defected and oxygen-excess defected structures. (a) Oxygen-deficient defects, (b) oxygen-excess defects.
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