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Ab initio cluster calculations on point defects in amorphous SiO2
Current Opinion in Solid State and Materials Science 5 (2001) 517–523
Ab initio cluster calculations on point defects in amorphous SiO 2 T. Uchino* Institute for Chemical Research, Kyoto University, Uji, Kyoto 611 -0011, Japan Received 16 January 2002; received in revised form 12 February 2002; accepted 12 February 2002
Abstract Recently, there have been considerable advances in quantum-chemical calculations on clusters of atoms designed to model local defect centers in amorphous materials. In particular, this review attempts to put into perspective the recent calculated results of the point defects in pure and doped a-SiO 2 , which have attracted renewed attention in view of fabrication of Bragg gratings in optical fibers and waveguides. Recent sophisticated calculations may challenge the conventional models of several defect centers in a-SiO 2 . 2002 Published by Elsevier Science Ltd.
1. Introduction The electrical and optical properties of Si-based amorphous materials, which are of special importance for their use in optical fiber technologies and optoelectronic devices, are determined mainly by local structural defects. Thus, considerable efforts have been made in the past decades to understand the structural, optical and electronic properties of point defects in amorphous SiO 2 . Recently, quantum-chemical calculations have proved increasingly useful for the study of the structure and properties associated with point defects in amorphous insulators and semiconductors. In particular, a cluster approach based on the ab initio molecular orbital method has provided several new insights into the microstructure of local defects in amorphous SiO 2 . It is often claimed that such cluster calculations may bridge the gap between the properties of isolated molecules and the condensed phase. According to the cluster approach, the structure of a defect center in amorphous solids is described by a finite number of atoms comprising the local defect and its surrounding environment. Model clusters are composed of |10–|100 atoms depending on the aim of the study and the available computer facilities. Geometries of the model clusters are optimized at the Hartree–Fock (HF), post-HF, and / or density functional theory (DFT) levels to search their local minimum configurations, and their structure, optical and vibrational properties, and excited states are *Departmeant of Chemistry, Kobe University, Nada-ku, Kobe 6578501, Japan. Tel.: 181-78-803-5681; fax: 181-78-803-5681. E-mail address: [email protected] (T. Uchino).
investigated at the respective levels of theory. This approach may not fully take into account the actual effect of condensed environments around the defect of interest. However, it is reasonable to expect that the electronic states associated with the defect are rather localized and do not extend through the corresponding solid, implying that the electronic structure of the defect in amorphous solids is reasonably modeled by the cluster calculations. This review will first highlight recent calculated results of intrinsic defects in pure amorphous SiO 2 (a-SiO 2 ), and will then turn to the extrinsic local defects in doped a-SiO 2 .
2. Point defects in pure a-SiO 2
2.1. The E9 centers Previously, a large number of theoretical studies has been dedicated to the structure and electronic states of point defects in a-SiO 2 [1]. Among other Si-related defect centers, E9 centers have been the subject of considerable theoretical investigation since the E9 centers are the major oxygen-deficiency-related paramagnetic defect in a-SiO 2 . Thus far, at least four different types of E9 centers have been observed in a-SiO 2 [2–4], with the only common feature being an unpaired electron on threefold coordinated silicon. These E9-center variants, as discussed below, will differ from each other in the second-coordination environments around the respective paramagnetic Si atoms, although their local structures have not been fully understood yet.
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2.1.1. The E 9g center According to Feigl et al. [5], trapping of a hole by an oxygen monovacancy site in crystalline a -quartz causes an asymmetric relaxation of the defect site, resulting in the paramagnetic center called the E 91 center. The unpaired electron in the E 91 center is localized solely on one of the two threefold-coordinated Si atoms in the oxygen vacancy site, whereas the hole is trapped at the other threefoldcoordinated Si atom (see Fig. 1a). This model of the E 91 center has been supported by recent theoretical calculations based on ab initio cluster [6] and super-cell [7–9] approaches. Since the E 9g center, which is a fundamental paramagnetic center in a-SiO 2 , exhibit similar electron paramagnetic resonance (EPR) characteristics to the E 91 center in a -quartz (a |420 G splitting of the hyperfine spectrum and an anisotropic g-tensor, g11 52.0018, g22 5 2.0006, g33 52.0003), it has commonly been believed over the past 25 years that these two E9-center variants, E 91 and E 9g , are essentially identical to each other. However, it has been suggested that in a-SiO 2 the original symmetry of the oxygen monovacancy site is likely to be low enough to drive such an asymmetric relaxation as seen in Fig. 1a, implying that there are some other defect sites that are responsible for the E 9g center in a-SiO 2 [1]. Indeed, there exist some experimental and theoretical indications that the E 9g center in a-SiO 2 may not have the same microscopic origin as that of the E 91 center in a -quartz [10]. Thus, Uchino et al. [10,11] have recently proposed an alternative model of the E 9g center, in which paramagnetic and positively charged threefold coordinated silicon atoms are bridged by a common oxygen atom (see Fig. 1b). This new
type of paramagnetic defect is referred to as a bridged hole-trapping oxygen-deficiency center (BHODC). It has been shown by the cluster calculations [10,11] that the BHODC model quantitatively reproduces the experimental 420 G hyperfine splitting observed for the E 9g center. Furthermore, this model can account for the diffusionlimited anneal mechanisms of the E 9g center associated with atomic hydrogen [10] and molecular oxygen [12], forming the E 9b center and the peroxy-radical defect, respectively. Although the BHODC model may not give a conclusive picture of the E 9g center in a-SiO 2 at the present stage, this model appears to have a reasonable advantage over the conventional E g9 -center model [10–12] and will surely challenge the experimenters to devise new experiments to prove or disprove its validity.
2.1.2. The E 9d center The E d9 center was first discovered by Griscom and Friebele [13] after X-ray irradiation in bulk a-SiO 2 . This defect was also observed at the surface of buried SiO 2 layers formed by oxygen-ion implantation of silicon crystals [14] and in thermally grown thin SiO 2 films [15]. The characteristic EPR features of the E 9d center are a highly isotropic g-tensor ( g11 52.0018, g22 5g33 52.0021) and a 100 G doublet hyperfine splitting. The observed EPR spectrum of the E d9 center implies that, unlike the other E9-center variants, the unpaired electron in this center is delocalized over multiple equivalent Si atoms. A theoretical study of the electronic structure of the E d9 center has been performed by Chavez et al. [16] using a cluster approach. According to their calculations, the E 9d
Fig. 1. (a) A conventional model of the E g9 center derived from the model of the E 91 center in a-quartz. (b) A newly proposed model of the E 9g center [10–12].
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however, such a lattice oxygen, which is inevitably located in a -quartz, may be absent [1]. Thus, it is probable that the symmetric relaxation occurs at the oxygen monovacancy site, especially in a-SiO 2 , and that the resultant paramagnetic center is a likely candidate for the delocalized E 9d defect.
Fig. 2. A model of the E 9d center proposed by Chavez et al. [16]. In this model, an unpaired electron is almost equally distributed over the two Si atoms in the defect.
center is attributed to a hole trapped at a simple oxygen monovacancy in which the unpaired electron is shared equally by two silicon atoms in the defect site (see Fig. 2). The hole trapping in this case results in a symmetric relaxation, leading to a slight increase in the interatomic distance between the two paramagnetic Si atoms. The calculated isotropic hyperfine coupling constants compare well with the corresponding observed values. Recent quantum-chemical calculations [6,10,17] have also supported the above E 9d -model. As for the oxygen monovacancy site in the corresponding crystalline a -quartz lattice, the hole trapping causes an asymmetric relaxation, forming the E 91 center as mentioned earlier. This suggests that structural constraints derived from a crystalline lattice are responsible for the asymmetric relaxation in the hole trapped oxygen monovacancy site. Indeed, it has been proposed that the asymmetric relaxation related to the formation of the E 91 center is facilitated with the help of the interaction between the hole-trapped Si site and its adjacent lattice oxygen, forming a puckered defect configuration [18]. In a-SiO 2 ,
2.1.3. The E 9a center The nature of the E 9a center is less certain as compared with other E9-center variants, and there has been no accepted model accounting for its microscopic structure. The E 9a center is stable only at low temperatures (, |100 K) and is observed to anneal at 200 K [19]. Another peculiar feature of the E 9a center is the large anisotropic component in the EPR g values ( g11 52.0018, g22 5 2.0013, g33 51.9998) although the observed isotropic hyperfine coupling (420 G) indicates that the unpaired electron in this defect center is most likely localized at one silicon atom, as in the case of the E 9g center. Thus far, only one quantum-chemical cluster approach [20] has been reported as to the microscopic structure of the E 9a center. It has been shown that the divalent Si defect can trap a hole and then tends to interact with a nearby bridging oxygen atom, forming a highly anisotropic threefold-coordinated paramagnetic Si site (see Fig. 3). Such an anisotropic nature of the defect is inherent in the fact that one of the oxygen atoms that are bonded to the paramagnetic silicon is a threefold coordinated oxygen. It has also been demonstrated [20] that the unpaired electron is localized mainly on the paramagnetic silicon and that the isotropic hyperfine coupling calculated for this silicon atom is in good agreement with that observed for the E 9a center. It should also be noted that the proposed structural transformation associated with the divalent Si defect is accomplished without accompanying complex atomic reconfigurations. This suggests that the hole-trapping center shown in Fig. 3 is apt to trap an electron to show an electron-hole recombination; in other words, this paramagnetic center may be stable only at low temperatures, in
Fig. 3. A proposed formation mechanism of the E a9 center [20]. In this model, an unpaired electron is localized mostly at the threefold coordinated silicon atom in the defect.
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accord with the experimental characteristics observed for the E 9a center.
2.2. The divalent Si defect The divalent Si (5Si:) defect has been the subject of considerable interest since the discovery of the photorefractive effect in a-SiO 2 , which has been recognized as having tremendous practical importance for Bragg-grating writing in silica-based optical fibers [21]. It has been suggested that the observed photosensitivity of pure and doped a-SiO 2 is closely related to the transformation of the divalent Si (and / or Ge) defect(s) [4], and, consequently, their microscopic structure and optical properties have been extensively studied using the cluster approach. Singlet-to-singlet (S0 →S1 ) and singlet-to-triplet (S0 →T 1 ) excitation energies of the divalent Si defect were calculated by Zhang and Raghavachari [22], Stefanov and Raghavachari [23], and Pacchioni and Ferrario [24] using different cluster models and different levels of theory. These studies yield almost the same calculated results concerning the S0 →S1 (|5 eV) and S0 →T 1 (|3 eV) transition energies, in good agreement with the corresponding photoabsorption bands at 5.0 and 3.15 eV [4], respectively. Thus, it is highly likely that the divalent Si defect is responsible for the observed 5-eV absorption band in a-SiO 2 and that observed bleaching of this band upon
ionizing irradiation is linked to the photoinduced transformations of the divalent Si defect. Recently, the transformation mechanism of the divalent Si defect has been investigated by several researchers [25–28]. It has been shown by ab initio cluster calculations that the divalent Si defect can be converted into various forms of E9 centers as well oxygen neutral vacancies (see Fig. 4) [25–27]. Similar reaction paths have also been proposed by recent ab initio Car–Parrinello molecular dynamics simulations [28].
3. Point defects in Ge-doped a-SiO 2 Ionizing radiation of Ge-doped a-SiO 2 induces several Ge-related paramagnetic defect centers that are analogous to the E9 centers in pure a-SiO 2 . Since the photosensitivity and the resulting photorefractive effect of Ge-doped a-SiO 2 is much higher than that of pure a-SiO 2 , local defects in the GeO 2 -SiO 2 system have attracted special attention in terms of fabrication of fiber Bragg gratings [21]. Although the defect formation mechanism in Ge-doped a-SiO 2 is expected to be similar to that in pure a-SiO 2 , there exist additional paramagnetic defect centers in Gedoped a-SiO 2 [21]. A photoinduced defect center called the germanium electron center (GEC) is peculiar to Ge-doped a-SiO 2 , and the formation and the subsequent conversion
Fig. 4. A proposed interconversion mechanism [25,26] among neutral oxygen vacancies and E9-center variants in a-SiO 2 during ionizing irradiation, recombination and relaxation processes.
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of GECs are believed to be associated with the highly photosensitive nature of this system [29]. A systematic ab initio cluster calculation on GECs along with other possible paramagnetic centers in Ge-doped a-SiO 2 has been performed by Pacchioni and Mazzeo [30]. They found that an orthorhombic distortion occurs when an electron is trapped at a GeO 4 site (see Fig. 5a) and that the structure of the negatively charged GeO 4 unit is more stable than the neutral one by 0.12 eV at the HF level and by 1.61 eV in DFT. They also found that the electroncapture process does not occur at the corresponding SiO 4 site but occurs only at the GeO 4 site. These results indicate that the electron trapping is a specific characteristic of a fourfold coordinated Ge center, explaining the high photosensitivity in Ge-doped a-SiO 2 . Furthermore, Uchino et al. [31] recently proposed that the electron-capture process occurs not only at the GeO 4 site but also at the O 3 Ge–GeO 3 (neutral oxygen monovacancy) site. As for the latter defect site, an electron is captured at one of the two Ge atoms in the defect, and an orthorhombic distortion also occurs, as in the case of the normal fourfold coordinate Ge site. However, the resultant germanium electron center is highly distorted (see Fig. 5b). If such a GEC as seen in Fig. 5b exists in Ge-doped a-SiO 2 , one will obtain an EPR line shape that is different from that observed for the GEC shown in Fig. 5a. Experimentally, two different EPR signals associated with GECs [Ge(1) and Ge(2)] have actually been observed [32]. Thus far, there has been no accepted model to account for the Ge(2) EPR signal, and the microscopic origin of Ge(2) is still the subject of intense discussion [33–35]. These two types of GECs are characterized by the same isotropic hyperfine coupling constant (28 mT), in harmony with the present calculations (see Fig. 6). Accord-
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ing to the Ge(1) EPR signal, Ge(1) is expected to be an ideal orthorhombic structure, suggesting that this signal is responsible for the GEC shown in Figs. 5a and 6a [30]. On the other hand, the Ge(2) EPR signal exhibits a strong anisotropic nature [32], and, therefore, the Ge(2) will be rather deformed from an orthorhombic structure. This suggests that the anisotropic Ge(2) EPR signal is attributed to the electron center shown in Figs. 5b and 6b [31].
4. Summary This short review has described recent ab initio cluster calculations on local defect centers in pure and doped a-SiO 2 . Some defect models are unprecedented and, therefore, may challenge several conventional defect structures proposed for a-SiO 2 . Besides the point defect in a-SiO 2 , ab initio cluster approaches have been used to model various phenomena associated directly and / or indirectly with defect centers, for example, oxidation processes of silicon surfaces [36], H-induced defect formation reactions at Si–SiO 2 interfaces [37], optical excitations of nanocrystalline silicon [38], and photoinduced structural changes in amorphous As 2 S 3 [39]. It should be mentioned, however, that there is a caution in using the cluster approach. As mentioned in the Introduction, the most crucial problem is that the effect of condensed environments is taken into account only in an approximate way. It is hence necessary to check whether the results obtained depend on the size and the shape of the cluster employed. When one keeps the above limitations in mind, the ab initio cluster approach will provide us with valuable information and a theoretical basis concerning the
Fig. 5. (a) An electron-capture process at the fourfold coordinated Ge site [30]. (b) An electron-capture process at the O 3 Ge–GeO 3 site proposed in [31].
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Fig. 6. Cluster models of (a) a GeO 2 4 unit and (b) a negatively charged oxygen monovacancy in the SiO 2 -GeO 2 system [31]. The optimized structures were obtained at the B3LYP/ 6-31G(d) level by assuming a total charge of 21. Principal structural parameters, Mulliken atomic charges, q, spin densities, r, and isotropic hyperfine coupling constants, A (in mT) are also shown.
structural and electronic properties of defects in amorphous materials.
References [1] Edwards AH, Fowler WB, Robertson J. Theory of electronic and structural properties of point defects in SiO 2 . In: Devine RAB, ´ E, editors, Structure and imperfections in Duraud JP, Dooryhee amorphous and crystalline silicon dioxide, Chichester: Wiley, 2000, pp. 253–91. [2] Griscom DL. Defect structure of glasses: some outstanding questions in regard to vitreous silica. J Non-Cryst Solids 1985;73:51–77. [3] Weeks RA. The many varieties of E9 centers: a review. J Non-Cryst Solids 1994;179:1–9.
[4] Skuja L. Optically active oxygen-deficiency-related centers in amorphous silicon dioxide. J Non-Cryst Solids 1998;239:16–48. [5] Feigl FJ, Fowler WB, Yip KL. Oxygen vacancy model for the E 19 center in SiO 2 . Solid State Commun 1974;14:225–9. [6] Pacchioni G, Ierano` G. Optical absorption and nonradiative decay mechanism of E9 center in silica. Phys Rev Lett 1998;81:377–80. [7] Boero M, Pasquarello A, Sarnthein J. Structure and hyperfine parameters of E 91 center in a-quartz and vitreous SiO 2 . Phys Rev Lett 1997;78:887–90. ¨ [8] Blochl PE. First-principles calculations of defects in oxygen-deficient silica exposed to hydrogen. Phys Rev B 2000;62:6158–79. [9] Carbonaro CM, Fiorentini V, Bernardini F. Proof of the thermodynamical stability of the E9 center in SiO 2 . Phys Rev Lett 2001;86:3064–7. [10] Uchino T, Takahashi M, Yoko T. E9 centers in amorphous SiO 2 revisited: a new look at an old problem. Phys Rev Lett 2001;86:5522–5. [11] Uchino T, Takahashi M, Yoko T. Model of oxygen-deficiencyrelated defects in SiO 2 glass. Phys Rev B 2000;62:2983–6. [12] Uchino T, Takahashi M, Yoko T. Structure and generation mechanism of the peroxy-radical defect in amorphous silica. Phys Rev Lett 2001;86:4560–3. [13] Griscom DL, Friebele EJ. Fundamental radiation-induced defect centers in synthetic fused silicas: atomic chlorine, delocalized E9 centers, and triplet state. Phys Rev B 1986;34:7524–33. [14] Stesmans A, Vanheusden K. Generation of delocalized E d9 defects in buried Si oxide by hole injection. J Appl Phys 1994;76:1681–5. [15] Conley Jr. JF, Lenahan PM, Evans HL, Lowry RK, Morthorst TJ. Observation and electronic characterization of ‘‘new’’ E9 center defects in technologically relevant thermal SiO 2 on Si: an additional complexity in oxide charge trapping. J Appl Phys 1994;76:2872–80. [16] Chavez JR, Kara SP, Vahneusden K, Brothers CP, Pugh RD, Singaraju BK, Devine RAB. Microscopic structure of the E 9d center in amorphous SiO 2 : a first principles quantum mechanical investigation. IEEE Trans Necl Sci 1997;44:1799–803. [17] Pienda AC, Karna SP. Effect of hole trapping on the microscopic structure of oxygen vacancy site in a-SiO 2 . J Phys Chem A 2000;104:4699–703. [18] Rudra JK, Fowler WB. Oxygen vacancy and the E 91 center in crystalline SiO 2 . Phys Rev B 1987;35:8223–30. [19] Griscom DL. Characterization of three E9-center variants in x- and g -irradiated high purity a-SiO 2 . Nucl Inst Methods Phys Res B 1984;1:481–8. [20] Uchino T, Takahashi M, Yoko T. Structure and formation mechanism of the E9 center in amorphous SiO 2 . Appl Phys Lett 2001;78:2730–2. [21] Othonos A, Kalli K. Fiber Bragg gratings. Norwood: Artech House, 1999. [22] Zhang BL, Raghavachari K. Photoabsorption and photoluminescence of divalent defects in silicate and germanosilicate glasses: first-principles calculations. Phys Rev B 1997;55:R15993–6. [23] Stefanov BB, Raghavachari K. Cluster models for the photoabsorption of divalent defects in silicate glasses: basis set and cluster size dependence. Appl Phys Lett 1997;71:770–2. [24] Pacchioni G, Ferrario R. Optical transitions and EPR properties of two-coordinated Si, Ge, Sn and related H(I), H(II), and H(III) centers in pure and doped silica from ab initio calculations. Phys Rev B 1998;58:6090–6. [25] Uchino T, Takahashi M, Yoko T. Mechanism of interconversion among radiation-induced defects in amorphous silicon dioxide. Phys Rev Lett 2001;86:1777–80. [26] Uchino T, Takahashi M, Yoko T. Models of radiation-induced structural changes in pure and Ge-doped silica. In: Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest, Washington: Optical Society of America, 2001:BWC5-1-3. [27] Garapon J, Poumellec B, Orcel G. Conversion mechanism between oxygen deficient centers in silica glass. In: Bragg Gratings, Photo-
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[33]
sensitivity, and Poling in Glass Waveguides, OSA Technical Digest, Washington: Optical Society of America, 2001:BWC2-1-3. Donadio D, Bernasconi M, Boero M. Ab initio simulations of photoinduced interconversions of oxygen deficient centers in amorphous silica. Phys Rev Lett 2001;87:195504-1-4. Nishii J, Kintaka K, Hosono H, Kawazoe H, Kato M, Muta K. Pair generation of Ge electron centers and self-trapped hole centers in GeO 2 –SiO 2 glasses by KrF excimer-laser irradiation. Phys Rev B 1999;60:7166–9. Pacchioni G, Mazzeo C. Paramagnetic centers in Ge-doped silica: a first-principles study. Phys Rev B 2000;62:5452–60. Uchino T, Takahashi M, Yoko T. Mechanism of electron trapping in Ge-doped SiO 2 glass. Appl Phys Lett 2001;79:359–61. Friebele EJ, Griscom DL, Sigel Jr. GH. Defect centers in germanium-doped silica-core optical fiber. J Appl Phys 1974;45:3424– 8. Tsai TE, Williams GM, Friebele EJ. Uniform component of index structure induced in Ge-SiO 2 fibers by spatially modulated ultraviolet light. Appl Phys Lett 1998;72:3243–5.
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[34] Neustruev VB. Color centers in germanosilicate glass and optical fibers. J Phys: Condens Matter 1994;6:6901–36. [35] Fujimaki M, Watanabe T, Katoh T, Kasahara T, Miyazaki N, Ohki Y. Structures and generation mechanisms of paramagnetic centers and absorption bands responsible for Ge-doped SiO 2 optical-fiber gratings. Phys Rev B 1998;57:3920–6. [36] Wang LS, Nicholas JB, Dupuis M, Wu H, Closon SD. Si 3 Oy ( y51–6) clusters: models for oxidation of silicon surfaces and defect sites in bulk oxide materials. Phys Rev Lett 1997;78:4450–3. [37] Chadi DJ. Intrinsic and H-induced defects at Si–SiO 2 interfaces. Phys Rev B 2001;64:195403-1-6. ¨ ¨ S, Chelikowsky JR. Ab initio absorption spectra and [38] Vasileiv I, Ogut optical gaps in nanocrystalline silicon. Phys Rev Lett 2001;86:1813–6. [39] Uchino T, Clary DC, Elliott SR. Mechanism of photoinduced changes in the structure and optical properties of amorphous As 2 S 3 . Phys Rev Lett 2000;85:3305–8.
Ab initio cluster calculations on point defects in amorphous SiO 2 T. Uchino* Institute for Chemical Research, Kyoto University, Uji, Kyoto 611 -0011, Japan Received 16 January 2002; received in revised form 12 February 2002; accepted 12 February 2002
Abstract Recently, there have been considerable advances in quantum-chemical calculations on clusters of atoms designed to model local defect centers in amorphous materials. In particular, this review attempts to put into perspective the recent calculated results of the point defects in pure and doped a-SiO 2 , which have attracted renewed attention in view of fabrication of Bragg gratings in optical fibers and waveguides. Recent sophisticated calculations may challenge the conventional models of several defect centers in a-SiO 2 . 2002 Published by Elsevier Science Ltd.
1. Introduction The electrical and optical properties of Si-based amorphous materials, which are of special importance for their use in optical fiber technologies and optoelectronic devices, are determined mainly by local structural defects. Thus, considerable efforts have been made in the past decades to understand the structural, optical and electronic properties of point defects in amorphous SiO 2 . Recently, quantum-chemical calculations have proved increasingly useful for the study of the structure and properties associated with point defects in amorphous insulators and semiconductors. In particular, a cluster approach based on the ab initio molecular orbital method has provided several new insights into the microstructure of local defects in amorphous SiO 2 . It is often claimed that such cluster calculations may bridge the gap between the properties of isolated molecules and the condensed phase. According to the cluster approach, the structure of a defect center in amorphous solids is described by a finite number of atoms comprising the local defect and its surrounding environment. Model clusters are composed of |10–|100 atoms depending on the aim of the study and the available computer facilities. Geometries of the model clusters are optimized at the Hartree–Fock (HF), post-HF, and / or density functional theory (DFT) levels to search their local minimum configurations, and their structure, optical and vibrational properties, and excited states are *Departmeant of Chemistry, Kobe University, Nada-ku, Kobe 6578501, Japan. Tel.: 181-78-803-5681; fax: 181-78-803-5681. E-mail address: [email protected] (T. Uchino).
investigated at the respective levels of theory. This approach may not fully take into account the actual effect of condensed environments around the defect of interest. However, it is reasonable to expect that the electronic states associated with the defect are rather localized and do not extend through the corresponding solid, implying that the electronic structure of the defect in amorphous solids is reasonably modeled by the cluster calculations. This review will first highlight recent calculated results of intrinsic defects in pure amorphous SiO 2 (a-SiO 2 ), and will then turn to the extrinsic local defects in doped a-SiO 2 .
2. Point defects in pure a-SiO 2
2.1. The E9 centers Previously, a large number of theoretical studies has been dedicated to the structure and electronic states of point defects in a-SiO 2 [1]. Among other Si-related defect centers, E9 centers have been the subject of considerable theoretical investigation since the E9 centers are the major oxygen-deficiency-related paramagnetic defect in a-SiO 2 . Thus far, at least four different types of E9 centers have been observed in a-SiO 2 [2–4], with the only common feature being an unpaired electron on threefold coordinated silicon. These E9-center variants, as discussed below, will differ from each other in the second-coordination environments around the respective paramagnetic Si atoms, although their local structures have not been fully understood yet.
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2.1.1. The E 9g center According to Feigl et al. [5], trapping of a hole by an oxygen monovacancy site in crystalline a -quartz causes an asymmetric relaxation of the defect site, resulting in the paramagnetic center called the E 91 center. The unpaired electron in the E 91 center is localized solely on one of the two threefold-coordinated Si atoms in the oxygen vacancy site, whereas the hole is trapped at the other threefoldcoordinated Si atom (see Fig. 1a). This model of the E 91 center has been supported by recent theoretical calculations based on ab initio cluster [6] and super-cell [7–9] approaches. Since the E 9g center, which is a fundamental paramagnetic center in a-SiO 2 , exhibit similar electron paramagnetic resonance (EPR) characteristics to the E 91 center in a -quartz (a |420 G splitting of the hyperfine spectrum and an anisotropic g-tensor, g11 52.0018, g22 5 2.0006, g33 52.0003), it has commonly been believed over the past 25 years that these two E9-center variants, E 91 and E 9g , are essentially identical to each other. However, it has been suggested that in a-SiO 2 the original symmetry of the oxygen monovacancy site is likely to be low enough to drive such an asymmetric relaxation as seen in Fig. 1a, implying that there are some other defect sites that are responsible for the E 9g center in a-SiO 2 [1]. Indeed, there exist some experimental and theoretical indications that the E 9g center in a-SiO 2 may not have the same microscopic origin as that of the E 91 center in a -quartz [10]. Thus, Uchino et al. [10,11] have recently proposed an alternative model of the E 9g center, in which paramagnetic and positively charged threefold coordinated silicon atoms are bridged by a common oxygen atom (see Fig. 1b). This new
type of paramagnetic defect is referred to as a bridged hole-trapping oxygen-deficiency center (BHODC). It has been shown by the cluster calculations [10,11] that the BHODC model quantitatively reproduces the experimental 420 G hyperfine splitting observed for the E 9g center. Furthermore, this model can account for the diffusionlimited anneal mechanisms of the E 9g center associated with atomic hydrogen [10] and molecular oxygen [12], forming the E 9b center and the peroxy-radical defect, respectively. Although the BHODC model may not give a conclusive picture of the E 9g center in a-SiO 2 at the present stage, this model appears to have a reasonable advantage over the conventional E g9 -center model [10–12] and will surely challenge the experimenters to devise new experiments to prove or disprove its validity.
2.1.2. The E 9d center The E d9 center was first discovered by Griscom and Friebele [13] after X-ray irradiation in bulk a-SiO 2 . This defect was also observed at the surface of buried SiO 2 layers formed by oxygen-ion implantation of silicon crystals [14] and in thermally grown thin SiO 2 films [15]. The characteristic EPR features of the E 9d center are a highly isotropic g-tensor ( g11 52.0018, g22 5g33 52.0021) and a 100 G doublet hyperfine splitting. The observed EPR spectrum of the E d9 center implies that, unlike the other E9-center variants, the unpaired electron in this center is delocalized over multiple equivalent Si atoms. A theoretical study of the electronic structure of the E d9 center has been performed by Chavez et al. [16] using a cluster approach. According to their calculations, the E 9d
Fig. 1. (a) A conventional model of the E g9 center derived from the model of the E 91 center in a-quartz. (b) A newly proposed model of the E 9g center [10–12].
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however, such a lattice oxygen, which is inevitably located in a -quartz, may be absent [1]. Thus, it is probable that the symmetric relaxation occurs at the oxygen monovacancy site, especially in a-SiO 2 , and that the resultant paramagnetic center is a likely candidate for the delocalized E 9d defect.
Fig. 2. A model of the E 9d center proposed by Chavez et al. [16]. In this model, an unpaired electron is almost equally distributed over the two Si atoms in the defect.
center is attributed to a hole trapped at a simple oxygen monovacancy in which the unpaired electron is shared equally by two silicon atoms in the defect site (see Fig. 2). The hole trapping in this case results in a symmetric relaxation, leading to a slight increase in the interatomic distance between the two paramagnetic Si atoms. The calculated isotropic hyperfine coupling constants compare well with the corresponding observed values. Recent quantum-chemical calculations [6,10,17] have also supported the above E 9d -model. As for the oxygen monovacancy site in the corresponding crystalline a -quartz lattice, the hole trapping causes an asymmetric relaxation, forming the E 91 center as mentioned earlier. This suggests that structural constraints derived from a crystalline lattice are responsible for the asymmetric relaxation in the hole trapped oxygen monovacancy site. Indeed, it has been proposed that the asymmetric relaxation related to the formation of the E 91 center is facilitated with the help of the interaction between the hole-trapped Si site and its adjacent lattice oxygen, forming a puckered defect configuration [18]. In a-SiO 2 ,
2.1.3. The E 9a center The nature of the E 9a center is less certain as compared with other E9-center variants, and there has been no accepted model accounting for its microscopic structure. The E 9a center is stable only at low temperatures (, |100 K) and is observed to anneal at 200 K [19]. Another peculiar feature of the E 9a center is the large anisotropic component in the EPR g values ( g11 52.0018, g22 5 2.0013, g33 51.9998) although the observed isotropic hyperfine coupling (420 G) indicates that the unpaired electron in this defect center is most likely localized at one silicon atom, as in the case of the E 9g center. Thus far, only one quantum-chemical cluster approach [20] has been reported as to the microscopic structure of the E 9a center. It has been shown that the divalent Si defect can trap a hole and then tends to interact with a nearby bridging oxygen atom, forming a highly anisotropic threefold-coordinated paramagnetic Si site (see Fig. 3). Such an anisotropic nature of the defect is inherent in the fact that one of the oxygen atoms that are bonded to the paramagnetic silicon is a threefold coordinated oxygen. It has also been demonstrated [20] that the unpaired electron is localized mainly on the paramagnetic silicon and that the isotropic hyperfine coupling calculated for this silicon atom is in good agreement with that observed for the E 9a center. It should also be noted that the proposed structural transformation associated with the divalent Si defect is accomplished without accompanying complex atomic reconfigurations. This suggests that the hole-trapping center shown in Fig. 3 is apt to trap an electron to show an electron-hole recombination; in other words, this paramagnetic center may be stable only at low temperatures, in
Fig. 3. A proposed formation mechanism of the E a9 center [20]. In this model, an unpaired electron is localized mostly at the threefold coordinated silicon atom in the defect.
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accord with the experimental characteristics observed for the E 9a center.
2.2. The divalent Si defect The divalent Si (5Si:) defect has been the subject of considerable interest since the discovery of the photorefractive effect in a-SiO 2 , which has been recognized as having tremendous practical importance for Bragg-grating writing in silica-based optical fibers [21]. It has been suggested that the observed photosensitivity of pure and doped a-SiO 2 is closely related to the transformation of the divalent Si (and / or Ge) defect(s) [4], and, consequently, their microscopic structure and optical properties have been extensively studied using the cluster approach. Singlet-to-singlet (S0 →S1 ) and singlet-to-triplet (S0 →T 1 ) excitation energies of the divalent Si defect were calculated by Zhang and Raghavachari [22], Stefanov and Raghavachari [23], and Pacchioni and Ferrario [24] using different cluster models and different levels of theory. These studies yield almost the same calculated results concerning the S0 →S1 (|5 eV) and S0 →T 1 (|3 eV) transition energies, in good agreement with the corresponding photoabsorption bands at 5.0 and 3.15 eV [4], respectively. Thus, it is highly likely that the divalent Si defect is responsible for the observed 5-eV absorption band in a-SiO 2 and that observed bleaching of this band upon
ionizing irradiation is linked to the photoinduced transformations of the divalent Si defect. Recently, the transformation mechanism of the divalent Si defect has been investigated by several researchers [25–28]. It has been shown by ab initio cluster calculations that the divalent Si defect can be converted into various forms of E9 centers as well oxygen neutral vacancies (see Fig. 4) [25–27]. Similar reaction paths have also been proposed by recent ab initio Car–Parrinello molecular dynamics simulations [28].
3. Point defects in Ge-doped a-SiO 2 Ionizing radiation of Ge-doped a-SiO 2 induces several Ge-related paramagnetic defect centers that are analogous to the E9 centers in pure a-SiO 2 . Since the photosensitivity and the resulting photorefractive effect of Ge-doped a-SiO 2 is much higher than that of pure a-SiO 2 , local defects in the GeO 2 -SiO 2 system have attracted special attention in terms of fabrication of fiber Bragg gratings [21]. Although the defect formation mechanism in Ge-doped a-SiO 2 is expected to be similar to that in pure a-SiO 2 , there exist additional paramagnetic defect centers in Gedoped a-SiO 2 [21]. A photoinduced defect center called the germanium electron center (GEC) is peculiar to Ge-doped a-SiO 2 , and the formation and the subsequent conversion
Fig. 4. A proposed interconversion mechanism [25,26] among neutral oxygen vacancies and E9-center variants in a-SiO 2 during ionizing irradiation, recombination and relaxation processes.
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of GECs are believed to be associated with the highly photosensitive nature of this system [29]. A systematic ab initio cluster calculation on GECs along with other possible paramagnetic centers in Ge-doped a-SiO 2 has been performed by Pacchioni and Mazzeo [30]. They found that an orthorhombic distortion occurs when an electron is trapped at a GeO 4 site (see Fig. 5a) and that the structure of the negatively charged GeO 4 unit is more stable than the neutral one by 0.12 eV at the HF level and by 1.61 eV in DFT. They also found that the electroncapture process does not occur at the corresponding SiO 4 site but occurs only at the GeO 4 site. These results indicate that the electron trapping is a specific characteristic of a fourfold coordinated Ge center, explaining the high photosensitivity in Ge-doped a-SiO 2 . Furthermore, Uchino et al. [31] recently proposed that the electron-capture process occurs not only at the GeO 4 site but also at the O 3 Ge–GeO 3 (neutral oxygen monovacancy) site. As for the latter defect site, an electron is captured at one of the two Ge atoms in the defect, and an orthorhombic distortion also occurs, as in the case of the normal fourfold coordinate Ge site. However, the resultant germanium electron center is highly distorted (see Fig. 5b). If such a GEC as seen in Fig. 5b exists in Ge-doped a-SiO 2 , one will obtain an EPR line shape that is different from that observed for the GEC shown in Fig. 5a. Experimentally, two different EPR signals associated with GECs [Ge(1) and Ge(2)] have actually been observed [32]. Thus far, there has been no accepted model to account for the Ge(2) EPR signal, and the microscopic origin of Ge(2) is still the subject of intense discussion [33–35]. These two types of GECs are characterized by the same isotropic hyperfine coupling constant (28 mT), in harmony with the present calculations (see Fig. 6). Accord-
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ing to the Ge(1) EPR signal, Ge(1) is expected to be an ideal orthorhombic structure, suggesting that this signal is responsible for the GEC shown in Figs. 5a and 6a [30]. On the other hand, the Ge(2) EPR signal exhibits a strong anisotropic nature [32], and, therefore, the Ge(2) will be rather deformed from an orthorhombic structure. This suggests that the anisotropic Ge(2) EPR signal is attributed to the electron center shown in Figs. 5b and 6b [31].
4. Summary This short review has described recent ab initio cluster calculations on local defect centers in pure and doped a-SiO 2 . Some defect models are unprecedented and, therefore, may challenge several conventional defect structures proposed for a-SiO 2 . Besides the point defect in a-SiO 2 , ab initio cluster approaches have been used to model various phenomena associated directly and / or indirectly with defect centers, for example, oxidation processes of silicon surfaces [36], H-induced defect formation reactions at Si–SiO 2 interfaces [37], optical excitations of nanocrystalline silicon [38], and photoinduced structural changes in amorphous As 2 S 3 [39]. It should be mentioned, however, that there is a caution in using the cluster approach. As mentioned in the Introduction, the most crucial problem is that the effect of condensed environments is taken into account only in an approximate way. It is hence necessary to check whether the results obtained depend on the size and the shape of the cluster employed. When one keeps the above limitations in mind, the ab initio cluster approach will provide us with valuable information and a theoretical basis concerning the
Fig. 5. (a) An electron-capture process at the fourfold coordinated Ge site [30]. (b) An electron-capture process at the O 3 Ge–GeO 3 site proposed in [31].
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Fig. 6. Cluster models of (a) a GeO 2 4 unit and (b) a negatively charged oxygen monovacancy in the SiO 2 -GeO 2 system [31]. The optimized structures were obtained at the B3LYP/ 6-31G(d) level by assuming a total charge of 21. Principal structural parameters, Mulliken atomic charges, q, spin densities, r, and isotropic hyperfine coupling constants, A (in mT) are also shown.
structural and electronic properties of defects in amorphous materials.
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