Optical absorption and nonradiative decay mechanism of E′ center in silica

VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998 Optical Absorption and Nonradiative Decay Mechanism of E000 Center in Silica Gianfranco Pacchioni* and Gianluigi Ieranò Istituto Nazionale di Fisica della Materia, Dipartimento di Scienza dei Materiali, Università di Milano, via Emanueli 15, 20126 Milano, Italy Antonio M. Márquez Departamento de Quimica Fisica, Facultad de Quimica, Universidad de Sevilla, 41012 Sevilla, Spain (Received 17 March 1998) We report ab initio configuration interaction calculations on the optical transitions of the E0center, a hole trapped at an oxygen vacancy, s—Od3Si≤1SisO—d3, in silica. We found two competing excitation mechanisms: (1) promotion of one electron from an Os2pdvalence band orbital to the singly occupied Si dangling bond; (2) charge transfer (CT) transition from s—Od3Si≤to 1SisO—d3. The two excitations occur at similar energies, ø5.8 6eV (5.85 eV in the experiment), but only the CT has a strong intensity. The excitation is followed by a complex nonradiative decay process which may explain the absence of luminescence for this center. [S0031-9007(98)06572-7] PACS numbers: 61.72.Bb, 42.70.Ce, 61.72.Ji, 78.20.–e Point defects in silica are of fundamental importance in metal-oxide semiconductor field effect transistors and fiber optics technology [1]. One of the most abundant and best characterized defects in SiO2is the E0center, a hole trapped at an oxygen vacancy, V1 O. The E0center is a fundamental radiation-induced defect in amorphous silica, a-SiO2[1–6], and an important source of degradation in SiySiO2based devices [4]. Several variants of the E0centers exist: E0 1, and H-associated E0 2, and E0 4,ina-quartz; E0 gand E0 dcenters in a-SiO2.E0 gis the closest analog to the E0 1in a-quartz [3]. Thanks to the combined use of optical absorption, OA [1], and electron paramagnetic resonance, EPR [1,6], spectroscopies, and theoretical calculations [7–11], the ground state structure of the E0 1and E0 gcenters is now quite well understood. The E0derives from the removal of a lattice oxygen to form a neutral oxygen vacancy, VO, followed by hole trapping to give V1 O. According to the first model proposed in 1974 by Feigl, Fowler, and Yip [7], FFY, the defect consists of a sp3hybridized — — —Si≤dangling bond and of a nearly planar — — —Si1 unit, — — —Si1≤Si— — —(— — —represents three Si-O bonds). The FFY model, however, does not account for the large hyperfine splitting, HFS, of ø420 G of the unpaired electron with the 29Si nuclide [6]. A refined model, suggested by Rudra and Fowler in 1985 [8], is based on an asymmetrical relaxation of the positively charged Si atom in a puckered position where it binds to a lattice oxygen which becomes three-coordinated. This structure was then confirmed by other studies including accurate first principle calculations [9–12]. The E0 1ground state structure, as obtained from the present cluster calculations, is illustrated in Fig. 1(a). It is generally accepted that the E0 gin a-SiO2has a very similar structure. Much less is known about the E0excited state properties. A typical OA band in bulk silica at 5.85 eV with an oscillator strength of 0.14 60.04 has been assigned to the E0 gcenter by Weeks and Sonder based on a strong correlation with a characteristic EPR signal [2]. Two recent studies further reinforced the original assignment of the 5.85 eV band to E0 gcenters [13,14]. The nature of the transition, however, is still unclear. It could involve a charge transfer, CT, from — — —Si≤to — — —Si1, as tentatively suggested back in 1980 by Griscom and Fowler [15], or simply a transition from the valence band to the partially filled Si sp3hybrid orbital. Furthermore, differently from many other defects in SiO2which exhibit typical photoluminescence, PL, bands, emission upon exciting in the E0 g-absorption band has never been observed. No mechanism has been proposed so far to elucidate this anomalous behavior. Another aspect which needs clarification is that on the surface of mechanically activated silica OA bands around 6.2 eV have been attributed to surface E0 scenters [16], consisting of a — — —Si≤dangling bond. In this case the CT mechanism is not possible since there is no — — —Si1unit in the vicinity of the — — —Si≤groups. The scope of this Letter is to present an accurate quantum-mechanical study of the absorption properties of the E0bulk and surface centers, and to provide a mechanism for the dissipation of the absorbed energy in the bulk through nonradiative decay. The computational approach is the same adopted recently to elucidate the OA and PL properties of VO[17] and of other defects in silica [18]. We used SiO2clusters (with no symmetry) with the broken bonds saturated by H atoms placed along the O-Si directions of the crystal. The position of all the Si and O atoms, initially taken from a-quartz [19], has been reoptimized by computing analytical gradients of the total energy [20]. The H atoms were kept fixed to provide a representation of the mechanical embedding of the solid. A relatively large cluster fSi14O16H26g1 (Fig. 1) was used to determine the geometry of ground and excited states of V1 O. All electron, AE, Hartee-Fock wave 0031-9007y98y81(2)y377(4)$15.00 © 1998 The American Physical Society 377 VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998 FIG. 1. fSi14O16H26g1model of a E0center in a a-quartz. White spheres: Si; grey spheres, O; small white spheres: H. (a) Ground state minimum, E0 g; (b) excited state minimum; (c) metastable E0 d; (d) C !A transition state; see Fig. 3. functions have been constructed using a 6-31Gbasis set on Si and O [21]. Smaller clusters were used to perform accurate calculations of the transition energies, Te.On these smaller clusters we used an effective core potential [22], ECP, on Si to reduce the size of the configuration interaction (CI) calculations and a double-zeta, DZ, basis [22]. Diffuse sand p, plus one d, polarization functions have been added to Si. Te’s have been determined by performing multireference CI calculations, MRD CI [23,24]. Single and double excitations from the 12 highest occupied levels (24 electrons) have been generated with respect to a set of main (M) configurations; for further details see Refs. [17] and [18]. Absorption intensities have been estimated by means of the oscillator strength, f, a dimensionless quantity, using the dipole-length operator formula, fsrd 2 3jkC0jerjCnlj2sEn2E0d. Typical values of f for allowed transitions are between 0.1 and 1. Radiative lifetimes, t, have also been determined. Both Te’s and intensities are determined with some uncertainty connected to the cluster and basis set size. These uncertainties are difficult to estimate: for the Te’s they are at least of the order of 60.4 eV. We start the discussion from the ground state structure of the E0center in bulk SiO2as obtained with the fSi14O16H26g1cluster, Fig. 1(a). The defect is characterized by a rather long Si1-Si2distance, 4.06 Å, and by a short distance, 1.81 Å, between the positively charged Si2and the three-coordinated oxygen. The isotropic HFS on Si1, 364 G, is in reasonable agreement with the experimental value, 420 G [6]. These data are consistent with those reported in the literature for the E0 gcenter [7–12]. To study the nature of the lowest excitations, we have considered two smaller models, one for the surface and one for the bulk. The model of a surface E0 s center is sHOd3Si≤, Fig. 2(a). For the bulk, we used a sHOd3Si≤1SisOHd3-sOH2dcluster; see Fig. 2(b), which includes also the three-coordinated oxygen of the E0 gground state structure. This latter cluster has been derived from the larger one, Fig. 1(a), but it has been fully reoptimized with the H atoms fixed. The optimal distances are similar to those obtained with the larger cluster. All the Teare computed from minimum structures. The E0 ssHOd3Si≤ model allows us to analyze in detail the dependence of the Teon the level of treatment. The lowest doubletto-doublet transition corresponds to the excitation of one electron from a nonbonding O 2pvalence band orbital to FIG. 2. Cluster models of surface (a) and bulk (b) E0centers used to compute Te’s. 378 VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998 the Si dangling bond. Usinga 6-31GpAE basis set on both O and Si plus diffuse sand pfunctions on Si, we obtain a Teof 6.21 eV, in excellent agreement with the experiment [16]. Using an ECP on Si and a comparable basis, the Teis slightly lower, 5.94 eV, Table I. The intensity of the transition is predicted to be low, fsrdø1022. The inclusion of a dfunction on O, cf. 6-31Gand 6-31Gpbasis sets in Table I, changes Teby only 60.1 eV. In conclusion, an absorption band of weak intensity due to a transition from an Os2pdlevel to a Si dangling bond is expected around ø6eV for E0 scenters at the SiO2surface. For the bulk E0center model we searched three roots in the CI secular problem: the ground state, the O s2pd! — — —Si≤transition described above, and the CT transition where one electron is excited from Si1to Si2. Strictly speaking, the Os2pd!— — —Si≤is also a CT transition, but for clarity we refer only to the excitation from the two nonbonded Si atoms as CT. The CI results show that the two excited states have very small mixing and similar Te,ø5.7 5.8 eV; they are separated by ø0.2 eV, but the relative ordering depends also on the details of the calculation, Table I. It is not possible to predict in a firm way which is the lowest transition in bulk E0based on the Te’s. However, the two transitions exhibit different intensities: the CT is about 10 times stronger than the Os2pd!— — —Si≤transition. Experimentally, it has been observed that the transition at 5.85 eV associated with the E0 gcenter has an oscillator strength of ø0.14 eV [2]. Thus, both Teand fsrdare in agreement with the CT transition computed here while the predicted intensity of the valence band transition is too low. Consequently, the CT transition is expected to have a much shorter lifetime, tø1029sec, and to occur much more rapidly than the Os2pd!— — —Si≤transition, tø1028sec. This latter transition, however, may dominate at the surface of the material. Having established the nature of the 5.85 eV band in aquartz and a-SiO2, we consider now the decay mechanism. As we mentioned above, no luminescence is stimulated by the OA at 5.85 eV. In the bulk, the CT FranckCondon excitation leads to a structure where one electron has been transferred from Si1to Si2; see point A0in Fig. 3. The neutralization of Si2destabilizes the puckered structure, Fig. 1(a), because of the repulsion with the threecoordinated oxygen. The Si2-O distance increases and the system undergoes a strong geometrical relaxation until it reaches a minimum; see Fig. 1(b) and point Bin Fig. 3. In this minimum the unpaired electron is in a Si2sp3dangling bond, while Si1becomes almost flat because of the positive charge. Notice that no puckering of Si1occurs in this case because of the much longer distance with the lattice oxygen, Fig. 1(b). Starting the geometry optimization from a cluster where Si1has been inverted and puckered inside the ring results spontaneously in the structure shown in Fig. 1(b). In this respect the asymmetric nature of aquartz is very important. From the excited state minimum, see Fig. 1(b) and point Bin Fig. 3, the system could in principle decay radiatively. However, a barrier separates this minimum from another important reconstruction. This can be described as the inversion of Si2through the plane of the three O atoms with displacement of the unpaired electron toward the center of the cavity. It is reminiscent of the inversion doubling in a trigonal pyramidal molecule like NH3. In an adiabatic picture, it is conceivable that the strong relaxation following the excitation provides enough vibrational energy to the system to overcome this barrier or that the electron can tunnel through the barrier and show up on the other side of Si2. A more detailed analysis of the potential energy surface around this barrier shows that it actually originates from an avoided crossing of two states; see dotted lines in Fig. 3. In a diabatic picture the vertical CT transition from the E0ground state promotes one electron in a highly excited vibrational level; see A!A0in Fig. 3. The electron can then decay to lower vibration levels and, through an internal conversion, into the minimum of the upper state curve, Fig. 3, and from here can cross the narrow gap with emission of a lowfrequency photon. Whatever description is used, adiabatic TABLE I. Transition energies, Te, and oscillator strength, fsrd,ofE 0centers at the surface and in the bulk of SiO2. Os2pd!— — —Si≤— — —Si≤!1Si— — — transition CT transition Cluster O basis Si basis Te(eV) fsrdTe(eV) fsrd sHOd3Si≤, surface E0 s 6-31G6-31Gp1s1p6.28 0.01 ··· ··· 6-31Gp6-31Gp1s1p6.21 0.01 ··· ··· 6-31GECP-DZ 1s1d5.81 0.01 ··· ··· 6-31GpECP-DZ 1s1d5.94 0.03 ··· ··· Experiment [16] 6.2 60.1 ··· ··· sHOd3Si≤1SisOHd3-sOH2d, bulk E0 6-31GECP-DZ 1s1d5.7a0.03 5.8a0.30 Experiment [2] ··· ··· 5.85 0.14 60.04 aAverage value of different CI treatments. 379 VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13JULY 1998 FIG. 3. Schematic energy profile of the excitationdeexcitation mechanism of the E0center in bulk SiO2. The energies are plotted versus the distance between Si2and the “three-coordinated” O. See Figs. 1(a), 1(b), 1(c), and 1(d) for the structure of the stationary points A,B,C, and D, respectively. or diabatic, the system gains enough vibrational energy through the CT excitation to escape from the minimum of the excited state potential, Fig. 3. Once the barrier is overcome, the system undergoes another important relaxation which leads to a metastable variant of the E0ground state structure. In this local minimum, point Cin Fig. 3, the unpaired electron is shared among the two Si atoms of the vacancy, Fig. 1(c). The substantial delocalization of the spin is shown by the existence of two HFS’s of 118 G (Si1) and 62 G (Si2). The electron remains trapped between the two Si atoms, a situation reminiscent of F centers in alkali halides; the Si-Si distance, 2.67 Å, is not too far from that of the regular lattice, 3.06 Å. This structure is not unprecedented and corresponds to the E0 ddescribed by Snyder and Fowler [10] and by Boero et al. [11] and probably observed in Cl-containing glasses by Griscom and Friebele [25]. The E0 dis a metastable form of the E0ground state. In our approach it is 0.64 eV higher than the global minimum; the barrier separating the local, Fig. 1(c), and the global, Fig. 1(a), minima is 0.32 eV and corresponds, as shown by a full vibrational analysis, to a true transition state, Fig. 1(d), and point Din Fig. 3. The barrier is small enough that the lattice vibrations following the nonradiative decay will lead to a depopulation of the E0 dstructure in favor of the asymmetric E0 gground state, explaining why the E0 dhas not been clearly identified in EPR experiments so far. In this way, the system returns back to the original structure from which the CT transition has occurred and dissipates completely the absorbed energy through a nonradiative decay mechanism. In conclusion, we have shown that E0centers at the surface and in the bulk of SiO2have similar absorption energies which, however, originate from different mechanisms. In bulk silica the excitation seems to have CT character; the absence of luminescence may be explained as due to a complex nonradiative decay mechanism which completely dissipates the energy of the adsorbed photon. Stimulating discussions with Professor Beall Fowler are gratefully acknowledged. *Electronic address: [email protected] [1] The Physics of Technology of Amorphous SiO2,edited by J. Arndt, R. Devine, and A. Revesz (Plenum, New York, 1988). [2] R.A. Weeks and E. Sonder, in Paramagnetic Resonance, Vol. II, edited by W. Low (Academic Press, New York, 1963), p. 869. [3] R.A. Weeks, J. Non-Cryst. Solids 179, 1 (1994). [4] D.L. Griscom and M. Cook, J. Non-Cryst. Solids 182, 119 (1995). [5] H.S. Witham and P.M. Lenahan, Appl. Phys. Lett. 51, 1007 (1987). [6] D.L. Griscom, E.J. Friebele, and G.H. Siegel, Solid State Commun. 15, 479 (1974). [7] F.J. Feigl, W.B. Fowler, and K.L. Yip, Solid State Commun. 14, 225 (1974). [8] J.K. Rudra and W.B. Fowler, Phys. Rev. B 35, 8223 (1987). [9] D.C. Allan and M.P. Teter, J. Am. Ceram. Soc. 73, 3247 (1990). [10] K.C. Snyder and W.B. Fowler, Phys. Rev. B 48, 13238 (1993). [11] M. Boero et al., Phys. Rev. Lett. 78, 887 (1997). [12] G. Pacchioni, A.M. Ferrari, and G. Ieranò, Faraday Discuss. 106, 155 (1997). [13] R. Boscaino et al., Nucl. Instrum. Methods Phys. Res., Sect. B 16, 373 (1996). [14] H. Nishikawa et al., J. Non-Cryst. Solids 179, 179 (1994). [15] D.L. Griscom and W.B. Fowler, in The Physics of MOS Insulators, edited by G. Lucovsky et al. (Pergamon Press, New York, 1981), p. 97. [16] V.A. Radtzig, Chem. Phys. Rep. 14, 1206 (1995). [17] G. Pacchioni and G. Ieranò, Phys. Rev. Lett. 79, 753 (1997). [18] G. Pacchioni and G. Ieranò, Phys. Rev. B 57, 818 (1998). [19] Y. Le Page, L.D. Calvert, and E.J. Gabe, J. Phys. Chem. Solids 41, 721 (1980). [20] M. Dupuis, F. Johnston, and A. Marquez, HONDO 8.5 for CHEMStation (IBM Co., Kingston, 1994). [21] W.J. Here, R. Ditchfield, and J.A. Pople, J. Chem. Phys. 56, 2257 (1972). [22] P.J. Hay and W.R. Wadt, J. Chem. Phys. 82, 270 (1985). [23] R.J. Buenker and S.D. Peyerimhoff, Theor. Chim. Acta 35, 33 (1974). [24] M.F. Guest and P. Sherwood, GAMESS-UK Reference Manual (SERC, Daresbury Laboratory, Daresbury, 1992). [25] D.L. Griscom and E.J. Friebele, Phys. Rev. B 34, 7524 (1986). 380