- Email: [email protected]
Resonant absorption and emission from localized core-hole states in Al2O3 and SiO2
320
Nuclear
Instruments
and Methods
in Physics Research
B56/57
(1991) 320-323 North-Holland
Resonant absorption and emission from localized core-hole states in Al,O, and SiO, W.L. O’Brienl,
J. Jia, Q-Y. Dong and T.A. Callcott
University of Tennessee,
Knoxville,
J.-E. Rubensson,
D.L. Mueller
National Institute
of Standards
TN 37996, USA
and D.L. Ederer
and Technology,
Gaithersburg,
MD 20899, USA
We have compared the Al L,, and Si L,, emission and reflection spectra of Al,O, and SiO, to obtain information on the nature of the excited states in the presence of the L,, holes. A 5 m Rowland spectrometer, using a 600 l/mm grating mounted in grazing incidence was used to detect both electron excited soft X-ray emission and near normal soft X-ray reflection. We report fine structure in the emission spectra above the L,, edges which coincides with structure in the reflection spectra. These features appear both in the bandgap and in the conduction band. Such features within the bandgap are typically identified as excitons, while those in the conduction band must be localized excited states. Therefore, measurements of e2, for SiO, and Al,O, above the L,, edge should be interpreted in terms of localized excitations in the presence of a core hole, rather than interband transitions.
1. Introduction The SiO,
electronic
[lo-141
retical
and
properties emission
Both
subject
the
experimental (SXE)
band
of
been
of cw-Al,O,
spectroscopy vestigated
structure
have
by
been
spectroscopy
studied [2]
absorption
photoelectron structure
Al,O,
yield
calculations
[l-9]
and
of numerous
investigations. have
[3]. The
both
and spectra
Valence
band
by soft
X-ray
photoemission has
-measurements [4-61
theo-
and
been
in[2,7].
cluster
have been employed to describe the experimental emission and absorption spectra of (YAl,O,. While much of the theoretical work on ol-Al,O, attempts to explain the emission spectra through calculations of the occupied density of states we concentrate on the absorption process and its description in terms of localized excitations as opposed to interband transitions. Brytov and Romashchenko [2] measured the photoelectron yield above the L,, threshold for a-A1203. They interpreted the fine structure in the absorption spectra in terms of localized excitations in the [A10,1P9 cluster as determined by Tossell [l]. Tossell used a self-consistent field (SCF) Xa molecular orbital calculation to determine the excited states of the [A10,1P9 cluster. More recently Balzarotti et al. [7] have percalculations
[1,7]
’ Present address: Brookhaven National UlOA, Upton, NY 11973, USA. 0168-583X/91/$03.50
Labs, NSLS, Beamline
0 1991 - Elsevier Science Publishers
formed CND0/2 calculations on the [AlO,]molecule to explain the experimental photoelectron yield spectra. Band structure calculations have also been performed on a-A1203. These calculations employed the semi-empirical Mulliken-Rudenberg [4] method, and tight binding methods [5,6]. These calculations give reasonable values for the widths of the conduction band and some of the more prominent features as determined by SXE. There are, however, difficulties in defining the absorption spectra using these band models since they each neglected the presence of unoccupied Al 3d orbitals in the basis set. This is important for the identification of features in the L,, yield spectra since dipole selection rules are obeyed. A similar discussion can be made for SiO,. Both band structure models and cluster calculations have been used to explain the absorption spectra. In general, cluster calculations are appropriate when interpreting excitations which are localized. In alkali halides the core exciton associated with the positive ion is often found to be energetically identical to an excitation of the free ion [15,24]. This suggests highly localized non-screened excited states in the solid. Highly localized excited states are found in f-metals [16] and compounds [17], where d-f resonant emission and absorption has been used to explain spectral features. We have investigated both the reflection and emission from Al,O, and SiO, to determine the degree of localization of the excited states.
B.V. (North-Holland)
W.L. O’Brien et al. / Reflection
2. Experimental
and emission
fromAlJO
and SiO,
321
700
The L,, reflection and emission spectra of cll-Al,O, and fused SiO, are shown in fig. 1 and fig. 2, respectively. The soft X-ray emission (SXE) spectra shows only the fine structure above the valence band. The integrated intensity of these features are < 1% of the main band. The valence band spectra are similar to published spectra [2], and from our spectra we determine the VBM to be at 69.84 and 97.30 eV for Al,O, and SiOz respectively. Reflection spectra in this energy range follow the sample absorption. This is shown by writing the expression for normal incidence reflection in terms of the complex index of refraction n + ik,
0
1~~~1~~~1l’l~I~“““I
102
106
104
110
108
112
photon energy (ev)
Fig. 2. SiO, reflection and emission spectra. The vertical line marks the CBM as described in the text. The emission spectra
(n + 1)’ + k2 For photon energies in this energy range n = 1, thus and Rae:, where e2 is the imaginary part of the complex dielectric function. Thus, changes in the reflection spectra should follow changes in the absorption spectra. In fact the details in the reflection spectra for ol-Al,O, (fig. 1) are identical to those in published photoelectron yield spectra [2,7] with the exception that feature A apptiars more intense in reflection and is resolved as a doublet. Both the reflection and emission spectra were obtained with a 5 m Rowland spectrometer, using a 600 l/mm grating mounted in grazing incidence [18]. Specular reflection spectra were obtained 15” off normal. White light from beamline UlOA at the NSLS BNL was focussed onto the samples which were located in front R
was obtained
with an electron
excitation
energy of 500 eV.
ak2
600
reflection
5 $500
of the input slits of the Rowland spectrometer. The reflection spectra obtained in this manner show excellent agreement with published spectra [9,13]. Emission spectra were obtained with electron beam excitation. The spectra shown have been corrected for detector efficiency and bremsstrahlung background. The intensity of the bremsstrahlung background was typically ten times the peak heights of the features. For ol-AlzO, excitation energies of 1 and 2 keV were used. The peaks at 75 and 87 eV in the 2 keV excited spectra are due to higher orders of the 0 K emission. Features C and D, fig. 1, do not show the effects of self-absorption, 2 keV excited spectra, as do features A and B. The reason for this could be in our background subtraction or the features, and and D, could be an experimental artifact. We intend to continue this study in order to remove any uncertainty. For SiO, the emission spectra was obtained using 500 eV excitation to insure no 0 K emission. This was important since 0 K emission in 5 order appears at 104 eV.
3. Results and discussion
74
76
78
80 82 84 photon energy (eV)
86
88
90
Fig. 1. a-Al,O, reflection and emission spectra. The vertical line marks the CBM as described in the text. The emission spectra were obtained with electron excitation energies of 1 and 2 keV. Self absorption is evident in the comparison of the two emission spectra. The features at 75 and 87 eV are due to high orders of 0 K emission which has a low cross section at 1 keV excitation.
In fig. 1 it can be seen that doublet A and features B, C and D appear in both the reflection and emission spectra with approximately the same relative intensities. Similarly, in fig. 2, doublet A and feature B occur in both the reflection and emission spectra for Siq. The conduction band minimum (CBM) relative to the L3 level is shown in each figure. The CBM was determined by combining optical band gap measurements, 9.5 eV for Al,O, [19] and 9.3 eV for SiO, [20], to our measurements of the valence band maximum relative to the L, level. Each of these optical band gaps has an uncertainty of 0.5 eV based on the different values sited in the literature. I. ATOMIC/MOLECULAR
PHYSICS
322
W.L. O’Brien et al. / Reflection and emission from AI,O,
The doublet features, A, in the reflection spectra for both n-A1203 and SiO* appear in the band gap and have been defined as local excitations or core excitons [S,ll]. Core excitons are localized excitations which are typically described by their binding energy relative to the CBM. They give strong signals at the absorption threshold and definite but weak signals, in SXE. Features B, C, and D in fig. 1 and feature B in fig. 2 appear in the conduction band. Since they appear in emission as well as reflection they must be due to Iocalized resonant excitations. If they were due to absorption to a Bloch state within the continuum they would not appear as part of the emission process. Furthermore, since their intensities relative to the gap excitons are similar in both reflection and emission it appears that autoionization is not predominant, and that these L-states remain localized on a time scale equal to the lifetime of the core hole. The splittings in the doublet A features were determined by fitting the reflection spectra in these regions with gaussians of variable widths, and positions. The energy splittings were found to be 0.48 and 0.61 eV while the intensity ratios were found to be 1.8 : 1 and 0.9 : 1 in the Al,O, and SiO, spectra respectively. The atomic values for the L,, spin orbit splitting are 0.43 and 0.61 eV for Al and Si respectively while the statistical intensity ratio would be 0.5 : 1. Emission from localized states is expected to be broadened and shifted towards lower energies when compared to absorption [21,22]. This is due to the creation of phonons in the absorption process and emission from partially relaxed states. LOW energy broadening is evident in both fig. 1 and fig. 2. It is difficult to determine relaxation shifts due to sclf-absorption as evident by the changes in the emission doublet with excitation energy, fig. 1. 700 I
S
200~““““““““““‘~ 10 A 6 8
WI
12 energy above
d
14
d
a16 ‘,
I
I
18
/
I
and SiO,
600
6a
6t
I2
500
0’ * 6
r * , t
I
reflection
I
I
10
8
energy Fig. 4. SiO,
I
I’
above
I
c
I
VBM
spectra compared tion of Tossell [lo].
I
I
14
12
I
t
1
16
(eV) with cluster
calcula-
We conclude from this analysis that the L,, reflection {absorption) spectra of a-Al@, and SiO, give information due primarily to localized excitations of the and not on interband Al L,, and Si L,, electrons transitions, This is similar to an explanation for the absorption spectra of alkali halides [23]. It is therefore relevant to compare our reflection spectra with excitation energies predicted from cluster calculations. In fig. 3 we compare the Al,O, reflection spectra with the absorption features predicted by Balzarotti [7] using the unit [A10,1e9. Good agreement is found with feature A and the excitation to an orbital of s character using Balzarotti’s calculations. Balzarotti’s other levels appear to be too high in energy, and the level at 12 eV is primarily p type, dipole forbidden. Balzarotti (71 states that changing Pople’s [24] parameter, p in the CNDO/Z calculation lowers the d states below the p state, but that the band gap obtained is unrealistic. In fig. 4 we compare the SiO1 reflection with Tossells [lo] calculations on [SiOJ4 clusters. The agreement is quite good for the two main features if the levels Gt, and 6a, are shifted to lower energies by 2 eV. This assignment has already been made by Brytov et al. [2]. To our knowledge this is the first discussion of resonant absorption/ emission for localized excited states of other than f symmetry above the CBM. This analysis should stimulate more accurate calculations of localized excitations in Al,O,, SiO, and perhaps other wide band gap insulators.
I
20
VBM (eV)
Fig. 3. oc-Al,O, reflection spectra compared with cluster calculation of Balzarotti [7]. The symmetries of the orbitals are given. The orbital at 12 eV is primarily p type, dipole forbidden.
Acknowledgements One of us (W.L.O.) would like to thank CC. Kao for a number of discussions regarding the electronic properties of a-Al,O,.
W.L. O’Brien et al. / Reflection and emission from AI,O, References [l] J.A. Tossell, J. Phys. Chem. Solids 36 (1975) 1273. [2] LA. Brytov and Y.N. Romashchenko, Sov. Phys. Solid State 20 (1978) 384. [3] A. Balzarrotti and A. Bianconi, Phys. Status Solidi B76 (1976) 689. [4] R.A. Evarestov, A.N. Ermoshkin and V.A. Lovchikov, Phys. Status Solidi B99 (1980) 387. [5] I.P. Barta, J. Phys. Cl5 (1982) 5399. [6] S. Ciraci and I.P. Barta, Phys. Rev. BZ8 (1983) 982. [7] A. Balzzarotti, F. Antonangeli, R. Girlanda and G. Martino, Phys. Rev. B29 (1984) 5903. [S] A. Balzzarotti, F. Antonangeli, R. Girlanda and G. Martino, Solid State Commun. 44 (1982) 275. [9] T. Tomiki, T. Futemma, H. Kato, T. Miyahara, Y. Aiura, H. Fukutani and T. Shikenbaru, J. Phys. Sot. Jpn. 58 (1989) 1486. [lo] J.A. Tossell, J. Am. Chem. Sot. 97 (1975) 4840. [ll] F.C. Brown, R.Z. Bachrach and M. Skibowski, Phys. Rev. B15 (1977) 4781. [12] P. Deak, J. Kazsoki and J. Giber, Phys. Lett. 66A (1978) 395.
and SiO,
323
[13] E.O. Filatova, A.S. Vinogradov and T.M. Zimkina, Sov. Phys. Solid State 27 (1985) 606. [14] R. Dovesi, C. Pisani and C. Roetti, J. Chem. Phys. 86 (1987) 6967. [15] C.E. Moore, Atomic Energy Levels, Natl. Bur. Stds. Circ. No. 467 (U.S. GPO, Washington, DC, 1949). [16] J.M. Mariot and R.C. Karnatak, J. Phys. F4 (1974) L223. [17] P. Motais, E. Belin and C. Bonnelle, Phys. Rev. B25 (1982) 5492. [18] T.A. Callcott, K.L. Tsang, C.H. Zhang, D.L. Ederer and E.T. Arakawa, Rev. Sci. Instr. 57 (1986) 2680. [19] E.T. Arakawa and M.W. Williams, J. Phys. Chem. Solids 29 (1969) 795; E.R. Ilmas and A.I. Kuznetsov, Fiz. Tverd. Tela (Leningrad) 14 (1972) 1464. [20] N.M. Ravindra and J. Narayan, J. Appl. Phys. 61 (1987) 2017. [21] C.O. Almbladh, Phys. Rev. B16 (1977) 4343. [22] G.D. Mahan, Phys. Rev. B15 (1977) 4587. [23] S.T. Pantelides, Phys. Rev. Bll (1974) 2391. 1241 J.A. Pople and G.A. Segal, J. Chem. Phys. 44 (1966) 3289.
I. ATOMIC/MOLECULAR
PHYSICS
Nuclear
Instruments
and Methods
in Physics Research
B56/57
(1991) 320-323 North-Holland
Resonant absorption and emission from localized core-hole states in Al,O, and SiO, W.L. O’Brienl,
J. Jia, Q-Y. Dong and T.A. Callcott
University of Tennessee,
Knoxville,
J.-E. Rubensson,
D.L. Mueller
National Institute
of Standards
TN 37996, USA
and D.L. Ederer
and Technology,
Gaithersburg,
MD 20899, USA
We have compared the Al L,, and Si L,, emission and reflection spectra of Al,O, and SiO, to obtain information on the nature of the excited states in the presence of the L,, holes. A 5 m Rowland spectrometer, using a 600 l/mm grating mounted in grazing incidence was used to detect both electron excited soft X-ray emission and near normal soft X-ray reflection. We report fine structure in the emission spectra above the L,, edges which coincides with structure in the reflection spectra. These features appear both in the bandgap and in the conduction band. Such features within the bandgap are typically identified as excitons, while those in the conduction band must be localized excited states. Therefore, measurements of e2, for SiO, and Al,O, above the L,, edge should be interpreted in terms of localized excitations in the presence of a core hole, rather than interband transitions.
1. Introduction The SiO,
electronic
[lo-141
retical
and
properties emission
Both
subject
the
experimental (SXE)
band
of
been
of cw-Al,O,
spectroscopy vestigated
structure
have
by
been
spectroscopy
studied [2]
absorption
photoelectron structure
Al,O,
yield
calculations
[l-9]
and
of numerous
investigations. have
[3]. The
both
and spectra
Valence
band
by soft
X-ray
photoemission has
-measurements [4-61
theo-
and
been
in[2,7].
cluster
have been employed to describe the experimental emission and absorption spectra of (YAl,O,. While much of the theoretical work on ol-Al,O, attempts to explain the emission spectra through calculations of the occupied density of states we concentrate on the absorption process and its description in terms of localized excitations as opposed to interband transitions. Brytov and Romashchenko [2] measured the photoelectron yield above the L,, threshold for a-A1203. They interpreted the fine structure in the absorption spectra in terms of localized excitations in the [A10,1P9 cluster as determined by Tossell [l]. Tossell used a self-consistent field (SCF) Xa molecular orbital calculation to determine the excited states of the [A10,1P9 cluster. More recently Balzarotti et al. [7] have percalculations
[1,7]
’ Present address: Brookhaven National UlOA, Upton, NY 11973, USA. 0168-583X/91/$03.50
Labs, NSLS, Beamline
0 1991 - Elsevier Science Publishers
formed CND0/2 calculations on the [AlO,]molecule to explain the experimental photoelectron yield spectra. Band structure calculations have also been performed on a-A1203. These calculations employed the semi-empirical Mulliken-Rudenberg [4] method, and tight binding methods [5,6]. These calculations give reasonable values for the widths of the conduction band and some of the more prominent features as determined by SXE. There are, however, difficulties in defining the absorption spectra using these band models since they each neglected the presence of unoccupied Al 3d orbitals in the basis set. This is important for the identification of features in the L,, yield spectra since dipole selection rules are obeyed. A similar discussion can be made for SiO,. Both band structure models and cluster calculations have been used to explain the absorption spectra. In general, cluster calculations are appropriate when interpreting excitations which are localized. In alkali halides the core exciton associated with the positive ion is often found to be energetically identical to an excitation of the free ion [15,24]. This suggests highly localized non-screened excited states in the solid. Highly localized excited states are found in f-metals [16] and compounds [17], where d-f resonant emission and absorption has been used to explain spectral features. We have investigated both the reflection and emission from Al,O, and SiO, to determine the degree of localization of the excited states.
B.V. (North-Holland)
W.L. O’Brien et al. / Reflection
2. Experimental
and emission
fromAlJO
and SiO,
321
700
The L,, reflection and emission spectra of cll-Al,O, and fused SiO, are shown in fig. 1 and fig. 2, respectively. The soft X-ray emission (SXE) spectra shows only the fine structure above the valence band. The integrated intensity of these features are < 1% of the main band. The valence band spectra are similar to published spectra [2], and from our spectra we determine the VBM to be at 69.84 and 97.30 eV for Al,O, and SiOz respectively. Reflection spectra in this energy range follow the sample absorption. This is shown by writing the expression for normal incidence reflection in terms of the complex index of refraction n + ik,
0
1~~~1~~~1l’l~I~“““I
102
106
104
110
108
112
photon energy (ev)
Fig. 2. SiO, reflection and emission spectra. The vertical line marks the CBM as described in the text. The emission spectra
(n + 1)’ + k2 For photon energies in this energy range n = 1, thus and Rae:, where e2 is the imaginary part of the complex dielectric function. Thus, changes in the reflection spectra should follow changes in the absorption spectra. In fact the details in the reflection spectra for ol-Al,O, (fig. 1) are identical to those in published photoelectron yield spectra [2,7] with the exception that feature A apptiars more intense in reflection and is resolved as a doublet. Both the reflection and emission spectra were obtained with a 5 m Rowland spectrometer, using a 600 l/mm grating mounted in grazing incidence [18]. Specular reflection spectra were obtained 15” off normal. White light from beamline UlOA at the NSLS BNL was focussed onto the samples which were located in front R
was obtained
with an electron
excitation
energy of 500 eV.
ak2
600
reflection
5 $500
of the input slits of the Rowland spectrometer. The reflection spectra obtained in this manner show excellent agreement with published spectra [9,13]. Emission spectra were obtained with electron beam excitation. The spectra shown have been corrected for detector efficiency and bremsstrahlung background. The intensity of the bremsstrahlung background was typically ten times the peak heights of the features. For ol-AlzO, excitation energies of 1 and 2 keV were used. The peaks at 75 and 87 eV in the 2 keV excited spectra are due to higher orders of the 0 K emission. Features C and D, fig. 1, do not show the effects of self-absorption, 2 keV excited spectra, as do features A and B. The reason for this could be in our background subtraction or the features, and and D, could be an experimental artifact. We intend to continue this study in order to remove any uncertainty. For SiO, the emission spectra was obtained using 500 eV excitation to insure no 0 K emission. This was important since 0 K emission in 5 order appears at 104 eV.
3. Results and discussion
74
76
78
80 82 84 photon energy (eV)
86
88
90
Fig. 1. a-Al,O, reflection and emission spectra. The vertical line marks the CBM as described in the text. The emission spectra were obtained with electron excitation energies of 1 and 2 keV. Self absorption is evident in the comparison of the two emission spectra. The features at 75 and 87 eV are due to high orders of 0 K emission which has a low cross section at 1 keV excitation.
In fig. 1 it can be seen that doublet A and features B, C and D appear in both the reflection and emission spectra with approximately the same relative intensities. Similarly, in fig. 2, doublet A and feature B occur in both the reflection and emission spectra for Siq. The conduction band minimum (CBM) relative to the L3 level is shown in each figure. The CBM was determined by combining optical band gap measurements, 9.5 eV for Al,O, [19] and 9.3 eV for SiO, [20], to our measurements of the valence band maximum relative to the L, level. Each of these optical band gaps has an uncertainty of 0.5 eV based on the different values sited in the literature. I. ATOMIC/MOLECULAR
PHYSICS
322
W.L. O’Brien et al. / Reflection and emission from AI,O,
The doublet features, A, in the reflection spectra for both n-A1203 and SiO* appear in the band gap and have been defined as local excitations or core excitons [S,ll]. Core excitons are localized excitations which are typically described by their binding energy relative to the CBM. They give strong signals at the absorption threshold and definite but weak signals, in SXE. Features B, C, and D in fig. 1 and feature B in fig. 2 appear in the conduction band. Since they appear in emission as well as reflection they must be due to Iocalized resonant excitations. If they were due to absorption to a Bloch state within the continuum they would not appear as part of the emission process. Furthermore, since their intensities relative to the gap excitons are similar in both reflection and emission it appears that autoionization is not predominant, and that these L-states remain localized on a time scale equal to the lifetime of the core hole. The splittings in the doublet A features were determined by fitting the reflection spectra in these regions with gaussians of variable widths, and positions. The energy splittings were found to be 0.48 and 0.61 eV while the intensity ratios were found to be 1.8 : 1 and 0.9 : 1 in the Al,O, and SiO, spectra respectively. The atomic values for the L,, spin orbit splitting are 0.43 and 0.61 eV for Al and Si respectively while the statistical intensity ratio would be 0.5 : 1. Emission from localized states is expected to be broadened and shifted towards lower energies when compared to absorption [21,22]. This is due to the creation of phonons in the absorption process and emission from partially relaxed states. LOW energy broadening is evident in both fig. 1 and fig. 2. It is difficult to determine relaxation shifts due to sclf-absorption as evident by the changes in the emission doublet with excitation energy, fig. 1. 700 I
S
200~““““““““““‘~ 10 A 6 8
WI
12 energy above
d
14
d
a16 ‘,
I
I
18
/
I
and SiO,
600
6a
6t
I2
500
0’ * 6
r * , t
I
reflection
I
I
10
8
energy Fig. 4. SiO,
I
I’
above
I
c
I
VBM
spectra compared tion of Tossell [lo].
I
I
14
12
I
t
1
16
(eV) with cluster
calcula-
We conclude from this analysis that the L,, reflection {absorption) spectra of a-Al@, and SiO, give information due primarily to localized excitations of the and not on interband Al L,, and Si L,, electrons transitions, This is similar to an explanation for the absorption spectra of alkali halides [23]. It is therefore relevant to compare our reflection spectra with excitation energies predicted from cluster calculations. In fig. 3 we compare the Al,O, reflection spectra with the absorption features predicted by Balzarotti [7] using the unit [A10,1e9. Good agreement is found with feature A and the excitation to an orbital of s character using Balzarotti’s calculations. Balzarotti’s other levels appear to be too high in energy, and the level at 12 eV is primarily p type, dipole forbidden. Balzarotti (71 states that changing Pople’s [24] parameter, p in the CNDO/Z calculation lowers the d states below the p state, but that the band gap obtained is unrealistic. In fig. 4 we compare the SiO1 reflection with Tossells [lo] calculations on [SiOJ4 clusters. The agreement is quite good for the two main features if the levels Gt, and 6a, are shifted to lower energies by 2 eV. This assignment has already been made by Brytov et al. [2]. To our knowledge this is the first discussion of resonant absorption/ emission for localized excited states of other than f symmetry above the CBM. This analysis should stimulate more accurate calculations of localized excitations in Al,O,, SiO, and perhaps other wide band gap insulators.
I
20
VBM (eV)
Fig. 3. oc-Al,O, reflection spectra compared with cluster calculation of Balzarotti [7]. The symmetries of the orbitals are given. The orbital at 12 eV is primarily p type, dipole forbidden.
Acknowledgements One of us (W.L.O.) would like to thank CC. Kao for a number of discussions regarding the electronic properties of a-Al,O,.
W.L. O’Brien et al. / Reflection and emission from AI,O, References [l] J.A. Tossell, J. Phys. Chem. Solids 36 (1975) 1273. [2] LA. Brytov and Y.N. Romashchenko, Sov. Phys. Solid State 20 (1978) 384. [3] A. Balzarrotti and A. Bianconi, Phys. Status Solidi B76 (1976) 689. [4] R.A. Evarestov, A.N. Ermoshkin and V.A. Lovchikov, Phys. Status Solidi B99 (1980) 387. [5] I.P. Barta, J. Phys. Cl5 (1982) 5399. [6] S. Ciraci and I.P. Barta, Phys. Rev. BZ8 (1983) 982. [7] A. Balzzarotti, F. Antonangeli, R. Girlanda and G. Martino, Phys. Rev. B29 (1984) 5903. [S] A. Balzzarotti, F. Antonangeli, R. Girlanda and G. Martino, Solid State Commun. 44 (1982) 275. [9] T. Tomiki, T. Futemma, H. Kato, T. Miyahara, Y. Aiura, H. Fukutani and T. Shikenbaru, J. Phys. Sot. Jpn. 58 (1989) 1486. [lo] J.A. Tossell, J. Am. Chem. Sot. 97 (1975) 4840. [ll] F.C. Brown, R.Z. Bachrach and M. Skibowski, Phys. Rev. B15 (1977) 4781. [12] P. Deak, J. Kazsoki and J. Giber, Phys. Lett. 66A (1978) 395.
and SiO,
323
[13] E.O. Filatova, A.S. Vinogradov and T.M. Zimkina, Sov. Phys. Solid State 27 (1985) 606. [14] R. Dovesi, C. Pisani and C. Roetti, J. Chem. Phys. 86 (1987) 6967. [15] C.E. Moore, Atomic Energy Levels, Natl. Bur. Stds. Circ. No. 467 (U.S. GPO, Washington, DC, 1949). [16] J.M. Mariot and R.C. Karnatak, J. Phys. F4 (1974) L223. [17] P. Motais, E. Belin and C. Bonnelle, Phys. Rev. B25 (1982) 5492. [18] T.A. Callcott, K.L. Tsang, C.H. Zhang, D.L. Ederer and E.T. Arakawa, Rev. Sci. Instr. 57 (1986) 2680. [19] E.T. Arakawa and M.W. Williams, J. Phys. Chem. Solids 29 (1969) 795; E.R. Ilmas and A.I. Kuznetsov, Fiz. Tverd. Tela (Leningrad) 14 (1972) 1464. [20] N.M. Ravindra and J. Narayan, J. Appl. Phys. 61 (1987) 2017. [21] C.O. Almbladh, Phys. Rev. B16 (1977) 4343. [22] G.D. Mahan, Phys. Rev. B15 (1977) 4587. [23] S.T. Pantelides, Phys. Rev. Bll (1974) 2391. 1241 J.A. Pople and G.A. Segal, J. Chem. Phys. 44 (1966) 3289.
I. ATOMIC/MOLECULAR
PHYSICS