- Email: [email protected]
Core excitons and inner well resonances in surface soft x-ray absorption (SSXA) spectra
Surface Science 89 (1979)41-50 © North-Holland Publishing Company
CORE EXCITONS AND INNER WELL RESONANCES IN SURFACE SOFT
X-RAY ABSORPTION (SSXA) SPECTRA Antonio BIANCONI * Instituto di Fisica Universitd di Camerino, 62032 Camerino, Italy Received 22 February 1979
The surface soft X-ray absorption (SSXA) spectra of about one monolayer of AI203and of SiO2 has been measured. We demonstrate that the near L2,3 edge structures (Kossel structures), due to "core excitons" and "inner well resonances" can give both structural and electronic information of local character which are important in surface physics. A comparison with the structural information which can be extracted from SEXAFS structures appearing at higher photon energies is discussed. We have found that the local structure of the oxide monolayers is formed by Si-O4 and Al-O6 complexes. The binding energy of surface and bulk core excitons are the same in spite of the shift of the initial state energy. Information on the surface density of states of the conduction band of the Si(ll l) surface have been extracted from the SSXA spectrum of the clean Si surface.
1. Introduction Using synchrotron radiation sources and photoemission techniques it is now possible to measure the surface soft X-ray absorption (SSXA) spectra of solids over a large energy range [ 1]. Unique structural information like the interatomic distance and the coordination number (CN) can be extracted from the analysis of the surface EXAFS (SEXAFS) modulations extending far above the photoabsorption edge [2]. Here we concentrate our attention on discussing the information that can be extracted from the near edge structures (once called Kossel structures). The soft X-ray absorption (SXA) spectroscopy of bulk materials has grown rapidly by using synchrotron radiation [3]. The SXA spectroscopy historically deals with the structures within 30 eV from the photoabsorption threshold. It has been demonstrated that the chemical state o f the absorbing atom, the site symmetry and the nature of the nearest neighbouring atoms determine the SXA near-edge structures in bulk materials. In this paper the physics of SXA spectroscopy is applied to surface physics. It is well established that the strong absorption bands near the L or K edge of a * Also at Instituto di Fisica, Universitfi di Roma, Roma, Italy and PULS, Laboratori Nazionali di Frascati, Frascati, Italy. 41
42
.4. B&ncom / Core excitons and inner well resonances
positive ion surrounded by electronegative ions are due to "core excitons" below the photocoaduction threshold and above to "inner well resonances" degenerate with tile continuum [4-6]. The "inner well resonances" are molecular excited states localized inside the molecule. In molecules like CF4 [6] or SF6 [3], where a central atom fc)ims polar bonds with the first neighbours an effective potential barrier occurs ou the outer rim of molecules where bonding electrons accumulate on electronegati,ve atoms. The region of space between the positive central atom and the electrom,gative cage is called "inner well". If the central atom is symmetrically surrounded by electronegative atoms, states localized inside the "inner well" exist also at positi~. " energies above the continuum threshold. In the photoionization of an inner sheh :;t the central atom the excited internal photoelectron can be injected into the inner }~ell or in the outer well. The structures in the SXA spectra due to "inner well resonances" are very strong for large spatial overlap between the final and initial sta~es. In materials like SiO: and a-A1203 each positive metal ion is surrounded by four oxygen atoms forming an electronegative cage. Therefore localized quasi-molecular "inner well resonances" typical of the microscopic molecular unit MO4 appear. Below the continuum threshold discrete inner well states called "core excitons" are present. This interpretation of the soft X-ray absorption spectra assumes that they are determined essentially by the first coordination sphere of the cation. Here we discuss the "core excitons" and the "inner well resonances" in the SSXA spectra of about one monolayer of A1203 and of SiO2 in comparison with bulk SXA spectra. SSXA spectroscopy has been already applied to study the oxygen chemisorption on aluminium [1 ] and silicon [7,8] single crystals. Here we discuss fundamental aspects of surface "core excitons" and "inner well resonances" by comparison between bulk and surface spectra. The local character of this spectroscopy is demonstrated by the similarity of the shapes of SSXA and bulk SXA spectrao First the local structure of the oxide monolayers has been determined. In fact Si can have only a tetrahedral coordination (CN = 4) but AI can have both tetrahedral, as in a-AI203, and octahe&al coordination (CN = 6), as in co~rundum (c~-Al20~). The relative intensity of the peaks in the SSXA spectrum of A1203 indicates a prevalence of octahedral coordination in the first oxide monolayer formed on the AI(111) surface also if the thick oxide (d > 20 A) grown at room temperarare is amorphous and has a tetrahedral coordination. A large interest has grown recently on surface core excitons and on their binding energy in comparison with b u ~ CAk.ltUll~ .... :. . . . ~.~nd V ~ ¢ excitons r,, ~enuconuucwrslarge -- l~m a l - s t h' t e. . . . I t ~ , l v ,,,~ l .... " .... ~ ....... • In s..... u r l a c~e effects with increasing surface ionicity have been observed [11 ]. Surface core excitons have been observed alse in ionic materials like NaC1 [12] and MgO [13] both in single crystal surfaces and in thin films. In SiO2 a shift of ~1 eV toward lower energies of the absolute energy of the surface core exciton is observed in the SSXA spectrum. This is only an apparent shift of the core exciton binding energy which is the same, within experimental error, as in the bulk. In fact the shift is due to a variation of the binding energy of the core hole in the surface monolayer. This
A. Bianconi / Core excitons and inner well resonances
43
shows that it is very important to measure at the same time the core level binding energy, for the localization of the continuum threshold, and the photoabsorption. The results show that the binding energies of core excitons, Eb ~-- 1 eV in A1203 and Eb ~ 1.8 eV in SiO2, are similar to that of VUV excitons in agreement with ref. [ 10]. The effects of the extra-atomic relaxation of the core hole and of the ionicity of the Si-O bond on the inner well resonances in the oxide monolayers are disctissed.
2. Experimental The surface soft X-ray absorption (SSXA)spectra have been measured by recording the intensity of Auger electrons of energy E* = const as a function of the incident photon energy. The kinetic energy of collected Auger electrons has been selected to have the best surface contrast. For A1203 the interatornic Auger [ 1] line L2,3L 1V at E* = 45 eV and for SiO 2 the L 2 , a W Auger line at E* = 63 eV, involving the 4al and 4t2 valence orbitals [14], have been selected. The SSXA spectrum of the clean Si(111) 2 X 1 surface has been measured by recording the intensity of secondary electrons at a fixed kinetic energy E* = 50 eV. The electron escape depth fiE*) i~ Si and SiO 2 is 5 A and in A12Oa is 3 A. The thickness of the probed surface layer [2] is h = 21(E*) cos 0, where 0 is the ,ngle between the direction of the collected electrons and the surface normal, 0 = 42 ° in our experimental conditions. The surface slab of thickness h contributes to 86% of the measured SSXA spectrum of a clean surface (a slab of thickness 1.5h will contribute to 95%). Therefore the SSXA spectra of Si and SiO2 concern a h = 7.4 A tlfick surface layer and for A1203, h = 4.5 A. The oxide layers have been formed by exposure of clean AI(111) and Si(111) surfaces to oxygen at room temperature. The AI(111) surface has been exposed to 106 L and the Si(111) has been cleaved in atmospheric pressure of molecular oxygen for an exposure of 5 × 10 ~1 L [7]. The oxide thickness d has been extimated by the formula d = I(E*)ln(R[K + 1), where R is the ratio of the areas under the 2p chemically shifted photoemission peak'of the oxide and of the 2p peak of the substrate, and K is the ratio of the 2p peaks of the bulk oxide and of the bulk substrate. We have found d(A1203) ~-d(SiO2) -~, 5 fit. In the SSXA spectra of the SiO2 monolayer there is a contribution from the Si substrate, as it is expected since h >dox. To obtain the SSXA spectrum of SiO2 the Si contribution has been subtracted. Experimental details are described in refs. [ 1] and [7].
3. Results and discussion Fig. 1 shows the SSXA spectrum of the AI203 monolayer d ~ 5 A, together with the SXA spectra of [15] ~-A1203 and a-A1203 [16]. These spectra are dominated by the core exciton A below the photoconduction threshold Ec and by the "inner
44
A. Bianconi / Core excitons and inner well resonances
~~f~=77"8'v°'2e
D
_1 i
1 I I
I I "i I!
3
\ '~\ -AIzO=
Z
~I~
8O
9O
100 11o ENER6Y{eV) Fig. 1. Surface soft X-ray absorption (SSXA) spe:trum of a AI2O 3 monolayer (d = 5 A) and bulk SXA spectra of amorphous "alumina (a-AI203) and of crystalline a-AI203. Here, E c (monolayer) = E~p + 4, = 75.8 + 2 eV = 77.8 eV [ 1l; Ec (a-A1203) = Ebp + ~ = 75.7 + 2 eV = 77.7 eV; Ec (a-AI203) = E~p +Eg = 70.2 + 9.9 eV = 80.1 eV [17].
well resonances" B, C, D. In this figure we compare the spectrum of the A1203 monolayer of unknown microscopic structure with the bulk spectra of a-AI203 and ~-A1203 compounds. Since AI can have both tetrahedral coordination (like a-A1203) [17] and octahedral coordhnation (like a-A1203), the comparison between the spectra ha fig. I can tell us something about the preferred coordination in the surface r'nonolayer. The similarity between the relative intensities of peaks A, B, C, D in the /~203 monolayer and in o~-A]203 seems to indicate that the octahedral coordina~n (CN = 6) prevails in the monolayer. In :fact the intensity ratio of the peaks A and B and the splitting of peak D are similar to that found in a-A12Oa which is formed by &lO6 complexes. The theoretical interpretation of the L2,3SXA spectra of the microscopic struco turzl units i~JO6 and AI04 has been given by Tossel [ 18]. Using the SCF-Xt~ scatter-
A. Bianconi / Core excitons and inper well resonances
45
ing wave cluster Me method he has found that the peaks A and B in A10~9 cluster with octahedral symmetry are associated with final state molecular orbitals 7alg (from A1 s atomic orbitals) and 2t2g-3eg (from p and d atomic orbitals) respectively. For the tetrahedral geometry in A10~ s there is an inversion of the symmetry and the peaks A and B are now due to 6t2-2e (from p and d atomic orbitals) and 6al (from s atomic orbitals) respectively. This inversion of the symm~try for the first excited states is experimentally associated with an inversion of the relative oscillator strengths [15] of the A and B transitions in a-A1203 and ~t-A1203. More detailed calculations concerning also the shape and intensities of the photoabsorption structures would be really useful for a better interpretation of the spectra. The peak D is due to d-like orbitals and o- measured spectra indicate that it is split by the molecular field in oetahedral syn, ~try. Using the Z + 1 analogy [3], the peaks C and D correspond respectively to optical transitions to A13p and A13d derived orbitals. The binding energy of the exciton A has been calculated by the experimental determination of the photoconduction thresholds E¢. Generally Ee i,~ determined by the ~ m of L2,3 binding energy E~p below the top of the valence band (VBM), taken from photoemission spectra, and the optical band gap Eg taken from reflectivity spectra. E¢ measured in this way has a large error due to long tail of the density of states at the top of the valence band. An alternative way to measure Ec, with a smaller error [16], is to sum the 1.2,3 binding energy Eb2pin the oxide below the Fermi level in the metal and the potential barrier • between the metal Fermi level and the oxide conduction band, measured by tunnelling experiments. The results are reported in fig. 1. For ot-A12Oa we have found Ec = 80.1 eV about 2 eV higher than for amorphous oxide; Ec = 77.7 eV [ 1], which has a band gap about 2 eV smaller than the crystal. The calculated binding energy Eb of the core exciton A (Eb ~ 1 eV) is about the same in all the spectra and i~ is similar to the exciton bindmg energy in the VUV reflectivity spectra of Al2Oa [17]. It is necessary to be very careful to calculate reliable values of Ec. The XPS, reflectivity, photoconductivity and SXA should be taken on the same sample or in similar well characterized sampies. The structures S~ and $2 in the SSXA spectra are due to interface transitions discussed in ref. [ 1]. Fig. 2 shows the SSXA spectrum of about one SiO2 monolayer, d = 5 A, compared with the bulk SXA spectrum [19] of SiO2. The strong similarity between the bulk and the surface spectra reveals that the oxide rnonolayer is formed by SiO4 microscopic structural units as in SiO2. This is in agreement with the consideration that Si generally prefers only the tetra_hedr~ coordLnation. The siw':larity between the bulk spectrum and the spectrum of an oxide monolayer gives strong experimental evidence that the SXA spectra are determined by the sho~ range order. The Si-SiO2 interface in the present samples is nearly abrupt [20]. No SiOx thick interface layer has been found. The structural modifications in the oxide monolayer concern the angle ~ of the Si-O-Si bond cormecting two nearby tetrahedra and the Si second neighbours around the central Si atom. In aSiO2 the angle/3 = 144° and
46
A. Bianconi / Core excitons and inner well resonances
c==I07.2-~0.2
Z
! I
~02 ...
Lt3e~e
i
0
B
I
m
t..2
c
-
1
! I ~ y--,^r, =I'I \
~
"-~ ,'
,
j.
n - - , 7 . .E. .~. .T m ~ , 100
II0
, 120
,
, 130
PHOTONENER6Y(eV) Fig. 2. SSXA spectrum of a 5 A layer of SiO2 on Si(l 11) and the bulk SXA spectrum of SiO2.
in a-SiO2, 13 has a random distribution. In SiO2 each of the SiO4 oxygens is linked to a second Si atom. These atoms can be missing in the monolayer or toward the interface can be in an intermediate oxidation state. On an ideal (111) abrupt interface these Si ions will have a Si-Si30 configuration. The intermediate ,oxidation of a Si atom has been revealed by the intermediate, 1.6 eV, chemical shift of the Si* 2p level [7]. These structural differences will infer only changes in the details of the SSXA spectra. Therefore let us now analyse the differencies between the SSXA and the SXA spectra. The surface core exciton A in the SSXA spectrum in fig. 2 is at about 1 eV lower energy than the corresponding peak m the bulk spectrum. In order to avoid calibration errors comparing results of different groups we have compared the shift of the L2,3 threshold energy of the oxide spectrum with respect to the L3 edge of silicon (see fig. 4) taken in the same experiment. Lukirskii [19] and Brown [19] have found a shift of the oxide L2,3 edge of 6.2 + 0.2 eV in the bulk SXA spectra. This shift ~,,ln=Lu~l~ be ,-,m,,~r~a with +h~ ~.2 + 0.2 eV shift found in this. work in the oxide monolayer. Britov et al. [15] have found a peak at 105.4 eV below the main peak A at 106 eV in the total electron yield spectra of bulk SIO2. By comparison with our results this peak should be assigned to the surface core exciton. To calculate the binding energy of the exc~ton we have taken from ref. [7] the measured binding energy Eb2p of the 2p core lewd in the same sample Eb2p = 102.8 +--0.1 eV and the Si-SiO2 potential barrier [21] • = 4.4 +- 0.1 eV which is independent on
A. Bianconi / Core excitons and inner well resonances
47
the thickness of the oxide. Therefore Ec = 107.2 +--0.2 eV and the s.',face core exciton binding energy is Eb = 1.8 -+0.3 eV. It has been found [22] that for thicker oxide layers the binding energy E2bp shifts toward higher energy up to the value 103.6 eV, constant for oxide layers between 20 and 400 A. Taking this value for bulk SiO2 we have found Ee = 108 + 0.3 eV in the bulk SXA spectra. Therefore the continuum threshold E¢ shifts together with the absolute energy of the exciton A. The binding energy of the bulk and surface core excitons are agahn the same withi:a experimental error. It is interesting to remark that the binding energy of the core exciton is similar to that of the VUV exciton at h ~ = 10.4 eV in the ultraviolet reflectivity spectra of SiO2 [8]. This exciton occurring above the photoconductioa threshold (9 eV) has an extimated binding energy of 1.5-2 eV [23]. In conclusion the core exciton absolute energy shift is associated with the 2p core level shift. B~at there is not a rigid shift of the inner well resonances B, C, D with the exciton A. This is due to different effects on the excited states of the modified molecular potential. The observed shift of the Si 2p initial state and of the core exciton A in the monolayer can be related with the structural and electronic differences between the bulk and the monolayer. First a change of the S i - O - S i bonding angle on the surface will modify the ionicity [24] of the Si-O bond and the Si central atom will have a smaller positive effective charge and the Si 2p level a smaller binding energy. The oxygen atoms will have a smaller negative charge and the electronegative barrier will be modified. Second, the lack of the second neighbour Si atoms linked to the SiO4 tetrahedron or their different ionization state will also change the molecular potential, and a modificaticn ot the extra-atomic relaxation of the core hole is expected in the monolayer. In fact these structural differencies change the distribution of the screening electrons on the O 2p levels. Third, the electrostatic Madelung potential is lower in the surface layer. The high energy rt;sonances B, C, D are clearly affected by these modifications of the molecular potential in the SiO2 monolayer. The different shifts of these peaks between bulk and surface spectra are due to their different symmetry and spatial distribution. The Madelung potential, for example, is expected to induce different shifts of the orbitals with different syrmnetries [8]. Moreover we should take into account the Stark effect on the excited states in the surface electric fiAd due to the gradient of the Madelung potential at the surface [13]. The first strong discrete excited state (the exciton A) seems to follow more closely than others the shift of the initial core state. A similar effect can be found in SXA spectra of molecules [6]. The peak S~ with the thres,tu~u at ,ul 1 -. 70.0 is an intenace transition Ill from the Si* zp level (1.6 eV shift) in the intermediate oxidation state to the Si substrate conduction band and it has been discussed in ref. [7]. Fig. 3 shows an energy scheme of Si, SiO2 monolayer and bulk SiO2. Fig. 4 shows the SSXA spectrum of Si(111) surface. In metals and low gap semiconductors the SXA spectra in the energy range between 1 and 10 eV above the edge are largely dominated by transitions to delocalized states and it is possible to
A. Bianconi I Core excitons and inner well resonances
48
"' ] monolayer
d ~20t t
d=5A ./11
4- - t
T
colt txCllol 2-
O-2--
T
g •'.',<'
l./j/ll
/
4.4i (11c
El i
I
!~///////1/11
I
.,:,1 III i<
-6
-101-
! I
-~-Si2p
1
103.6±0.2 b
Fig. 3. Energy scheme and optical transitions of Si, SiO2 monolayer and bulk SiO2. Some data have been taken from the following references: (a) refs. [7,81; (b) ref. [22]; (c) ref. [21]; (d) ref. [19].
correlate the spectra with the density of states of the conduction band (DOS). Brown [3] has found a good correlation between the structures of the Si L2, 3 absorption spectrum in this energy range and the calculated DOS. From SSXA spectra of clean AI(100) a surface resonance correlated with a partial gap ha the projected energy bands has been found [25]. Collecting the secondaries at E* = 4 eV we measure an absorption coefficient of a more than 20 A thick layer, coincident with the bulk SXA spectrum measured by optical transmission [19]. The yield spectrum with E* = 50 eV probes an about 7 A thick layer. The only significative difference between t:,.e surface (E* = 50 eV) and bulk spectra (E* = 4 eV) is for the p--~v ~+ ,~,~.,,+ ~ ~ e V a~" . . . . . . U~ ~. the conduction band r,-,c. in the surface u u v. v. . . t h e 1_ UOttUll spectrum it becomes broader and a 4.0 eV shift is observed. This structure at 2.9 eV above Ec in the SSXA spectrum is assigned to a transition to the fiat surface band between M and I~ directions at about 3 eV above Ec in the Si(111)energy bands calculated by Schlfiter [26] and Del Sole [27]. No shift of the L2, 3 threshold due to a different binding energy of the surface core excitons has been observed in fig. 4. •, ~
at
a u v u t
r.,.a
A. Bianconi / Core excitons and inner well resonances
49
Si (111)(2xl1
N
11
',
I ,
'
t
99'
,
0 I
~, 100
\
1 ,
/
2 3 E-Ec (eV) •
101 '
e=4 .
1
102
.
I
4 ,
103
1
104
" ,
I
105
,
I
106
PHOTON E~ERGY (eV)
Fig. 4. L2,3 SSXA spectra of the Si(111) 2 X 1 surface of a h ~ 7 A thick layer (E* = 50 eV) and of a h >~ 20 A thick layer (E* = 4 eV).
4. Conclusions In conclusion we have discussed the application of the SSXA spectroscopy to surface physics in several materials. The analysis of the near-edge structures contain a lot of information on the local structure which is complementary to other spectroscopies. SEXAFS, for example, gives the interatomic distance and the coordination number SSXA gives the symmetry around the central atom and its ionization state, related to the ionicity of the bond. Moreover information on the surface electronic structure can be obtained from SSXA spectroscopy. An upper limit of about 0.3 eV for the difference of the electron-hole interaction between core and valence excitons and bulk and surface excitons in A1203 and SiO2 has been founa. Some of the material incorporated in this work was developed with the financial support of the National Science Foundation (under Contract No. DMR7727489) in cooperation with the US Department of Energy. Portions of this work were carried out while the author wa~; at SSRL, Stanford University.
References [1] A. Bianconi, R.Z. Bachrach and S.A. Flodstr6m, Solid State Commun. 24 (1977)539; Phys. Rev. B19 (1979) 3879. [2] A. Bianconi and R.Z. Baehrach, Phys. Revo Letters 42 (1979) 104. [31 E.E. Koch, C. Kunz and B. Sonntag, Phys. Rept. 29C (1977) 155; F.C. Brown, Solid. State Phys. 29 (1974) 1. [41 J.L. Dehmer, J. Chem. Phys, 56 (1972) 4496.
50
A. Bianconi / Core excitons and inner well resonances
151 T. Aberg and J.L. Dehmer, J. Phys. C6 (1973) 1450. 161 F.C. Brown, R.Z. Bachrach and A. Bianconi, Chem. Phys. Letters 54 (1978) 425. 171 A. Bianconi and R.S. Bauer, to be published; R.S. Bauer, J.C. McMenamin, R.Z. Bachrach, A. Bianconi, L. Johansson and H. Petersen, in: Proc. 14th Conf. on the Physics of Semiconductors, Ed. B.L. Wilson, Inst. Phys. Conf. Ser. 43 (1978) 797. [81 S.T. Pantelides, Ed., The Physics of SiO2 and its Interfaces, (Pergamon, 1978): See: R.S. Bauer, J.C. ~,icMenamin and H. Petersen and A. Bianconi, p. 401. [91 F. Bassa~, G. Margaritondo and G. Tinivella, in: Proc. 14th Conf. on the Physics of Semiconductors, Ed. B.L. Wilson (Plessey, 1978). tl01 M. Altarell, G. Bachelet and R. Del Sole, to be published. [111 J.C. McMenamin and R.S. Bauer, J. Vacuum Sci. Technol. 15 (1978) 1262 1121 V. Rehcer, W. Gudat, R.G. Hayes and C. Kunz, in: Proc. 7th Intern. Vacut, m Congr. and 3rd Intern. Conf. on Solid Surfaces, Eds. R. Dobrozemsky et al. (Berger, Vienna, 1977) p. 453. 1131 V.E. Heu-~,ch, G. Dresselhaus and lt.J. Zeiger, Phys. Rev. Letters 36 (1976) 158. !141 D.E. R~m~ker, J.S. Murday, N.H. Turner, G. Moore, M.G. Lagally and J. Houston, ref.
181, p. 99. [151 I.A. Britov and Y_u.N. Romashenko, Soviet Phys.-Solid State 20 (1978) 384. [161 A. Balzarotti, A. Bianconi, E. Burattini, M. Grandolfo, R. Habel and M. Piacentini, Phys. Status Solidi Co) 63 (1974) 77. [171 A. Balzarotti and A. Bianconi, Phys. Status Solidi (b) 76 (1976) 689 and references cited therein. 1181 J.A. Tossel, J. Phys. Chem. Solids 36 (1975) 1273;J. Am. Chem. Soc. 97 (1975)4840. [191 O.A. Ershov and A.P. Lukirskii, Soviet Phys.-Solid State 8 (1967) 1699; F.C. Brown, R.Z. Bachrach and M. Skibowski Phys. Rev. B15 (1977) 4781. I2Ol S.T. Pantelides, ref. [81, p. 339. 1211 r.H. Di Stefano, J. Vacuum Sci. Technol. 13 (1976) 856; T.H. Di Stefano, ref. [81, p. 362. [221 S.l. Raider and R. Flitsh, ref. [8], p. 384; T. Hattori and T. Nishina, ref. [8], p. 379; G. HoUinger and Tran Minh Duc, in: Proc. 7th Conf. on Amorphous and Liquid Semiconductors, Ed. W.E. Spear (1977) p. 87; G. HollJnger, Y. Yugnet, P. Pertosa and Tran Mirth Duc, Chem. Phys. Letters 36 (1975) 441. I231 N.F. Mott, ref. [81, p. 1; J.R. Chelikowsky and M. Schliiter, Phys. Rev.B15 (1977) 4020; S.T. Pantelides and W.A. Harrison, Phys. Rev. B13 (1976) 2667; S.T. Pantelides and W.A. Harrison, ref. [8], p. 80. [241 K. Hfibner, Phys. Status Solidi (a) 42, (1977) 501; K. Hiabner and A. Lehmann, Phys. Status Solidi (a) 46 (1978) 451. [251 R.Z. Bachrach, D.J. Chadi and A. Bianconi, Solid State Commun. 28 (1978) 931. [261 M. Schltiter and M.L. Cohen, Phys. Rev. B17 (1978) 716. I271 R. Del Sole and W. Hanke, Solid State Commun., to be published.
CORE EXCITONS AND INNER WELL RESONANCES IN SURFACE SOFT
X-RAY ABSORPTION (SSXA) SPECTRA Antonio BIANCONI * Instituto di Fisica Universitd di Camerino, 62032 Camerino, Italy Received 22 February 1979
The surface soft X-ray absorption (SSXA) spectra of about one monolayer of AI203and of SiO2 has been measured. We demonstrate that the near L2,3 edge structures (Kossel structures), due to "core excitons" and "inner well resonances" can give both structural and electronic information of local character which are important in surface physics. A comparison with the structural information which can be extracted from SEXAFS structures appearing at higher photon energies is discussed. We have found that the local structure of the oxide monolayers is formed by Si-O4 and Al-O6 complexes. The binding energy of surface and bulk core excitons are the same in spite of the shift of the initial state energy. Information on the surface density of states of the conduction band of the Si(ll l) surface have been extracted from the SSXA spectrum of the clean Si surface.
1. Introduction Using synchrotron radiation sources and photoemission techniques it is now possible to measure the surface soft X-ray absorption (SSXA) spectra of solids over a large energy range [ 1]. Unique structural information like the interatomic distance and the coordination number (CN) can be extracted from the analysis of the surface EXAFS (SEXAFS) modulations extending far above the photoabsorption edge [2]. Here we concentrate our attention on discussing the information that can be extracted from the near edge structures (once called Kossel structures). The soft X-ray absorption (SXA) spectroscopy of bulk materials has grown rapidly by using synchrotron radiation [3]. The SXA spectroscopy historically deals with the structures within 30 eV from the photoabsorption threshold. It has been demonstrated that the chemical state o f the absorbing atom, the site symmetry and the nature of the nearest neighbouring atoms determine the SXA near-edge structures in bulk materials. In this paper the physics of SXA spectroscopy is applied to surface physics. It is well established that the strong absorption bands near the L or K edge of a * Also at Instituto di Fisica, Universitfi di Roma, Roma, Italy and PULS, Laboratori Nazionali di Frascati, Frascati, Italy. 41
42
.4. B&ncom / Core excitons and inner well resonances
positive ion surrounded by electronegative ions are due to "core excitons" below the photocoaduction threshold and above to "inner well resonances" degenerate with tile continuum [4-6]. The "inner well resonances" are molecular excited states localized inside the molecule. In molecules like CF4 [6] or SF6 [3], where a central atom fc)ims polar bonds with the first neighbours an effective potential barrier occurs ou the outer rim of molecules where bonding electrons accumulate on electronegati,ve atoms. The region of space between the positive central atom and the electrom,gative cage is called "inner well". If the central atom is symmetrically surrounded by electronegative atoms, states localized inside the "inner well" exist also at positi~. " energies above the continuum threshold. In the photoionization of an inner sheh :;t the central atom the excited internal photoelectron can be injected into the inner }~ell or in the outer well. The structures in the SXA spectra due to "inner well resonances" are very strong for large spatial overlap between the final and initial sta~es. In materials like SiO: and a-A1203 each positive metal ion is surrounded by four oxygen atoms forming an electronegative cage. Therefore localized quasi-molecular "inner well resonances" typical of the microscopic molecular unit MO4 appear. Below the continuum threshold discrete inner well states called "core excitons" are present. This interpretation of the soft X-ray absorption spectra assumes that they are determined essentially by the first coordination sphere of the cation. Here we discuss the "core excitons" and the "inner well resonances" in the SSXA spectra of about one monolayer of A1203 and of SiO2 in comparison with bulk SXA spectra. SSXA spectroscopy has been already applied to study the oxygen chemisorption on aluminium [1 ] and silicon [7,8] single crystals. Here we discuss fundamental aspects of surface "core excitons" and "inner well resonances" by comparison between bulk and surface spectra. The local character of this spectroscopy is demonstrated by the similarity of the shapes of SSXA and bulk SXA spectrao First the local structure of the oxide monolayers has been determined. In fact Si can have only a tetrahedral coordination (CN = 4) but AI can have both tetrahedral, as in a-AI203, and octahe&al coordination (CN = 6), as in co~rundum (c~-Al20~). The relative intensity of the peaks in the SSXA spectrum of A1203 indicates a prevalence of octahedral coordination in the first oxide monolayer formed on the AI(111) surface also if the thick oxide (d > 20 A) grown at room temperarare is amorphous and has a tetrahedral coordination. A large interest has grown recently on surface core excitons and on their binding energy in comparison with b u ~ CAk.ltUll~ .... :. . . . ~.~nd V ~ ¢ excitons r,, ~enuconuucwrslarge -- l~m a l - s t h' t e. . . . I t ~ , l v ,,,~ l .... " .... ~ ....... • In s..... u r l a c~e effects with increasing surface ionicity have been observed [11 ]. Surface core excitons have been observed alse in ionic materials like NaC1 [12] and MgO [13] both in single crystal surfaces and in thin films. In SiO2 a shift of ~1 eV toward lower energies of the absolute energy of the surface core exciton is observed in the SSXA spectrum. This is only an apparent shift of the core exciton binding energy which is the same, within experimental error, as in the bulk. In fact the shift is due to a variation of the binding energy of the core hole in the surface monolayer. This
A. Bianconi / Core excitons and inner well resonances
43
shows that it is very important to measure at the same time the core level binding energy, for the localization of the continuum threshold, and the photoabsorption. The results show that the binding energies of core excitons, Eb ~-- 1 eV in A1203 and Eb ~ 1.8 eV in SiO2, are similar to that of VUV excitons in agreement with ref. [ 10]. The effects of the extra-atomic relaxation of the core hole and of the ionicity of the Si-O bond on the inner well resonances in the oxide monolayers are disctissed.
2. Experimental The surface soft X-ray absorption (SSXA)spectra have been measured by recording the intensity of Auger electrons of energy E* = const as a function of the incident photon energy. The kinetic energy of collected Auger electrons has been selected to have the best surface contrast. For A1203 the interatornic Auger [ 1] line L2,3L 1V at E* = 45 eV and for SiO 2 the L 2 , a W Auger line at E* = 63 eV, involving the 4al and 4t2 valence orbitals [14], have been selected. The SSXA spectrum of the clean Si(111) 2 X 1 surface has been measured by recording the intensity of secondary electrons at a fixed kinetic energy E* = 50 eV. The electron escape depth fiE*) i~ Si and SiO 2 is 5 A and in A12Oa is 3 A. The thickness of the probed surface layer [2] is h = 21(E*) cos 0, where 0 is the ,ngle between the direction of the collected electrons and the surface normal, 0 = 42 ° in our experimental conditions. The surface slab of thickness h contributes to 86% of the measured SSXA spectrum of a clean surface (a slab of thickness 1.5h will contribute to 95%). Therefore the SSXA spectra of Si and SiO2 concern a h = 7.4 A tlfick surface layer and for A1203, h = 4.5 A. The oxide layers have been formed by exposure of clean AI(111) and Si(111) surfaces to oxygen at room temperature. The AI(111) surface has been exposed to 106 L and the Si(111) has been cleaved in atmospheric pressure of molecular oxygen for an exposure of 5 × 10 ~1 L [7]. The oxide thickness d has been extimated by the formula d = I(E*)ln(R[K + 1), where R is the ratio of the areas under the 2p chemically shifted photoemission peak'of the oxide and of the 2p peak of the substrate, and K is the ratio of the 2p peaks of the bulk oxide and of the bulk substrate. We have found d(A1203) ~-d(SiO2) -~, 5 fit. In the SSXA spectra of the SiO2 monolayer there is a contribution from the Si substrate, as it is expected since h >dox. To obtain the SSXA spectrum of SiO2 the Si contribution has been subtracted. Experimental details are described in refs. [ 1] and [7].
3. Results and discussion Fig. 1 shows the SSXA spectrum of the AI203 monolayer d ~ 5 A, together with the SXA spectra of [15] ~-A1203 and a-A1203 [16]. These spectra are dominated by the core exciton A below the photoconduction threshold Ec and by the "inner
44
A. Bianconi / Core excitons and inner well resonances
~~f~=77"8'v°'2e
D
_1 i
1 I I
I I "i I!
3
\ '~\ -AIzO=
Z
~I~
8O
9O
100 11o ENER6Y{eV) Fig. 1. Surface soft X-ray absorption (SSXA) spe:trum of a AI2O 3 monolayer (d = 5 A) and bulk SXA spectra of amorphous "alumina (a-AI203) and of crystalline a-AI203. Here, E c (monolayer) = E~p + 4, = 75.8 + 2 eV = 77.8 eV [ 1l; Ec (a-A1203) = Ebp + ~ = 75.7 + 2 eV = 77.7 eV; Ec (a-AI203) = E~p +Eg = 70.2 + 9.9 eV = 80.1 eV [17].
well resonances" B, C, D. In this figure we compare the spectrum of the A1203 monolayer of unknown microscopic structure with the bulk spectra of a-AI203 and ~-A1203 compounds. Since AI can have both tetrahedral coordination (like a-A1203) [17] and octahedral coordhnation (like a-A1203), the comparison between the spectra ha fig. I can tell us something about the preferred coordination in the surface r'nonolayer. The similarity between the relative intensities of peaks A, B, C, D in the /~203 monolayer and in o~-A]203 seems to indicate that the octahedral coordina~n (CN = 6) prevails in the monolayer. In :fact the intensity ratio of the peaks A and B and the splitting of peak D are similar to that found in a-A12Oa which is formed by &lO6 complexes. The theoretical interpretation of the L2,3SXA spectra of the microscopic struco turzl units i~JO6 and AI04 has been given by Tossel [ 18]. Using the SCF-Xt~ scatter-
A. Bianconi / Core excitons and inper well resonances
45
ing wave cluster Me method he has found that the peaks A and B in A10~9 cluster with octahedral symmetry are associated with final state molecular orbitals 7alg (from A1 s atomic orbitals) and 2t2g-3eg (from p and d atomic orbitals) respectively. For the tetrahedral geometry in A10~ s there is an inversion of the symmetry and the peaks A and B are now due to 6t2-2e (from p and d atomic orbitals) and 6al (from s atomic orbitals) respectively. This inversion of the symm~try for the first excited states is experimentally associated with an inversion of the relative oscillator strengths [15] of the A and B transitions in a-A1203 and ~t-A1203. More detailed calculations concerning also the shape and intensities of the photoabsorption structures would be really useful for a better interpretation of the spectra. The peak D is due to d-like orbitals and o- measured spectra indicate that it is split by the molecular field in oetahedral syn, ~try. Using the Z + 1 analogy [3], the peaks C and D correspond respectively to optical transitions to A13p and A13d derived orbitals. The binding energy of the exciton A has been calculated by the experimental determination of the photoconduction thresholds E¢. Generally Ee i,~ determined by the ~ m of L2,3 binding energy E~p below the top of the valence band (VBM), taken from photoemission spectra, and the optical band gap Eg taken from reflectivity spectra. E¢ measured in this way has a large error due to long tail of the density of states at the top of the valence band. An alternative way to measure Ec, with a smaller error [16], is to sum the 1.2,3 binding energy Eb2pin the oxide below the Fermi level in the metal and the potential barrier • between the metal Fermi level and the oxide conduction band, measured by tunnelling experiments. The results are reported in fig. 1. For ot-A12Oa we have found Ec = 80.1 eV about 2 eV higher than for amorphous oxide; Ec = 77.7 eV [ 1], which has a band gap about 2 eV smaller than the crystal. The calculated binding energy Eb of the core exciton A (Eb ~ 1 eV) is about the same in all the spectra and i~ is similar to the exciton bindmg energy in the VUV reflectivity spectra of Al2Oa [17]. It is necessary to be very careful to calculate reliable values of Ec. The XPS, reflectivity, photoconductivity and SXA should be taken on the same sample or in similar well characterized sampies. The structures S~ and $2 in the SSXA spectra are due to interface transitions discussed in ref. [ 1]. Fig. 2 shows the SSXA spectrum of about one SiO2 monolayer, d = 5 A, compared with the bulk SXA spectrum [19] of SiO2. The strong similarity between the bulk and the surface spectra reveals that the oxide rnonolayer is formed by SiO4 microscopic structural units as in SiO2. This is in agreement with the consideration that Si generally prefers only the tetra_hedr~ coordLnation. The siw':larity between the bulk spectrum and the spectrum of an oxide monolayer gives strong experimental evidence that the SXA spectra are determined by the sho~ range order. The Si-SiO2 interface in the present samples is nearly abrupt [20]. No SiOx thick interface layer has been found. The structural modifications in the oxide monolayer concern the angle ~ of the Si-O-Si bond cormecting two nearby tetrahedra and the Si second neighbours around the central Si atom. In aSiO2 the angle/3 = 144° and
46
A. Bianconi / Core excitons and inner well resonances
c==I07.2-~0.2
Z
! I
~02 ...
Lt3e~e
i
0
B
I
m
t..2
c
-
1
! I ~ y--,^r, =I'I \
~
"-~ ,'
,
j.
n - - , 7 . .E. .~. .T m ~ , 100
II0
, 120
,
, 130
PHOTONENER6Y(eV) Fig. 2. SSXA spectrum of a 5 A layer of SiO2 on Si(l 11) and the bulk SXA spectrum of SiO2.
in a-SiO2, 13 has a random distribution. In SiO2 each of the SiO4 oxygens is linked to a second Si atom. These atoms can be missing in the monolayer or toward the interface can be in an intermediate oxidation state. On an ideal (111) abrupt interface these Si ions will have a Si-Si30 configuration. The intermediate ,oxidation of a Si atom has been revealed by the intermediate, 1.6 eV, chemical shift of the Si* 2p level [7]. These structural differences will infer only changes in the details of the SSXA spectra. Therefore let us now analyse the differencies between the SSXA and the SXA spectra. The surface core exciton A in the SSXA spectrum in fig. 2 is at about 1 eV lower energy than the corresponding peak m the bulk spectrum. In order to avoid calibration errors comparing results of different groups we have compared the shift of the L2,3 threshold energy of the oxide spectrum with respect to the L3 edge of silicon (see fig. 4) taken in the same experiment. Lukirskii [19] and Brown [19] have found a shift of the oxide L2,3 edge of 6.2 + 0.2 eV in the bulk SXA spectra. This shift ~,,ln=Lu~l~ be ,-,m,,~r~a with +h~ ~.2 + 0.2 eV shift found in this. work in the oxide monolayer. Britov et al. [15] have found a peak at 105.4 eV below the main peak A at 106 eV in the total electron yield spectra of bulk SIO2. By comparison with our results this peak should be assigned to the surface core exciton. To calculate the binding energy of the exc~ton we have taken from ref. [7] the measured binding energy Eb2p of the 2p core lewd in the same sample Eb2p = 102.8 +--0.1 eV and the Si-SiO2 potential barrier [21] • = 4.4 +- 0.1 eV which is independent on
A. Bianconi / Core excitons and inner well resonances
47
the thickness of the oxide. Therefore Ec = 107.2 +--0.2 eV and the s.',face core exciton binding energy is Eb = 1.8 -+0.3 eV. It has been found [22] that for thicker oxide layers the binding energy E2bp shifts toward higher energy up to the value 103.6 eV, constant for oxide layers between 20 and 400 A. Taking this value for bulk SiO2 we have found Ee = 108 + 0.3 eV in the bulk SXA spectra. Therefore the continuum threshold E¢ shifts together with the absolute energy of the exciton A. The binding energy of the bulk and surface core excitons are agahn the same withi:a experimental error. It is interesting to remark that the binding energy of the core exciton is similar to that of the VUV exciton at h ~ = 10.4 eV in the ultraviolet reflectivity spectra of SiO2 [8]. This exciton occurring above the photoconductioa threshold (9 eV) has an extimated binding energy of 1.5-2 eV [23]. In conclusion the core exciton absolute energy shift is associated with the 2p core level shift. B~at there is not a rigid shift of the inner well resonances B, C, D with the exciton A. This is due to different effects on the excited states of the modified molecular potential. The observed shift of the Si 2p initial state and of the core exciton A in the monolayer can be related with the structural and electronic differences between the bulk and the monolayer. First a change of the S i - O - S i bonding angle on the surface will modify the ionicity [24] of the Si-O bond and the Si central atom will have a smaller positive effective charge and the Si 2p level a smaller binding energy. The oxygen atoms will have a smaller negative charge and the electronegative barrier will be modified. Second, the lack of the second neighbour Si atoms linked to the SiO4 tetrahedron or their different ionization state will also change the molecular potential, and a modificaticn ot the extra-atomic relaxation of the core hole is expected in the monolayer. In fact these structural differencies change the distribution of the screening electrons on the O 2p levels. Third, the electrostatic Madelung potential is lower in the surface layer. The high energy rt;sonances B, C, D are clearly affected by these modifications of the molecular potential in the SiO2 monolayer. The different shifts of these peaks between bulk and surface spectra are due to their different symmetry and spatial distribution. The Madelung potential, for example, is expected to induce different shifts of the orbitals with different syrmnetries [8]. Moreover we should take into account the Stark effect on the excited states in the surface electric fiAd due to the gradient of the Madelung potential at the surface [13]. The first strong discrete excited state (the exciton A) seems to follow more closely than others the shift of the initial core state. A similar effect can be found in SXA spectra of molecules [6]. The peak S~ with the thres,tu~u at ,ul 1 -. 70.0 is an intenace transition Ill from the Si* zp level (1.6 eV shift) in the intermediate oxidation state to the Si substrate conduction band and it has been discussed in ref. [7]. Fig. 3 shows an energy scheme of Si, SiO2 monolayer and bulk SiO2. Fig. 4 shows the SSXA spectrum of Si(111) surface. In metals and low gap semiconductors the SXA spectra in the energy range between 1 and 10 eV above the edge are largely dominated by transitions to delocalized states and it is possible to
A. Bianconi I Core excitons and inner well resonances
48
"' ] monolayer
d ~20t t
d=5A ./11
4- - t
T
colt txCllol 2-
O-2--
T
g •'.',<'
l./j/ll
/
4.4i (11c
El i
I
!~///////1/11
I
.,:,1 III i<
-6
-101-
! I
-~-Si2p
1
103.6±0.2 b
Fig. 3. Energy scheme and optical transitions of Si, SiO2 monolayer and bulk SiO2. Some data have been taken from the following references: (a) refs. [7,81; (b) ref. [22]; (c) ref. [21]; (d) ref. [19].
correlate the spectra with the density of states of the conduction band (DOS). Brown [3] has found a good correlation between the structures of the Si L2, 3 absorption spectrum in this energy range and the calculated DOS. From SSXA spectra of clean AI(100) a surface resonance correlated with a partial gap ha the projected energy bands has been found [25]. Collecting the secondaries at E* = 4 eV we measure an absorption coefficient of a more than 20 A thick layer, coincident with the bulk SXA spectrum measured by optical transmission [19]. The yield spectrum with E* = 50 eV probes an about 7 A thick layer. The only significative difference between t:,.e surface (E* = 50 eV) and bulk spectra (E* = 4 eV) is for the p--~v ~+ ,~,~.,,+ ~ ~ e V a~" . . . . . . U~ ~. the conduction band r,-,c. in the surface u u v. v. . . t h e 1_ UOttUll spectrum it becomes broader and a 4.0 eV shift is observed. This structure at 2.9 eV above Ec in the SSXA spectrum is assigned to a transition to the fiat surface band between M and I~ directions at about 3 eV above Ec in the Si(111)energy bands calculated by Schlfiter [26] and Del Sole [27]. No shift of the L2, 3 threshold due to a different binding energy of the surface core excitons has been observed in fig. 4. •, ~
at
a u v u t
r.,.a
A. Bianconi / Core excitons and inner well resonances
49
Si (111)(2xl1
N
11
',
I ,
'
t
99'
,
0 I
~, 100
\
1 ,
/
2 3 E-Ec (eV) •
101 '
e=4 .
1
102
.
I
4 ,
103
1
104
" ,
I
105
,
I
106
PHOTON E~ERGY (eV)
Fig. 4. L2,3 SSXA spectra of the Si(111) 2 X 1 surface of a h ~ 7 A thick layer (E* = 50 eV) and of a h >~ 20 A thick layer (E* = 4 eV).
4. Conclusions In conclusion we have discussed the application of the SSXA spectroscopy to surface physics in several materials. The analysis of the near-edge structures contain a lot of information on the local structure which is complementary to other spectroscopies. SEXAFS, for example, gives the interatomic distance and the coordination number SSXA gives the symmetry around the central atom and its ionization state, related to the ionicity of the bond. Moreover information on the surface electronic structure can be obtained from SSXA spectroscopy. An upper limit of about 0.3 eV for the difference of the electron-hole interaction between core and valence excitons and bulk and surface excitons in A1203 and SiO2 has been founa. Some of the material incorporated in this work was developed with the financial support of the National Science Foundation (under Contract No. DMR7727489) in cooperation with the US Department of Energy. Portions of this work were carried out while the author wa~; at SSRL, Stanford University.
References [1] A. Bianconi, R.Z. Bachrach and S.A. Flodstr6m, Solid State Commun. 24 (1977)539; Phys. Rev. B19 (1979) 3879. [2] A. Bianconi and R.Z. Baehrach, Phys. Revo Letters 42 (1979) 104. [31 E.E. Koch, C. Kunz and B. Sonntag, Phys. Rept. 29C (1977) 155; F.C. Brown, Solid. State Phys. 29 (1974) 1. [41 J.L. Dehmer, J. Chem. Phys, 56 (1972) 4496.
50
A. Bianconi / Core excitons and inner well resonances
151 T. Aberg and J.L. Dehmer, J. Phys. C6 (1973) 1450. 161 F.C. Brown, R.Z. Bachrach and A. Bianconi, Chem. Phys. Letters 54 (1978) 425. 171 A. Bianconi and R.S. Bauer, to be published; R.S. Bauer, J.C. McMenamin, R.Z. Bachrach, A. Bianconi, L. Johansson and H. Petersen, in: Proc. 14th Conf. on the Physics of Semiconductors, Ed. B.L. Wilson, Inst. Phys. Conf. Ser. 43 (1978) 797. [81 S.T. Pantelides, Ed., The Physics of SiO2 and its Interfaces, (Pergamon, 1978): See: R.S. Bauer, J.C. ~,icMenamin and H. Petersen and A. Bianconi, p. 401. [91 F. Bassa~, G. Margaritondo and G. Tinivella, in: Proc. 14th Conf. on the Physics of Semiconductors, Ed. B.L. Wilson (Plessey, 1978). tl01 M. Altarell, G. Bachelet and R. Del Sole, to be published. [111 J.C. McMenamin and R.S. Bauer, J. Vacuum Sci. Technol. 15 (1978) 1262 1121 V. Rehcer, W. Gudat, R.G. Hayes and C. Kunz, in: Proc. 7th Intern. Vacut, m Congr. and 3rd Intern. Conf. on Solid Surfaces, Eds. R. Dobrozemsky et al. (Berger, Vienna, 1977) p. 453. 1131 V.E. Heu-~,ch, G. Dresselhaus and lt.J. Zeiger, Phys. Rev. Letters 36 (1976) 158. !141 D.E. R~m~ker, J.S. Murday, N.H. Turner, G. Moore, M.G. Lagally and J. Houston, ref.
181, p. 99. [151 I.A. Britov and Y_u.N. Romashenko, Soviet Phys.-Solid State 20 (1978) 384. [161 A. Balzarotti, A. Bianconi, E. Burattini, M. Grandolfo, R. Habel and M. Piacentini, Phys. Status Solidi Co) 63 (1974) 77. [171 A. Balzarotti and A. Bianconi, Phys. Status Solidi (b) 76 (1976) 689 and references cited therein. 1181 J.A. Tossel, J. Phys. Chem. Solids 36 (1975) 1273;J. Am. Chem. Soc. 97 (1975)4840. [191 O.A. Ershov and A.P. Lukirskii, Soviet Phys.-Solid State 8 (1967) 1699; F.C. Brown, R.Z. Bachrach and M. Skibowski Phys. Rev. B15 (1977) 4781. I2Ol S.T. Pantelides, ref. [81, p. 339. 1211 r.H. Di Stefano, J. Vacuum Sci. Technol. 13 (1976) 856; T.H. Di Stefano, ref. [81, p. 362. [221 S.l. Raider and R. Flitsh, ref. [8], p. 384; T. Hattori and T. Nishina, ref. [8], p. 379; G. HoUinger and Tran Minh Duc, in: Proc. 7th Conf. on Amorphous and Liquid Semiconductors, Ed. W.E. Spear (1977) p. 87; G. HollJnger, Y. Yugnet, P. Pertosa and Tran Mirth Duc, Chem. Phys. Letters 36 (1975) 441. I231 N.F. Mott, ref. [81, p. 1; J.R. Chelikowsky and M. Schliiter, Phys. Rev.B15 (1977) 4020; S.T. Pantelides and W.A. Harrison, Phys. Rev. B13 (1976) 2667; S.T. Pantelides and W.A. Harrison, ref. [8], p. 80. [241 K. Hfibner, Phys. Status Solidi (a) 42, (1977) 501; K. Hiabner and A. Lehmann, Phys. Status Solidi (a) 46 (1978) 451. [251 R.Z. Bachrach, D.J. Chadi and A. Bianconi, Solid State Commun. 28 (1978) 931. [261 M. Schltiter and M.L. Cohen, Phys. Rev. B17 (1978) 716. I271 R. Del Sole and W. Hanke, Solid State Commun., to be published.