Chemisorption on the SiO2 and silicon surfaces and the influence of infrared laser excitation

143

Surface Science 203 (1988) 143-154 North-Holland, Amsterdam

CHEMISORF’TION ON THE SiO, AND SILICON SURFACES AND THE INFLUENCE OF INFRARED LASER EXCITATION Arndt JENICHEN

and Hartwig JOHANSEN

Central Institute of Isotope and Radration Research, Academy of Sciences of the GDR, Permoserstrasse 1.5, Leipzig 7050, German Dem. Rep.

Received

6 July 1987; accepted

for publication

20 April

1988

Binding energies and vibrational frequencies of adsorbate-substrate clusters modelling chemisorption of F, CF,, and CF, on SiO, and silicon surfaces have been calculated using quantum chemical MNDO method. The calculated data are discussed with respect to mechanism of infrared laser-induced etching and with respect to the choice of the etch molecules and the laser frequencies for selective etching of SiO, and Si.

the the the gas

1. Introduction The transfer of pattern to the surface, known as etching, is an important step in the generation of integrated circuits. In. the past few years many studies have dealt with dry etching processes and their elementary mechanisms [l-8]. Reactive etching consists in the controlled removal of surface atoms from the surface under the influence of reactive species and, possibly, by the supply of energy. The essential steps are the formation of reactive species starting from proper etch gas molecules, the chemisorption of reactive species, surface reactions, and the desorption of surface complexes. A surface complex consists of a surface atoms and one or more reactive species or parts of them. If we also admit that these complexes are formed and remain, for some time, below the surface the formation of a thick surface reaction multilayer found on Si e.g. by McFeely [42] is possibly. For the non-spontaneous etching the supply of energy can cause the generation of the reactive species and the formation and desorption of surface complexes. The supply of energy by laser radiation in the laser-induced or enhanced etching shows some advantages in comparison with plasma etching, e.g. low radiation damages and the formation of desired reactive species. For the effective utilization of this method the knowledge of proper reactive species and laser frequencies is desirable. The object of our investigations is the 0039-6028/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

144

A. Jemchen,

H. Johansen

/ Chemisorption

on SiO, and sdicon

selective etching of SiO, and Si by utilizing the influence of etch gas molecules and infrared radiation of the pulsed CO, laser tunable between - 900 and 1100 cm-‘. Several experimental studies have dealt with this problem. Steinfeld and coworkers [9,10] used CF,Br and a frequency of 1083.5 cm- ’ for the etching process of SiO,. Chuang studied the etching of silicon by SF, [ll] and XeF, 1121 in dependence on the laser freqrlency in the 920.~-980 cm-~’ region. Recently Holland et al. [13] have investigated the etching of SiO, by means of OCF, and a laser frequency of 988.5 cm ‘. In all these cases SiF, has been formed. Several quantum chemical investigations with respect to the attack of reactive species on the silicon surface are known. Fricke et al. [14] performed calculations related to the reactive etching of silicon by atomic fluorine. See1 and Bagus [15] considered the interaction of atomic fluorine and chlorine with a Si(ll1) surface. The studies of Barone et al. [16-201 must be mentioned also. In this study we consider the attack of the reactive species F, CF,, and CF, on SiO, and Si surfaces. Geometries, binding energies, and vibrational frequencies of adsorbate-substrate clusters are calculated using the quantum chemical MNDO method. For the discussion of the data with regard to the reaction mechanism at the surface, we assume that the bond with the lowest binding energy is preferentially broken (weakest bond) and that the infraredlaser excitation is most effective if the surface is irradiated with a frequency some cm-’ lower than that of the fundamental vibrational frequency [21]. The first assumption is fulfilled by reason of the fast vibrational energy redistribution. The last is attributed to the anharmonicity of the vibrational modes. The results allow us to make conclusions with respect to the elementary mechanism of the etching process, the reactive species, the laser frequency, and the selectivity.

2. Clusters For the type of mechanistical investigations presented in this paper, only the strong bonds are considered because the etch products generally are molecules possessing the strongest bonds which can be formed (e.g. SiF,, OCF,, CO). During the formation of surface complexes, especially by supply of energy, the weaker bonds are predominantly broken and stronger bonds resist. For our mechanistical studies we assume that those species causing the weakest interactions do not selectively or not all influence the strong bonds. Therefore, we only include on-top chemisorption sites and exclude the other sites considered by See1 and Bagus [ZS] as well as Barone et al. [18].

A. Jenichen,

H. Johansen

/

”

“\

Si -0

Chemisorption

on SiO,

/I)

-Si’

* 5 H

\‘H H

lnal

X

1

H&

0 /

”

7

H ‘,/-H

‘Si’

I

H

Si

I

”

lSi

‘I “H

/”

IlKbl

F H

‘0

1

H

(Illal

F\ /F ’

W/-H

H

i-l

“\si/o

’

,&”

I

I

H

I”

H

Si

’

H

*

(161

X H

” H -\Si

145

and silicon

\

H”

\.SiiF / \/

Si

H Si ;H

H

L’H

F

FF \

\

I Si ‘I ”

/y P

Si 0

I

H

H

IYl

X=0”,

’ H

’

F, CF3,

Y = F, CF3,

/I\

I

I/ Si

I

0

lmbl

FFF

Ima)

I/ Si I 0

CF2

CF_,

0

1 H

Fig. 1. Selectedclustersfor MNDOcalculations. Chemisorption structures with unsaturated surface atoms are also excluded because we suppose that sufficient reactive species are available so as to saturate all dangling bonds immediately. Fig. 1 shows the clusters treated by the calculations. The dangling bonds of the cluster atoms extended into the substrate are saturated by hydrogen atoms. That ensures that every atom in the cluster has its proper atomic coordination. The hydrogen atoms force the cluster atoms to develop the bulk sp3 hybridization.

A. Jemchen, H. Johunsen / Chemisorptlon on .%Oz and srlicon

146

3. Method The quantum chemical calculations are carried out with the MNDO method [22] using the original parameters [22,23]. This method has been successfully applied in treatments of chemisorption problems [16-201. Contrary to other studies all the internal coordinates are optimized. We use the Davidson-Fletcher-Powell method [24-261. Experimental bond lengths and ideal (tetrahedral) angles are used for the starting geometric parameters [27]. The binding energy D is defined as the difference between the sum of the total energies, E,,,(F,) and E,,,(F,), of both isolated fragments of the cluster and the total energy, E,,,(C), of the adsorbate-substrate cluster:

D = 4, (5 >+ 4,, (Fz>- Em,CC>.

(1)

In the following we use the term “bond” to mark the position where the cluster is decomposed into fragments. The vibrational frequencies result from the matrix of mass-weighted Cartesian force constants [28]. The values obtained in this way deviate from the experimental frequencies by reason of neglect of anharmonicity and by reason of the approximate character of the quantum chemical method. Table 1 shows the quotients of experimental and calculated frequencies for SiF, (n < 4) stretching vibrational modes of molecules and surface structures. In general the quotients with respect to the same vibrational type agree well. This fact is used for the correction of the calculated stretching frequencies. The correction factors Q, for the vibrational types listed in table 2 are the averages of such quotients for reference molecules i: Q, = +

5 a;(obs) I=1

(2)

3; (talc)

Table 3 presents Si-F bond lengths and corrected stretching frequencies of different SiO, and Si clusters modelling the on-top chemisorption of a fluorine atom. In the second line the data calculated with all force constants and in the Table 1 Quotients

of experimental

and calculated

X

X ,SiF SiF stretching

H D Cl OSiH,(SiO, [29]) SiH,(Si 1301)

0.923 0.879 0.927 0.925 0.921

SiF, (n = 1-3)

stretching

X,SiF, SiF, stretching

frequencies XSiF, SiF, stretching

Asymm

Symm

Asymm

Symm

0.940 0.931 0.955

0.873 0.888 0.912 _

0.951 0.949 0.957

0.907 0.908 0.921

0.968

0.871

0.962

0.907

A. Jenichen, H. Johansen Table 2 Correction

factors

Vibrational

type

Q, for stretching

/ Chemisorption

on SO,

frequencies

Q,

Reference

0.856 0.925 0.942 \ 0.891 J

H,SiOSiH,, D,SiOSiD, FSiH, FSiCl 3

as s

Si-0-Si SiF SiF, SiF,

as s

SiF SiFz

0.952 0.912 >

Si-C Si-O(Y)

CF,SiH,, CI,SiOH CF,OO CF,OO CF,OO

CF2

0.479 0.931 0.840 0.772 0.837 0.667 0.735 >

(Si)O-H O-F CF,(Si) CF,(Si)

0.900 0.840 0.727 0.852 >

Cl,SiOH HOF

as

as s as s

as s

O-C(F,,) CF, CF, CF,

147

and silicon

F,SiH,, F,SiH,

molecules

F,SiD,, F,SiD,

F*SiCl z F,SiCl

CF,SiD,

HCF, , DCF, , CICF,

CF,SiH,,

CF3SiD,

third line the frequencies calculated without the dangling bond hydrogen force constants are shown. A comparison of these values with the experimental frequencies shows that a good agreement results if the clusters FSiO,Si,H, and FSiSi,H, are used and the hydrogen force constants are neglected. Therefore, we use the clusters II, III, and IV (see fig. 1) for the chemisorption at Si surface atoms and neglect the hydrogen force constants in the following cluster calculations.

Table 3 Si-F distances

R (A) and stretching

Calcularion R(Si-F) i(Si-F) (with H force constants) 7(Si-F) (without H force

Experiment P(Si-F) a) SiO, 1291. b, Si [30].

frequencies

t (cm-‘)

FSiO,H,

FSiO,Si,H,

1.633 975

1.637

963

944

945 =)

for various

clusters

FSiH,

FSiSi,H,

1.644 963

1.640 935

938

924

920 b,

148

A. Jenichen, H. Johansen / Chemisorption on SO,

and silicon

4. Results and discussion 4.1. Initial reactions

The clean SiO, surface is mainly based on siloxane bridges and hydroxyl groups, whereas the pure silicon surface consists of Si-Si bonds (between the nearest-neighbour Si atoms) and dangling bonds assumed to be saturated by OH groups. The atomic distances, the binding energies and the vibrational stretching frequencies of corresponding clusters are presented in table 4. Regarding SiO, the weakest bond is that between Si and 0 within the SiOH group. The best possibility for breaking this bond consists in the direct infrared laser excitation of the Si-O(H) stretching vibrational mode. The calculated frequency of 959 cm-’ agrees relatively well with the experimentally determined one being in the range of 965 to 980 cm-’ [31,32]. Djidjoev et al. [33] have found a dehydroxylation by CO, laser excitation with a frequency of 950 cm-‘. On the other hand the energy can be supplied by excitation of the asymmetric Si-0-Si stretching mode. The experimentally found band maximum (bulk) is localized in the range of 1070 to 1085 cm-’ and has a large half width [34,35]. The corrected MNDO frequencies of the assumed clusters are situated between 1096 and 1108 cm-‘. The resultant heating of the surface causes the rupture of the weakest bond (Si-O(H)). The calculated SiOSi stretching frequencies generally are not correct quantitatively because of the restricted cluster size taken into account. The values of the frequencies shall only illustrate the relative influence of the different chemisorbed species on the surface SiOSi frequencies. The comparison of these frequencies shows that the deviations of the values from the frequency of the H,SiOSiH, cluster are smaller than 15 cm-‘.

Table 4 Atomic distances R (A), binding energies D (kcal/mol), initial structures H,SiOSiH, R (Si-O/SipSi) R (Si-O(H)) R (O-H) D (Si-O/Si-Si) D (Si-O(H)) D (O-H) t (as SiOSi) F (Si-O(H)) 5 (OH)

1.642

126 _ 1098 _ _

and stretching frequencies 5 (cm- ‘) for

HOSiO,Si,H, 1.650 1.709 0.932 109 88 122 1108,‘1099/1096 959 3714

HOSiSi,H, 2.312 1.701 0.932 29 92 133 939

3706

A. Jenichen,

H. Johansen

/ Chemisorprion

149

on SiO-, andsilicon

In the case of silicon the Si-Si bond is weaker than the Si-O(H) bond. However, the Si-Si vibration cannot be excited directly to a sufficient degree [35,36]. The supply of energy by the CO, laser is only possible by multiphoton excitation of the Si-O(H) stretching vibration (MNDO: 939 cm-‘) or by heat transfer from other substrate layers, e.g. SiO,, or by excitation of vibrational modes connected with defects or by absorption as a result of free carrier excitation. The last is important at high temperatures [37,383. 4.2. Chemisorption

at surface silicon atoms

The results of the bond breaking described in the last section are threecoordinate surface silicon radicals being saturated with reactive species or, in the case of dissociative chemisorption, with parts of them. Table 5 presents the results for the clusters (Ila and IIb in fig. 1) XSiO,Si,H, and XSiSi,H, (X = F, CF,, and CF,). Concerning the SiO, surface, only the fluorine atom is more strongly bound to the Si surface atom in comparison to the Si-0 bond. On the other hand, CF, and CF, should be preferentially desorbed because the Si-C bond is the weakest one of the corresponding clusters. The energy can be supplied by laser excitation of the Si-F stretching vibration (MNDO: 944 cm-‘, experimental: 945 cm-’ [29]). However, the surface heating by means of the asymmetric Si-0-Si stretching vibration ought to be used because the CF, and CF, adsorbates do not strongly absorb below 1000 cm-‘. These species block up the surface sites and have to be desorbed. On the silicon surface all of the bond breaking processes demand a higher energy than that of a Si-Si bond. By reason of the low infrared absorption of Table S Atomic distances R (A), binding energies D (kcal/mol), the clusters IIa and IIb

R (C-F) R @i-X) R (Si-O/Si-Si) D (C-F) D @i-X) D (Si-O/Si-Si) c (as CF,) c (s CF,) v’ (X-Si:I v’ (as Si-0-a)

1.637 1.647 127 110 944 1106 1106 1101

i; (cm-‘)

XSiSi3H,

XSi0,Si3H, X=F

and stretching frequencies

CF3

C%

1.359 1.934 1.646 83 46 104 1114 1216 398 1105 1090 1085

1.315 1.826 1.652 139 53 99 1155 1221 379 1100 1097 1097

X=F

1.640 2.324 _ 127 27 924

CF, 1.361 1.930 2.301 93 47 42 1104 1208 394

CF, 1.311 1.847 2.297 117 45 26 1131 1155 358 -

for

150 Table 6 Atomic distances the clusters Illa,

R (Si-F) R (Si-O/Si-Si) D (Si-F) D (Si-O/Si-Si) C (as SiF,) a (s SiF,) i; (as Si-0-Si)

A. Jenichen,

H. Johansen

/ Chemisorptron

on SiO, and srlicon

R (A). binding energies IVa, IIIb, and IVb

D (kcal/mol)

and stretching

frequencies

i, (cm-‘)

F,SiO,Si,H,

F,SiOSiH,

F,SiSi,H,

F,SiSiH,

1.633 1.641 124 111 1001 879 1112

1.629 1.634 121 95 1021 855 1113

1.642 2.372 118 13 939 890 _

1.647 2.389 106 43 960 904 _

for

1105

the bulk (see also section 4.1) the excitation is only possible by means of chemisorption structures. Chemisorbed CF, has an asymmetric stretching mode with a fundamental frequency of 1104 cm-’ (MNDO) which can adsorb CO, laser radiation. Since the Si-C bond is only slightly stronger than the Si-Si bond and the energy is being redistributed to several Si-Si bonds by means of the Si-C bond, the CF, ought to be desorbed. Chemisorbed CF, does not cause absorption in the CO, laser frequency range. By reaction with a fluorine atom, chemisorbed CF, is formed and desorbed. Only chemisorbed fluorine atoms are able to form a strong bond to silicon and this bond absorbs at 924 cm-’ (MNDO). Experimentally a band was found at 920 cm-’ [30]. The results of the fragmentation processes are silicon radicals two-fold bound to the nearest-neighbour substrate atoms. After saturation by reactive species the next Si-0 or Si-Si bond should be broken, respectively. Unless SiF, (n < 4) species are previously desorbed, SiF, is formed and desorbed in the last step. Table 6 presents the data for the fluorine chemisorption on doubly and singly oxygen or silicon coordinate surface silicon atoms, respectively. For SiO, there is no essential change in the data in comparison with the chemisorption of a single fluorine atom. Only the frequencies of the asymmetric SiF, and SiF, stretching modes are higher than that of SiF. Since these SiF, (n < 4) frequencies are very different with respect to each other the excitation is not possible with a single laser frequency. Via the siloxane bridge vibrations, surface heating may be initiated. On silicon our calculated Si-Si(F,) binding energies (D( n = 2) < D(n = 1) < D( n = 3)) are in accordance with the product distribution C (C( n = 4) Z+ C(n = 2) = C( n = 1) > C( n = 3)) of the spontaneous reaction of XeF, or atomic fluorine with silicon found by Winters and Houle (391. Vasile and Stevie identified only SiF, and SiF, as gas phase etching products [40]. The high contribution of SiF, to the gas phase species can be attributed to the

A. Jenichen, H. Johansen

/ Chemisorption

on Si0,

and silicon

151

fluorination of the SiF, (n < 4) species in the gas phase, on the surface or below the surface. The different behaviour of the SiF, complexes on Si and SiO, surfaces is also confirmed by the discharge experiments of Matsumi et al. [41]. Their measurements provided that SiF, radicals are desorbed from the surface during the etching of silicon by fluorine atoms. They did not find any SiF, species during the etching of SiO,. Both statements are in agreement with our calculated Si-Si and Si-0 binding energies, respectively. The desorption of SiF, weakly bound to the Si surface can be promoted by excitation of the asymmetric SiF, stretching mode. By MNDO we calculated a frequency of 939 cm-’ for this mode. Chuang has found an enhancement of the etch rate in this frequency region by normal incidence of laser radiation onto the Si surface [11,12]. The other possibility is the formation of SiF, by Si-Si bond rupture and saturation with fluorine atoms. SiF, is relatively strongly bound to the surface. This is in agreement with the observation of McFeely et al. [42]. They found a thick, highly fluorinated reaction multilayer, dominated by trifluorosilyl moieties. The removal of the SiF, groups may be an important bottleneck in the etching process.

4.3. Chemisorption

at surface oxygen atoms

By the breaking of Si-0 bonds, surface oxygen, besides silicon, radicals are formed. The chemisorption on this oxygen is modelled by the smaller cluster YOSi(OH),) (V in fig. 1) because, as test-calculations have shown, the O-Y chemisorption bonds are not influenced and the Si-O(Y) bonds are only slightly influenced by enlargement of the surface clusters.

Table 7 Atomic distances R (A), binding energies D (kcal/mol), the clusters V (YOSiO,H,) Y=F R (C-F) R (O-Y) R (Si-0) D (C-F) D (O-Y) D @i-O) ? (as CF,) ij (s CF,) J (O-Y) Z (Si-0)

1.269 1.753 _ 46 84 _ 1448 798

and stretching frequencies

Y=CF,

Y=CF,

1.352 1.352 1.687 103 93 102 1244/1219 1049 1412 810

1.310 1.273 1.776 79 81 32 1768 960 1502 798

i (cm-‘)

for

152

A. Jenichen, H. J ohansen / Chemisorp lion on SO,

and silicon

The data of these clusters, given in table 7, show the following: The weakest chemisorption bond is formed by fluorine, The energy supply for the desorption of fluorine is only possible by means of the siloxane bridges. CF, is also preferentially desorbed. Besides the siloxane bridge vibrations the symmetric CF, stretching mode can be excited (MNDO: 1049 cm-‘). The only possibility to remove oxygen consists in the desorption of OCF, because the Si-0 bond is strongly weakened by chemisorption of CF,. For infrared absorption the symmetric CF, stretching mode (MNDO: 960 cm-‘) and the surface heating by the siloxane bridges is suitable. Experimentally COF, was found in the gas phase during the etching of SiO, [43]. However, the SiO, surface as origin of the oxygen atoms could not be traced unambiguously.

5. Summary With the quantum chemical MNDO method we have calculated binding energies and vibrational frequencies of clusters modelling the chemisorption of F, CFJ, and CF, on SiO, and silicon surface radicals. As far as experimental data are available the agreement between corrected MNDO stretching frequencies and observed values is good. Bond energies and vibrational frequencies calculated by a semi-empirical method cannot be expected to have experimental accuracy but should rather serve as a guide for the finding of the elementary mechanism of an etching process. The data are discussed with regard to the mechanisms of infrared laser-induced etching and with regard to the choice of reactive species and the laser frequency. On the assumption that the weakest bond is preferentially broken and the infrared laser excitation is most effective if the surface is irradiated with a laser frequency some cm-’ lower than the fundamental frequency the following mechanism results: For the SiO, etching in an initial step the Si-0 bonds of the surface hydroxyl groups are broken. The formed surface radicals are saturated with fluorine atoms. By successive breaking of the Si-0 bonds and simultaneous saturation of the arising radicals, SiF, molecules are produced and desorbed. The formed surface oxygen radicals are removed by CF,. For the infrared laser-induced etching of SiO, a laser frequency of about 1080 cm-’ should be used. With this frequency CF,, Br, CF,, and F are generated from CF,Br by multiphoton dissociation [21,44]. The asymmetric siloxane bridge modes are excited. The resulting surface heating promotes all the discussed processes. Since the silicon substrates and the fluorine adsorbates do not strongly absorb in the region of this frequency a selective etching of SiO, ought to be possible if the heat transfer from absorbing SiO, to the Si substrate is not too high. The formed bromine atoms are excluded from the considerations because

A. Jenichen, H. Johansen

/ Chemisorption

on SO,

and sdicon

153

the Si-Br and the 0-Br bonds are so weak that Br desorbs preferentially. In the case of silicon the binding energy between the Si atoms is lower than the binding energies of all the other bonds. The lowest desorption energy is obtained for SiF, (MNDO: 22 kcal/mol). For the laser-enhanced etching of silicon a frequency in the 920-940 cm-’ range should be used. This frequency excites the Si-0 stretching mode of the SiOH group in the initial step and the SiF, SiF, and partially SiF, stretching modes. As an etch gas SF, (experimental fundamental frequency: 948 cm-‘) [II] or XeF, [12] can be used. The results are in good agreement with the observed findings and demand further experimental and theoretical investigations.

References [l] [2] [3] [4] [5] (61 [7] [S] [9] [lo] Ill] [12] (131 [14] [lS] [16] [17] [18] [19] [20] [21] [22] (231 [24] [25) [26] [27] [28] [29]

J.W. Cobum and H.F. Winters, J. Vacuum Sci. Technol. 16 (1979) 391. T.J. Chuang, IBM J. Res. Develop. 26 (1982) 145. T.J. Chuang, J. Vacuum Sci. Technol. 21 (1982) 798. T.J. Chuang, Surface Sci. Rept. 3 (1983) 1. G. Turban, Pure Appl. Chem. 56 (1984) 215. A.J. van Roosmalen, Vacuum 34 (1984) 429. F.A. Home, Proc. SPIE 459 (1984) 110. F.A. Home, Appl. Phys. A 41 (1986) 315. J.I. Steinfeld, T.G. Anderson, C. Reiser, D.R. Denison, L.D. Hartsough and J.R. Hollahan, J. Electrochem. Sot. 127 (1980) 514. D. Harradine, F.R. McFeely, B. Roop, J.I. Steinfeld, D. Denison, L. Hartsough and J.R. Hollahan, Proc. SPIE 270 (1981) 52. T.J. Chuang, J. Chem. Phys. 74 (1981) 1453. T.J. Chuang, J. Chem. Phys. 74 (1981) 1461. R.J. Holland and S.L. Bernasek, J. Appl. Phys. 60 (1986) 2553. D.K. Fricke, H. Miiller and C. Opitz, Chem. Phys. Letters 94 (1983) 421. M. See1 and P.S. Bagus, Phys. Rev. B 28 (1983) 2023. G. Abbate, V. Barone, F. Lelj, E. Iaconis and N. Russo, Surface Sci. 152/153 (1985) 690. V. Barone, F. Lelj, N. Russo and M. Toscano, Surface Sci. 162 (1985) 230. V. Barone, F. Lelj, N. Russo and M. Toscano, Solid State Commun. 59 (1986) 433. V. Barone, F. Lelj, N. Russo, M. Toscano, F. Illas and J. Rubio, Phys. Rev. B 34 (1986) 7203. N. Russo, M. Toscano, V. Barone and F. LeIj, Surface Sci. 180 (1987) 599. A.S. Sudbo, P.A. Schulz, E.R. Grant, Y.R. Shen and Y.T. Lee, J. Chem. Phys. 68 (1978) 1306. M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899. M.J.S. Dewar, M.L. McKee and H.S. Rzepa, J. Am. Chem. Sot. 100 (1978) 3607. R. Fletcher and M.J.D. Powell, Comput. J. 6 (1963) 163. R. Fletcher, Comput. J. 8 (1965) 33. W.C. Davidson, Comput. J. 10 (1968) 406. L.E<. Sutton, Tables of Interatomic Distances and Configuration in Molecules and Ions (Chem. Sot., London, 1958). M.J.S. Dewar and C.P. Ford, J. Am. Chem. Sot. 99 (1977) 1685. P. Dumas, J. Corset, W. Carvalho, Y. Levy and Y. Neuman, J. Non-Cryst. Solids 47 (1982) 239.

154

A. Jenichen,

H. Johansen

/ Chemisorptwm

on SO,

and sdicon

[30] K. Yamamoto, T. Nakanishi, H. Kasahara and K. Abe, J. Non-Cryst. Solids 59/60 (1983) 213. [31] M. Huffman and P. McMillan, J. Non-Cryst. Solids 76 (1985) 369. [32] J.M. Krol and E.M. Rabinovich, J. Non-Cryst. Solids 82 (1986) 143. [33] MS. Djidjoev, R.V. Khokhlov, A.V. Kiselev, V.I. Lygin, V.A. Namiot, AI. Osipov, V.I. Panchenko and B.I. Provoforov, in: Tunable Lasers and Applications, Eds. A. Mooradian, T. Jaeger and P. Stokseth (Springer, Berlin. 1976) p. 100. [34] J. Etchepare, M. Merian and L. Smetankine, J. Chem. Phys. 60 (1974) 1873. [35] I.W. Boyd and J.I.B. Wilson, J. Appl. Phys. 53 (1982) 4166. [36] J. Humlicek and K. Vojtechovsky, Phys. Status Solidi (a) 92 (1985) 249. [37] M. Miyao, K. Ohyu and T. Tokuyama, Appl. Phys. Letters 35 (1979) 227. [38] J.R. Meyer, F.J. Bartoli and M.R. Kruer, Phys. Rev. B 21 (1980) 1559. [39] H.F. Winters and F.A. Home, J. Appl. Phys. 54 (1983) 1218. [40] M.J. Vasile and F.A. Stevie, J. Appl. Phys. 53 (1982) 3799. [41] Y. Matsumi, S. Toyoda, T. Hayashi and M. Miyamura, J. Appl. Phys. 60 (1986) 4102. [42) F.R. McFeely, J.F. Morar and F.J. Himpsel, Surface Sci. 165 (1986) 277. [43] N. Selamoglu, M.J. Rossi and D.M. Golden, J. Chem. Phys. 84 (1986) 2400. [44] E. Wlirzberg. L.J. Kovalenko and P.L. Houston, Chem. Phys. 35 (1978) 317.