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Photon-induced bound-free transitions of ions at solid surfaces
PHYSICS LETTERS A
Physics LettersA 181 (1993) 413—416 North-Holland
Photon-induced bound-free transitions of ions at solid surfaces A.I. Agafonov and E.A. Manykin Russian Research Center “Kurchatov !nstitute’~123182 Moscow, Russian Federation Received 16 February 1993; revised manuscript received 5 August 1993; acceptedfor publication 2 September 1993 Communicatedby A. Lagendijk
Transitions of ions from the groundbound state at the surface into a continuous spectrum in an electromagnetic field without any electronic excitation are investigated. For single-photon absorption by surface ions the expression for the transition cross section is obtained. A new mechanism of laser-induced desorption is discussed.
I. Introduction Laser-induced desorption (LID) of surface atoms is one of the elementary processes of laser—solid interaction. It is established that photons can, by a quantum process, cause the ejection of atomic partides from solid surfaces. The understanding of the basic mechanisms responsible for this phenomenon is of substantial current interest [1]. LID from polar surfaces of semiconductors and insulators such as GaP [2], CdSe [3], CdS [4], GaAs [5], InP [6], A1203 [7,8], silver and alkali halides [9] has been investigated. Photon energies were both above and below the band gaps. It has been shown that the major part of the species ejectedfrom the surface consists of atomic and molecular neutrals. As a rule, LID yields of charged species are very small as compared with neutrals. Usually the desorption yield is linearly proportional to the photon flux over many orders of magnitude when the power density in the beam is such that thermal effects are negligible [7,9]. Also a superlinear dependence of the yield from the laser pulse fluence was observed [2—4,6].In the latter case, there is an apparent threshold laser fluence above which the ejection of particles becomes detectable for the experimental setups used [10]. The energy spectrum of the ejected atoms has been measured in refs. [2—5,7].It has been shown that particles may have both a relatively low kinetic energy (~-.~0.1 eV) and a high energy (>1 eV). MeaElsevier Science Publishers B’!
surements of the wavelength dependence of the desorption have been reported only for GaP [2]. The absolute desorption yield has not yet been decided in most cases. The mechanism of LID is a topic of further investigations. At present LID is suggested to be due to electronic excitations at the surfaces, either through direct excitations or through energy transfer from the bulk [2,9,10]. Since the bulk excitation cross section for photons of subband gap energies is negligible for pure crystals, electronic transitionsare considered at the surface states [2]. The theory of desorption by subband gap lasers was developed [11] on the presumption [12] that twohole localization can lead to rupture ofa surface bond and, finally, to ejection of an atom from the surface. However, a concrete mechanism correlating the nipture of bonds to the ejection of neutrals was not discussed. In this Letter a theory of interaction betweenbound ions at the surface and incident radiation is presented. This theory is based on the channel of boundfree transitions of the surface ion which are induced by photon absorption by the particle. We consider the transitions from the bound state of the deep potential well formed by the ground electronic state of the particle—surface system, into states of a continuous spectrum. This interaction channel is not necessary for initial electronic excitations in the system because the photoexcitedparticle is moving over the ground electronic state, but it is due to the particle— 413
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PHYSICS LETTERS A
surface bond and the effective charge of the surface atom. These transitions may result in LID of both neutral and charged species. For the single-photon absorption we will obtain the expression for the cross section of the bound-free transition and compare our results with experimental data ofLID ofGa atoms from GaP ( T Ti) surfaces.
25 October 1993
energies ofthe electromagnetic field in the initial Ii> and the final f> states, respectively. Equations (1) —(4) allow to investigate multiphoton absorption processes by bound ions. Here we restrict to the case of the single-photon process. It is suggested that the photon energy 11w> Cb.
3. Cross section of single-photon bound-free transitions
2. The model The Hamiltonian for surface ions interacting with the incident radiation may be presented as follows,
We consider the plane-polarized electromagnetic wave with the polarization vector s lain in the plane (x, z) and the incident angle 0~measured from the
H= Hrad + H,
0~+ H1~1. (1) Here Hrad is the unperturbed energy of the electromagnetic field. The second term, ~ is the unperturbed energy of surface ions,
axis z coincident with the external normal to the surface. Axes x and y are parallel to the surface. From eq. (4) and in the dipole approximation the differential cross section of the transition is given by
H10~= ~
c9a
(2)
,
S
where c~and are the creation annihilation operators for thec2eigenstate I ~.> andand energy e~.These eigenstates include both bound states at the surface and free-particle states of the continuous spectrum. The third term, ~ is the interaction ocerator between the particle and the radiation field, H 1~~ =
—
J
dr
W~A•pyi+
$
dr
+ ~“
where q and areis the the mass ofparthe particle,p = M ihV, the charge impulseand operator of the tide, A is the vector potential operator of the elec—
tromagnetic field and W=1A C
5 I )~>.
The initial state I ~o> corresponds to the ground bound state in the potential well. The final state corresponds to the free-particle state with wave vector g and quantum number m. Thethe transition amplitude B(gm; connected with S matrix, determined by A~)is eqs. (l)—(3) in the interaction picture, as follows, 2itiô(E~ E, )B(gm; 2~) —
=
0>Ii> (4) where E, = b + e~,Ef= Cgm + Cf, ~b is the bound energy of the particle in the I ~o> state, ~gm is the energy of the particle in the 1gm> state, e, and e~are the —
414
~
$
dgg
2(egm+eb—hw).
0>1
(5) Here a is the fine structureconstant, e is the electron charge, Q, is the normalization volume of the 1gm> state. For the calculations of any particle—surfacepotential the Morse potential is usually chosen as a typical
(3)
—
x
q~ hQ1 2l
form for the interaction. It is known [131 that for from the well this potential the wave function of 2z) the ground bound state decays as exp ( —11’ (2MA)” minimum position at z> a —1, where A and a are the two parameters ofthe potential. A bound wave function with the same spatial decay was used in ref. [141 where sticking of atomic particles at the surface was investigated. Here the initial wave function is represented in the form 312 K ~~>= --j-j~exp(—icr),
K=ht(2Meb)lt2.
(6)
From eq. (6), the transition matrix element in eq. (5) is calculated in the neighbourhood of the well minimum with a radius of about (2—3 )ic ‘.A typical value of ~c’ of about 102 A is estimated from eq. (6). In this spatial region one may neglect the parabolic variation of the potential energy in the Schrodinger equation for the 1gm> state. Taking into
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PHYSICS LETTERS A
account the selection rules for dipole transitions, for the final state we obtain [15] 1gm> =G~Qj”2 (g*r Y”2J312(g~r)Yim(O, 9,) (7) 2(eb+E 2, Yim(0, 9,) is the where g5=11’(2M)” spherical function, m=0, ±5)” 1 and Gm =
—
ltx 6”2[m
sin ~ sin 0~
+2”2i(1—m2) cos öcos O~].
(8)
Here cosOg=gz/g and 8(g) is the phase shift which for the free particle is determined by the potential energy near the surface. Using eqs. (6)— (8), for the matrix element in eq. (5) one obtains 2~”~ 2x ~TThX7t1
25 October 1993
The peak in the photon energy dependence of the cross section is predicted by eq. (12). The maxi-
7’2xitaq2 112 mum value of c is am(0 7 0) 217/2 ~ at the photon energy hw=
~b•
(13) Then the kinetic en-
ergy of the free particles is equal to e~=~Eb. Near the photon energy threshold at 11w = Eb the cross section increases as (hw—b)’’2. At higher values 11W>Eb it decreases as (hwY7t2. LID of Ga atoms from the GaP (ITT) surface has been studied in ref. [2]. Photons of energies below the indirect band gap have been used. The detection limit of the experimental setup was evaluated to be ,, 10—s ofa monolayer of Ga atoms per laser pulse. The threshold laser pulse fluence for the Ga detec-
0>=Q~”
(~b + c 12 Gm M”4(2eb +e~)2 5)’
tion depends on the photon energy and is equal to Eth~0.lJ/cm2 at hw=2.14 eV. Fromthese data one may estimate the cross section,
~ 3’2~’4
X[(l—m2)sin0o—2”2mcos0o]
(9)
.
Substitutingeq. (9) into eq. (5) andusingcg=112g2/ 2M, finally, the differential cross section is given by -~
=26a q2 h2e~2(hw—eb)”2 e2 M (hw+eb)4 F(ô, 0g~0~), (10)
where
a= ~0.4x 1022 cm2. According to ref. [16] there are several types of defect sites for Ga atoms at the GaP surface. At hw=2.14 eV the desorption due to single-photon bound-free transitions may occur from the following sites: Ga adatom (Eb~ 1.70 eV), P vacancy (E~n~ 1.46 —~-~-
eV), Ga—P divacancy (Ebn~ 1.32 eV) and P(Ga) antisite (Eb 0.44 eV). We estimate the transition cross section for Ga adatom sites where the Ga~ions lo-
F(ö, O~,0~)= cos 28 cos 20~sin 20o + ~ sin~8S~fl2Ogcos2O 0.
(11)
calize with charge equal toe [11]. From eq. (12) for
1.7 eV, hw=2.14 eV, C=0.2 one ob2. q=e This and estimation is well tains a=0.6x l0_22 cm consistent with the cross section obtained above from the experimental LID data from the GaP (IT I) surEb=
4. Discussion According to eq. (11) the function F determines the angular distribution of the photoexcited partides. This distribution depends on the phase shift 8(g) which is due to scattering of the free particle at the surface. Here we introduce ~= (2x)’.fFdO~ which depends on the potential energy near the surface. From eq. (11) we have 0<~const—1. Further ~ is considered as a constant parameter. Then from eq. (10) one obtains q2
h2e~/2
(hCO.b)112
M
(hw+eb)
a
4 2
.
(12)
face [2]. Note that although the charge of the Ga adatom is equal to e at the surface, the ground electronic state of the Ga adatom—GaP (III) system which determines the potential energy for photoexcited partides, must correspond to the neutral state Ga°+[GaP(ITT)]° at a large distance from the surface. This is concerned with the ionization potential of the Ga atoms which is equalto 6.0 eV whereas the work function from the GaP (III) surface is equal to 3.2 eV [17]. Thus, finally, neutral species are desorbed. 415
Volume 181, number 5
PHYSICS LETTERS A
If the bound energy of the ions in the bulk is less than the photon energy then in an electromagnetic field single-photon bound-free transitions may occur in the crystal lattice. These transitions result in photon-induced generation and diffusion of defect ions in the bulk of semiconductors [18]. Photoexcited particles which diffuse toward the surface, may contribute to LID from the surface.
Acknowledgement The Russian Found of Fundamental Investigations is thanked for founding this work.
References [1] 0. Betz and P. Varga, eds., Desorption induced by electronic transitions (Springer, Berlin, 1990). [2]K. Hattori, Y. Nakai and N. Itoh, Surf. Sci. 227 (1990) Ll 15.
416
25 October 1993
[3] N. Nakayma, Surf. Sci. 133 (1983) 101. [4] A. Namilci, K. Watabe, H. Fukano, S. Nishigaki andT. Noda, J. Phys. Soc.T.Japan 54 Y. (1985) 3162. [5] A. Namiki, Kawai, Yasuda and T. Nakamura, Japan j. APPI. Phys. 24 (1985) 270. [6] J.M. Moison and M. Bensoussan, J. Vac. Sci. Technol. 21 (1982) 315. [7] R.W. Dreyfus, RE. Walkup and R. Kelly, Radiat. Eff. 99 (1986) 199. [8] M.A. Schildbach and A.V. Hamza, Phys. Rev. B 45 (1992) 9878. [9] H. Kansaki and T. Mori, Phys. Rev. B 29 (1984) 3573. [10] N. Itoh, Nuci. Instrum. Methods B 27 (1987) 155. [1l]H.Sumi,Surf.Sci.248 (1991) 382. [12] N. Itoh, T. Nakayama and T.A. Tombrello, Phys. Lett. A 108 (1985) 480. [13] L.D. Landau and E.M. Lifshitz, Quantum mechanics (Nauka, Moscow, 1974) p. 96. [14] T.B. Grimley, Chem. Phys. Lett. 177 (1991)129. [15] A.I. Agafonov and T.M. Makhviladze, AppI. Surf. Sci. 46 (1990) 288. [16] C.K. Ong, G.S. Khoo, K. Hattori, Y. Nakai and N. Itoh, Surf. Sci. 259 (1991 L787. [17] J. Derrien, F. Arnaud D’Avitaya and A. Glachant, Surf. Sci. 47(1975)162. [18] Al. Agafonov, Phisica B (1993), lobe published.
Physics LettersA 181 (1993) 413—416 North-Holland
Photon-induced bound-free transitions of ions at solid surfaces A.I. Agafonov and E.A. Manykin Russian Research Center “Kurchatov !nstitute’~123182 Moscow, Russian Federation Received 16 February 1993; revised manuscript received 5 August 1993; acceptedfor publication 2 September 1993 Communicatedby A. Lagendijk
Transitions of ions from the groundbound state at the surface into a continuous spectrum in an electromagnetic field without any electronic excitation are investigated. For single-photon absorption by surface ions the expression for the transition cross section is obtained. A new mechanism of laser-induced desorption is discussed.
I. Introduction Laser-induced desorption (LID) of surface atoms is one of the elementary processes of laser—solid interaction. It is established that photons can, by a quantum process, cause the ejection of atomic partides from solid surfaces. The understanding of the basic mechanisms responsible for this phenomenon is of substantial current interest [1]. LID from polar surfaces of semiconductors and insulators such as GaP [2], CdSe [3], CdS [4], GaAs [5], InP [6], A1203 [7,8], silver and alkali halides [9] has been investigated. Photon energies were both above and below the band gaps. It has been shown that the major part of the species ejectedfrom the surface consists of atomic and molecular neutrals. As a rule, LID yields of charged species are very small as compared with neutrals. Usually the desorption yield is linearly proportional to the photon flux over many orders of magnitude when the power density in the beam is such that thermal effects are negligible [7,9]. Also a superlinear dependence of the yield from the laser pulse fluence was observed [2—4,6].In the latter case, there is an apparent threshold laser fluence above which the ejection of particles becomes detectable for the experimental setups used [10]. The energy spectrum of the ejected atoms has been measured in refs. [2—5,7].It has been shown that particles may have both a relatively low kinetic energy (~-.~0.1 eV) and a high energy (>1 eV). MeaElsevier Science Publishers B’!
surements of the wavelength dependence of the desorption have been reported only for GaP [2]. The absolute desorption yield has not yet been decided in most cases. The mechanism of LID is a topic of further investigations. At present LID is suggested to be due to electronic excitations at the surfaces, either through direct excitations or through energy transfer from the bulk [2,9,10]. Since the bulk excitation cross section for photons of subband gap energies is negligible for pure crystals, electronic transitionsare considered at the surface states [2]. The theory of desorption by subband gap lasers was developed [11] on the presumption [12] that twohole localization can lead to rupture ofa surface bond and, finally, to ejection of an atom from the surface. However, a concrete mechanism correlating the nipture of bonds to the ejection of neutrals was not discussed. In this Letter a theory of interaction betweenbound ions at the surface and incident radiation is presented. This theory is based on the channel of boundfree transitions of the surface ion which are induced by photon absorption by the particle. We consider the transitions from the bound state of the deep potential well formed by the ground electronic state of the particle—surface system, into states of a continuous spectrum. This interaction channel is not necessary for initial electronic excitations in the system because the photoexcitedparticle is moving over the ground electronic state, but it is due to the particle— 413
Volume 181, number 5
PHYSICS LETTERS A
surface bond and the effective charge of the surface atom. These transitions may result in LID of both neutral and charged species. For the single-photon absorption we will obtain the expression for the cross section of the bound-free transition and compare our results with experimental data ofLID ofGa atoms from GaP ( T Ti) surfaces.
25 October 1993
energies ofthe electromagnetic field in the initial Ii> and the final f> states, respectively. Equations (1) —(4) allow to investigate multiphoton absorption processes by bound ions. Here we restrict to the case of the single-photon process. It is suggested that the photon energy 11w> Cb.
3. Cross section of single-photon bound-free transitions
2. The model The Hamiltonian for surface ions interacting with the incident radiation may be presented as follows,
We consider the plane-polarized electromagnetic wave with the polarization vector s lain in the plane (x, z) and the incident angle 0~measured from the
H= Hrad + H,
0~+ H1~1. (1) Here Hrad is the unperturbed energy of the electromagnetic field. The second term, ~ is the unperturbed energy of surface ions,
axis z coincident with the external normal to the surface. Axes x and y are parallel to the surface. From eq. (4) and in the dipole approximation the differential cross section of the transition is given by
H10~= ~
c9a
(2)
,
S
where c~and are the creation annihilation operators for thec2eigenstate I ~.> andand energy e~.These eigenstates include both bound states at the surface and free-particle states of the continuous spectrum. The third term, ~ is the interaction ocerator between the particle and the radiation field, H 1~~ =
—
J
dr
W~A•pyi+
$
dr
+ ~“
where q and areis the the mass ofparthe particle,p = M ihV, the charge impulseand operator of the tide, A is the vector potential operator of the elec—
tromagnetic field and W=1A C
5 I )~>.
The initial state I ~o> corresponds to the ground bound state in the potential well. The final state corresponds to the free-particle state with wave vector g and quantum number m. Thethe transition amplitude B(gm; connected with S matrix, determined by A~)is eqs. (l)—(3) in the interaction picture, as follows, 2itiô(E~ E, )B(gm; 2~) —
=
0>Ii> (4) where E, = b + e~,Ef= Cgm + Cf, ~b is the bound energy of the particle in the I ~o> state, ~gm is the energy of the particle in the 1gm> state, e, and e~are the —
414
~
$
dgg
2(egm+eb—hw).
0>1
(5) Here a is the fine structureconstant, e is the electron charge, Q, is the normalization volume of the 1gm> state. For the calculations of any particle—surfacepotential the Morse potential is usually chosen as a typical
(3)
—
x
q~ hQ1 2l
form for the interaction. It is known [131 that for from the well this potential the wave function of 2z) the ground bound state decays as exp ( —11’ (2MA)” minimum position at z> a —1, where A and a are the two parameters ofthe potential. A bound wave function with the same spatial decay was used in ref. [141 where sticking of atomic particles at the surface was investigated. Here the initial wave function is represented in the form 312 K ~~>= --j-j~exp(—icr),
K=ht(2Meb)lt2.
(6)
From eq. (6), the transition matrix element in eq. (5) is calculated in the neighbourhood of the well minimum with a radius of about (2—3 )ic ‘.A typical value of ~c’ of about 102 A is estimated from eq. (6). In this spatial region one may neglect the parabolic variation of the potential energy in the Schrodinger equation for the 1gm> state. Taking into
Volume 181, number 5
PHYSICS LETTERS A
account the selection rules for dipole transitions, for the final state we obtain [15] 1gm> =G~Qj”2 (g*r Y”2J312(g~r)Yim(O, 9,) (7) 2(eb+E 2, Yim(0, 9,) is the where g5=11’(2M)” spherical function, m=0, ±5)” 1 and Gm =
—
ltx 6”2[m
sin ~ sin 0~
+2”2i(1—m2) cos öcos O~].
(8)
Here cosOg=gz/g and 8(g) is the phase shift which for the free particle is determined by the potential energy near the surface. Using eqs. (6)— (8), for the matrix element in eq. (5) one obtains 2~”~ 2x ~TThX7t1
25 October 1993
The peak in the photon energy dependence of the cross section is predicted by eq. (12). The maxi-
7’2xitaq2 112 mum value of c is am(0 7 0) 217/2 ~ at the photon energy hw=
~b•
(13) Then the kinetic en-
ergy of the free particles is equal to e~=~Eb. Near the photon energy threshold at 11w = Eb the cross section increases as (hw—b)’’2. At higher values 11W>Eb it decreases as (hwY7t2. LID of Ga atoms from the GaP (ITT) surface has been studied in ref. [2]. Photons of energies below the indirect band gap have been used. The detection limit of the experimental setup was evaluated to be ,, 10—s ofa monolayer of Ga atoms per laser pulse. The threshold laser pulse fluence for the Ga detec-
0>=Q~”
(~b + c 12 Gm M”4(2eb +e~)2 5)’
tion depends on the photon energy and is equal to Eth~0.lJ/cm2 at hw=2.14 eV. Fromthese data one may estimate the cross section,
~ 3’2~’4
X[(l—m2)sin0o—2”2mcos0o]
(9)
.
Substitutingeq. (9) into eq. (5) andusingcg=112g2/ 2M, finally, the differential cross section is given by -~
=26a q2 h2e~2(hw—eb)”2 e2 M (hw+eb)4 F(ô, 0g~0~), (10)
where
a= ~0.4x 1022 cm2. According to ref. [16] there are several types of defect sites for Ga atoms at the GaP surface. At hw=2.14 eV the desorption due to single-photon bound-free transitions may occur from the following sites: Ga adatom (Eb~ 1.70 eV), P vacancy (E~n~ 1.46 —~-~-
eV), Ga—P divacancy (Ebn~ 1.32 eV) and P(Ga) antisite (Eb 0.44 eV). We estimate the transition cross section for Ga adatom sites where the Ga~ions lo-
F(ö, O~,0~)= cos 28 cos 20~sin 20o + ~ sin~8S~fl2Ogcos2O 0.
(11)
calize with charge equal toe [11]. From eq. (12) for
1.7 eV, hw=2.14 eV, C=0.2 one ob2. q=e This and estimation is well tains a=0.6x l0_22 cm consistent with the cross section obtained above from the experimental LID data from the GaP (IT I) surEb=
4. Discussion According to eq. (11) the function F determines the angular distribution of the photoexcited partides. This distribution depends on the phase shift 8(g) which is due to scattering of the free particle at the surface. Here we introduce ~= (2x)’.fFdO~ which depends on the potential energy near the surface. From eq. (11) we have 0<~const—1. Further ~ is considered as a constant parameter. Then from eq. (10) one obtains q2
h2e~/2
(hCO.b)112
M
(hw+eb)
a
4 2
.
(12)
face [2]. Note that although the charge of the Ga adatom is equal to e at the surface, the ground electronic state of the Ga adatom—GaP (III) system which determines the potential energy for photoexcited partides, must correspond to the neutral state Ga°+[GaP(ITT)]° at a large distance from the surface. This is concerned with the ionization potential of the Ga atoms which is equalto 6.0 eV whereas the work function from the GaP (III) surface is equal to 3.2 eV [17]. Thus, finally, neutral species are desorbed. 415
Volume 181, number 5
PHYSICS LETTERS A
If the bound energy of the ions in the bulk is less than the photon energy then in an electromagnetic field single-photon bound-free transitions may occur in the crystal lattice. These transitions result in photon-induced generation and diffusion of defect ions in the bulk of semiconductors [18]. Photoexcited particles which diffuse toward the surface, may contribute to LID from the surface.
Acknowledgement The Russian Found of Fundamental Investigations is thanked for founding this work.
References [1] 0. Betz and P. Varga, eds., Desorption induced by electronic transitions (Springer, Berlin, 1990). [2]K. Hattori, Y. Nakai and N. Itoh, Surf. Sci. 227 (1990) Ll 15.
416
25 October 1993
[3] N. Nakayma, Surf. Sci. 133 (1983) 101. [4] A. Namilci, K. Watabe, H. Fukano, S. Nishigaki andT. Noda, J. Phys. Soc.T.Japan 54 Y. (1985) 3162. [5] A. Namiki, Kawai, Yasuda and T. Nakamura, Japan j. APPI. Phys. 24 (1985) 270. [6] J.M. Moison and M. Bensoussan, J. Vac. Sci. Technol. 21 (1982) 315. [7] R.W. Dreyfus, RE. Walkup and R. Kelly, Radiat. Eff. 99 (1986) 199. [8] M.A. Schildbach and A.V. Hamza, Phys. Rev. B 45 (1992) 9878. [9] H. Kansaki and T. Mori, Phys. Rev. B 29 (1984) 3573. [10] N. Itoh, Nuci. Instrum. Methods B 27 (1987) 155. [1l]H.Sumi,Surf.Sci.248 (1991) 382. [12] N. Itoh, T. Nakayama and T.A. Tombrello, Phys. Lett. A 108 (1985) 480. [13] L.D. Landau and E.M. Lifshitz, Quantum mechanics (Nauka, Moscow, 1974) p. 96. [14] T.B. Grimley, Chem. Phys. Lett. 177 (1991)129. [15] A.I. Agafonov and T.M. Makhviladze, AppI. Surf. Sci. 46 (1990) 288. [16] C.K. Ong, G.S. Khoo, K. Hattori, Y. Nakai and N. Itoh, Surf. Sci. 259 (1991 L787. [17] J. Derrien, F. Arnaud D’Avitaya and A. Glachant, Surf. Sci. 47(1975)162. [18] Al. Agafonov, Phisica B (1993), lobe published.