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On the absence of oxygen spectral lines in sputtering
Surface Science 109 (1981) L5455L548 North-Holland Publishing Company
L545
SURFACE SCIENCE LETTERS ON THE ABSENCE OF OXYGEN SPECTRAL LINES IN SPUTTERING
E. VEJE Physics Laboratory II, H.C. f$rsted Institute, Universitetsparken Denmark
Received
19 February
1981; accepted
for publication
5, DK-2100
Copenhagen
0,
6 May 1981
It is well established that atomic oxygen spectral lines are normally not observed in optical studies of sputtering processes. We suggest that this can be explained in terms of local variations in the electron density along the solid surface. The model outlined is in accordance with the finding that the yields of secondary ions, secondary electrons, and secondary photons are normally enhanced by presence of oxygen at the target surface.
It is well established that a fraction of the particles sputtered from a solid exposed to heavy ion bombardment leaves the surface in an excited state. The excitation of atomic species in sputtering can readily be studied by observing photons emitted from the sputtered particles, and a great number of works has been carried out in which intense line radiations have been observed from metal atoms or ions. However, although many measurements have been done under such vacuum conditions, that the target surface was known to be at least partly covered by oxygen, observation of oxygen spectral lines in sputtering has only been reported in very few cases. Thus, in an early work, done under poor vacuum conditions, we bombarded magnesium with 50 keV xenon ions and observed many intense lines from Mg I and Mg II. In addition, we saw a spectral feature which was identified as a transition in MgO [ 11. This indicated directly the presence of oxygen as a target impurity, but despite this, no oxygen spectral lines were observed. Similarly, no radiation from oxygen was observed in a work in which aluminium was bombarded with 40 keV argon ions, and oxygen was admitted deliberately to the target chamber, to study changes of aluminium spectral line intensities caused by the presence of oxygen [2]. Also, Tsong and Tsuji [3], Thomas and de Kluizenaar [4], and Kerkdijk and Kelly [S] have studied photon intensities from a number of metals under heavy ion bombardments, as functions of the oxygen pressure in the target chamber, and no oxygen lines were reported. When dealing with excitation of atomic oxygen, it must first of all be remembered that the spectrum of atomic oxygen has only very few lines in that wavelength interval which is most popular to study in sputtering experiments, namely 200-500 nm [6]. However, there are in atomic oxygen some levels with excitation 0039-6028/8
l/0000-0000/$02.50
0 198 1 North-Holland
energies of ~ppr~x~m~tel~ 12 eV which decay by emitting lines in this wavelength interval. Nonetheless, such oxygen lines have not been observed in sputtering, whereas excitation of levels with 12 eV excitation energy or more in Mg’ has been observed with certainty in a work with magnesium 171. Also, in our old work ]I] we observed fairly strong excitation of hydrogen to levels with approximately 13 eV excitation energy. Therefore, it. seems fair to say that the absence of oxygen lines in sputtering cannot be explained solely by arguing that the relevant excited levels of neutral oxygen are high-lying, and consequently, their excitation is improbable. Furtllermore, the s~rigly~harged oxygen ion (0 II> has an optical spectrum which is very rich in lines in the above-~l~ent~ou~d wavelength region [t;]. Ionic spectral iines are often observed from sputtered metals [I ,2>7]. Therefore, the general absence of Q fl lines is worth noting, e.g. in the above-rnen~~oned experiments where oxygen was known to be present at the target surface [l--5]. In a recent experiment in which B20a or elemental boron in the presence of oxygen were used as targets, several 0 If Iines were however observed in the wavelength region 200-500 nm [S ] _ This observation is of great ~rnpor~nce~ because it demonstrates that excitation of sputtered oxygen (or, in fact a combination of ionization and excitation, since 0 If lines were seen> depends on the properties of the target material, 0 If tines are observed when elemental boron is bombarded in an oxygen atmosphere [S], but not when metals are bombarded under similar circumstances ]l-51. We shah here speculate that the general absence of oxygen spectral Iines in the air region of the s~~ctrum as well as the presence of 0 II lines when boron containing targets are bombarded is associated with localization of the electron density at the target surface. The discussion will follow a model proposed by Prival [9], which we recently have apphed for expIaining atomic excitation in sputtering [7]. In construc~~ii~ a model for the ion sputtering process, Prival 191 started with the Sommerfeld model of a metal, according to which the atoms forming the metal are situated in a lattice immersed in a “gas” of free electrons contributed by the valence electrons of the individual atoms [ 10]. Ions OKneutral atoms ejected during heavy-ion induced sputtering are then hypothesized initiaIly to be ion cores sitting in the SonlnlerfeId electron “gas”. Thus, they are initially positive ions not by virtue of collisional charge transfer processes, but simply because, according to the S~mmerfeld model [IO], almost all atoms in a metal exist in an ionized state. However, as the ionic cores move away from {or pass through the target surface. only it very small fraction of them will survive neutralization caused by efectron pick-up. Therefore, almost aII sputtered atoms will end up as neutral particles. The observed sputtered ion yield consists of just those sputtered ions which have survived neutralization. Atomic excitation in sputtering is easily ~~lcorporated in Privaf’s model for ion emission f9] I When the atomic ion is neutralized during its take-off from the target, the picked-up electron(s) may well be transferred from the valence band to an excited state instead of to the ground state of the sputtered atom f7]. Thus, excitation results from eiectron pick-up into an excited state rather than from some
E. Veje /Absence of oxygen spectral lines in sputtering
Is47
collision-induced excitation process starting from the atomic ground state. The model of Prival was proposed for ion sputtering from a pure metal target [9]. Now, if the target is not a pure metal, but also contains oxygen, the electron density will be higher where the oxygen atoms are situated. In a crude picture, the oxygen atoms are sitting more or less as negative ions in the target. If, during heavy ion bombardment, an oxygen atom receives so much kinetic energy that it is sputtered from the target, it will during such an event, initially be in a negative ion state. Thus, to end up with a neutral, excited oxygen atom will involve not only excitation of an electron, but also removal of an electron (or maybe of more electrons). Such more complex processes are naturally much less probable than the one-electron pick-up into an excited state which has been proposed [7] to explain excitation of metal atoms in sputtering, as repeated briefly above. Lack of excitation for oxygen is thus explained basically from local electron densities in the target, and we note that the same model explains excitation of metal ions as-well as absence of excitation of oxygen atoms sputtered from the same matrix. The observation of 0 II lines when I&O3 or elemental boron in the presence of oxygen are bombarded with heavy ions [8] is also qualitatively understandable in the picture outlined above. Boron is a non-metal. Therefore, when oxygen is bound to a target containing boron, the electron density will not be enhanced where the oxygen atoms are localized. Rather, the valence electrons of the boron and oxygen atoms will form a common electron cloud. Therefore, when an oxygen atom is sputtered from such a matrix, it will be initially in a state somewhat resembling that of a positive ion carrying more than one unit of charge. Such an initial state can readily lead to emission of an excited ion during sputtering, through capture of one electron into an excited state. It is well established experimentally that the emission yields of secondary ions (111, electrons 1121, and photons [2,3] will change strongly if oxygen is present as a surface impurity. Normally, all three secondary emission yields increase rapidly with increasing concentration of oxygen at the surface. Such features can also be understood from the model proposed here. Presence of oxygen at the surface will lead to local variations in the electron density aIong the surface, resulting in an increased electron density along the surface, resulting in an increased electron density at the sites of the oxygen atoms, and consequently to a reduced electron density in the metal ion surroundings. This will naturally reduce the overall probability for electron pick-up for the metal ions during sputtering, and following Prival’s picture [9], the secondary ion emission yield will consequently increase with increasing oxygen concentration at the surface, in accordance with experimental findings [ I 1] . We shall explain the enhancement of secondary photon [2,3] and electron emissions [ 121 caused by the presence of oxygen atoms at the surface in the following way, which partly has been proposed by Williams [13]. When the projectile penetrates the surface, electrons will become excited at the same time as the nuclear motions which lead to sputtering are initiated. For clean metals, the relaxation
L548
E. Veje /Absence of oxygen spectral lines in sputtering
times are much shorter than the total time evolutions of the sputtering processes [ 131. Therefore, for clean metals, the sputtered atoms will interact with a surface which mainly has relaxed. This is however not the case for surfaces containing oxygen. The localization of electrons on the oxygen atoms will lead to a significant increase in the electron relaxation time at such sites. The relaxation times will become comparable to or maybe even longer than the time evolutions of the sputtering events [13]. Sputtered atoms departing close to the sites of surface oxygen atoms will therefore interact with a surface region more highly excited than is the case for atoms sputtered from a clean surface. In other words, a metal ion leaving such a region will interact with electrons with reduced binding energies, due to the excitations caused by the projectile. This will clearly favor electron pick-up to excited states rather than to the ground state, because electron pick-up processes take place preferentially to levels of same binding energy (resonant charge transfer). At the same time, the momentarily reductions in electron binding energies together with the concentration of electrons to such sites will imply an increased secondary electron emission from such regions. It has been customary to explain the enhancements of photon yields caused by presence of oxygen in terms of a blocking of the non-radiative decay channel due to the change of band structure of the solid, see e.g. refs. [2] and [13]. It is however difficult to imagine that the band structure should change smoothly with the concentration of oxygen, as demanded by measurements [2]. Also, there are experimental data which are not in accordance with the band structure model [2]. However, the model outlined above does not involve the band structure, but it is clearly in accordance with the finding that there is a gradual increase of photon intensities with increasing oxygen coverage of the surface [2,3]. The basic hypothesis of the model described here is that sputtered particles are initially emitted from a surface in the same charge state as they exist in the undisturbed medium. Neutralization as well as excitation are the results of electron transfer processes during the sputtering events. We note that such a picture can explain (i) secondary ion emission, cf. the article of Prival [9], (ii) atomic excitation in sputtering [7], (iii) the absence of oxygen spectral lines in sputtering, (iiii) the enhancements of secondary ion, secondary electron, and secondary photon yields caused by presence of oxygen at the target surface. Also, it can be said that the picture outlined here is very similar to the independent-electron model proposed for beam-foil excitations [ 141. According to that model, the valenceshell and the outer shells of the projectile cannot prevail undisturbed as long as the projectile is inside the solid foil. This is simply because the geometrical sizes of the valence shell and the outer shells are comparable to or even larger than the mean distance between two neighbor foil atoms. Therefore, Rydberg-state excitations observed downstream from the foil will be created by processes in which electrons are transferred from the valence band of the foil to the excited projectile state. Such electron pick-up processes take place when the projectile leaves the back of the foil [ 141. There has recently been found experimental evidence for this beam-foil
E. Veje /Absence
of oxygen spectral lines in sputtering
L549
model in studies of relative1 level excitations in 0 VI, F VII [ 1.51, Ar VIII and Kr VIII [16]. In beam-foil processes, the projectile core will normally be multiply charged, so that the electrons, during the pick-up processes at the back of the foil, will feel strong attractive forces towards the projectile core as well as back towards the foil [ 141, and the mutual electron-electron repulsions will be much weaker. Therefore, as a first approach, an independent-electron model can be applied to beam-foil processes [ 141. In sputtering, on the contrary, the mutual electron-electron interactions may well be relatively large, or at least comparable to any electron-ion interaction. Thus, beam-foil and sputtering processes have the common feature that excitation results from transfer of electrons from the solid and into the excited atomic state. But whereas the electrons can be treated as independent particles-in beam-foil interactions, this will most presumably not be the case in sputtering. At the end we want to mention that the picture outlined here should not be taken as the only one possible, but only one out of a multitude. There may well be additional features, see e.g. the review articles by Williams 2131, by Balise and Nourtier [ 111, and by Thomas [ 171. We want to thank Drs. R. Kelly, G.E. Thomas and P. Williams most sincerely for pleasant and helpful correspondence, which has improved the quality of the manuscript considerably.
References K. Jensen and E. Veje, 2. Physik 269 (1974) 293. M. Braun, Phys. Scripta 19 (1979) 33. I.S.T. Tsong and S. Tsuji, Surface Sci. 94 (1980) 269. G.E. Thomas and E.E. de Kluizenaar, Vide 167 (1973) 190. C.B. Kerkdijk and R. Kelly, Surface Sci. 47 (1975) 294. A.R. Striganov and N.S. Sventitskii, Tables of Spectral’ Lines of Neutral and Ionized Atoms (IFI/Plenum, New York, Washington, 1968); S. Bashkin and J.O. Stoner, Jr., Atomic Energy Levels and Grotrian Diagrams, Vol. 1 (North-Ho~and, Amsterdam, 197.5). [ 71 N. Andersen, B. Andresen and E. Veje, to be published. [8] R. Kelly, S. Dzioba, N.H. Tolk and J.C. Tully, Surface Sci. 102 (1981) 486. [ 91 H.G. Prival, Surface Sci. 76 (1978) 443. [ 101 A. Sommerfeld, Naturwissenschaften 41 (1927) 82.5. [ 111 See, e.g., G. Blaise and A. Nourtier, Surface Sci. 90 (1979) 495. [ 121 See, e.g., L.A. Dietz and J.C. Sheffield, J. Appl. Phys. 46 (1975) 4361. [ 131 P. Williams, Surface Sci. 90 (1979) 588. (141 E. Veje, Phys. Rev. Al4 (1976) 2077. [ 151 B. Andresen, B. Denne, J.O. Ekberg, L. Engstrom, S. Huldt, I. Martinson and E. Veje, Phys. Rev. A, to be published. [ 161 S. Bashkin, H. Oona and E. Veje, to be published. [ 171G.E. Thomas, Surface Sci. 90 (1979) 381. (11 [2] [3] [4] [5] [6]
L545
SURFACE SCIENCE LETTERS ON THE ABSENCE OF OXYGEN SPECTRAL LINES IN SPUTTERING
E. VEJE Physics Laboratory II, H.C. f$rsted Institute, Universitetsparken Denmark
Received
19 February
1981; accepted
for publication
5, DK-2100
Copenhagen
0,
6 May 1981
It is well established that atomic oxygen spectral lines are normally not observed in optical studies of sputtering processes. We suggest that this can be explained in terms of local variations in the electron density along the solid surface. The model outlined is in accordance with the finding that the yields of secondary ions, secondary electrons, and secondary photons are normally enhanced by presence of oxygen at the target surface.
It is well established that a fraction of the particles sputtered from a solid exposed to heavy ion bombardment leaves the surface in an excited state. The excitation of atomic species in sputtering can readily be studied by observing photons emitted from the sputtered particles, and a great number of works has been carried out in which intense line radiations have been observed from metal atoms or ions. However, although many measurements have been done under such vacuum conditions, that the target surface was known to be at least partly covered by oxygen, observation of oxygen spectral lines in sputtering has only been reported in very few cases. Thus, in an early work, done under poor vacuum conditions, we bombarded magnesium with 50 keV xenon ions and observed many intense lines from Mg I and Mg II. In addition, we saw a spectral feature which was identified as a transition in MgO [ 11. This indicated directly the presence of oxygen as a target impurity, but despite this, no oxygen spectral lines were observed. Similarly, no radiation from oxygen was observed in a work in which aluminium was bombarded with 40 keV argon ions, and oxygen was admitted deliberately to the target chamber, to study changes of aluminium spectral line intensities caused by the presence of oxygen [2]. Also, Tsong and Tsuji [3], Thomas and de Kluizenaar [4], and Kerkdijk and Kelly [S] have studied photon intensities from a number of metals under heavy ion bombardments, as functions of the oxygen pressure in the target chamber, and no oxygen lines were reported. When dealing with excitation of atomic oxygen, it must first of all be remembered that the spectrum of atomic oxygen has only very few lines in that wavelength interval which is most popular to study in sputtering experiments, namely 200-500 nm [6]. However, there are in atomic oxygen some levels with excitation 0039-6028/8
l/0000-0000/$02.50
0 198 1 North-Holland
energies of ~ppr~x~m~tel~ 12 eV which decay by emitting lines in this wavelength interval. Nonetheless, such oxygen lines have not been observed in sputtering, whereas excitation of levels with 12 eV excitation energy or more in Mg’ has been observed with certainty in a work with magnesium 171. Also, in our old work ]I] we observed fairly strong excitation of hydrogen to levels with approximately 13 eV excitation energy. Therefore, it. seems fair to say that the absence of oxygen lines in sputtering cannot be explained solely by arguing that the relevant excited levels of neutral oxygen are high-lying, and consequently, their excitation is improbable. Furtllermore, the s~rigly~harged oxygen ion (0 II> has an optical spectrum which is very rich in lines in the above-~l~ent~ou~d wavelength region [t;]. Ionic spectral iines are often observed from sputtered metals [I ,2>7]. Therefore, the general absence of Q fl lines is worth noting, e.g. in the above-rnen~~oned experiments where oxygen was known to be present at the target surface [l--5]. In a recent experiment in which B20a or elemental boron in the presence of oxygen were used as targets, several 0 If Iines were however observed in the wavelength region 200-500 nm [S ] _ This observation is of great ~rnpor~nce~ because it demonstrates that excitation of sputtered oxygen (or, in fact a combination of ionization and excitation, since 0 If lines were seen> depends on the properties of the target material, 0 If tines are observed when elemental boron is bombarded in an oxygen atmosphere [S], but not when metals are bombarded under similar circumstances ]l-51. We shah here speculate that the general absence of oxygen spectral Iines in the air region of the s~~ctrum as well as the presence of 0 II lines when boron containing targets are bombarded is associated with localization of the electron density at the target surface. The discussion will follow a model proposed by Prival [9], which we recently have apphed for expIaining atomic excitation in sputtering [7]. In construc~~ii~ a model for the ion sputtering process, Prival 191 started with the Sommerfeld model of a metal, according to which the atoms forming the metal are situated in a lattice immersed in a “gas” of free electrons contributed by the valence electrons of the individual atoms [ 10]. Ions OKneutral atoms ejected during heavy-ion induced sputtering are then hypothesized initiaIly to be ion cores sitting in the SonlnlerfeId electron “gas”. Thus, they are initially positive ions not by virtue of collisional charge transfer processes, but simply because, according to the S~mmerfeld model [IO], almost all atoms in a metal exist in an ionized state. However, as the ionic cores move away from {or pass through the target surface. only it very small fraction of them will survive neutralization caused by efectron pick-up. Therefore, almost aII sputtered atoms will end up as neutral particles. The observed sputtered ion yield consists of just those sputtered ions which have survived neutralization. Atomic excitation in sputtering is easily ~~lcorporated in Privaf’s model for ion emission f9] I When the atomic ion is neutralized during its take-off from the target, the picked-up electron(s) may well be transferred from the valence band to an excited state instead of to the ground state of the sputtered atom f7]. Thus, excitation results from eiectron pick-up into an excited state rather than from some
E. Veje /Absence of oxygen spectral lines in sputtering
Is47
collision-induced excitation process starting from the atomic ground state. The model of Prival was proposed for ion sputtering from a pure metal target [9]. Now, if the target is not a pure metal, but also contains oxygen, the electron density will be higher where the oxygen atoms are situated. In a crude picture, the oxygen atoms are sitting more or less as negative ions in the target. If, during heavy ion bombardment, an oxygen atom receives so much kinetic energy that it is sputtered from the target, it will during such an event, initially be in a negative ion state. Thus, to end up with a neutral, excited oxygen atom will involve not only excitation of an electron, but also removal of an electron (or maybe of more electrons). Such more complex processes are naturally much less probable than the one-electron pick-up into an excited state which has been proposed [7] to explain excitation of metal atoms in sputtering, as repeated briefly above. Lack of excitation for oxygen is thus explained basically from local electron densities in the target, and we note that the same model explains excitation of metal ions as-well as absence of excitation of oxygen atoms sputtered from the same matrix. The observation of 0 II lines when I&O3 or elemental boron in the presence of oxygen are bombarded with heavy ions [8] is also qualitatively understandable in the picture outlined above. Boron is a non-metal. Therefore, when oxygen is bound to a target containing boron, the electron density will not be enhanced where the oxygen atoms are localized. Rather, the valence electrons of the boron and oxygen atoms will form a common electron cloud. Therefore, when an oxygen atom is sputtered from such a matrix, it will be initially in a state somewhat resembling that of a positive ion carrying more than one unit of charge. Such an initial state can readily lead to emission of an excited ion during sputtering, through capture of one electron into an excited state. It is well established experimentally that the emission yields of secondary ions (111, electrons 1121, and photons [2,3] will change strongly if oxygen is present as a surface impurity. Normally, all three secondary emission yields increase rapidly with increasing concentration of oxygen at the surface. Such features can also be understood from the model proposed here. Presence of oxygen at the surface will lead to local variations in the electron density aIong the surface, resulting in an increased electron density along the surface, resulting in an increased electron density at the sites of the oxygen atoms, and consequently to a reduced electron density in the metal ion surroundings. This will naturally reduce the overall probability for electron pick-up for the metal ions during sputtering, and following Prival’s picture [9], the secondary ion emission yield will consequently increase with increasing oxygen concentration at the surface, in accordance with experimental findings [ I 1] . We shall explain the enhancement of secondary photon [2,3] and electron emissions [ 121 caused by the presence of oxygen atoms at the surface in the following way, which partly has been proposed by Williams [13]. When the projectile penetrates the surface, electrons will become excited at the same time as the nuclear motions which lead to sputtering are initiated. For clean metals, the relaxation
L548
E. Veje /Absence of oxygen spectral lines in sputtering
times are much shorter than the total time evolutions of the sputtering processes [ 131. Therefore, for clean metals, the sputtered atoms will interact with a surface which mainly has relaxed. This is however not the case for surfaces containing oxygen. The localization of electrons on the oxygen atoms will lead to a significant increase in the electron relaxation time at such sites. The relaxation times will become comparable to or maybe even longer than the time evolutions of the sputtering events [13]. Sputtered atoms departing close to the sites of surface oxygen atoms will therefore interact with a surface region more highly excited than is the case for atoms sputtered from a clean surface. In other words, a metal ion leaving such a region will interact with electrons with reduced binding energies, due to the excitations caused by the projectile. This will clearly favor electron pick-up to excited states rather than to the ground state, because electron pick-up processes take place preferentially to levels of same binding energy (resonant charge transfer). At the same time, the momentarily reductions in electron binding energies together with the concentration of electrons to such sites will imply an increased secondary electron emission from such regions. It has been customary to explain the enhancements of photon yields caused by presence of oxygen in terms of a blocking of the non-radiative decay channel due to the change of band structure of the solid, see e.g. refs. [2] and [13]. It is however difficult to imagine that the band structure should change smoothly with the concentration of oxygen, as demanded by measurements [2]. Also, there are experimental data which are not in accordance with the band structure model [2]. However, the model outlined above does not involve the band structure, but it is clearly in accordance with the finding that there is a gradual increase of photon intensities with increasing oxygen coverage of the surface [2,3]. The basic hypothesis of the model described here is that sputtered particles are initially emitted from a surface in the same charge state as they exist in the undisturbed medium. Neutralization as well as excitation are the results of electron transfer processes during the sputtering events. We note that such a picture can explain (i) secondary ion emission, cf. the article of Prival [9], (ii) atomic excitation in sputtering [7], (iii) the absence of oxygen spectral lines in sputtering, (iiii) the enhancements of secondary ion, secondary electron, and secondary photon yields caused by presence of oxygen at the target surface. Also, it can be said that the picture outlined here is very similar to the independent-electron model proposed for beam-foil excitations [ 141. According to that model, the valenceshell and the outer shells of the projectile cannot prevail undisturbed as long as the projectile is inside the solid foil. This is simply because the geometrical sizes of the valence shell and the outer shells are comparable to or even larger than the mean distance between two neighbor foil atoms. Therefore, Rydberg-state excitations observed downstream from the foil will be created by processes in which electrons are transferred from the valence band of the foil to the excited projectile state. Such electron pick-up processes take place when the projectile leaves the back of the foil [ 141. There has recently been found experimental evidence for this beam-foil
E. Veje /Absence
of oxygen spectral lines in sputtering
L549
model in studies of relative1 level excitations in 0 VI, F VII [ 1.51, Ar VIII and Kr VIII [16]. In beam-foil processes, the projectile core will normally be multiply charged, so that the electrons, during the pick-up processes at the back of the foil, will feel strong attractive forces towards the projectile core as well as back towards the foil [ 141, and the mutual electron-electron repulsions will be much weaker. Therefore, as a first approach, an independent-electron model can be applied to beam-foil processes [ 141. In sputtering, on the contrary, the mutual electron-electron interactions may well be relatively large, or at least comparable to any electron-ion interaction. Thus, beam-foil and sputtering processes have the common feature that excitation results from transfer of electrons from the solid and into the excited atomic state. But whereas the electrons can be treated as independent particles-in beam-foil interactions, this will most presumably not be the case in sputtering. At the end we want to mention that the picture outlined here should not be taken as the only one possible, but only one out of a multitude. There may well be additional features, see e.g. the review articles by Williams 2131, by Balise and Nourtier [ 111, and by Thomas [ 171. We want to thank Drs. R. Kelly, G.E. Thomas and P. Williams most sincerely for pleasant and helpful correspondence, which has improved the quality of the manuscript considerably.
References K. Jensen and E. Veje, 2. Physik 269 (1974) 293. M. Braun, Phys. Scripta 19 (1979) 33. I.S.T. Tsong and S. Tsuji, Surface Sci. 94 (1980) 269. G.E. Thomas and E.E. de Kluizenaar, Vide 167 (1973) 190. C.B. Kerkdijk and R. Kelly, Surface Sci. 47 (1975) 294. A.R. Striganov and N.S. Sventitskii, Tables of Spectral’ Lines of Neutral and Ionized Atoms (IFI/Plenum, New York, Washington, 1968); S. Bashkin and J.O. Stoner, Jr., Atomic Energy Levels and Grotrian Diagrams, Vol. 1 (North-Ho~and, Amsterdam, 197.5). [ 71 N. Andersen, B. Andresen and E. Veje, to be published. [8] R. Kelly, S. Dzioba, N.H. Tolk and J.C. Tully, Surface Sci. 102 (1981) 486. [ 91 H.G. Prival, Surface Sci. 76 (1978) 443. [ 101 A. Sommerfeld, Naturwissenschaften 41 (1927) 82.5. [ 111 See, e.g., G. Blaise and A. Nourtier, Surface Sci. 90 (1979) 495. [ 121 See, e.g., L.A. Dietz and J.C. Sheffield, J. Appl. Phys. 46 (1975) 4361. [ 131 P. Williams, Surface Sci. 90 (1979) 588. (141 E. Veje, Phys. Rev. Al4 (1976) 2077. [ 151 B. Andresen, B. Denne, J.O. Ekberg, L. Engstrom, S. Huldt, I. Martinson and E. Veje, Phys. Rev. A, to be published. [ 161 S. Bashkin, H. Oona and E. Veje, to be published. [ 171G.E. Thomas, Surface Sci. 90 (1979) 381. (11 [2] [3] [4] [5] [6]