- Email: [email protected]
Energy loss spectra of H+ and He+ scattered off clean and K-covered Pd surfaces
Nuclear Instruments and Methods in Physics Research B 93 (1994) 113-116 North-Holland
NIIM B
6-m Intwmtlonr with Matdais & Atoms
Energy loss spectra of H+ and He+ scattered off clean and K-covered Pd surfaces C. Htifner ‘, A. NBrrnann and W. Heiland Vniversitiit Osnabriick, Fachbereich Physik, Barbarastrasse 7, D-49069 Osnabriick, Germany
Received 21 December 1993 and in revised form 18 February 1994
In the last years we studied the energy loss of low-energy (OS-5 keV) particles incident under grazing incidence on metal surfaces for some simples systems, e.g. He and W on Ni and Pd surfaces [FL Derks et al., Nucl. Instr. and Meth. B44 (19891125, A. Niirmann et al., Phys. Rev. L&t. 64 (19901 1601, A. NIrmann et al., Nucl. Instr. and Meth. B69 (1992) 1581.The detector is placed in specular direction. In this way we only probe the surface region. We want to investigate the effect on energy loss when using systems with different electronic structure. This was performed by depositing layers of potassium onto a metal surface and thereby varying the electron density at the surface. The question is, how can we explain the experimental results, which description of the surface properties does fit the experimental results best?
1. intr~uction Incident particles in our energy range (OS-5 keV) and geometrical configuration (5” grazing incidence and specular detection) only probe the surface region and do not penetrate into the bulk. The energy loss is practically only due to inelastic effects. Therefore we measure the inelastic energy loss Q as the difference between the elastic peak position and the maximum of the energy distribution of the scattered particles. By depositing potassium on the surface we aim at changing the electron density at the Pd(ll0) surface.
The experimental system used has been described previously [1,2]. It is a UHV system with a magnetically analyzed ion beam, an electrostatic energy analyzer for surface chemical analysis and a time-of-flight (TOF) system. The TOF detector [3] is placed at a laboratory scattering angle of 10” and has an angle of acceptance of 1.2” (full width). Cleanliness and surface structure are controlled by ion scattering spectrometry and surface channeling [4]. The preparation of the Pd(ll0) surface was performed by grazing incidence Nef bom-
* Corresponding author. Tel. + 49 541969 0, fax + 49 541969 2670, e-mail ch~~er~dosun~t.bitnet.
bardment with 2 keV followed by annealing by low temperature f < 3OOOC). The K-coverage is achieved by means of an alkali dispenser and monitored by a Kelvin probe [2,5] that allows the measurement of only work function differences At+. In order to be sure that we worked with K-coverages of about one “physical monolayer” [6] in this series of experiments, we measured the time-dependent change of the work function while depositing K on the Pd(llO) surface [2]. The work function Ar$ decreases nearly linearly at “low coverages”, then more slowly, passes through a minimum and finally approaches approximately the work function of the bulk alkali metal f2,7,8]. The experiments were done at A# _ 3 eV, in the area “behind” the A# minimum. In this region the adlayer can be treated as a physical monolayer [8]. Rue to the high vapor pressure of K at room temperature it cannot form second and higher adlayers [7]. Several experiments about alkali metal adsorption on Ni surfaces [6,7] show the tendency to form one dimensionally incoherent, close-packed hexagonal structures at coverages approaching one physical monolayer on surfaces [6,9]. Because of the similarity of Ni and Pd 121we assume to have nearly the same alkali adsorption behaviour. The K-coverage is achieved by means of an alkali dispenser and monitored by a Kelvin probe [Z,S]. In this series of experiments we worked with I(-coverages of about one monolayer. For the experiments discussed here, we only scattered along a random azimuthal direction. ‘“Random” direction means a not low-indexed direction.
Ot68-583X/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSD$ 0168-583)3(94)00158-R
114
C. Hifner et al./Nucl. fnsfr. and Meth. in Phys.Res. B 93 (1994) 113-116 500 0 0
‘-s. 8 6
He+->K:Pd(l 10)
150100
b g
2 .
He+->Pd(l IO)
0
0
0
*
400 t
0
H+->K:Pd(l 10)
;
H+->Pd(llO)
l
He+->Pd(llO)
-
50-
0 O
:
0
i
8 0
I
I
2000
1
ol*:
4000
3. Results The eperimentai results of He scattering (Fig. 1) show that the basic effect of the K-coverage is a tendency to enhance the energy loss of the scattered particles as well as the width of the ene& loss distribution (Fig. 2). For scattered hydrogen particles we have measured the same behaviour. Fig. 3 shows the comparison between energy losses of two types of scattered particles depending on their incident velocity. The energy loss after scattering H+ particles is smaller compared to the He+ case. Density functional (DF) calculations of the stopping power d E/dx of H and He particles [lo] in an electron gas as a function of the free-electron-radius rS show that dE/dx decreases with increasing r, (i.e. decreasing the electron density n,). The free-electronradius is defined by the relation n, = ($rrz)-‘. For Pd
1
I
0 l
He*->K:Pd(l 10) He+->Pd(l 10)
0 *
0 0
0
01
a
e
L
2000
70
where y(s) is the friction coefficient, ds a path segment along the particle’s trajectory and o the velocity of the particle, which we assume to be constant. After transformation of variables we obtain 6uz, Sin ff
0 a
8
we find a free-electron-radius of rS = 3.8 a.u. [ll] and for K a value of r, = 4.7 a.u. We therefore expect n, to decrease on a K-covered surface. DF calculations thus predict less energy Ioss after scattering from K-covered surfaces. In the experiment we see just the contrary. The above comparison is somewhat misleading. The DF predictions apply to bulk interactions, whereas we are comparing them to surface scattering experiments. The most striking difference between bulk and surface electron densities is its spatial dependence which we have not accounted for yet. Neglecting electron capture or loss during the particle-surface interaction we derive the total energy loss Q as follows
Q=-
200 --
..
6
Fig. 3. Peak energy loss for incident H+ and He+ on a Pd surface without (filled symbols) and with potassium coverage (open symbols) as a function of incident velocity.
0
0
100
4
velocity in 1O5 m/s
Fig. 1. Peak energy loss vs. incident energy for incident He+ ions on a Pd surface without (0) and with (0) K-coverage.
300 A.
1
:
2
energy / eV
_;
LJ
He+->K:Pd(llO)
4000
energy I eV Fig. 2. Full width at half maximum of the energy loss distribution vs. incident energy for incident He+ ions on a Pd surface without (0) and with (0) K-coverage.
s--Y(r,). mdrs
R
rs
where R = rf exp(z,,/(3z,)) is the lower limit of integration, a! is the angle of incidence, z0 the distance of closest approach to the surface (obtained from MARLOWE calculations [12]), z1 the decay length of the electron density, and r,” the free-eiectron radius corresponding to the electron density at the last atomic layer, i.e. we assumed a z-dependence (normal to the surface) of the electron density of the form n(z) = n, exp(z/zl). Note that we do not have to introduce a trajectory-length parameter since the integration covers the whole trajectory. In this way we have expressed the energy loss after the surface interaction by an integral over the r,-de-
11s
C. Hiifner et al. /Nucl. Instr. and Meth. in Phys. Res. B 93 (1994) 113-116 Q(r,z)
for 3 keV H -)
Q(r,z)
Pd and Pd/K
for 3 keV He -)
Pd and Pd/K
Fig. 4. Contout plot for Q(rS,zI) for 3 keV H (a) and He (b). The thicker lines mark the experimental energy loss results (on clean Pd at lower, on K-covered Pd at higher energy losses).
pendent stopping power. The two parameters involved are r: and ,rr. As an estimate for y = y(r,) we take the density functional calculation in ref. [lo]. First we investigate the beha~our of Q for incident H with a primary energy of 5 keV, i.e. u - 0.41 a.u. The friction coefficient can be approximated by
This is a fit to the DF data, which were determined
for
r, e 6. In order to anaiyse these results we need a compari-
son to another projectile-target system in which the prujectile follows about the same trajectory as the 5 keV H trajectory. This assures that the particle “sees” the same electron density profile along the trajectory. From BLOC c~culations we dete~ined that the penetration depth for 5 keV He and H is about the same. The friction coefficient of He can be approximated from the DF data to be (rs < 6)
r(rshe -3Ar,
Q(r,z)
exp
for
-&
a.u.
(.)
5 keV H -)
Pd and Pd,‘K
In both cases (He and H) the probabihties
for neutrdization are very high [13,14]. As a first approximation one might assume that the charge state does not change during the interaction. In order to further analyse the experimental results we plot the Q(rp,z,) dependence two dimensionally (Figs. 4 and 5) as a contour plot for the two types of projectiles. The energy loss values are drawn as contour lines. The thicker drawn contours in the lower energy region represent the experimental energy losses Q for scattering off the clean, those in the higher energy region for scattering off K covered Pd(ll0) surfaces. The spread of the thick lines corresponds to the experimental uncertainty. The common area when matching the two plots restricts the range of r, and zr values. Thus we can determine from the overlap the r, and zr values for the clean and the K-covered Pd(l~O~ surface. The resulting numbers are listed in Table 1. The errors are obtained from the experimental errors of the energy loss. When applying this line of argument we see a change in the decay length z1 of the electron density
Q(r,z)
for
5 keV He
-)
Pd and Pd/K
Fig. 5. Contour plot for Q(~,,z,> for 5 keV fI (a) and He tbb).The thicker lines mark the experimental energy loss results (ONclean Pd at lower, on K-covered Pd at higher energy losses).
C. HGfner et al. /Nucl. fnstr. and Meth. in Phys. Rex B 93 (1994) 113-116
116
Table 1 Values of r,” and zt obtained from Figs. 4 and 5
3 keV 3 keV 5 keV
5 keV
r,” (au.)
zt (au.)
Pd K:Pd
3.18kO.22 2.9 *0.25
2.25 f 0.25 3.00 f 0.40
Pd K:Pd
2.95+ 0.25 2.90+ 0.25
2.4 +0.4 3.8 &OS
when depositing potassium onto the PdCllO) surface. The z, value of the K-covered Pd(l101 surface is larger than the one for the clean surface. Therefore the effective interaction region is enhanced in the case of covered surfaces thus leading to higher energy losses. This is in accordance with theoretical calculations by Lang [15] and Feibelman and Hamann [16]. In both papers it is concluded that adsorption of an alkali layer onto a “free electron gas” leads to a decrease of the work function that is associated with an increase in electron charge density at the surface. We would like to point the reader’s attention also to an experimental paper by Brown et al. [17] that dealt with long-range poisoning of D, dissociative chemiso~tion on Ptilll) by coadsorbed K. As a result they propose that the origin of the poisoning is due to the lowering of the work function which causes the Pt 5s electrons to tail off more slowly into the vacuum. We want to mention that this line of reasoning is a very simple way of explaining the experimental results. We neglect electron capture and loss during the particle-surface interaction and assume that the distance of the particle to the clean and K-covered Pd(llO1 surface is the same. The results presented here are preliminary and we are currently looking into how to include electron capture and loss into this description.
4. Summary We presented measurements of energy loss of He and H particles after scattering off clean and K-covered Pd(ll0) surfaces. As a result we find the energy loss to be higher on K-covered surfaces. We use the two sets
of experiments
to estimate electron density parameters at the surface within a very simple, preliminary model. The higher energy losses on the covered surfaces might result from an electron density which extends further into the vacuum as compared to the clean surface. Acknowledgement We thank the Deutsche (DFG) for financial support.
Forschungsgemeinschaft
References [l] B. Willerding, H. Steininger, K.J. Snowdown and W. Heiland, Nucl. Instr. and Meth. B2 (1984) 453. [2] K. Schmidt, Ph.D. Thesis, Universitat Osnabriick, Germany (1993). [3] D. Rathmann, N. Exeler and B. Willerding, J. Phys. E 18 (1985) 17. [4] A. Niehof and W. Heiland, Nucl. Instr. and Meth. B48 (1990) 306. [5] S. Schubert, Ph.D. Thesis, Universitlt Osnabriick, Germany (1989). [6] R.L. Gerlach and T.N. Rhodin, Surf. Sci. 17 (1969132. [7] R.L. Geriach and T.N. Rhodin, Surf. Sci. 19 (1970) 403. [S] R. Bhrszczyszyn, M. BIaszczyszyn and R. Ml;clewski, Surf. Sci. 51 (1975) 396. [9] Proc. 4th. Int. Materials Symp. on the Structure and Chemistry of Solid Surfaces, University of California, Berkeley, June 19-21, 1968, pp. 55-l. [lo] A. Arnau, Ph.D. Thesis, Euskal Herriko Unibertsitatea/ Universidad de1 Pais Vasco, Spain (1989). [ll] J.S. Dugdale, The Electrical Properties of Metals and Alloys (Arnold, 1977). [12] C. Hiifner, A. NZrmann and W. Heiland, Nucl. Instr. and Meth. B72 (1992) 177. [13] A. Nfrmann, K. Schmidt, C. Hiifner, W. Heiland and A. Arnau, Nucl. Instr. and Meth. B78 (1993) 72. [14] A. Narmann, W. Heiland, R. Monreal, F. Flares and P.M. Echenique, Phys. Rev. B44 (1991) 2003. 1151 N.D. Lang, Solid State Physics Series 28 (1973) 225. [16] P.J. Feibelman and D.R. Hamann, Surf. Sci. 149 (198% 48. [17] J.K. Brown, AC. Luntz and P.A. Schultz, J. Chem. Phys. 95 (1991) 3767.
NIIM B
6-m Intwmtlonr with Matdais & Atoms
Energy loss spectra of H+ and He+ scattered off clean and K-covered Pd surfaces C. Htifner ‘, A. NBrrnann and W. Heiland Vniversitiit Osnabriick, Fachbereich Physik, Barbarastrasse 7, D-49069 Osnabriick, Germany
Received 21 December 1993 and in revised form 18 February 1994
In the last years we studied the energy loss of low-energy (OS-5 keV) particles incident under grazing incidence on metal surfaces for some simples systems, e.g. He and W on Ni and Pd surfaces [FL Derks et al., Nucl. Instr. and Meth. B44 (19891125, A. Niirmann et al., Phys. Rev. L&t. 64 (19901 1601, A. NIrmann et al., Nucl. Instr. and Meth. B69 (1992) 1581.The detector is placed in specular direction. In this way we only probe the surface region. We want to investigate the effect on energy loss when using systems with different electronic structure. This was performed by depositing layers of potassium onto a metal surface and thereby varying the electron density at the surface. The question is, how can we explain the experimental results, which description of the surface properties does fit the experimental results best?
1. intr~uction Incident particles in our energy range (OS-5 keV) and geometrical configuration (5” grazing incidence and specular detection) only probe the surface region and do not penetrate into the bulk. The energy loss is practically only due to inelastic effects. Therefore we measure the inelastic energy loss Q as the difference between the elastic peak position and the maximum of the energy distribution of the scattered particles. By depositing potassium on the surface we aim at changing the electron density at the Pd(ll0) surface.
The experimental system used has been described previously [1,2]. It is a UHV system with a magnetically analyzed ion beam, an electrostatic energy analyzer for surface chemical analysis and a time-of-flight (TOF) system. The TOF detector [3] is placed at a laboratory scattering angle of 10” and has an angle of acceptance of 1.2” (full width). Cleanliness and surface structure are controlled by ion scattering spectrometry and surface channeling [4]. The preparation of the Pd(ll0) surface was performed by grazing incidence Nef bom-
* Corresponding author. Tel. + 49 541969 0, fax + 49 541969 2670, e-mail ch~~er~dosun~t.bitnet.
bardment with 2 keV followed by annealing by low temperature f < 3OOOC). The K-coverage is achieved by means of an alkali dispenser and monitored by a Kelvin probe [2,5] that allows the measurement of only work function differences At+. In order to be sure that we worked with K-coverages of about one “physical monolayer” [6] in this series of experiments, we measured the time-dependent change of the work function while depositing K on the Pd(llO) surface [2]. The work function Ar$ decreases nearly linearly at “low coverages”, then more slowly, passes through a minimum and finally approaches approximately the work function of the bulk alkali metal f2,7,8]. The experiments were done at A# _ 3 eV, in the area “behind” the A# minimum. In this region the adlayer can be treated as a physical monolayer [8]. Rue to the high vapor pressure of K at room temperature it cannot form second and higher adlayers [7]. Several experiments about alkali metal adsorption on Ni surfaces [6,7] show the tendency to form one dimensionally incoherent, close-packed hexagonal structures at coverages approaching one physical monolayer on surfaces [6,9]. Because of the similarity of Ni and Pd 121we assume to have nearly the same alkali adsorption behaviour. The K-coverage is achieved by means of an alkali dispenser and monitored by a Kelvin probe [Z,S]. In this series of experiments we worked with I(-coverages of about one monolayer. For the experiments discussed here, we only scattered along a random azimuthal direction. ‘“Random” direction means a not low-indexed direction.
Ot68-583X/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSD$ 0168-583)3(94)00158-R
114
C. Hifner et al./Nucl. fnsfr. and Meth. in Phys.Res. B 93 (1994) 113-116 500 0 0
‘-s. 8 6
He+->K:Pd(l 10)
150100
b g
2 .
He+->Pd(l IO)
0
0
0
*
400 t
0
H+->K:Pd(l 10)
;
H+->Pd(llO)
l
He+->Pd(llO)
-
50-
0 O
:
0
i
8 0
I
I
2000
1
ol*:
4000
3. Results The eperimentai results of He scattering (Fig. 1) show that the basic effect of the K-coverage is a tendency to enhance the energy loss of the scattered particles as well as the width of the ene& loss distribution (Fig. 2). For scattered hydrogen particles we have measured the same behaviour. Fig. 3 shows the comparison between energy losses of two types of scattered particles depending on their incident velocity. The energy loss after scattering H+ particles is smaller compared to the He+ case. Density functional (DF) calculations of the stopping power d E/dx of H and He particles [lo] in an electron gas as a function of the free-electron-radius rS show that dE/dx decreases with increasing r, (i.e. decreasing the electron density n,). The free-electronradius is defined by the relation n, = ($rrz)-‘. For Pd
1
I
0 l
He*->K:Pd(l 10) He+->Pd(l 10)
0 *
0 0
0
01
a
e
L
2000
70
where y(s) is the friction coefficient, ds a path segment along the particle’s trajectory and o the velocity of the particle, which we assume to be constant. After transformation of variables we obtain 6uz, Sin ff
0 a
8
we find a free-electron-radius of rS = 3.8 a.u. [ll] and for K a value of r, = 4.7 a.u. We therefore expect n, to decrease on a K-covered surface. DF calculations thus predict less energy Ioss after scattering from K-covered surfaces. In the experiment we see just the contrary. The above comparison is somewhat misleading. The DF predictions apply to bulk interactions, whereas we are comparing them to surface scattering experiments. The most striking difference between bulk and surface electron densities is its spatial dependence which we have not accounted for yet. Neglecting electron capture or loss during the particle-surface interaction we derive the total energy loss Q as follows
Q=-
200 --
..
6
Fig. 3. Peak energy loss for incident H+ and He+ on a Pd surface without (filled symbols) and with potassium coverage (open symbols) as a function of incident velocity.
0
0
100
4
velocity in 1O5 m/s
Fig. 1. Peak energy loss vs. incident energy for incident He+ ions on a Pd surface without (0) and with (0) K-coverage.
300 A.
1
:
2
energy / eV
_;
LJ
He+->K:Pd(llO)
4000
energy I eV Fig. 2. Full width at half maximum of the energy loss distribution vs. incident energy for incident He+ ions on a Pd surface without (0) and with (0) K-coverage.
s--Y(r,). mdrs
R
rs
where R = rf exp(z,,/(3z,)) is the lower limit of integration, a! is the angle of incidence, z0 the distance of closest approach to the surface (obtained from MARLOWE calculations [12]), z1 the decay length of the electron density, and r,” the free-eiectron radius corresponding to the electron density at the last atomic layer, i.e. we assumed a z-dependence (normal to the surface) of the electron density of the form n(z) = n, exp(z/zl). Note that we do not have to introduce a trajectory-length parameter since the integration covers the whole trajectory. In this way we have expressed the energy loss after the surface interaction by an integral over the r,-de-
11s
C. Hiifner et al. /Nucl. Instr. and Meth. in Phys. Res. B 93 (1994) 113-116 Q(r,z)
for 3 keV H -)
Q(r,z)
Pd and Pd/K
for 3 keV He -)
Pd and Pd/K
Fig. 4. Contout plot for Q(rS,zI) for 3 keV H (a) and He (b). The thicker lines mark the experimental energy loss results (on clean Pd at lower, on K-covered Pd at higher energy losses).
pendent stopping power. The two parameters involved are r: and ,rr. As an estimate for y = y(r,) we take the density functional calculation in ref. [lo]. First we investigate the beha~our of Q for incident H with a primary energy of 5 keV, i.e. u - 0.41 a.u. The friction coefficient can be approximated by
This is a fit to the DF data, which were determined
for
r, e 6. In order to anaiyse these results we need a compari-
son to another projectile-target system in which the prujectile follows about the same trajectory as the 5 keV H trajectory. This assures that the particle “sees” the same electron density profile along the trajectory. From BLOC c~culations we dete~ined that the penetration depth for 5 keV He and H is about the same. The friction coefficient of He can be approximated from the DF data to be (rs < 6)
r(rshe -3Ar,
Q(r,z)
exp
for
-&
a.u.
(.)
5 keV H -)
Pd and Pd,‘K
In both cases (He and H) the probabihties
for neutrdization are very high [13,14]. As a first approximation one might assume that the charge state does not change during the interaction. In order to further analyse the experimental results we plot the Q(rp,z,) dependence two dimensionally (Figs. 4 and 5) as a contour plot for the two types of projectiles. The energy loss values are drawn as contour lines. The thicker drawn contours in the lower energy region represent the experimental energy losses Q for scattering off the clean, those in the higher energy region for scattering off K covered Pd(ll0) surfaces. The spread of the thick lines corresponds to the experimental uncertainty. The common area when matching the two plots restricts the range of r, and zr values. Thus we can determine from the overlap the r, and zr values for the clean and the K-covered Pd(l~O~ surface. The resulting numbers are listed in Table 1. The errors are obtained from the experimental errors of the energy loss. When applying this line of argument we see a change in the decay length z1 of the electron density
Q(r,z)
for
5 keV He
-)
Pd and Pd/K
Fig. 5. Contour plot for Q(~,,z,> for 5 keV fI (a) and He tbb).The thicker lines mark the experimental energy loss results (ONclean Pd at lower, on K-covered Pd at higher energy losses).
C. HGfner et al. /Nucl. fnstr. and Meth. in Phys. Rex B 93 (1994) 113-116
116
Table 1 Values of r,” and zt obtained from Figs. 4 and 5
3 keV 3 keV 5 keV
5 keV
r,” (au.)
zt (au.)
Pd K:Pd
3.18kO.22 2.9 *0.25
2.25 f 0.25 3.00 f 0.40
Pd K:Pd
2.95+ 0.25 2.90+ 0.25
2.4 +0.4 3.8 &OS
when depositing potassium onto the PdCllO) surface. The z, value of the K-covered Pd(l101 surface is larger than the one for the clean surface. Therefore the effective interaction region is enhanced in the case of covered surfaces thus leading to higher energy losses. This is in accordance with theoretical calculations by Lang [15] and Feibelman and Hamann [16]. In both papers it is concluded that adsorption of an alkali layer onto a “free electron gas” leads to a decrease of the work function that is associated with an increase in electron charge density at the surface. We would like to point the reader’s attention also to an experimental paper by Brown et al. [17] that dealt with long-range poisoning of D, dissociative chemiso~tion on Ptilll) by coadsorbed K. As a result they propose that the origin of the poisoning is due to the lowering of the work function which causes the Pt 5s electrons to tail off more slowly into the vacuum. We want to mention that this line of reasoning is a very simple way of explaining the experimental results. We neglect electron capture and loss during the particle-surface interaction and assume that the distance of the particle to the clean and K-covered Pd(llO1 surface is the same. The results presented here are preliminary and we are currently looking into how to include electron capture and loss into this description.
4. Summary We presented measurements of energy loss of He and H particles after scattering off clean and K-covered Pd(ll0) surfaces. As a result we find the energy loss to be higher on K-covered surfaces. We use the two sets
of experiments
to estimate electron density parameters at the surface within a very simple, preliminary model. The higher energy losses on the covered surfaces might result from an electron density which extends further into the vacuum as compared to the clean surface. Acknowledgement We thank the Deutsche (DFG) for financial support.
Forschungsgemeinschaft
References [l] B. Willerding, H. Steininger, K.J. Snowdown and W. Heiland, Nucl. Instr. and Meth. B2 (1984) 453. [2] K. Schmidt, Ph.D. Thesis, Universitat Osnabriick, Germany (1993). [3] D. Rathmann, N. Exeler and B. Willerding, J. Phys. E 18 (1985) 17. [4] A. Niehof and W. Heiland, Nucl. Instr. and Meth. B48 (1990) 306. [5] S. Schubert, Ph.D. Thesis, Universitlt Osnabriick, Germany (1989). [6] R.L. Gerlach and T.N. Rhodin, Surf. Sci. 17 (1969132. [7] R.L. Geriach and T.N. Rhodin, Surf. Sci. 19 (1970) 403. [S] R. Bhrszczyszyn, M. BIaszczyszyn and R. Ml;clewski, Surf. Sci. 51 (1975) 396. [9] Proc. 4th. Int. Materials Symp. on the Structure and Chemistry of Solid Surfaces, University of California, Berkeley, June 19-21, 1968, pp. 55-l. [lo] A. Arnau, Ph.D. Thesis, Euskal Herriko Unibertsitatea/ Universidad de1 Pais Vasco, Spain (1989). [ll] J.S. Dugdale, The Electrical Properties of Metals and Alloys (Arnold, 1977). [12] C. Hiifner, A. NZrmann and W. Heiland, Nucl. Instr. and Meth. B72 (1992) 177. [13] A. Nfrmann, K. Schmidt, C. Hiifner, W. Heiland and A. Arnau, Nucl. Instr. and Meth. B78 (1993) 72. [14] A. Narmann, W. Heiland, R. Monreal, F. Flares and P.M. Echenique, Phys. Rev. B44 (1991) 2003. 1151 N.D. Lang, Solid State Physics Series 28 (1973) 225. [16] P.J. Feibelman and D.R. Hamann, Surf. Sci. 149 (198% 48. [17] J.K. Brown, AC. Luntz and P.A. Schultz, J. Chem. Phys. 95 (1991) 3767.