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Effect of hydrogen adsorption on the charge exchange process in atom-surface collisions
245
Surface Science 182 (1987) 245-256 North-Holland, Amsterdam
EFFECT OF HYDROGEN ADSORPTION ON THE CHARGE EXCHANGE PROCESS IN ATOM-SURFACE COLLISIONS J.P. GAUYACQ Laboratoire des Collisions Atomiques 91405 Orsay, France
et MolPculaires
*, B&imeni
351, UniuersitC Pans-Sud,
and
J.J.C. GEERLINGS FOM Institute, Received
Kruislaan
407, 1098 SJ Amsterdam,
16 July 1986; accepted
for publication
The Netherlands 31 October
1986
~4 model of the effect of the adsorption of hydrogen atoms on a charge exchange process in atorn-surface collisions is presented. The adsorbed layer is represented by a 1D 6 potential. The model is applied to the problem of Hformation in H+-Cs/W surface collisions. In the presence of the adsorbed layer, the charge exchange process becomes a three-body problem: the electrons can jump from the collisional H atom, to the metal and to the adsorbed H atoms. As a net effect, this results in a decrease of the charge exchange interaction. The model results are found to account for the recent observations of van Amersfoort et al. [J. Appl. Phys. 59 (1986) 24111.
1. Introduction Electron capture by ions colliding with a surface has been the subject of numerous works over the past years (see, e.g., the proceedings of the workshop on IISC of 1982 [l]). Among those systems, the proton-cesiated-tungsten system has been investigated in some detail [2]. Experimental investigations of this collisional system revealed very large negative ion yields (up to 67%) while no proton was reflected from the surface [3]. The main characteristic of this particular surface (cesiated tungsten) is its ability to reach low work function values (down to 1.45 eV). When approaching the surface, the H- binding energy (0.75 eV at infinity) increases due to the image charge potential and the affinity level can thus become degenerate with the occupied metal states: the charge exchange process between an H- ion and the Cs/W surface thus * Laboratoire
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0039-6028/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
246
J. P. Guuyucq, J.J.C.
Geerlings / H adsorption and the collisional charge exchange
process
becomes a resonant process. Furthermore, the ionization energy of a hydrogen atom is much larger than its affinity and the neutralization of the incident proton and H- formation can be considered as independent. In this way, the HP formation problem can be reduced to a resonant charge exchange between a neutral H atom and the metal. Following this idea, a few theoretical descriptions of this process were developed: Hiskes and Schneider [4] considered H- ion formation occurring at small atom-surface distances followed by a partial recapture of the outer H- electron by the metal as the ion escapes from the surface. The charge exchange process was also studied by explicitly taking into account the charge exchange interaction as a function of the atom-surface distance and of the momentum of the metal electron. Rasser et al. [5] considered a treatment of the collision, termed the probability model [6], that describes the evolution of the charge state populations through a rate equation. Norskov and Lundqvist [7] and Brako and Newns [S] introduced another approximation, the amplitude model, that considers amplitudes instead of populations of electronic states. The probability model has been shown to be the semiclassical limit of the amplitude model [9]. In a previous work [3], we studied the particular case of HP formation in H+-Cs/W(llO) collisions in the 50-400 eV collision energy range. Using a free-wave description of the metal states and a separable approximation of the electron-hydrogen atom interaction, we obtained a theoretical description of the H- formation problem that accounts for the experimental findings. Recently, van Amersfoort et al. [lo] reported on the effect of hydrogen exposure on the charge exchange process in the same system. Several other authors also reported on qualitative studies of fluence dependences of the population of final states in ion-surface collisions. These concerned excited state population [ll] and charge fraction [12] measurements. These fluence dependences were tentatively attributed to some of the incident hydrogen forming an adsorbed layer on the target surface. While these fluence dependence studies were only qualitative, van Amersfoort et al. performed a detailed study of the effect of hydrogen exposure; in particular, they measured the negative ion charge fractions under controlled hydrogen exposures. As the main result of their experimental work: the negative ion yield in H+-cesiated tungsten surface collisions (cesium coverage corresponding to the minimum work function) is very quickly decreased by the coadsorption of hydrogen. However, the coadsorption of hydrogen yields almost no variation of the work function of the Cs/W(llO) surface up to rather large hydrogen coverages. This is a very striking feature since the work function can be considered as the key parameter for the charge exchange efficiency. The aim of the present paper is to develop a simple theoretical model for this effect, that can help understanding why adsorbed hydrogen atoms inhibit the charge exchange process. Basically, the idea of this description is to consider that the electrons can jump from the collisional H atom to the metal and to
J.P. Gauyacq, J.J.C.
Geerlings / H adsorption and the collisional charge exchange process
247
the adsorbed hydrogen atoms. The model is devised by adding the effect of an adsorbed layer of atoms to a previously developed model for H- formation in the H+-cesiated tungsten collision [3]. The treatment of the charge exchange process between the collisional H atom and the metal states perturbed by the adsorbed H atoms leads to a theoretical treatment of the coadsorption problem, the parameters of which can be obtained from the literature. This theoretical description will be shown to account for the experimental findings of van Amersfoort et al. [lo].
2. Formalism The basic aim of the model is to incorporate the effect of an adsorbed hydrogen layer into the previously developed model for H- formation in H’.-cesiated tungsten collisions [3]. Let us briefly recall the characteristics of the previous model. 2.1. Charge exchange between H and a Cs/ W surface The H--metal interaction is treated in a first-order perturbation theory following the work of Gadzuk [13]. The metal electrons are described by free waves in a potential box characterized by a work function and a bandwidth. Because of the charge exchange interaction, the affinity level acquires a finite width I? ~(z)=2~Cp(E,)I(kI~l~a)l*,
(1)
where the sum C runs over the continuum states 1k) degenerated with the affinity level ]a) at the energy E,, p is the density of continuum states and z is the atom-surface distance. V is the interaction between the collisional hydrogen atom and the electron. It is described by a separable potential [14] v=
-~lg)(sl,
(2)
where (r ] g) = &?% e -p’/r. The H- bound state is described as the bound state of the separable potential. Its energy is - a*/2 with cX==+iX-p. The (Y, p and X parameters are obtained from the H- ion and the e--H scattering characteristics [15]: (Y= 0.2355, p = 0.7858 and X = 0.5315. The z dependence of the affinity level energy is assumed to be a shifted image potential: E,(z)=
-[4(z+z,)]-‘.
(3)
The distance z, was determined by an adjustment to experimental data that yielded the value z, = 3.2 a,. When the hydrogen atom moves in front of the
24% J.P. Guuyucq, J.J.C.
Geerlings / H ud.wrp~~on and the collisional charge exchange
process
surface, the population of the affinity level P(z) changes due to the charge exchange interaction. This time evolution is described by a rate equation, through the width of the affinity level T(z). After integration, it yields the final negative ion yield:
where u is the collision velocity perpendicular to the surface (it is assumed to be a constant), z0 is the turning point of the trajectory, N-(z) is the affinity level population when the collisional hydrogen is at rest at distance z from the surface (we consider the metal to be at zero temperature). The collision velocity parallel to the surface has been shown by van Wunnik et al. [16] to affect the charge exchange process. Following these authors, we introduce the parallel velocity effect as a shift of the Fermi sphere in the k space for the determination of the width T(z) and the equilibrium charge fraction N-(z). The above treatment is often referred to as the probability model. It has been shown [9] to be a semiclassical limit of the more sophisticated “amplitude model” [7,8]. In the present case both models should yield similar results. 2.2. H/ Cs coadsorption
on W(II0)
Hydrogen adsorption on W(110) has been studied in some detail [17-191. One of the principal results is that the hydrogen sticking probability is very high on clean W(110): a saturation coverage is very quickly reached, at an exposure of a few tens of langmuir already, though the various studies do not agree on the adsorption kinetics. The hydrogen is adsorbed as atoms, in the “egg timer” regions of the W(110) surface [20]. Far fewer works have been devoted to the H/Cs coadsorption problem. The study of Papageorgopoulos and Chen [21] of H/Cs coadsorption on W(100) showed that the hydrogen atoms were adsorbed at the same places whichever of hydrogen and cesium atoms were adsorbed first. The hydrogen atoms then stick below the cesium layer, with an adsorption speed rapidly decreasing with increasing cesium coverage. For the minimum work function Cs/W surface (cesium coverage around 0.6 times the saturation coverage), van Amersfoort et al. [lo] obtained the relation between the hydrogen exposure and the number of adsorbed hydrogen atoms, and this will enable a detailed comparison between experimental and theoretical data. In contrast, of the adsorption kinetics of hydrogen on a saturated cesium layer nothing is known, except its extreme slowness. Another important feature, reported by van Amersfoort et al. [lo], concerns the variation of the cesiated tungsten surface work function under hydrogen adsorption: very little variation, if any, is observed up to hydrogen exposures of around lo3 L.
J.P. Gauyacq, J.J.C.
2.3. Presentation
Geerlings / H adsorpiion und the collisional charge exchange process
249
of the model
The theoretical model is derived from the above observations: since there is no sizable change of the work function, the potential box for the definition of the free metal states is chosen to be the same as in the cesiated tungsten case and the effect of the layer of adsorbed H atoms is superimposed on it. The work functions (1.45 and 2.15 ev> and bandwidths (1.57 and 1.95 eV) for the two cases studied below (half a cesium monolayer and a full cesium monolayer) were taken from ref. [2]. We assume that the hydrogen atoms are adsorbed on the W surface below the cesium layer. With respect to Gadzuk’s description of the metal states, this means that the hydrogen atoms are adsorbed inside the potential box defining the metal states. It is possible to get an estimate for its location in the box with the following arguments: first, when linking the electron density in the free-wave approximation with the electron density in the jellium calculation of Wojciechowski [22], the box edge appears to be around 6 a,, in front of the tungsten jellium edge. According to Nordlander et al. [20], the hydrogen atom is adsorbed in a region where the electron density is of the order of 10e2 ai3, i.e. close to the W jellium edge. Finally, Papageorgopoulos and Chen mentioned an outward shift (- 0.9 A) of the Cs layer due to the H adsorption. Thus one gets a rather rough estimate of the location of the adsorbed H atom, around 6-8 a0 inside the potential box. The interaction between electrons and the adsorbed hydrogen atoms can be represented in the zero range potential approximation (ZRP, see, e.g., Demkov and Ostrovskii [23]), i.e. by a Dirac 6 potential (the strength of which is linked to the hydrogen scattering length (singlet and triplet)). However, if the adsorbed hydrogen atom density is large enough, one can replace the layer of three-dimensional (3D) S potentials by a 1D 6 potential in a plane parallel to
v (2) t
Fig. 1. Sketch of the potentials
used in the present
model
250
J. P. Guuyacq, J.J. C. Geerlrngs / H adsorprion and the collkmul
charge exchange process
the surface. The strength of this 1D 6 potential is determined so as to give the same average value as the layer of 3D 6 potentials. For an adsorbed atom density p and a scattering length L the strength of the 1D S potential is 27pL. The replacement of a set of 3D S potentials by a 1D 6 potential requires a minimum density of hydrogen atoms which can be estimated to be in the range of a few 1014 atoms/cm*. The metal states are defined as the solutions of the following problem: a semi-infinite potential box in the region z c 0 and a 1D 6 potential located at z = -u (fig. l), with a strength A. In the absence of an adsorbed layer, the metal states are solutions of the potential box problem; the z dependence of the metal states is in this case: $=sin(k,z+6), $=A
forz
exp(-k,z),
forz>O,
with cotg 6 = - k,/k,,
IAj*=kf/k$
where k, and ki are the electron momenta perpendicular to the surface for the regions inside and outside the potential box, and k:/2 is the depth of the potential box. The lD-6 potential introduces a discontinuity in z = - a in the logarithmic derivative with respect to z of the electron wavefunction equal to -2X. The electron wavefunction is then: $=sin(kiz+p), +=Bsin(k,z+S), $=ABexp(-k,z),
forz<
-a,
for -aO.
In the region z > ---a, this wavefunction is simply proportional to the above solution in the absence of the 1D 6 potential. The proportionality factor B is such that IB12=
1 + cotg2(S - k,a), 1 + [cotg(b - kia) + 2X/ki12
The effect of hydrogen can very simply be implemented into the previous model, through the use of the eq. (5). It can also be tested directly, since this model does not contain any unknown or adjustable parameter. The factor B given by (5) can be larger and smaller than unity, depending on the value of the electron momentum k, perpendicular to the surface. Thus the hydrogen coadsorption could increase or decrease the charge exchange interaction. However, the width r(z) and equilibrium population NP (z) entering eq. (4) are obtained as averages over the various k values of the degenerated continuum states and as a result, the effect of coadsorption is not easily
J. P. Gauyacq, J.J. C. Geeriings / H adsorption and the collisional charge exchange process
4
251
8
Fig. 2. Width of the affinity level of H - in front of a Cs,IW(llO) surface, with various amounts of hydrogen adsorbed on the surface. Full lines: width in the random phase approximation: (1): clean Cs/w surface, (2): density of 3 x 1014 H atoms/cm*, (3): density of 7 x 1014 H atoms/cm*. Dashed lines: width obtained by eq. (5): (4): density of 3 X 1014 H atoms/cm* with a = 8 as, (5): density of 7 x lOI atoms/cm* with (I = 6 (I~.
guessed from eq. (5). Fig. 2 presents the width T(z) for different situations, compared with the width I’(z) in the absence of a hydrogen layer. It appears in fig. 2 that the width can be increased or decreased by the presence of a hydrogen layer. However, the intuitive idea would be that the adsorbed H atoms would attract the electrons towards the inside of the metal, and that would result in a decrease of the charge exchange interaction. This effect is hidden by a phase effect associated with the electron movement between the adsorbed H atom and the potential box edge (in the present model, both are sharp edges). Another approximation can be introduced that consists in a randomization of this phase (8 - k,a in eq. (5)). In this random phase appro~mation, the multip~cative factor B reduces to:
I B I&A= (1+
2P/k;)-*.
(6)
This expression corresponds to the intuitive idea that 1B 1 is smaller than unity, i.e., the adsorbed H atoms attract the electrons, and that reduces the tail of the electron wavefunction outside the metal. It shows that the net effect of
252
J. P. Gauyacq, J.J.C.
Geerfings / H adsorption and the coli~sronal charge exchange process
the coadsorption is to reduce the charge exchange interaction. This approximation corresponds to an averaging over the adsorbed atom positions, it can also be looked at as a way to take into account possible irregularities of the surface or of the H-Cs coverages. Fig. 2 also presents the affinity level width T(z) for various hydrogen coverages in the random phase approximation: in this approximation the width smoothly decreases with increasing hydrogen density.
3. Results The above model has been applied to the problem of hydrogen coadsorption on the electron capture by 400 eV H atoms scattered by a cesiated tungsten surface, studied by van Amersfoort et al. [lo]. Two situations were investigated: the ~nimum work function Cs/W surface (around 0.5 Cs layer) and the full cesium monolayer case. Fig. 3 presents the results for the minimum work function surface. It shows the relative negative ion fraction for 400 eV H, H- particles scattered at 70” from the surface normal, as a function of the hydrogen coverage. The theoretical results are obtained for distances The equal to 6 a0 and 8 a,, as well as in the random phase approximation.
N-h ,.,)/N-(O)
0.4 -
0.2 ---m-w-_ t 0
I
0.4
0.8
1
L
1.2
“H
Fig. 3. Negative fl- ion yield for a W surface partially covered with cesium and hydrogen, relative to a cesiated W surface, as a function of the hydrogen coverage. The c&urn coverage corresponds to the minimum work function Cs/W surface. The collision energy is 400 eV, with a 70° exit angle relative to the surface normal. Experimental results [IO]: 0. Present theoretical results:(------): u=~u,;(,-.-.): ic=Z3~,~;(): random phase approximation.
J. P. Gauvacq, J.J.C.
Geerlings / H adsorption and the collisional charge exchange process
253
N’@)/N-(0)
90
70
30
50
lo
P(des)
Fig. 4. Negative H- ion yield for a W surface partially covered with cesium and hydrogen, relative to a cesiated W surface as a function of the exit angle for a 400 eV collision. Experimental results [lo]: 0 (900 L hydrogen exposure). a = 8 aO: ( -):
Present
theoretical
results (10”
atoms/cm2):
(- - - - - -):
random phase approximation.
three sets of results are quite similar to the experimental data: in particular they all show that hydrogen adsorption results in a very fast decrease of the negative ion yield. Fig. 4 presents the same results for a 400 eV collision as a function of the scattering angle. The experimental results [lo] correspond to an exposure of 900 L, whereas the theoretical results correspond to a hydrogen coverage of 10” atoms/cm’. The latter overestimate the hydrogen adsorption effect as experimentally observed. The experimental results display a rather flat behaviour with the scattering angle (within the error bars), whereas the theoretical results slightly increase with increasing scattering angle, i.e. with decreasing perpendicular velocity. For the case of a thick cesium layer on a W(110) surface, a direct detailed comparison between theory and experiment is not possible. Indeed, the relation between hydrogen exposure and coverages is not known if the surface is cesiated first. If the surface is covered first with hydrogen, then the adsorption dynamics can be found in the literature [17,18]; however, in the experimental situation studied by van Amersfoort et al. [lo], it very quickly results in a saturation coverage in the range (0.7-0.8) x 1015 atoms/cm*. Papageorgopoulos and Chen [21] have also shown that the presence of hydrogen adsorbed on a W(100) surface results in an increase of the cesium saturation coverage. This might be correlated to the slight increase (- 0.15 ev) of the surface work function observed by van Amersfoort in that case. For all the above reasons, no detailed comparison was attempted
254
J. P. Guuyacq, .J..J.C. Geeriings / N adsorption and the collistonaLcharge exchange process
N-U/N-(O)
WW
1.
N’(O)
1.
0.5
0.5
t
~Ii; 0 10
100
o’5at/al12)
Fig. 5. Negative He- ion yield for a W surface partially covered with cesium and hydrogen, relative to a cesiated W surface, as a function of the hydrogen coverage. The cesium coverage corresponds to a full monolayer. The collision energy is 400 eV, with a 70° exit angle relative to the surface normal. Left: experimental results [lo] as a function of the hydrogen exposure. Right: present theoretical results in the random phase approximation as a function of the hydrogen coverage.
between expe~mental and theoretical results. We only performed c~culations in the random phase approximation to evaluate what would be the average effect of the hydrogen adsorption. The results are presented in fig. 5, for a 400 eV collision, at 70” from the surface normal as a function of the hydrogen coverage. The main feature is that the negative ion yield is only slightly affected by hydrogen adsorption for coverages below 1015 atoms/cm*. This is at variance with the results obtained in the ~nimum work function case and corresponds to the experimental observations [lo], also presented in fig. 4.
4. Conclusions We have reported on a model representing the effect of hydrogen adsorption on the charge exchange process between H atoms and a cesiated tungsten (110) surface. The model is able to reproduce the experimental findings of van Amersfoort et al. [lo]: for a minimum work function surface, the hydrogen adsorption results in a drastic decrease of the negative ion yield whereas for a W surface saturated with cesium, only small changes are obtained.
J.P. Gauyacq, J.J.C.
Geerlings / H adsorption und the collisional charge exchange process
255
As conclusive remarks, one can stress the characteristics of the model: it considers the electron jumps between three bodies: the metal represented by a potential box, a layer of adsorbed atoms and the collisional hydrogen atom. This three-body charge exchange process is reduced to the charge exchange between the collisional hydrogen atom and the perturbed metal states. On the average, it is found that hydrogen adsorption results in a decrease of the charge exchange interaction between the collisional hydrogen and the surface. Depending on the specificities of the case under study, namely of the strength of the charge exchange interaction with a “clean” surface, this interaction decrease can lead to various variations of the negative ion yield: the two cases we investigated exhibit two different ways of behaviour: fast decrease and almost constancy. Increase of the negative ion yield should be observed for situations where the charge exchange interaction with a “clean” surface is extremely large. The above discussion, as well as the examples treated above pertain to situations where the adsorbed layer is located inside the potential box. Indeed, for situations where the adsorbed layer is outside the potential box, the effect would be opposite and one should expect the charge exchange interaction to be increased by the presence of an adsorbed hydrogen layer.
Acknowledgments J.P. Gauyacq gratefully acknowledges a grant from the CNRS-ZWO exchange program which made this collaboration possible. The numerical calculations for this work were performed at the Centre Inter Regional de Calcul Electronique at Orsay (France).
References [l] Proc. 4th Intern. Workshop on Inelastic Ion-Surface Collisions, Middelfart, 1982. [Phys. Scripta T6 (1983)]. [2] J.N.M. van Wunnik, J.J.C. Geerlings and J. Los, Surface Sci. 131 (1983) 1. [3] J.J.C. Geerlings, P.W. van Amersfoort, L.F.Tz. Kwakman, E.H.A. Granneman. J. Los and J.P. Gauyacq, Surface Sci. 157 (1985) 151. [4] J.R. Hiskes and P.J. Schneider, Phys. Rev. B23 (1981) 949; J.R. Hiskes, J. Phys. (Paris) 40 (1979) C7-179. [5] B. Rasser, J.N.M. van Wunmk and J. Los, Surface Sci. 118 (1982) 697. [6] E.G. Overbosch, B. Rasser, A.D. Tenner and J. Los, Surface Sci. 92 (1980) 310. [7] J.K. Nsrskov and B.I. Lundqvist, Phys. Rev. B19 (1979) 5561. [8] R. Brako and D.M. Newns, Surface Sci. 108 (1981) 253. [9] J.J.C. Geerlings, J. Los, J.P. Gauyacq and N.M. Temme, Surface Sci. 172 (1986) 257. [lo] P.W. van Amersfoort, J.J.C. Geerlings, R. Rodink, E.H.A. Granneman and J. Los, J. Appl. Phys. 59 (1986) 241. [ll] H. Steininger, B. Willerding, K. Snowdon, N.H. Tolk and W. Eckstein, Nucl. Instr. Methods B2 (1984) 484.
256 [12] [13] [14] [15] [16] [17] [18] [191 [20] [21] [22] [23]
J. P. Gauyacq, J.J.C.
Geerlings / M adrorpiion and the colhsioncrl charge
exchange process
H. Verbeek, W. Eckstein and R.S. Bhattacharya, Nucl. Instr. Methods 170 (1980) 539. J.W. Gadzuk Surface Sci. 6 (1967) 133. Y. Yamagushi, Phys. Rev. 95 (1954) 1628. B.M. Smimov, Negative Ions (McGraw-Hill, New York, 1982). J.N.M. van Wunnik, R. Brako, K. Makoshi and D.M. Newns, Surface Sci. 126 (1983) 618. P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 54 (1971) 4775; 55 (1971) 4253. B.D. Bardford and R.R. Rye, J. Chem. Phys. 60 (1974) 1046. V.V. Gonchar, Yu.M. Kagan, O.V. Kanash, A.G. Naumovets and A.D. Fedorus, Soviet Phys. JETP 57 (1983) 142. P. Nordlander, A. Holloway and J.K. Nsrskov, Surface Sci. 136 (1984) 59. C.A. Papageorgopoulos and J.M. Chen, Surface Sci. 39 (1973) 283. K.F. Wojciechowski, Surface Sci. 55 (1976) 246. Yu.N. Demkov and V.N. Ostrovskii, Zero Range Potential Methods in Atomic Physics (Leningrad University Press, Leningrad, 1975).
Surface Science 182 (1987) 245-256 North-Holland, Amsterdam
EFFECT OF HYDROGEN ADSORPTION ON THE CHARGE EXCHANGE PROCESS IN ATOM-SURFACE COLLISIONS J.P. GAUYACQ Laboratoire des Collisions Atomiques 91405 Orsay, France
et MolPculaires
*, B&imeni
351, UniuersitC Pans-Sud,
and
J.J.C. GEERLINGS FOM Institute, Received
Kruislaan
407, 1098 SJ Amsterdam,
16 July 1986; accepted
for publication
The Netherlands 31 October
1986
~4 model of the effect of the adsorption of hydrogen atoms on a charge exchange process in atorn-surface collisions is presented. The adsorbed layer is represented by a 1D 6 potential. The model is applied to the problem of Hformation in H+-Cs/W surface collisions. In the presence of the adsorbed layer, the charge exchange process becomes a three-body problem: the electrons can jump from the collisional H atom, to the metal and to the adsorbed H atoms. As a net effect, this results in a decrease of the charge exchange interaction. The model results are found to account for the recent observations of van Amersfoort et al. [J. Appl. Phys. 59 (1986) 24111.
1. Introduction Electron capture by ions colliding with a surface has been the subject of numerous works over the past years (see, e.g., the proceedings of the workshop on IISC of 1982 [l]). Among those systems, the proton-cesiated-tungsten system has been investigated in some detail [2]. Experimental investigations of this collisional system revealed very large negative ion yields (up to 67%) while no proton was reflected from the surface [3]. The main characteristic of this particular surface (cesiated tungsten) is its ability to reach low work function values (down to 1.45 eV). When approaching the surface, the H- binding energy (0.75 eV at infinity) increases due to the image charge potential and the affinity level can thus become degenerate with the occupied metal states: the charge exchange process between an H- ion and the Cs/W surface thus * Laboratoire
associe
au CNRS
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0039-6028/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
246
J. P. Guuyucq, J.J.C.
Geerlings / H adsorption and the collisional charge exchange
process
becomes a resonant process. Furthermore, the ionization energy of a hydrogen atom is much larger than its affinity and the neutralization of the incident proton and H- formation can be considered as independent. In this way, the HP formation problem can be reduced to a resonant charge exchange between a neutral H atom and the metal. Following this idea, a few theoretical descriptions of this process were developed: Hiskes and Schneider [4] considered H- ion formation occurring at small atom-surface distances followed by a partial recapture of the outer H- electron by the metal as the ion escapes from the surface. The charge exchange process was also studied by explicitly taking into account the charge exchange interaction as a function of the atom-surface distance and of the momentum of the metal electron. Rasser et al. [5] considered a treatment of the collision, termed the probability model [6], that describes the evolution of the charge state populations through a rate equation. Norskov and Lundqvist [7] and Brako and Newns [S] introduced another approximation, the amplitude model, that considers amplitudes instead of populations of electronic states. The probability model has been shown to be the semiclassical limit of the amplitude model [9]. In a previous work [3], we studied the particular case of HP formation in H+-Cs/W(llO) collisions in the 50-400 eV collision energy range. Using a free-wave description of the metal states and a separable approximation of the electron-hydrogen atom interaction, we obtained a theoretical description of the H- formation problem that accounts for the experimental findings. Recently, van Amersfoort et al. [lo] reported on the effect of hydrogen exposure on the charge exchange process in the same system. Several other authors also reported on qualitative studies of fluence dependences of the population of final states in ion-surface collisions. These concerned excited state population [ll] and charge fraction [12] measurements. These fluence dependences were tentatively attributed to some of the incident hydrogen forming an adsorbed layer on the target surface. While these fluence dependence studies were only qualitative, van Amersfoort et al. performed a detailed study of the effect of hydrogen exposure; in particular, they measured the negative ion charge fractions under controlled hydrogen exposures. As the main result of their experimental work: the negative ion yield in H+-cesiated tungsten surface collisions (cesium coverage corresponding to the minimum work function) is very quickly decreased by the coadsorption of hydrogen. However, the coadsorption of hydrogen yields almost no variation of the work function of the Cs/W(llO) surface up to rather large hydrogen coverages. This is a very striking feature since the work function can be considered as the key parameter for the charge exchange efficiency. The aim of the present paper is to develop a simple theoretical model for this effect, that can help understanding why adsorbed hydrogen atoms inhibit the charge exchange process. Basically, the idea of this description is to consider that the electrons can jump from the collisional H atom to the metal and to
J.P. Gauyacq, J.J.C.
Geerlings / H adsorption and the collisional charge exchange process
247
the adsorbed hydrogen atoms. The model is devised by adding the effect of an adsorbed layer of atoms to a previously developed model for H- formation in the H+-cesiated tungsten collision [3]. The treatment of the charge exchange process between the collisional H atom and the metal states perturbed by the adsorbed H atoms leads to a theoretical treatment of the coadsorption problem, the parameters of which can be obtained from the literature. This theoretical description will be shown to account for the experimental findings of van Amersfoort et al. [lo].
2. Formalism The basic aim of the model is to incorporate the effect of an adsorbed hydrogen layer into the previously developed model for H- formation in H’.-cesiated tungsten collisions [3]. Let us briefly recall the characteristics of the previous model. 2.1. Charge exchange between H and a Cs/ W surface The H--metal interaction is treated in a first-order perturbation theory following the work of Gadzuk [13]. The metal electrons are described by free waves in a potential box characterized by a work function and a bandwidth. Because of the charge exchange interaction, the affinity level acquires a finite width I? ~(z)=2~Cp(E,)I(kI~l~a)l*,
(1)
where the sum C runs over the continuum states 1k) degenerated with the affinity level ]a) at the energy E,, p is the density of continuum states and z is the atom-surface distance. V is the interaction between the collisional hydrogen atom and the electron. It is described by a separable potential [14] v=
-~lg)(sl,
(2)
where (r ] g) = &?% e -p’/r. The H- bound state is described as the bound state of the separable potential. Its energy is - a*/2 with cX==+iX-p. The (Y, p and X parameters are obtained from the H- ion and the e--H scattering characteristics [15]: (Y= 0.2355, p = 0.7858 and X = 0.5315. The z dependence of the affinity level energy is assumed to be a shifted image potential: E,(z)=
-[4(z+z,)]-‘.
(3)
The distance z, was determined by an adjustment to experimental data that yielded the value z, = 3.2 a,. When the hydrogen atom moves in front of the
24% J.P. Guuyucq, J.J.C.
Geerlings / H ud.wrp~~on and the collisional charge exchange
process
surface, the population of the affinity level P(z) changes due to the charge exchange interaction. This time evolution is described by a rate equation, through the width of the affinity level T(z). After integration, it yields the final negative ion yield:
where u is the collision velocity perpendicular to the surface (it is assumed to be a constant), z0 is the turning point of the trajectory, N-(z) is the affinity level population when the collisional hydrogen is at rest at distance z from the surface (we consider the metal to be at zero temperature). The collision velocity parallel to the surface has been shown by van Wunnik et al. [16] to affect the charge exchange process. Following these authors, we introduce the parallel velocity effect as a shift of the Fermi sphere in the k space for the determination of the width T(z) and the equilibrium charge fraction N-(z). The above treatment is often referred to as the probability model. It has been shown [9] to be a semiclassical limit of the more sophisticated “amplitude model” [7,8]. In the present case both models should yield similar results. 2.2. H/ Cs coadsorption
on W(II0)
Hydrogen adsorption on W(110) has been studied in some detail [17-191. One of the principal results is that the hydrogen sticking probability is very high on clean W(110): a saturation coverage is very quickly reached, at an exposure of a few tens of langmuir already, though the various studies do not agree on the adsorption kinetics. The hydrogen is adsorbed as atoms, in the “egg timer” regions of the W(110) surface [20]. Far fewer works have been devoted to the H/Cs coadsorption problem. The study of Papageorgopoulos and Chen [21] of H/Cs coadsorption on W(100) showed that the hydrogen atoms were adsorbed at the same places whichever of hydrogen and cesium atoms were adsorbed first. The hydrogen atoms then stick below the cesium layer, with an adsorption speed rapidly decreasing with increasing cesium coverage. For the minimum work function Cs/W surface (cesium coverage around 0.6 times the saturation coverage), van Amersfoort et al. [lo] obtained the relation between the hydrogen exposure and the number of adsorbed hydrogen atoms, and this will enable a detailed comparison between experimental and theoretical data. In contrast, of the adsorption kinetics of hydrogen on a saturated cesium layer nothing is known, except its extreme slowness. Another important feature, reported by van Amersfoort et al. [lo], concerns the variation of the cesiated tungsten surface work function under hydrogen adsorption: very little variation, if any, is observed up to hydrogen exposures of around lo3 L.
J.P. Gauyacq, J.J.C.
2.3. Presentation
Geerlings / H adsorpiion und the collisional charge exchange process
249
of the model
The theoretical model is derived from the above observations: since there is no sizable change of the work function, the potential box for the definition of the free metal states is chosen to be the same as in the cesiated tungsten case and the effect of the layer of adsorbed H atoms is superimposed on it. The work functions (1.45 and 2.15 ev> and bandwidths (1.57 and 1.95 eV) for the two cases studied below (half a cesium monolayer and a full cesium monolayer) were taken from ref. [2]. We assume that the hydrogen atoms are adsorbed on the W surface below the cesium layer. With respect to Gadzuk’s description of the metal states, this means that the hydrogen atoms are adsorbed inside the potential box defining the metal states. It is possible to get an estimate for its location in the box with the following arguments: first, when linking the electron density in the free-wave approximation with the electron density in the jellium calculation of Wojciechowski [22], the box edge appears to be around 6 a,, in front of the tungsten jellium edge. According to Nordlander et al. [20], the hydrogen atom is adsorbed in a region where the electron density is of the order of 10e2 ai3, i.e. close to the W jellium edge. Finally, Papageorgopoulos and Chen mentioned an outward shift (- 0.9 A) of the Cs layer due to the H adsorption. Thus one gets a rather rough estimate of the location of the adsorbed H atom, around 6-8 a0 inside the potential box. The interaction between electrons and the adsorbed hydrogen atoms can be represented in the zero range potential approximation (ZRP, see, e.g., Demkov and Ostrovskii [23]), i.e. by a Dirac 6 potential (the strength of which is linked to the hydrogen scattering length (singlet and triplet)). However, if the adsorbed hydrogen atom density is large enough, one can replace the layer of three-dimensional (3D) S potentials by a 1D 6 potential in a plane parallel to
v (2) t
Fig. 1. Sketch of the potentials
used in the present
model
250
J. P. Guuyacq, J.J. C. Geerlrngs / H adsorprion and the collkmul
charge exchange process
the surface. The strength of this 1D 6 potential is determined so as to give the same average value as the layer of 3D 6 potentials. For an adsorbed atom density p and a scattering length L the strength of the 1D S potential is 27pL. The replacement of a set of 3D S potentials by a 1D 6 potential requires a minimum density of hydrogen atoms which can be estimated to be in the range of a few 1014 atoms/cm*. The metal states are defined as the solutions of the following problem: a semi-infinite potential box in the region z c 0 and a 1D 6 potential located at z = -u (fig. l), with a strength A. In the absence of an adsorbed layer, the metal states are solutions of the potential box problem; the z dependence of the metal states is in this case: $=sin(k,z+6), $=A
forz
exp(-k,z),
forz>O,
with cotg 6 = - k,/k,,
IAj*=kf/k$
where k, and ki are the electron momenta perpendicular to the surface for the regions inside and outside the potential box, and k:/2 is the depth of the potential box. The lD-6 potential introduces a discontinuity in z = - a in the logarithmic derivative with respect to z of the electron wavefunction equal to -2X. The electron wavefunction is then: $=sin(kiz+p), +=Bsin(k,z+S), $=ABexp(-k,z),
forz<
-a,
for -a
In the region z > ---a, this wavefunction is simply proportional to the above solution in the absence of the 1D 6 potential. The proportionality factor B is such that IB12=
1 + cotg2(S - k,a), 1 + [cotg(b - kia) + 2X/ki12
The effect of hydrogen can very simply be implemented into the previous model, through the use of the eq. (5). It can also be tested directly, since this model does not contain any unknown or adjustable parameter. The factor B given by (5) can be larger and smaller than unity, depending on the value of the electron momentum k, perpendicular to the surface. Thus the hydrogen coadsorption could increase or decrease the charge exchange interaction. However, the width r(z) and equilibrium population NP (z) entering eq. (4) are obtained as averages over the various k values of the degenerated continuum states and as a result, the effect of coadsorption is not easily
J. P. Gauyacq, J.J. C. Geeriings / H adsorption and the collisional charge exchange process
4
251
8
Fig. 2. Width of the affinity level of H - in front of a Cs,IW(llO) surface, with various amounts of hydrogen adsorbed on the surface. Full lines: width in the random phase approximation: (1): clean Cs/w surface, (2): density of 3 x 1014 H atoms/cm*, (3): density of 7 x 1014 H atoms/cm*. Dashed lines: width obtained by eq. (5): (4): density of 3 X 1014 H atoms/cm* with a = 8 as, (5): density of 7 x lOI atoms/cm* with (I = 6 (I~.
guessed from eq. (5). Fig. 2 presents the width T(z) for different situations, compared with the width I’(z) in the absence of a hydrogen layer. It appears in fig. 2 that the width can be increased or decreased by the presence of a hydrogen layer. However, the intuitive idea would be that the adsorbed H atoms would attract the electrons towards the inside of the metal, and that would result in a decrease of the charge exchange interaction. This effect is hidden by a phase effect associated with the electron movement between the adsorbed H atom and the potential box edge (in the present model, both are sharp edges). Another approximation can be introduced that consists in a randomization of this phase (8 - k,a in eq. (5)). In this random phase appro~mation, the multip~cative factor B reduces to:
I B I&A= (1+
2P/k;)-*.
(6)
This expression corresponds to the intuitive idea that 1B 1 is smaller than unity, i.e., the adsorbed H atoms attract the electrons, and that reduces the tail of the electron wavefunction outside the metal. It shows that the net effect of
252
J. P. Gauyacq, J.J.C.
Geerfings / H adsorption and the coli~sronal charge exchange process
the coadsorption is to reduce the charge exchange interaction. This approximation corresponds to an averaging over the adsorbed atom positions, it can also be looked at as a way to take into account possible irregularities of the surface or of the H-Cs coverages. Fig. 2 also presents the affinity level width T(z) for various hydrogen coverages in the random phase approximation: in this approximation the width smoothly decreases with increasing hydrogen density.
3. Results The above model has been applied to the problem of hydrogen coadsorption on the electron capture by 400 eV H atoms scattered by a cesiated tungsten surface, studied by van Amersfoort et al. [lo]. Two situations were investigated: the ~nimum work function Cs/W surface (around 0.5 Cs layer) and the full cesium monolayer case. Fig. 3 presents the results for the minimum work function surface. It shows the relative negative ion fraction for 400 eV H, H- particles scattered at 70” from the surface normal, as a function of the hydrogen coverage. The theoretical results are obtained for distances The equal to 6 a0 and 8 a,, as well as in the random phase approximation.
N-h ,.,)/N-(O)
0.4 -
0.2 ---m-w-_ t 0
I
0.4
0.8
1
L
1.2
“H
Fig. 3. Negative fl- ion yield for a W surface partially covered with cesium and hydrogen, relative to a cesiated W surface, as a function of the hydrogen coverage. The c&urn coverage corresponds to the minimum work function Cs/W surface. The collision energy is 400 eV, with a 70° exit angle relative to the surface normal. Experimental results [IO]: 0. Present theoretical results:(------): u=~u,;(,-.-.): ic=Z3~,~;(): random phase approximation.
J. P. Gauvacq, J.J.C.
Geerlings / H adsorption and the collisional charge exchange process
253
N’@)/N-(0)
90
70
30
50
lo
P(des)
Fig. 4. Negative H- ion yield for a W surface partially covered with cesium and hydrogen, relative to a cesiated W surface as a function of the exit angle for a 400 eV collision. Experimental results [lo]: 0 (900 L hydrogen exposure). a = 8 aO: ( -):
Present
theoretical
results (10”
atoms/cm2):
(- - - - - -):
random phase approximation.
three sets of results are quite similar to the experimental data: in particular they all show that hydrogen adsorption results in a very fast decrease of the negative ion yield. Fig. 4 presents the same results for a 400 eV collision as a function of the scattering angle. The experimental results [lo] correspond to an exposure of 900 L, whereas the theoretical results correspond to a hydrogen coverage of 10” atoms/cm’. The latter overestimate the hydrogen adsorption effect as experimentally observed. The experimental results display a rather flat behaviour with the scattering angle (within the error bars), whereas the theoretical results slightly increase with increasing scattering angle, i.e. with decreasing perpendicular velocity. For the case of a thick cesium layer on a W(110) surface, a direct detailed comparison between theory and experiment is not possible. Indeed, the relation between hydrogen exposure and coverages is not known if the surface is cesiated first. If the surface is covered first with hydrogen, then the adsorption dynamics can be found in the literature [17,18]; however, in the experimental situation studied by van Amersfoort et al. [lo], it very quickly results in a saturation coverage in the range (0.7-0.8) x 1015 atoms/cm*. Papageorgopoulos and Chen [21] have also shown that the presence of hydrogen adsorbed on a W(100) surface results in an increase of the cesium saturation coverage. This might be correlated to the slight increase (- 0.15 ev) of the surface work function observed by van Amersfoort in that case. For all the above reasons, no detailed comparison was attempted
254
J. P. Guuyacq, .J..J.C. Geeriings / N adsorption and the collistonaLcharge exchange process
N-U/N-(O)
WW
1.
N’(O)
1.
0.5
0.5
t
~Ii; 0 10
100
o’5at/al12)
Fig. 5. Negative He- ion yield for a W surface partially covered with cesium and hydrogen, relative to a cesiated W surface, as a function of the hydrogen coverage. The cesium coverage corresponds to a full monolayer. The collision energy is 400 eV, with a 70° exit angle relative to the surface normal. Left: experimental results [lo] as a function of the hydrogen exposure. Right: present theoretical results in the random phase approximation as a function of the hydrogen coverage.
between expe~mental and theoretical results. We only performed c~culations in the random phase approximation to evaluate what would be the average effect of the hydrogen adsorption. The results are presented in fig. 5, for a 400 eV collision, at 70” from the surface normal as a function of the hydrogen coverage. The main feature is that the negative ion yield is only slightly affected by hydrogen adsorption for coverages below 1015 atoms/cm*. This is at variance with the results obtained in the ~nimum work function case and corresponds to the experimental observations [lo], also presented in fig. 4.
4. Conclusions We have reported on a model representing the effect of hydrogen adsorption on the charge exchange process between H atoms and a cesiated tungsten (110) surface. The model is able to reproduce the experimental findings of van Amersfoort et al. [lo]: for a minimum work function surface, the hydrogen adsorption results in a drastic decrease of the negative ion yield whereas for a W surface saturated with cesium, only small changes are obtained.
J.P. Gauyacq, J.J.C.
Geerlings / H adsorption und the collisional charge exchange process
255
As conclusive remarks, one can stress the characteristics of the model: it considers the electron jumps between three bodies: the metal represented by a potential box, a layer of adsorbed atoms and the collisional hydrogen atom. This three-body charge exchange process is reduced to the charge exchange between the collisional hydrogen atom and the perturbed metal states. On the average, it is found that hydrogen adsorption results in a decrease of the charge exchange interaction between the collisional hydrogen and the surface. Depending on the specificities of the case under study, namely of the strength of the charge exchange interaction with a “clean” surface, this interaction decrease can lead to various variations of the negative ion yield: the two cases we investigated exhibit two different ways of behaviour: fast decrease and almost constancy. Increase of the negative ion yield should be observed for situations where the charge exchange interaction with a “clean” surface is extremely large. The above discussion, as well as the examples treated above pertain to situations where the adsorbed layer is located inside the potential box. Indeed, for situations where the adsorbed layer is outside the potential box, the effect would be opposite and one should expect the charge exchange interaction to be increased by the presence of an adsorbed hydrogen layer.
Acknowledgments J.P. Gauyacq gratefully acknowledges a grant from the CNRS-ZWO exchange program which made this collaboration possible. The numerical calculations for this work were performed at the Centre Inter Regional de Calcul Electronique at Orsay (France).
References [l] Proc. 4th Intern. Workshop on Inelastic Ion-Surface Collisions, Middelfart, 1982. [Phys. Scripta T6 (1983)]. [2] J.N.M. van Wunnik, J.J.C. Geerlings and J. Los, Surface Sci. 131 (1983) 1. [3] J.J.C. Geerlings, P.W. van Amersfoort, L.F.Tz. Kwakman, E.H.A. Granneman. J. Los and J.P. Gauyacq, Surface Sci. 157 (1985) 151. [4] J.R. Hiskes and P.J. Schneider, Phys. Rev. B23 (1981) 949; J.R. Hiskes, J. Phys. (Paris) 40 (1979) C7-179. [5] B. Rasser, J.N.M. van Wunmk and J. Los, Surface Sci. 118 (1982) 697. [6] E.G. Overbosch, B. Rasser, A.D. Tenner and J. Los, Surface Sci. 92 (1980) 310. [7] J.K. Nsrskov and B.I. Lundqvist, Phys. Rev. B19 (1979) 5561. [8] R. Brako and D.M. Newns, Surface Sci. 108 (1981) 253. [9] J.J.C. Geerlings, J. Los, J.P. Gauyacq and N.M. Temme, Surface Sci. 172 (1986) 257. [lo] P.W. van Amersfoort, J.J.C. Geerlings, R. Rodink, E.H.A. Granneman and J. Los, J. Appl. Phys. 59 (1986) 241. [ll] H. Steininger, B. Willerding, K. Snowdon, N.H. Tolk and W. Eckstein, Nucl. Instr. Methods B2 (1984) 484.
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J. P. Gauyacq, J.J.C.
Geerlings / M adrorpiion and the colhsioncrl charge
exchange process
H. Verbeek, W. Eckstein and R.S. Bhattacharya, Nucl. Instr. Methods 170 (1980) 539. J.W. Gadzuk Surface Sci. 6 (1967) 133. Y. Yamagushi, Phys. Rev. 95 (1954) 1628. B.M. Smimov, Negative Ions (McGraw-Hill, New York, 1982). J.N.M. van Wunnik, R. Brako, K. Makoshi and D.M. Newns, Surface Sci. 126 (1983) 618. P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 54 (1971) 4775; 55 (1971) 4253. B.D. Bardford and R.R. Rye, J. Chem. Phys. 60 (1974) 1046. V.V. Gonchar, Yu.M. Kagan, O.V. Kanash, A.G. Naumovets and A.D. Fedorus, Soviet Phys. JETP 57 (1983) 142. P. Nordlander, A. Holloway and J.K. Nsrskov, Surface Sci. 136 (1984) 59. C.A. Papageorgopoulos and J.M. Chen, Surface Sci. 39 (1973) 283. K.F. Wojciechowski, Surface Sci. 55 (1976) 246. Yu.N. Demkov and V.N. Ostrovskii, Zero Range Potential Methods in Atomic Physics (Leningrad University Press, Leningrad, 1975).