Parallel velocity assisted charge transfer: F− ion formation at Al(111) and Ag(110) surfaces

Surface Science 429 (1999) 46–53

www.elsevier.nl/locate/susc

Parallel velocity assisted charge transfer: F− ion formation at Al(111) and Ag(110) surfaces N. Lorente, A.G. Borisov *, D. Teillet-Billy, J.P. Gauyacq Laboratoire des Collisions Atomiques et Mole´culaires (UMR no. 8625), Baˆtiment 351, Universite´ Paris-Sud, 91405 Orsay Cedex, France Received 6 September 1998; accepted for publication 29 January 1999

Abstract Theoretical results on the F− ion formation in scattering from Al and Ag surfaces are presented. Negative ion fractions are studied over a wide range of incident energies and scattering angles. Our description of the ion–surface charge transfer takes into account the multistate effects originating from the 2p6 closed shell structure of the F− ion. Based on the parameter-free study of the dynamics of resonant charge transfer we find that the parallel velocity effects are quite important down to projectile energies of 0.5 keV. This is further confirmed by comparison between the present results and available experimental data [S. Ustaze et al., Surf. Sci. 414 (1998) L938; M. Maazouz et al., Surf. Sci. 409 (1998) 189; S. Ustaze, L. Guillemot, V.A. Esaulov, personal communications]. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Atom–solid interactions; Ion emission; Ion–solid interactions, scattering, channelling

1. Introduction Charge transfer processes play an important role in gas–surface interactions. They directly determine the charge states of projectiles in the scattered or sputtered beams [1–3]. They are also involved as an intermediate step in various reactions at surfaces e.g. reactive scattering [4], excitation of adsorbed molecules [5], electron- and photon-stimulated desorption [6,7], quenching of excited states of projectiles [8,9], etc. For atomic/molecular projectiles with low binding energies of electronic states participating in the charge transfer at surfaces (negative ions, alkali atoms in ground and excited states) multielectron * Corresponding author. Fax: +33-(1)69-41-76-71. E-mail address: [email protected] (A.G. Borisov)

Auger charge transfer processes [10,11] are not efficient. The projectile–surface interaction is dominated by the resonant charge transfer (RCT ) process, which corresponds to one-electron energy conserving transitions between electronic states of the projectile and the surface. Owing to its importance, the RCT process has been a subject of detailed experimental and theoretical studies (for reviews see Refs. [1,2,12–14]). On the theoretical side, two problems have to be addressed: (i) the determination of the energies of the electronic levels of the projectile in front of the surface and of the charge transfer couplings (static part); (ii) the description of the dynamics of the electron transfer during a collision. Early descriptions of the dynamics of the RCT process were based on the time-dependent spinless Newns– Anderson Hamiltonian associated with estimated

0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 99 ) 0 03 2 2 -2

N. Lorente et al. / Surface Science 429 (1999) 46–53

or adjusted energies and couplings [15,16 ]: H=E (Z)C+ C +∑ E C+ C a a a k k k k +∑ [V (Z)C+ C +cc] (1) ak a k k where Z is the projectile–surface distance, E is a the energy of the projectile level in front of the surface, E stands for the energies of the conduck tion band states, C+ and C are creation and annihilation operators and V is the coupling ak between the projectile state and the conduction band states. The time dependence comes from the projectile motion [Z=Z(t)]. Developments in the treatment of the RCT process concerned both the dynamical and static parts. For the dynamical treatment, the multielectron effects (correlation between electrons with different spins, existence of different atomic states, degeneracy of the atomic states) have received a lot of attention [12,14,17–21]. The development of the Newns–Anderson Hamiltonian formalism led to the prediction of interesting effects like the influence of the Kondo effect on the RCT [22,23]. Also, a semiquantitative explanation of projectile charge state formation in surface scattering experiments was obtained [18–20]. In parallel, the possibility of the description of the RCT process via a rate equation approach has been investigated [14,15,24]. It was shown that under certain conditions (broad conduction band, high temperature, semiclassical conditions, or large parallel to the surface velocity component of the scattered beam V ), a rate equation description is valid, in which d the populations of the various states evolve following rates linked with the level widths. The multistate aspects of the RCT appear in the presence of a few terms in the rate equations and of unequal rates for electron capture and loss [25]. Quantitative studies of the RCT process became possible with the development of nonperturbative treatments of the static problem of an atom (molecule) interacting with a jellium surface [26–31], yielding the atomic level energies and widths. The connection between these and existing studies based on the Newns–Anderson formulation is not obvious, since, in order to obtain the RCT couplings V , one inverts the relation between the ak

47

V and the level width [18–20,22,23]. This requires ak extra assumptions, the validity of which have not yet been assessed (e.g. charge transfer couplings V were considered to be independent on the ak direction of the metal–state momentum k). In contrast, the level energies and widths can be used directly in a rate equation approach. A quantitative account for a large spectrum of experimental data was obtained in this way. In particular, experimental results on the parallel-velocity-assisted charge transfer in grazing scattering collisions were successfully reproduced [32–35]. In this paper we report on a theoretical study of the F− ion formation at metal surfaces [Al(111) and Ag(110)] over a wide range of scattering conditions (collision energies and scattering angles). It is well established that kinematic V d effects [36 ] determine the charge fractions of the projectiles in grazing scattering of high energy beams [1,33–35,37–39]. Below, we demonstrate that kinematic effects are very important for the fluorine projectiles even for energies as low as 0.5 keV. We compare our results with available experimental data [40–43] and with a previously reported study on the same system performed with a Newns–Anderson Hamiltonian including manybody (multielectron) effects but ignoring parallel velocity effects [40]. Our approach is based on the nonperturbative coupled angular mode (CAM ) method that was successfully applied to the study of the RCT process between metal surfaces and atomic systems with several electrons occupying a p-shell [21,27,35]. It provides the static properties of the F− ion in front of the metal surface. Those static properties are further used as inputs for the treatment of the dynamics of the charge transfer that is described within the multistate rate equation approach. Parallel velocity V effects are incorpod rated via the ‘shifted Fermi sphere’ model [13,36 ].

2. Theoretical description of the charge transfer For the details of the theoretical description we refer to the publication devoted to the I −, F− and Cl− formation in fast grazing collisions on the Al(111) surface [44]. Only a brief discussion

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N. Lorente et al. / Surface Science 429 (1999) 46–53

will be given here. We use atomic units unless otherwise specified (B=m=e=1). The F− ion has a closed-shell (2p6) structure with six equivalent electrons which can a priori participate in the charge transfer process. Depending on the spin and angular momentum orientation of the electron ejected by the decaying negative ion, different states of the parent atom can be formed [21,27,35]. We use a reference frame with the z-axis normal to the surface and going through the collisional atom centre, x- and y-axis are parallel to the surface with x-axis pointing in the V direction. The decay of the F− ion can be d schematically presented in the following way:

G

(1)e(p )+F : C x px px F−(1S) (2)e(p )+F : C py y py (3)e(p )+F : C z pz pz

(2)

where p stands for the angular part of the wave x,y,z function of the emitted electron, F denotes px,py,pz the fluorine atom with a hole on the 2p , 2p , or x y 2p orbital, and C are the partial decay rates z px,py,pz into the various channels. These rates take into account the existence of two possible spin orientations for the transferred electron. The basis of the p states is well adapted to treat the small angle x,y,z scattering from the surface when the only symmetry is that with respect to the (x, z) scattering plane. Then the p states are symmetric with x,z respect to the scattering plane and the p state is y antisymmetric. In the absence of the parallel velocity effect (static case) the system has cylindrical symmetry with respect to the z-axis and the (1) and (2) channels are degenerate: C =C . As we px py will see below, inclusion of the parallel velocity effects lifts the degeneracy of these channels. The static properties of the F− ion in front of the metal surfaces (decay rates into the different channels, energy of the negative ion resonance and the angular distributions of the electron transfer probability [33,34]) have been obtained within a nonperturbative study based on the CAM method [27]. This is a one-electron multistate approach that uses a free-electron representation of the metal target. The energy of the negative ion level is presented in Fig. 1a. It roughly follows the image-

Fig. 1. (a) Energy of the F− level in front of an Al surface as function of the ion–surface distance Z. Dots: CAM results; solid line: level energy estimated from the image-potential. The horizontal line defines the position of the Fermi level. (b) Partial decay rates of the F− ion for the various decay channels [see Eq. (2)] as functions of the ion–surface distance. Solid line: decay by the emission of the p electron (C ); Dashed line: z p decay by the emission of the p or p electron z(C =C ). x y px py

potential dependence: E (Z)$E (2)−1/(4Z), a a where Z is the ion–surface distance measured from the image plane. E (2) corresponds to the binding a energy of the electron in the free F− ion and is equal to −3.41 eV. The decay rates into the different channels are presented in Fig. 1b and can be approximately parametrized as C=C × 0 exp(−cZ), where the exponential factor is due to the exponentially decreasing overlap between the metal states and the negative ion state. For the same distance from the surface, the decay rate for the p channel is larger than that for the p or p z x y channels. This is because the p orbital oriented z along the surface normal is more coupled to the

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N. Lorente et al. / Surface Science 429 (1999) 46–53

continuum of metal states than the p or p orbitals x y lying in the plane parallel to the surface. Let us consider the grazing scattering of a 0.5 keV fluorine beam. When performing a transformation from the metal reference frame to the projectile frame, metal states appear at the energies E =(k+V )2/2 [36 ], and the parallel velocity k d broadening of the Fermi distribution can be estimated as DE =2k v . (3) F F d From Eq. (3) we obtain DE #1 eV and F DE #1.4 eV for the Ag and Al surface respecF tively. This parallel velocity broadening of the Fermi distribution is quite large and its effect is similar to that of an extremely high temperature of the surface. The recent study of the F− formation in 0.5 keV collisions with an Ag(110) surface [40] has shown that, owing to semiclassical conditions, the treatment of the RCT dynamics based on the generalised Newns–Anderson Hamiltonian yields results almost identical to those of the multistate rate equation approach. The parallel velocity effects were ignored in Ref. [40]. The inclusion of the V effect should strengthen the d validity of the rate equation approach. Within our treatment the evolution of the populations of the different states is described within a multistate rate equation approach: dP− dt

A

B

=− ∑ Gloss P−+∑ Gcapt P i i Fi i i

dP Fi =−Gcapt P +Gloss P− i Fi i dt

(4)

where P− and P are the populations of the F negative ion and ineutral atom substates, and i={p , p , p }. Gloss and Gcapt are the electron loss x y z i i and capture rates respectively. The capture and loss rates are calculated from the static results using the shifted Fermi spheremodel [13,33,36 ] (h, w are polar coordinates of the metal-state wave vector k with respect to the zaxis):

G

H

G HP

Gcapt (Z) 1 i =C (Z) 2 i Gloss (Z) 1 i

p/2 0

sin h dh

P

G

H

f (k+V ) d . (5) dw |s (h, w, Z)|2 i 1−f (k+V ) 0 d In Eq. (5), C (Z ) are the ‘static’ loss rates defined i for different decay channels by Eq. (1). The factor 1 for the capture rate arises from the spin statistics. 2 |s (h, w, Z)|2 is the angular distribution function i (for the details see Ref. [33]). It gives the probability of the negative ion decay toward the various metal states |k within the ith channel. This angular distribution function is normalized as ×

P

p/2

2p

P

2p

dw |s (h, w, Z)|2=1 (6) i 0 0 f(k+V ) is the ‘Fermi–Dirac’ function in the rest d frame of the moving ion. For a vanishing temperature it can be expressed by the step-function H (V along the x-axis): d k2+v2 d −v k sin h cos w f (k+V )=H E − d d F 2 sin h dh

A

B

(7) where E is the Fermi energy and k¬|k| is fixed F by the resonance condition k=앀2[(U −E (Z)], 0 a where U is the bottom of the conduction band 0 (we use U =15.9 eV for the Al case and 0 U =9.79 eV for the Ag case). Because of the 0 parallel velocity effect, the degeneracy of the 2p x and 2p decay channels is lifted owing to the y different angular distribution functions, and Gloss/capt ≠Gloss/capt . 2pz 2p Eq. (4) hasy been integrated numerically along the outgoing path of the trajectory of the scattered particle. The starting point of the integration is Z =2–3 a.u. (measured from the image plane). ini Close to the surface the F− affinity level lies well below the Fermi level of the surface (see Fig. 1) and the RCT process reduces to the F− formation by electron capture from the surface. Owing to the large charge transfer rates at small distances from the surface, the F− population quickly attains unity and any memory of the initial charge state is lost, as confirmed in a few experiments. Therefore, we consider the initial state of the projectile to be an F− ion and we study its survival when leaving the surface. We use an ionic trajec-

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tory of the projectile that takes into account the interaction of the singly charged fluorine ion with the metal surface via the image potential d2Z dt2

=−

1

1

4M Z2

with dZ dt

K

=v (2)=앀2E /M sin a, ) Proj

Z2 where M and E stand for the mass and the proj energy of the projectile, v is the velocity compo) nent perpendicular to the surface and a is the experimentally measured angle between the outgoing beam and the surface plane (exit angle). In Fig. 2 we present an example of the evolution of the population of the negative ion along the trajectory. The 0.5 keV projectile leaves the Ag(100) surface at the angle a=3.5°. To stress the influence of the parallel velocity effects, we also present in the Fig. 2 the results obtained with V d set to zero. As is seen in Fig. 2, the parallel velocity effect strongly modifies the dynamics of the charge transfer process even for this low projectile energy. Indeed, the F− affinity level crosses the Fermi level

of the surface at a distance Z of about 10.8 a.u. c [we use a work function value of 4.25 eV for the Ag(110) surface as explained below]. When the kinematic effects are neglected, the projectile moves away as a negative ion up to this crossing distance. For larger distances, the ion decays by electron loss and, finally, when the distance gets sufficiently large the charge transfer stops. The evolution of the negative ion population P− can then be described as

CP

P−=exp −

Z C(s)

D

(8) ds v (s) Zc ) where C=C +C +C is the total decay rate. p py pz The situation xis quite different if the parallel velocity effects are included into the treatment. The clear-cut energy separation between occupied and unoccupied metal states is smeared out as seen from the reference frame of the projectile. For the parallel velocity of 0.03 a.u. (energy of the projectile 0.5 keV ) the decay of the negative ion already starts at 8 a.u. from the surface, because the affinity level gets into dynamical resonance with unoccupied metal states. Therefore, the parallel velocity effect favours the negative ion destruction in the present case. Note, that even for such a slow collision where one might think that the kinematic effects are not important, they are important and their neglect leads to an overestimation of the final negative ion fraction by more than 10%. The neutral fraction is underestimated by a factor two.

3. Results and discussion

Fig. 2. Population of the F− ion as function of the projectile– surface distance in the outgoing trajectory path. The exit angle is 3.5° with respect to the surface and projectile energy is 0.5 keV. The integration of the rate equations is started at Z =2a with F− ion as initial charge state. The work function ini 0 of the surface eW=4.25 eV. Solid line: kinematic (V ) effects are d included into the treatment of the RCT; dashed line: V is set d to zero.

In Fig. 3a and b we compare experimental [40– 43] and calculated F− fractions for collisions at Al and Ag surfaces with a fixed exit angle a=3.5°. The negative ion fraction is presented as a function of the energy of the scattered beam. The workfunction of the samples could not be directly determined in the experiments. However, by studying low energy cutoffs of the electron spectra induced by ion scattering, it was found that the work functions eW of Al(111) and Ag(110) surfaces do not differ by more than 20 meV [43]. A 4.3±0.1 eV

N. Lorente et al. / Surface Science 429 (1999) 46–53

(a)

(b) Fig. 3. (a) F− negative ion fraction as a function of the projectile energy for the scattering of Fluorine atoms from an Ag surface. The exit angle is 3.5° with respect to the surface plane. Symbols with error bars represent experimental results for different targets. Dots: Ag(110) surface; squares: polycrystalline Ag surface (from Refs. [40–43]). Thick and thin lines represent theoretical results obtained with work function values eW=4.25 eV and eW=4.3 eV respectively. Solid lines: kinematic (V ) effects d are included into the treatment of the RCT; dashed line: V is d set to zero. (b) F− negative ion fraction as a function of the projectile energy for the scattering of fluorine atoms from an Al(111) surface. The exit angle is 3.5° with respect to the surface plane. Dots with error bars: experimental results (from Refs. [40–43]). Lines: see caption for (a).

value of the surface work function has been measured for Ag(110) by Canepa et al. [45]. For the Al(111) surface an eW value of 4.25 eV has been reported [46 ]. Therefore, we performed our studies for the two work function values 4.25 and 4.3 eV. The calculated negative ion fractions are found to be quite sensitive to the choice of the work function value. The best agreement with experiment is obtained for the eW=4.25 eV. In Fig. 3a and b we also present results of the

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calculations done without inclusion of the parallel velocity effects. The disagreement with experiment is obvious in this case. Indeed, if the kinematic effects are neglected, the negative ion fraction at the end of the collision is described by Eq. (8) with Z=2. For fixed angle scattering, the increase of the projectile energy leads to the increase of the velocity component perpendicular to the surface and, correspondingly, to the increase of the negative ion fraction. The experimental data and the results of the calculation including kinematic effects show an opposite behaviour with the energy, which is the result of the V effect. As was discussed d in Fig. 2, increase of the V (energy) favours the d region of projectile–surface separations where the negative ion can be destroyed via electron loss towards the metal. This effect overcompensates the increasing survival of the negative ion when v ) increases and finally leads to a decrease of the negative ion fraction. In Fig. 4a and b we compare experimental [41– 43] and theoretical results for the F− formation at Ag and Al surfaces as functions of the exit angle for a fixed projectile energy. We use a work function value of 4.25 eV for both surfaces and obtain a good agreement with experimental data, consistent with the results reported in Fig. 3a and b. Within the angular range presented in Fig. 4a and b, the V component of the projectile velocity d slowly decreases with increasing angle, whereas the v component rapidly increases, favouring ) survival of the negative ions. This explains why the negative ion fraction increases with the increase of the outgoing angle from the surface. Results of the calculations neglecting the kinematic effects are also presented in Fig. 4a and b. Though the shape of the angular dependence is reproduced in this case owing to the dominant role played by the change of v , the negative ion fractions are overes) timated. The difference with respect to the calculation including the V effect is particularly large at d small exit angles. It is interesting to discuss the results presented in Fig. 3a in connection with the theoretical results of Ustaze et al. [40] who studied the F−– Ag(110) charge transfer neglecting the parallel velocity effects for the 0.5 keV projectile energy. They compared the results of the rate equation

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N. Lorente et al. / Surface Science 429 (1999) 46–53

(a)

(b) Fig. 4. (a) F− negative ion fraction as a function of the exit angle with respect to the surface plane for the scattering of the 0.5 keV fluorine atoms from an Ag surface. Symbols with error bars represent experimental results for different targets. Dots: Ag(110) surface; squares: polycrystalline Ag surface (from Refs. [41–43]). Lines represent theoretical results obtained with work function value eW=4.25 eV. Solid line: kinematic (V ) d effects are included into the treatment of the RCT; dashed line: V is set to zero. (b) F− negative ion fraction as a function of d the exit angle with respect to the surface plane for the scattering of the 1 keV fluorine atoms from an Al surface. Symbols with error bars represent experimental results for different targets. Dots: Al(111) surface; squares: polycrystalline Al surface (from Refs. [41–43]). Lines: see caption for (a).

approach with those of a full quantum mechanical treatment of the RCT based on the Newns– Anderson Hamiltonian and including multistate and multielectron effects. They found that the rate equation (RE ) approach agrees with the full quantum mechanical (QM ) treatment within 1%: |P− −P− |/P− ≤10−2. It thus appears that, for RE QM RE this system, the multistate rate equation approach takes into account the major many-body effects. They are due to correlation effects in the projectile

side (only one projectile level can be populated at a time) and lead to the spin statistical factors in Eq. (5). Quantitatively, the results of Ustaze et al. [40] are similar to those obtained in the present study. Apparently, for a fixed energy the different work function (4.4 eV ) compensates the absence of the parallel velocity effect in their approach. The above difference between the results of the RE and QM treatments is negligible compared with the parallel velocity effect found in the present study. Therefore, even at a collision energy as low as 0.5 keV, the inclusion of the kinematic effects has a much more important consequence on the description of the RCT process than the possible error introduced by the use of rate equations. In addition, as was pointed out by a number of authors [13,23,24], the parallel velocity smearing of the Fermi distribution destroys coherence effects and further justifies the use of rate equations. Unfortunately, the theoretical developments allowing one to incorporate the parallel velocity effects directly into the generalised dynamical Newns– Anderson Hamiltonian have not been reported yet. Thus, the rate equation approach seems, at the moment, to be the only treatment allowing one to describe correctly the RCT process when parallel velocity effects are important.

4. Concluding summary The F− fractions in scattering from Al and Ag surfaces were studied theoretically. Our treatment is based on the nonperturbative parameter-free calculation of the static properties of the F− ion quasi-stationary state coupled to the metal electronic continuum. It is a one-electron multistate approach that takes into account the fact that any of the six p-electrons of the F− ion can participate in the charge transfer process. The dynamics of the RCT process are described within the rate equation approach where the parallel velocity effects are incorporated via the ‘shifted Fermi sphere’ model. We take full account of the multistate aspect of the charge transfer originating from the 2p6 structure of the F− ion. Quantitative agreement between theoretical results and available experimental data is obtained.

N. Lorente et al. / Surface Science 429 (1999) 46–53

We demonstrate that in the present system the kinematic (parallel velocity) effects on the RCT are important even at such a low collision energy as 0.5 keV, so that they have to be included into the theoretical description of the RCT process in order to get accurate results.

Acknowledgements We are indebted to S. Ustaze, L. Guillemot, and V.A. Esaulov for providing us with unpublished experimental results, large interest in this work and stimulating discussions. Discussions with P. Nordlander are gratefully acknowledged. N.L. acknowledges a postdoctoral grant by la Fundacio´n Ramo´n Areces.

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