Electronic processes in molecule–surface scattering

Nuclear Instruments and Methods in Physics Research B 140 (1998) 265±272

Electronic processes in molecule±surface scattering I.A. Wojciechowski a, V.Kh. Ferleger a, M.V. Medvedeva a, M. Vicanek b, K. Br uning c, c,* W. Heiland b

a Arivov Institute of Electronics, Tashkent 700143, Uzbekistan Institut f ur Theoretische Physik, Technische Universit at, D-38023 Braunschweig, Germany c Universit at Osnabr uck, D-49069 Osnabr uck, Germany

Received 30 September 1997; received in revised form 6 January 1998

Abstract Recent experimental data on H02 and H‡ 2 scattering from Pd (1 1 0) and Pd (1 1 1) as well from Al (1 1 0) surfaces is analyzed in terms of the electron exchange model. The main features of dissociative scattering of H02 and H‡ 2 from Pd can be explained with this model. For the H‡ ! Al (1 1 0) system we consider, beside the electron capture processes 2 for a description of the molecular survival probability as a function of translational energy, an additional process of dissociation: collision induced excitation of the triplet state. Ó 1998 Elsevier Science B.V.

1. Introduction There are two pictures describing the interaction of fast small molecules with solid surfaces. One of them has been proposed by Bitensky and Parilis [1] for the description of non-dissociative scattering of fast molecules. The model is based on the consideration of molecular scattering in terms of independent elastic collisions of the molecular atoms with solid surface atoms. According to another description, inelastic (electronic) processes govern the interaction of a molecule with solid at scattering. The mechanism of molecule dissociation due to resonant neutral-

* Corresponding author. Tel.: +49 541 969 26 75; fax: +49 541 969 26 70; e-mail: [email protected].

ization of a molecule ion into the repulsive state was proposed [2] and then further developed [3,4]. Regarding the ®nal state of a scattered molecule, current assessments of the relative importance of electronic processes vs. elastic rovibrational excitation are di€erent. It is usually supposed that the former picture is valid when the normal kinetic energy E? ˆ E0 sin2 w considerably exceeds the dissociation energy  …E0 is the initial translational energy per molecule atom and w is the glancing angle) [1]. The collisional model dominates in case of inert molecules, e.g. N2 [5]. The latter picture, on the other hand, is often used for charged molecules or for grazing incidence when E? 6  [3,6±8]. A comprehensive theory of these phenomena has to join both these models for a correct description of molecular scattering in the whole range of

0168-583X/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 1 0 4 - 9

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initial parameters. However, at present neither of these descriptions is suciently well developed to allow their uni®cation. This is especially true for the latter model because at present, there is no clear understanding of electron exchange processes and the role of manybody e€ects such as dissolving of the molecular bond in the vicinity of a metal surface due to the screening by metal electrons [9]. Scattering of neutral molecules, where charge transfer processes are suppressed, has been investigated [8±13]. These experiments show that neutral molecules under grazing incidence do dissociate, although the number of surviving molecules is higher than that for charged molecules. The dissociation of neutral H2 molecules has been described in terms of rotational excitation [12,13] following from the collision between the incident species and a single surface atom. The dissociation fraction was found to scale by the combination E0 H2 , where H is the total scattering angle. However in these experiments only ionised secondary species were analysed. The E0 H2 scaling ®ts the experimental data of [12,13] rather well, but the agreement with recent experimental data of [10,14], where the neutral secondary species were analysed, is poor. Moreover, there is a great di€erence in the dissociated fraction at low energies between charged and neutral hydrogen molecules, when the neutral secondaries are analysed. In addition, the average kinetic energy released in the center of mass of a molecule after dissociation was measured [15]. It turned out that this energy does not depend strongly on the initial energy of a molecule in the case of Al-targets. It should also be noted that computer simulations of scattering trajectories [5] underestimate the dissociation fraction at low energies even for the inert N2 molecule. The authors of this work took great care in developing a realistic potential of molecule±surface interaction, particularly taking into account the attractive part of the potential. All these facts point out the importance of electronic processes at low primary energies of a molecule. The aim of this article is to analyze the experimental data on hydrogen scattering obtained re-

cently [10,11,14±16] in terms of the inelastic interaction model. 2. Scattering of hydrogen from Pd In the experiments of Refs. [10,11,14,16] the dissociative fractions of hydrogen scattered from Pd (1 1 0), Pd (1 1 1) and from Pd covered by po0 tassium were measured. H‡ 2 and H2 molecules were used as primary particles. The main experimental results were the following.: 1. At low primary energies …E0 6 1 keV) the dissociation faction YD for H‡ 2 molecules as primary particles is higher than for a neutral incoming beam. 2. YD rises rather weakly with increasing E0 in the experiments with H‡ 2 . YD only varies by about 10% within the energy range from 330 to 1000 eV. 3. In the experiments with H02 , the dissociated fraction YD increases linearly with E0 within the same range of E0 , thus varying by more than a factor of four. 4. YD is about as high (within 10%) in the Pd (1 1 1) experiments as in the Pd (1 1 0) experiments. 5. For K covered surfaces YD is lower by approximately a factor of two compared to clean Pd surfaces. The most probable channel for H‡ 2 dissociation is dissociative neutralization into the antibonding P [2,3,7]. Auger capture into the ground state b3 P‡ u leads mainly to surviving molecules. state X 1 ‡ g In a previous work [6] the additional process of collisionally induced excitation into the triplet state of a molecule after capturing an electron into the ground state has been taken into account. Also considered was the possibility of Auger relaxation into the ground state of a molecule after capture of an electron into the triplet excited state. The latter process has to be considered more closely. The typical time of molecule dissociation from the repulsive state is less than 10ÿ14 s. Because the typical molecule-surface distance for resonant capture into the triplet state is larger than the typical distance for the Auger process, the dissociation event may occur before the de-excitation takes place.

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Presumably, the contribution of this process is rather small and we will not take that into account in our analysis. There are three elementary processes determining the ®nal state of molecule. The rate coecients for these processes are: 1. wtc for resonant dissociative capture into the triplet state; 2. wsc for electron capture into the ground state of H02 ; 3. wex for collisionally induced excitation from the ground state into the repulsive triplet state. The electron capture processes (1) and (2) are adiabatic. Therefore, dependencies of wtc and wsc on projectile energy E0 will be rather weak at low energies …E0 6 1 keV). Collisionally induced excitation, on the other hand, is a non-adiabatic process and thus strongly depends on E0 . Because the quantum mechanical expressions for the rates of these processes include a statistical factor, both wsc and wtc depend on the electron density n at the metal surface. The resonant process is a oneelectron process, so wtc  n. In the Auger process, two electrons are involved and wsc  n2 . To describe the process of the ®nal state formation of the scattered molecules we use a semiclassical model according to which the relative numbers of molecules in a certain state in a certain point of the scattering trajectory are determined from the following equations. For the scattering of neutral molecules: dN 0 ˆ ÿwex …t†N 0 …t†; dt N 0 …t ˆ ÿ1† ˆ 1; N 0 …t† ‡ Q…t† ˆ 1:

…1†

For the scattering of molecular ions: dN ‡ ˆ ÿwtc …t†N ‡ …t† ÿ wsc …t†N ‡ …t†; dt N ‡ …t ˆ ÿ1† ˆ 1; dN 0 …t† ˆ ÿwsc …t†N ‡ …t† ÿ wex …t†N 0 …t†; dt N 0 …t ˆ ÿ1† ˆ 0;

…2†

N ‡ …t† ‡ N 0 …t† ‡ Q…t† ˆ 1; where N 0 …t† is the relative number of neutral molecules in the ground state, N ‡ …t† is the relative

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number of charged molecules, and Q…t† is the relative number of dissociated neutral molecules. The transition rates are de®ned by the expressions: wtc …t† ˆ A exp ‰ÿaz…t†Š; wsc …t† ˆ B exp ‰ÿbz…t†Š;

…3†

wex …t† ˆ C…E0 † exp ‰ÿcz…t†Š; where a; b; and d are inverse decay lengths of the respective rates and z is the distance from the surface. A, B and C(E) are the rates at z ˆ 0: The rate C…E0 † can be written as [6] C…E0 † ˆ nrex v;

…4†

where v is the velocity of molecule, rex is the cross section of the excitation of the triplet state depending on E0 according to: 8 E0 < Et ; > < 0; rex  …E0 =Et †k E0 P Et ; …5† > : const; E0  E t ; where Et is the threshold energy, and k  1. Thus 3=2 for E0 P Et we have C…E0 † ˆ cE0 : Solving Eqs. (1) and (2) with the input from Eqs. (3) and (5) for a certain scattering trajectory, we can obtain the dependencies of dissociation (or survival) probabilities on both the initial energy and the surface electron density of the (metallic) target. First we estimate the orders of magnitude of the rates from the experimental data. For a given length l0 of the scattering trajectory consider the transition rates w averaged both along the trajectory and over all molecular axis orientations. In this case the solutions of Eqs. (1) and (2) are: N 0 …H20 † ˆ exp ‰ÿwex l0 =vŠ;

…6†

N ‡ ˆ exp ‰ÿwtc ‡ wsc l0 =vŠ;

…7†

N 0 …H2‡ † ˆ

wsc exp ‰wex l0 =vŠ: wtc ‡ wsc ÿ wex

…8†

Eqs. (6)±(8) allow to estimate the average values of the transition rates from experimental data.

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Knowing the experimental values for N …1†; N 0 …H02 † and N 0 …H‡ 2 †; the rates can be calculated by the following equations: ‡

wex ˆ ÿw0 ln N

0

…H20 †;

N 0 …H ‡ † wsc ˆ ÿw0 0 20 ln N 0 …1†; N …H2 † wtc ˆ ÿw0

N 0 …H20 † ÿ N 0 …H20 † ln N 0 …1†; N 0 …H20 †

…9† …10† …11†

where w0 ˆ t0ÿ1 ; t0 ˆ l0 =v: The average transition rates were estimated for 0 H‡ 2 [4] and H2 scattered from Pd (1 1 0) for the initial parameters …E0 ˆ 360 eV; w ˆ 5 †. The trajectory length calculated by the MARLOWE code is  [10]. The average transiof the order of l0 ˆ 20 A tion rates evaluated by experimental yields of survived and dissociated particles …N ‡ …1†  10ÿ4 ; N 0 …H02 † ˆ 0:6 and N 0 …H‡ 2 † ˆ 0:24† [11] are: wtc ˆ 5:5  1014 sÿ1 ; wsc ˆ 3:7  1014 sÿ1 ; 14

…12†

ÿ1

wex ˆ 0:5  10 s : The values of transition rates for the resonant and for the Auger capture are reasonable. Indeed, setting the average distance between the image  and plane and the projectile trajectory z0 ˆ 1:3 A assuming the inverse decay length to be of the orÿ1 , we get wtc …z ˆ 0† ˆ 0:75  1016 sÿ1 der of 1.5 A in good agreement with the typical value of resonant transition rates. Taking into account the promoting and the broadening of the molecule ground state level during the molecule±surface interaction, the value wsc appears reasonable, too. (However, we do not discard the possibility that the ground state level may be populated via a resonant transition.) Eqs. (1) and (2) have been solved numerically for the average trajectories of H2 scattered from faces (1 1 0) and (1 1 1) of Pd with initial energies ranging form 300 to 1500 eV. The trajectories were obtained by computer simulations using the code described in [17]. We used the following values of parameters

A ˆ 4  1015 sÿ1 ; B ˆ 1  1015 sÿ1 ; c ˆ 4  108 sÿ1 eVÿ3=2 ; ÿ1 ; b ˆ 1:8 A ÿ1 ; c ˆ 0:8 A ÿ1 : a ˆ 1:5 A The results of the calculations are compared with the experimental data of [10] in Fig. 1, where we show the dissociated fraction of H2 molecules as a function of E0 H2 for both H02 and H‡ 2 scattered from Pd (1 1 0). The dependence YD on E0 enters only through the dependence of wex on E0 . In the next section we will show that the increase of YD with increasing E0 in the case of H02 may be understood in this way. Taking into consideration that the electron densities are di€erent for di€erent faces of the target, n…PD…1 1 0†† S0 …1 1 1† ˆ 1:63; ˆ n…PD…1 1 1†† S0 …1 1 0† where S0 is the surface area per atom, we calculated YD for PD (1 1 1). The results of the calculations for Pd (1 1 0) and Pd (1 1 1) are shown in Fig. 2. It is seen that the dissociated fraction is higher for scattering from Pd (1 1 1), which is in qualitative agreement with the experimental data [16]. It should be noted that in terms of the elastic collision model the probability of molecule dissociation would be lower for the (1 1 1) face because it is less corrugated.

Fig. 1. Dissociated fraction for H02 and H‡ 2 scattered from Pd (1 1 0) as a function of E0 H2 .

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kinetic equations to determine the molecular survival probability:

Fig. 2. Dissociated fraction for H‡ 2 scattered from Pd (1 1 1) as a function of E0 H2 .

The fact that the dissociation probability is higher for a clean Pd surface than for a surface covered by one monolayer of potassium can be understood from the di€erence in surface electron densities of a clean metal and a metal covered by K. Thus the main features of dissociative scattering of H02 and H‡ 2 from Pd can be explained at low energies, i.e. E0 H2 < 30 eV rad2 , in terms of the electron exchange model.

dN ‡ ˆ ÿwtc N ‡ ÿ wscN ‡ ; N ‡ …ÿ1† ˆ 1; dt …13† dN 0 ˆ wsc N 0 ; N ‡ …ÿ1† ˆ 0: dt For simplicity we assume: 1. straight-line incoming and outgoing scattering trajectories; 2. the electronic surface y0 ˆ 0 is located at the distance of closest molecule approach, independent of initial energy. This assumption is justi®ed because in the planar-potential approximation, the distance of closest approach of the center of mass of H2 within initial energy 400± 4000 eV impinging in an Al (1 1 0) surface at  The main a glancing angle of 4 is less than 1 A. contribution to electron capture processes, however, occurs at distances signi®cantly exceeding  [3]; 1A 3. the rates of the electron capture processes as function of the separation between molecule and surface are determined by Eq. (3). Under these conditions we can rewrite Eq. (13) as dN ‡ ˆ ÿ…wtc ‡ wsc †N ‡ ; N ‡ …ÿ1† ˆ 1; dy dN 0 ˆ wsc N ‡ ; N ‡ …ÿ1† ˆ 0;  v? dy

 v?

…14†

3. Scattering of hydrogen from Al The rates wtc and wsc of the electron capture processes were calculated in Ref. [3] for H‡ 2 ! Al (1 1 0) as functions of both the distance from the surface and molecule axis orientation. This allows us to study the dependence of the dissociated or survived molecule fraction on the initial energy in more detail. For Pd comparable theoretical data are not available, therefore we restrict the following study of the collisional excitation process from the H2 singlet to the triplet state in the case of Al for a comparison we use the experimental data of [15]. Qualitatively, however, similar results may be expected for Pd. At ®rst we take into account the electron capture processes. In this case we have the following

where v? is the component of the molecule velocity normal to the surface. The minus sign represents the molecule trajectory before the turning point, y ˆ ÿv? t; while the plus sign applies afterwards, y ˆ v? t: Solving this system we get for surviving molecules Ns0 ˆ Nÿ0 ‡ N‡0 ; Nÿ0

…15†

is the relative number of molecules at the where turning point, and N‡0 is the fraction formed along the outgoing part of the trajectory. Noting that all electronic processes are nearly completed before the turning point [3], we neglect the second term in Eq. (15). Then, for Ns0 we obtain

270

Ns0

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1 ˆ v?



Z1 wsc exp

ÿ

0

 vA ÿay vB ÿby dy; e ÿ e v? v?

…16†

where vA ˆ A=a and vB ˆ B=b. Changing the integration variable in Eq. (16), we get Ns0

vB ˆ v?



Z1 wsc exp 0

ÿ

 vA aby vB t ÿ t dt: v? v?

…17†

In general, this integral can be found only numerically. But it is seen that if a ˆ b; we get a formula of Hagstrum's type [18],    vB vA ‡ vB vB 0 1 ÿ exp ÿ ÿ t ; …18† Ns ˆ vA ‡ vB v? v? for surviving molecules. It is seen that if vA  vB  v? then Ns0  const. For the case vA  vB  v? the number of surviving molecules has to decrease with increasing normal velocity. For an arbitrary relation between the decay lengths of singlet a and triplet b electron capture processes the dependence on v? may be di€erent. The range of variation of v? in the experiments of [15] is from 1:5  104 to 4:3  104 m/s. The values of vA and vB obtained in (3) for H2‡ ! Al for a molecule axis orientation normal to the surface For the case signi®cantly exceed v? : vA =v?  1; vB =v?  1; vA  vB and a=b 6 1 one can estimate the integral Eq. (17) analytically. It is easy to show that in the zero order approximab=aÿ1 tion Ns0 / v? : It is seen that if a < b the molecular survival probability has to increase with increasing normal velocity. Neutralization into the antibonding state occurs at a distance from the surface larger than that of neutralization into the ground state. A faster molecule has a better chance to reach without dissociative neutralization the surface, where electron capture into the ground state occurs with a comparable probability as the dissociative capture. For molecule axis orientations parallel to the surface, the rate of the singlet capture process signi®cantly exceeds the rate of the dissociative capture at all distances between molecule and surface. In this case we get a Hagstrum's type formula for the molecular survival probability. To compare the results of the calculations with exper-

imental data we have to average Eq. (17) over all molecule axis orientations. Taking into account both more accurate approximations for the rates obtained by Imke et al. [3] and the rate dependence on c …c is the angle between molecule axis and surface), we numerically solved Eq. (14) for 0 6 c 6 90 with a stepsize of 5 for di€erent normal velocities. Then we averaged Ns0 assuming an isotropic molecule axis orientation distribution. The results of these calculations are shown in Fig. 3 (dashed line). It is seen that the number of surviving molecules is practically independent of normal velocity for the given range. That is in contradiction with the experimental data of [15], where the survival probability decreases by almost a factor of two within the same range of velocities. In order to ®t the experimental data of [15] we have to allow for an additional dissociation mechanism, the rate of which depends on the energy of the molecule. An obvious candidate is collisionally induced excitation from the singlet to the triplet state which is followed by dissociation. However, as was shown experimentally, the average kinetic energy of the molecule atoms released after dissociation does not depend on E. For a collisional mechanism, one would expect the energy release to in-

Fig. 3. Molecular survival probability as a function of the normal velocity component averaged over molecule axis orientations. The dashed line shows the calculation using results of [3], the solid line includes the process of collisional triplet state excitation.

I.A. Wojciechowski et al. / Nucl. Instr. and Meth. in Phys. Res. B 140 (1998) 265±272

crease with increasing bombarding energy. Therefore, the dissociation process in question is very likely an electronic process. We consider therefore the electron spin-¯ip excitation from the ground state into the antibonding stage. Adding a corresponding term in the right- and side of the second equation in (14) we get  v?

dN ‡ ˆ ÿ…wtc ‡ wsc †N ‡ ; dy

N ‡ …ÿ1† ˆ 1;

dN 0 ˆ wsc N ‡ ÿ wex N ‡ ;  v? dy

0

N …ÿ1† ˆ 0: …19†

0

The solution for N is 0 1 Z1 1 wex dy A N 0 ˆ Q exp @ ÿ v? 0

‡

1 v?

Z1 0

0

B 1 f …y† exp @ÿ v?

Z1

1 C wex …t† dtA dy; …20†

y

where Q is the number of neutral molecules at the turning point, 8 9 Z1 Z1 < = 1 1 wsc exp ÿ ‰wsc …t† ‡ wtc …t†Š dt Qˆ : v? ; v? 0

y

2

 exp 4 ÿ

1 v?

Zy

3

wex …t† dt5dy;

0

f …y† ˆ N ‡ …0†wsc …y† 8 9 < 1 Zy = ‰wsc …t† ‡ wtc …t†Š dt dy:  exp ÿ : v? ; 0

We calculated the integrals in Eq. (20) numerically using the parameters c = 9:8  108 sÿ1 eVÿ3=2 ; d ˆ 1:8 A. The dependence of Ns0 …v? † is shown in Fig. 3 (dashed line). It is seen that the molecular survival probability is decreased almost by a factor two within the displayed range of v? , which qualitatively agrees with experimental data [15].

271

Thus in order to describe the experimental data for H‡ 2 ! Al in terms of the electronic process model we have to take into account molecule dissociation due to a collisional excitation into the triplet state. 4. Conclusions We have analyzed recent experimental data on H02 and H‡ 2 scattering from Pd (1 1 0) and Pd (1 1 1) as well as from Al (1 1 0) in terms of the electron exchange model. Three elementary electronic processes determining the ®nal state of H02 and H‡ 2 scattered have been taken into account: 1. resonant dissociative capture into the antibonding state; 2. electron capture into the ground state; 3. collisionally induced excitation from the ground state into the repulsive triplet state. Using a semiclassical model we calculated dissociated fractions for H02 and H‡ 2 scattered from Pd (1 1 0) and Pd (1 1 1) as functions of the combination of the initial parameters E0 H2 . The results of the calculations are in a good agreement with the experimental data using reasonable values for the model parameters. It has been shown that for the H‡ 2 ! Al (1 1 0) system it is not sucient to only consider the electron capture processes in order to describe the molecular survival probability as a function of translational energy. An additional process of dissociation ± collision-induced excitation of the triplet state ± has to be invoked. It would be interesting to obtain experimentally the molecular survival probabilities for E0 < 300 eV. At these initial energies a contribution of the collision-induced excitation to the dissociation process is negligible. Due to the di€erence of the decay lengths of singlet and triplet electron capture processes, the molecular survival probability is expected to be independent of E0 : Thus, using the simple model of electron exchange processes, we explained qualitatively the main features of recent experiments on scattering of H02 and H‡ 2 from metal surfaces.

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Acknowledgements This work was supported in part by Grant No USB 005-96 within the framework of the Program of Scienti®c and Technological Cooperation between Germany and Uzbekistan. The experiments are supported by the Deutsche Forschungsgemeinschaft. References [1] I.S. Bitensky, E.S. Parilis, Nucl. Instr. and Meth. B 2 (1984) 384. [2] W. Heiland, U. Beitat, E. Taglauer, Phys. Rev. B 19 (1979) 1677. [3] U. Imke, K.J. Snowdon, W. Heiland, Phys. Rev. B 34 (1986) 41±48. [4] J.M. Schins, R.B. Vrijen, W.J. van der Zande, J. Los, Surf. Sci. 280 (1993) 145. [5] T. Schlath olter, T. Schlath olter, M. Vicanek, W. Heiland, Surf. Sci. 352 (1996) 195. [6] I.S. Bitensky, E.S. Parilis, I.A. Wojciechowski, Nucl. Instr. and Meth. B 47 (1992) 243; ibid B 73 (1993) 333.

[7] W. Tappe, A. Niehof, K. Schmidt, W. Heiland, Europhys. Lett. 15 (1991) 405. [8] K.J. Snowdon, R. Harder, A. Nesbitt, Surf. Sci. 363 (1996) 42. [9] K. Schmidt, T. Schlath olter, A. N arman, W. Heiland, Chem. Phys. Lett. 200 (1992) 465. [10] K. Schmidt, H. Franke, T. Schlath olter, C. H ofner, A. N armann, W. Heiland, Surf. Sci. 301 (1994) 326. [11] T. Schlath olter, W. Heiland, Nucl. Instr. and Meth. B 100 (1995) 352. [12] U. van Slooten, D.R. Andersson, A.W. Kleyn, E.A. Gislason, Surf. Sci. 274 (1992) 1. [13] U. van Slooten, A.W. Kleyn, Chem. Phys. 177 (1993) 509. [14] W. Heiland, T. Schlath olter, M. Vicanek, Phys. Stat. Sol. (b) 192 (1995) 301. [15] K. Br uning, T. Schlath olter, A. N armann, W. Heiland, to be published. [16] T. Schlath olter, T. Schlath olter, M. Vicanek, W. Heiland, in: P. Varga, F. Aumayr (Eds.), Symposium on Surface Science 3S' 95, Institut f ur Allgemeine Physik, TU Wien, A±1040 Wien, Austria, 1995. [17] M. Vicanek, T. Schlath olter, W. Heiland, Nucl. Instr. and Meth. B 115 (1996) 206. [18] H.D. Hagstrum, Phys. Rev. 96 (1954) 336.