Formation of negative ions in grazing scattering from insulator surfaces

Transcription

1 PHYSICAL REVIEW A VOLUME 57, NUMBER 1 JANUARY 1998 Formation of negative ions in grazing scattering from insulator surfaces C. Auth, A. Mertens, and H. Winter Institut für Physik der Humboldt-Universität zu Berlin Invalidenstrasse 110, Berlin, Germany A. G. Borisov and V. Sidis Laboratoire des Collisions Atomiques et Moléculaires, Bâtiment 351, Université Paris Sud, Orsay Cedex, France Received 13 March 1997 Substantial fractions of fast atoms or ions are converted to negative ions during grazing scattering from a clean and flat monocrystalline surface of alkali-metal halides. We interpret the experimental data by a model of local electron capture from the halogen sites of the crystal in binary-type collision events. Due to the band gap of the insulator, the probability for subsequent electron loss is low, resulting in large fractions of negative ions that survive from the collisional formation. S PACS numbers: Rf, e I. INTRODUCTION In recent years there has been increasing activity concerning the scattering of atomic projectiles from insulator surfaces, in particular alkali-metal halides. A variety of processes have been studied by application of different methods, e.g., sputtering and secondary-ion emission for a brief review see Ref. 1, charge exchange under large-angle impact 2, or electron-emission phenomena 3. Recently, also studies with multicharged projectiles have been reported 4 9 that clearly show that the understanding of interaction processes is far from the level currently achieved for metal targets. In this respect we performed studies on the effects of an image charge acceleration on the trajectories of multicharged ions 10 scattered under a grazing angle of incidence from a LiF100 surface 6. From the analysis of our data with respect to the neutralization dynamics of multicharged ions we concluded that in front of the surface of an ionic crystal for a very short period of time neutral atoms with highly inverted populations of Rydberg states, so-called hollow atoms, are formed. In those experiments we noticed for some atomic species substantial fractions of projectiles that were converted to negative ions 11. These at first glance, somewhat surprising observations initiated detailed studies on this problem. In this paper we will report our experiments on the formation of negative ions in grazing scattering from surfaces of alkali-metal halides, here LiF100, KCl100, and KI100. The experimental data reveal some systematic features that are interpreted by a model of local electron capture from negatively charged sites of a ionic crystal. We will demonstrate that the interplay of capture of localized electrons in binary-type collision events and the subsequent suppression of electron loss due to the band gap of insulators results in substantial fractions of negative ions. Our studies represent an interesting alternative scheme concerning negative-ion conversion via scattering from surfaces, where metal surfaces with low work functions achieved by alkalimetal atom adsorption have been primarily considered so far 12,13. II. EXPERIMENT In our experimental studies we scattered a number of different sorts of atoms and ions primarily hydrogen, oxygen, sodium, and fluorine from the 100 faces of monocrystalline LiF, KCl, and KI samples. The ions are produced in an electron cyclotron resonance ion source and accelerated or decelerated to final energies ranging from some 100 ev to some 100 kev, achieved by mounting the ion source and analyzing the magnet on a high-voltage platform. The targets have a cylindrical shape about 10 mm in diameter and about 2 mm thick and are mounted on a tantalum block with bores for tungsten wires for Ohmic heating up to 500 C. The 100 surfaces are prepared via cleaving and subsequent mechanical polishing before inserting the samples into the UHV chamber at a base pressure in the upper mbar regime. For scattering experiments with fast ions under grazing incidence any macroscopic charging up of the insulating target has to be avoided. For alkali-metal halides this difficulty can be avoided by heating the target up to some 100 C, where those samples show sufficient conductivity 1. Since this item is an essential prerequisite for experiments with ions, we have investigated this problem in detail by using primary ion beams with relatively high currents in the microampere domain on the target in the actual studies on negative-ion conversion currents typically less than 1 na are applied. From these studies we can deduce that under our conditions target temperatures above about 150 C are sufficient to avoid a deflection of projectiles by the accumulation of charge on the target. The in situ preparation of the target surface and the scattering experiments were performed at target temperatures between 250 C and 330 C. For annealing the temperatures are raised for several minutes up to about 400 C. The target surface is prepared by sputtering with 25-keV Ar ions under a grazing angle of incidence in 1.6. This type of cleaning and reducing the density of defect structures from the topmost layers of the surface has been shown to provide high-quality surfaces for metals since erosion phenomena present for impact under large angles are widely avoided. In order to reduce directional effects during this /98/571/35111/$ The American Physical Society

2 352 AUTH, MERTENS, WINTER, BORISOV, AND SIDIS 57 FIG. 1. Target current as a function of azimuthal angle during sputtering of the LiF100 surface with 25-keV Ar ions under in 1.6. FIG. 2. Simple sketch of the experimental setup. Measured angular distributions for 25-keV Ar ions scattered from a LiF100 surface. The distribution after one month in situ preparation full circles of the crystal surface is compared with the distribution at an early stage open circles. procedure, the target is azimuthally rotated in intervals of about 1.5 with a sputtering time of 1 2 s per position. This procedure is controlled with a small computer under simultaneous recording of the effective current measured from the target surface to the ground. In Fig. 1 we display a typical dependence of the target current on the azimuthal angle in an advanced state of preparation of the target surface. Whereas in an early state this curve does not show any structures, here defined peaks can be seen in the data. It is straightforward to identify the most prominent peaks with the 100 directions in the LiF100 surface, separated by angular intervals of 90. Also the 110 directions can be deduced at 45 between the prominent peaks. The origin of this structure is ascribed here in a similar way as for metal targets 14 by an enhanced kinetic emission of electrons for trajectories determined by axial channeling along low-indexed directions in the surface plane. Thus these structures in the target current provide a precise method for the azimuthal adjustment of the target relative to the direction of the projectile beam. Most measurements are performed for an azimuthal orientation along a high-indexed random direction, where the scattering from the surface is not affected by axial channeling effects 15. Important information on the conditions for a surface scattering experiment is obtained from angular distributions of scattered projectiles. A sketch of the collision geometry and the experimental procedure is given in the upper part of Fig. 2 see also the more detailed drawing in Fig. 3. The well-collimated beam 0.2-mm slits separated by a distance of 0.7 m is directed onto a LiF100 target kept at a constant temperature of 330 C. A residual fraction of the incoming beam passes above the target without scattering, so that the intense peak due to these projectiles serves as a reference for the direction of the incoming beam. In the lower part of Fig. 2 we show angular distributions at early and advanced states of preparation, respectively. In the beginning of the preparation cycles a very broad and undefined angular distribution with a full width at half maximum FWHM of several degrees is observed, indicating a high density of defect structures on the target surface. This distribution is gradually improved with increasing efforts in the preparation of the target. After a great number of preparation cycles over a period of about three weeks for the LiF100 surface, a well-defined angular distribution with a FWHM 0.3 for 25-keV Ar projectiles is recorded. This means that most of the projectiles are scattered under planar channeling conditions 16 with well-defined trajectories for an ensemble of scattered particles. Note that the improvement of the quality of the target surface is reflected also in a kind of condensation with respect to the flux density of the scattered beams. For the data shown in Fig. 2 the peak intensity is enhanced by a factor of about 60 for the better prepared surface. In our studies on charge exchange outlined below, these scattered beams are analyzed with respect to the charge states of the projectiles emerging from the surface. In general, measurements of charge fractions of fast beams are conceptually simple. It turns out, however, that in particular for grazing surface scattering those measurements bear conceptual problems that make a reliable analysis of charge fractions nontrivial. A dominant contribution in this respect is caused by the effect of the image charge interaction on the trajectories of charged projectiles 17. The forces due to this attractive interaction deflect trajectories of outgoing ions towards the surface plane, whereas trajectories of neutral atoms are not affected. Thus the angular distributions for particles emerging from the surface as ions are shifted with respect to those distributions for neutral particles. This angular shift has to be taken into account in measurements of charge fractions. In cases where the charge fractions are dominated by a singly charged and a neutral component here N and N 0

3 57 FORMATION OF NEGATIVE IONS IN GRAZING FIG. 3. Sketch of the experimental setup for measurements of angular distributions separated with respect to the charge states of scattered projectiles CEM: channel electron multiplies; HV: high voltage. with N N 0 1, a difference method has been shown to provide reliable data with respect to trajectory effects 17,18. In Fig. 3 we show a more detailed sketch of our setup, where the angular distributions for charged as well as neutral particles are separated by means of electric-field plates between the target and detector. The detector is positioned about 70 cm behind the target on a precision manipulator and can be translated within the plane of scattering via a stepmotor drive under computer control. The fast particles are detected with a channeltron VALVO X919BL, where the 0.5-mm-diam entrance aperture is covered with a thin carbon foil several g/cm 2 thick in order to achieve a charge state equilibrium for transmitted ions and atoms and thus the same response of the detector irrespective of the charge state of an incoming projectile. A typical result obtained with this technique is displayed in Fig. 4 for 10-keV O atoms scattered from a LiF100 surface, where the fast atoms are produced in a gas target mounted in the beamline between the accelerator and the UHV chamber. The gas target was operated with air. The FIG. 4. Angular distributions for emerging O atoms full circles and O ions open circles for the scattering of 10-keV oxygen atoms from a LiF100 surface. The solid lines represent fits to the data by a Gaussian line shape. FIG. 5. Negative-ion fractions for grazing scattering of 7-keV full circles, 20-keV full triangles, and 60-keV full squares oxygen atoms from a LiF100 surface as functions of the energy for the motion parallel to the surface normal. main reason for using neutral projectiles here is to avoid image charge effects on the incident part of the trajectories, which would enhance the initial energies for the motion normal to the surface plane 10,17. The data show a pronounced angular shift between the angular distributions for emerging O atoms obtained from the signal with biased field plates and for O ions obtained from the difference signals for grounded and biased field plates. O atoms are scattered under a mean scattering angle s and O ions under s It is straightforward to show that the reduction of normal energy for the ions E z is obtained from E z E 0 sin 2 s 0 /2sin 2 s s 0 /2 where E 0 is the kinetic energy of scattered projectiles. Since the energy loss is relatively small, we can take the initial projectile energy here to a good approximation and deduce E z 0.65 ev. We will discuss below that we can obtain from E z important information on the distance of effective formation of O ions. From the peak heights arbitrarily normalized in Fig. 4 we deduce the negative-ion fractions. The solid lines represent best fits to a Gaussian line shape for the analysis of data. In Fig. 5 we display O fractions as functions of the normal energy E z E 0 sin 2 in for the projectile energies E 0 7, 20, and 60 kev; E z is adjusted here by setting the angle of incidence in. We observe a pronounced enhancement of the O fractions with increasing normal energies and a saturation for E z 5eVatallE 0. In Fig. 6 we have plotted the O fractions for three normal energies E z 1, 2, and 5 ev as functions of the projectile velocity v and reveal a kinematic resonance structure. A striking feature of the data are negative-ion yields larger than 60% for velocities of about a.u., which correspond to E 0 20 kev. These large yields are quite surprising at first glance since occupied electronic states of LiF have binding energies larger than 12 ev see below. On the other hand, experiments with clean Al or Au targets with binding energies work functions of about 4.3 and 5.3 ev, respectively, showed O fractions of only 3 5 % 19,20. In Fig. 7 we show a study on the dependence of the O fractions on the azimuthal orientation of the target relative to 1

4 354 AUTH, MERTENS, WINTER, BORISOV, AND SIDIS 57 FIG. 6. Negative-ion fractions for the scattering of fast oxygen atoms from a LiF100 surface as functions of the projectile velocity. Circles, E z 1 ev; triangles, E z 2 ev; squares, E z 5 ev. The solid and dashed lines are drawn to guide the eye. the direction of the incoming beam. We observe no pronounced effects for scattering along low-indexed directions axial surface channeling or at random directions planar surface channeling. Before we present more experimental data for other atomic projectiles and alkali-metal halide targets, we give an outline of a model that allows us to explain essential features of the experiments. III. MODEL FOR THE ELECTRON CAPTURE IN GRAZING SCATTERING FROM THE IONIC CRYSTAL SURFACES A. General outline Two processes are responsible for the formation of negative ions in grazing scattering of atomic projectiles from the surface of an ionic crystal. Those are electron capture of the projectile from the surface and electron loss from the negative ion to the surface. Final negative-ion fractions result from the interplay of the two processes. Electron loss is suppressed owing to the large electronic band gap of the ionic crystal. In Fig. 8 we show schematic band structures of the FIG. 7. Negative-ion fractions for the scattering of oxygen atoms from a LiF100 surface under an angle of incidence of in 1 as functions of the azimuthal angle. Triangles, v0.14 a.u.; circles, v0.39 a.u.; squares, v0.50 a.u. FIG. 8. Sketch of the energies of the bands of LiF, KCl, and KI; the affinity levels of F, O, and H; and the 3s level of Na. surfaces relevant for our studies together with the energies of the negative-ion states. It is evident that in case of the scattering from the LiF surface, there are no states in resonance with the H,O, and F affinity levels towards which an electron loss can proceed. This holds for the F -KCl and F -KI systems, while for H and O ions in front of the KCl and KI surfaces electron loss towards the conduction band seems possible, though only the states close to the bottom of the band can participate in this process. In general, we expect that electron-loss processes via resonant electron transfer are suppressed at low projectile velocities. Now we consider the problem how electrons can be captured from an alkali-metal halide surface despite the large energy difference between electronic states of the projectile and occupied electronic states of the target. It is tempting to explain the large negative-ion fractions in the outgoing beam by the presence of occupied states with low binding energies at the surface of the alkali-metal halide crystal 9,21. In this case negative-ion formation will proceed via resonant electron capture from those states and basically the formalism to describe negative-ion formation at metal surfaces can be applied. Although this model is able to explain the efficient negative-ion formation and its dependence on velocity, it contradicts other experimental data available on charge transfer at alkali-metal halide surfaces. Indeed, experiments on alkali-metal atom or ion scattering demonstrate that there are no surface states with binding energies comparable to the ionization potentials of ground or excited states of alkali-metal atoms 25. Note that binding energies of negative ions electron affinities are in the same energy range as ionization potentials of alkali-metal atoms. Furthermore, a suppression of Auger electron capture was observed for the He and Ne projectiles in the scattering from a LiF100 surface 26. This can only be explained by the large binding energies of valence-band electrons in alkali-metal halides and would not be possible if the occupied states with low binding energies were present with sufficient density at the surface. In fact, such surface states are found neither in metastable helium deexcitation spectroscopy 27 nor in ab initio band-structure calculations 28. In recent works 11,29,30 we proposed a model for the negative-ion formation based on the property of the alkalimetal halide crystals to have alternating positively charged

5 57 FORMATION OF NEGATIVE IONS IN GRAZING For simplicity we will neglect polarization effects including image potentials. In addition we will consider a range of distances R between the projectile and the active site large enough so that electronic clouds of the Hal active site and the projectile do not overlap significantly. With these approximations we have EHal active site AE Hal E A i j q i q j r i r j i q i r i. 4 FIG. 9. Sketch of the binary interaction model. The lower plane represents a portion of the crystal lattice surrounding the Ha active site. The dashed upper line shows a trajectory of the projectile A in the plane (X,Y,ZZ 0 ). alkali-metal ions (Alk ) and negatively charged halogen ions (Hal ) at lattice sites. The valence band originates from the Hal (np x,y,z ) orbitals and the valence-band electrons are localized at the Hal sites The binding energies of the valence-band electrons can be well approximated by the affinity of a free Hal ion increased by the Madelung potential of the crystal. Further contributions come from the polarization effects and finite bandwidths 35. Electron-transfer processes between a projectile (A) and the surface of an alkali-metal halide crystal involve localized valence-band electrons. Therefore, it can be viewed as a series of binary interactions between the projectile and Hal ions at the crystal sites Fig. 9 29,30 Hal active site A Hal active site A, where active site specifies the actual crystal site involved in the binary interaction. It is taken at the origin of the frame. Other ions of the crystal are spectators and considered as point charges. Note that, owing to the flat and narrow valence bands of the alkali-metal halide crystals, the mobility of a hole is low. Therefore, removal of an electron from the Hal ion at the crystal site keeps the corresponding hole localized at that site for the time scale of the collision 35. We will present here a simple qualitative discussion of the process of the electron capture, given by Eq. 2. Some formulas will be derived, which can be used to analyze the experimental data. This approach is actually supported by parameter-free calculations on negative-ion formation in grazing scattering from alkali-metal halide surfaces 29,30. B. Energy-level confluence The probability of the electron-transfer reaction Eq. 2 is determined by the energy difference between final-like (Hal active site A ) and initial-like (Hal active site A) diabatic states during the collision: ER EHalactive site A EHal active site A. E(R ) is the energy that is needed to move an electron from the Hal ion at the surface to the projectile located at R Fig E Hal and E A are the total energies of the free Hal ion and projectile A, respectively. The q i 1 are the point charges at the crystal sites located at r i relative to the active site. The third term in Eq. 4 gives the interaction energy between the point charges of the crystal excluding the active site. The last term is the interaction energy between the active site having a charge 1 and all other sites of the crystal. In the same way we have EHal active site A E Hal E A i j i q i R r i. q i q j r i r j From Eqs. 4 and 5 we obtain the energy difference ER Hal A i q i r i i q i R r i, where Hal E Hal E Hal and A E A E A are electron affinities of the free Hal ion and the free projectile, respectively. The last two terms give the difference between the Madelung potentials created by the point charges at the Hal site E Mad (0)E Mad and at the point R E Mad (R ). Sofinally Eq. 5 can be written as ER Hal A E Mad E Mad R. In order to understand the mechanism of electron transfer, let us consider the case R a, where a is the lattice constant. For a distant charge, a hole created in the neutral crystal by the removal of a negative charge at the active site is seen as a 1 charge. In this case E Mad (R )1/R (RR ) and Eq. 6 gives ER Hal A E Mad 1/R a Equation 8a pinpoints the basic phenomenon that initiates a confluence of the relevant energy levels and therefore enables the electron capture from halogen sites. It is essentially due to the Coulomb interaction in the final-like state between the negative projectile and the hole created in the neutral crystal by the removal of an electron. The above derivation of the energy difference between final-like and initial-like states can also be applied to the more general case of electron capture by a projectile with charge q (A q ) from the alkali-metal halide crystal surface. In this case one obtains 30

6 356 AUTH, MERTENS, WINTER, BORISOV, AND SIDIS 57 FIG. 11. Negative-ion fractions of scattered oxygen atoms with E z 2eVfull triangles and neutral fractions of scattered sodium ions full circles as functions of projectile velocity. FIG. 10. a Energy difference between initial-like and final-like states for O formation at distances Z a.u. solid line, Z a.u. dashed line, and Na neutralization Z a.u. dotted line in front of a LiF100 surface as a function of X. b Energy difference for O full line and F dashed line formation at a distance Z a.u. in front of a KI100 surface as a function of X. ER Hal A q1e Mad q1/r, 8b where A g1 is the binding energy of the projectile A q1.it is evident from Eq. 8b that the energy-level confluence will not occur for the neutralization of positive ions. Indeed, if the initial charge of the projectile is q1, then for R a we have E(R ) Hal IE Mad const, where I is the ionization potential of the atom. In order to obtain the efficiency of the charge-transfer process one has to know E(R ) over the whole trajectory of the projectile. Important are the small separations between the collisional atom and an active halogen site where the electron-transfer interaction between initial-like and finallike adiabatic states is comparable with E(R ) and leads to electronic transitions. In Figs. 10a and 10b we show E(R ) calculated from Eq. 7 for O and F formation at LiF100 and KI100 surfaces O 1.46 ev, F 3.4 ev, I 3.37 ev, and the spin-orbit interaction in the neutral I atom is removed. We also show E(R ) for Na neutralization by electron capture from F sites at a LiF surface. We consider a part of the trajectory of the projectile close to the turning point and therefore parallel to the surface: R (t)(xvt,0,z), where v is the projectile velocity. The scattered beam is assumed to be parallel to the 100 direction. Only positive values of the X coordinate are shown. The case Y 0 corresponds to the passage on top of the active site at the surface. The calculations show that for negative-ion formation E decreases essentially as soon as the active site is approached. This facilities electron transfer from the active site to the projectile. For Na neutralization, however, the energy defect of the reaction E remains large Fig. 10a. Therefore, a high velocity of the projectile is needed to bridge the energy gap between initiallike (F active site Na ) and final-like (F active site Na) states and to neutralize the Na ion. Oscillations present for all curves result from the passage over or point charges at the surface. The calculated energy differences E for Na neutralization and O formation at a LiF surface Fig. 10a qualitatively explain the experimental results presented in Fig. 11. Indeed, in the range of projectile velocities, where O atoms grazingly scattered from a LiF surface are efficiently transformed into O ions, Na projectiles will hardly capture electrons. As follows from Eq. 7, E is reduced for an increasing electron affinity of the projectile. This is illustrated in Fig. 10b, where the energy defect E is presented for the O and F formation via electron capture from I active site of a KI100 surface. E is smaller for the F ion and electron transfer will proceed under nearly resonance conditions. In this case we predict an efficient negative-ion conversion of fluorine atoms at a KI100 surface. A further important feature seen in Fig. 10 consists in a remarkable difference between O formation at LiF100 and KI100 surfaces. The energy defect for the charge transfer E is much smaller in the case of the KI100 surface for the same ion surface distance Z. This can be explained by the larger lattice constant of the KI crystal (a13.34a 0 ) compared to LiF (a7.592a 0 ). As follows from Eq. 7, the energy difference E is governed by the difference of the Madelung potentials at the active site and at the position R of the projectile. Since the characteristic size of the variation of the Madelung field is given by the lattice constant a, the smaller the ratio R/a, the smaller the difference E Mad E Mad (R ). For the same reasons a reduction of the

7 57 FORMATION OF NEGATIVE IONS IN GRAZING projectile-surface distance Z leads to a reduction of E compare the solid and dashed lines in Fig. 10a. From the results presented in Fig. 10 the following conclusions can be drawn: i The larger the electron affinity of the negative ion, the more efficiently it will be formed at the surface; ii the increase of the lattice constant of the target will reduce the projectile velocity required for the efficient negative ion formation; and iii the negative-ion formation proceeds on the part of the projectile trajectory close to the surface. The last conclusion is supported by the experimental data on the image forces affecting the trajectories of negative ions. As discussed above see Fig. 4, image potentials of the order of 0.65 ev are measured for the O ions formed at LiF100. Based on dynamical response theory 36, velocity-dependent image potentials can be evaluated for singly charged projectiles in front of the LiF surface 6. Negative-ion formation distances of Z3 a.u. can then be deduced from the experimentally measured angular shifts. This negative-ion formation distance corresponds to the distance of closest approach to the surface as obtained from the Ziegler-Biersack-Littmark ZBL binary interaction potentials 37. C. Population buildup A nearly constant energy difference E between initiallike and final-like states in the electron-transfer region close to the active site can be seen in Fig. 10. Therefore, we will apply the Demkov near-resonance electron-transfer model 38 to describe the probability of the process defined in Eq. 2. We should point out that the results of the parameter-free studies 29,30 justify the validity of this approximation see below. Assuming an exponential dependence on R of the electron-transfer interaction V transfer that couples initial-like and final-like states, one obtains 38 P binary 1 2 sech2 2 E v, 9 where P binary is the probability for negative-ion formation in the binary collision with the Hal active site. characterizes the exponential decay of the electron-transfer interaction V transfer V 0 e R/. The factor 1 2 in Eq. 9 arises from the averaging over the trajectories with different impact parameters. The parameter can be estimated from the decay length of the wave functions of the collision partners: Hal E Mad 2 A. 10 Equation 9 can be adjusted in a phenomenological way to include the effect of the translational factors arising from the projectile motion with respect to the active site 39: P binary 1 2 sech2 2 Ev 2 /2 v. 11 In grazing scattering experiments projectiles spend a long part of their trajectory close to the surface and experience a number of binary collisions with Hal sites at the surface. The final probability of the negative-ion formation during an interaction with the surface is then given by P final 11P binary N, 12 where N is the number of binary collisions. Note that the final negative-ion formation probability can be large even for small P binary, provided the number of binary collisions N is large. Equations 11 and 12 can be used to analyze on a simple qualitative level the experimental results. The values of E and N can be only estimated within this approach and used as adjustable parameters representing an effective energy difference E and an effective number of collisions N along the projectile trajectory. D. Parameter-free calculations of the F formation in grazing scattering at a LiF 100 surface For details on the parameter-free study of negative-ion formation in grazing scattering on alkali-metal halide surfaces we refer to recent work 29,30. Here we will give only a brief outline of its results justifying the qualitative discussion presented in the preceding subsection. Consider the case of F ion formation in grazing scattering at a LiF100 surface. Owing to the open p-shell structure of the halide atom three substates emerge in the initial-like (F active site F collisional ) and final-like (F active site F collisional ) states. Those levels correspond to the permutation of the hole among three 2p orbitals 2p x,2p y, and 2p z of the collisional F atom and F atom at the active site. We use a reference frame with the z axis along R. This is the natural choice for a treatment of the binary collision given by Eq. 2. Hartree-Fock-Roothan self-consistent field SCF schemes are used then to calculate the Hamiltonian H matrix within the diabatic basis of the states formed by the hole permutation among the 2p x,y,z orbitals of F active site and F collisional atoms. The collisional F atom and the F atom at the active site are treated explicitly, while all the other ions in the crystal are presented by possibly polarizable point charges. In Fig. 12 we present the energy differences E and F electron-transfer interactions V transfer between 2p collisional z and F 2p active site F z and also between 2p collisional F x and 2px active site. In addition we show E calculated from the point charge estimate Eq. 6. We consider a trajectory of the projectile in the 100 direction and parallel to the surface: R (X,0,Z 2.5a 0 ). Only positive values of the X coordinate are shown. The case Y 0 corresponds to the passage on top of the active site at the surface. As seen in the figure, the point charge estimate for E is rather close to SCF results. The differences arise from distortions of the electronic clouds of the collisional partners polarization effects caused by the field of the point charges. These polarization effects are present in the SCF calculation, but completely ignored in Eq. 6. The electron-transfer interaction V transfer is much stronger between the p z states oriented along the molecular axis than the p x states lying in the parallel planes results for the p y states are very close to those of p x states. From the distance dependence of the energy differences and electron-transfer interactions presented in Fig. 12 we can estimate on the applicability of the Demkov model to describe transitions between the states. Favorable regions for electron transfer E 2V transfer 38 are indicated in the figure by hatched bars.

8 358 AUTH, MERTENS, WINTER, BORISOV, AND SIDIS 57 FIG. 13. Negative-ion fractions as functions of projectile velocity for hydrogen, oxygen, and fluorine atoms scattered from LiF100. The dashed lines show the ion fraction obtained with Eqs. 11 and 12 O, long-dashed line; F, short-dashed line and the solid line results from parameter-free calculations. model for electron capture, the velocity threshold v th for the negative-ion formation is given by v th E. 13 FIG. 12. Diabatic energy differences E HF and electron transfer interaction V transfer from parameter-free calculations at Z2.5 a.u. solid lines. The dashed line is obtained from Eq. 6. The hatched bars indicate the distances X where quasiresonant electron transitions described by the Demkov model take place. For details see the text. From the time-dependent Schrödinger equation the probability of the electron transfer from the active F site to the collisional F atom is evaluated. Finally, those transition probabilities were summed over the trajectory of the projectile to obtain the negative-ion fractions. We point out that calculations of this type are time consuming. Therefore, the simple expressions in Eqs. 7, 11, and 12 are quite useful for a simple analysis of the data and even for predictions on a certain level. IV. FURTHER EXPERIMENTAL RESULTS AND DISCUSSION First we discuss results presented in Figs. 5 and 6. The experimental data show a decrease of the O fraction when the normal energy component E z is reduced. A qualitative understanding of the experimentally observed features can be obtained with the help of the model, presented in Sec. III. The decrease of the energy for the motion normal to the surface leads to the increase of the distance of closest approach to the surface. It follows from Fig. 10 that the energy difference E increases with increasing Z. This will reduce the probabilities for electron transfer from the surface to the projectile. In Fig. 13 we present experimental data on the H,O, and F formations at a LiF100 surface see also Refs. 11, 40. As discussed in Sec. III, an increase of the electron affinity of the negative ion A decreases the energy difference E see Eq. 6 and Fig. 10b. Within the Demkov This is the Massey criterion, well established in atomic collision physics 41. Therefore, an increase of the electronic affinity of the projectile should lead to lower parallel velocity thresholds for negative-ion conversion of neutral projectiles. This is indeed confirmed by the experimental results. We also present results of the parameter-free study of F formation 30 and fits to the low-velocity part of the experimental data, based on Eqs. 11 and 12. N30 collisions between a neutral projectile and negatively charged surface sites were roughly estimated from the projectile trajectory calculated from binary potentials. The parameter was evaluated from Eq. 10. The energy differences for oxygen and fluorine projectiles E O 4.3 ev and E F 3.0 ev, respectively, are obtained from best fits to the low-velocity part of the data. Note that E O E F F O, with electron affinities of fluorine and oxygen equal to F ev and O ev, respectively. Actually this relation is quite independent of the choice of the parameters N and. This is exactly what one would expect from Eq. 7, provided comparable ranges of projectile-surface separations contribute to the negative-ion formation in both cases. For the case of hydrogen a fit was not performed for reasons given below. Based on the results for E O and E F, we estimate E H to be of the order of 5eV( H 0.75 ev). As can be seen in Fig. 13, theory reproduces quite well the low-velocity part of the experimental data for the O and F formations. For large velocities the theoretical results saturate within the velocity range considered here, while the measured negative-ion fractions decrease. This discrepancy is due to the neglect of possible electron-loss processes in our model. As discussed in Sec. III see also Fig. 8, owing to the large band gap of the LiF surface, the electron losses are not active for small velocities. There are no states of the surface in resonance with the negative-ion states. An increase of the projectile velocity, however, opens channels for electron-loss processes. One of the possibilities is kinematic

9 57 FORMATION OF NEGATIVE IONS IN GRAZING FIG. 14. Negative-ion fractions as functions of projectile velocity for oxygen atoms or ions scattered from KI full squares, KCl full triangles, and LiF full circles 100 surfaces. Solid lines are drawn to guide the eye. tuning of the projectile level into resonance with conductionband states 40,42. So our model describes the experimental results only for small parallel velocities where electron losses are either not active or small compared to electron capture. At large velocities electron losses will dominate electron capture so that our model fails to reproduce the experimental data. An increase of the electron affinity of the projectile decreases E and increases, on the other hand, the separation between the affinity level and conduction-band states see Fig. 8. As a result, electron capture is favored and electron loss is suppressed, which leads to the overall increase of the negative-ion fractions. The competition between loss and capture processes explains the poor agreement over the whole velocity range between experimental data and theoretical estimate for the H case. Indeed, E H is quite large, so that large velocities are needed for electron capture. On the other hand, owing to the small affinity of the negative hydrogen ion it is quite close in energy to the bottom of the conduction band. As a result, the velocity regions for efficient electron-loss and capture processes overlap in this case. In Fig. 14 we present experimental results for the O formation at LiF100, KCl100, and KI100 surfaces. Lattice constants for the targets are a LiF 7.6a 0, a KCl 11.9a 0, and a KI 13.3a 0. As we have seen in Fig. 10, for a given projectile-surface distance Z, the energy difference E decreases when increasing the lattice constant. This is ascribed in Sec. III to properties of the Madelung field of the crystal. Therefore, one would expect a shift of the O formation threshold towards smaller velocities when going from LiF100 to KCl100 and KI100. The projectile-surface separations as estimated from binary ZBL potentials 37 are comparable for those surfaces. The experimental results indeed demonstrate the shift of the thresholds for the negativeion formation in the order predicted by our model. On the other hand, the maximum of the negative-ion fractions does not change significantly. This is due to the fact that an increase of the lattice constant reduces the band gap of the crystal and brings the bottom of the conduction band closer to the affinity level of the O ion see Fig. 8. This should enable electron losses at smaller velocities when going from a LiF100 to a KCl100 andaki100 surface. Then a FIG. 15. Negative-ion fractions as functions of projectile velocity for fluorine atoms or ions scattered from KI full squares, KCl full triangles, and LiF full circles 100 surfaces. Solid lines are drawn to guide the eye. more efficient electron loss and a more efficient electron capture counteract. Results for the F formation at LiF100, KCl100, and KI100 surfaces are presented in Fig. 15. The order of the velocity thresholds for the different targets is the same as that of Fig. 14. As discussed in Sec. III see Fig. 10b, the energy defect of the electron-transfer reaction (E) is very small for the F formation at KI100. Negative ions in the outgoing beam are formed already at the smallest collision velocities accessible in our measurements. The experimental data do not show a velocity threshold for the negative-ion formation in this case. Note that the theoretically predicted saturation of the negative-ion fraction is indeed observed for F /KI100. This is due to the efficient capture from the I sites at small velocities where loss is still suppressed. An interesting aspect can be seen from the data for F /KI100. Based on the approaches developed to treat kinematically assisted coherent processes in atom-crystal interactions 43,44, it was argued 40 that the velocity threshold for the kinematically assisted electron losses into conduction-band states (v loss ) can be estimated from v loss E c F /g, 14 where E c is the binding energy of the electron at the bottom of the conduction band of the order of 2 ev in the case of the KI crystal 45. g 0.668a 0 1 is the reciprocal vector of the two-dimensional surface. From Eq. 14 we estimate v loss to be of the order of 0.09 a.u. This closely corresponds to the onset of the decrease of the F ion fractions from the saturation with velocity in the experimental data. V. CONCLUSIONS From studies on the formation of negative ions in grazing scattering from the surface of ionic crystals we deduce important information on charge-transfer mechanisms for the interaction of atoms in front of insulator surfaces. At first glance surprisingly large fractions of negative ions in the scattered beams can be understood with a model of local capture of electrons from halogen sites at the surface of

10 360 AUTH, MERTENS, WINTER, BORISOV, AND SIDIS 57 alkali-metal halide crystal. Based on a simple model as well as a sophisticated parameter-free approach, we describe the energy confluence and the electron capture in a sequence of binary collisions and are able to reproduce gross features of the experimental results: i a shift of the kinematic ion formation thresholds and increase of the negative ion fractions with increasing electron affinity of the scattered projectiles, ii a decrease of the negative-ion fractions with the normal velocity component, and iii a shift of the kinematic thresholds towards smaller velocities for the scattering from targets with increasing lattice constant. An additional important aspect with respect to charge exchange is based on the large band gap of insulators that is the origin of a pronounced suppression of electron-loss processes. This feature is clearly different from metal targets, where the high density of unoccupied states of the conduction band gives rise to an efficient resonant ionization of atomic levels with low binding energies. Thus, when an electron is captured by the atom in front of the surface of an insulator, the probability for the projectile to keep its charge state here a negative ion is high. It is clear, however, that this situation is changed for sufficiently high velocities, where kinematic effects can result in electron-loss processes by transfer to, e.g., the conduction band. These loss mechanisms, not included in our model, have to be considered in order to describe the complete velocity dependence observed in the experiments. Work on this problem is in progress. The interaction of atoms with insulators is a potential attractive alternative scheme for negative-ion conversion, in particular, when suitable insulators with low binding energies of valence-band electrons and band gaps possibly extending to vacuum energies can be applied. Finally, we mention that the interesting physics of charge transfer between atoms and insulator is not restricted to negative-ion formation. Also the neutralization of noble-gas ions show phenomena concerning electron capture: Auger neutralization rates can be considerably affected by the band gaps of insulators 26. ACKNOWLEDGMENT This work was supported by the DFG Contract No. Wi1336. Laboratoire des Collisions Atomiques et Moléculaires is Unité de Recherche Associée au CNRS No. D P. Varga and U. Diebold, in Low Energy Ion-Surface Interactions, edited by J. W. Rabalais Wiley, New York, 1994, p R. Souda, K. Yamamoto, W. Hayami, B. Tilley, T. Aizawa, and Y. Ishizawa, Surf. Sci. Lett. 324, L S. Dieckhoff, H. 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