Simulation of fast electron emission from surfaces

Nuclear Instruments and Methods in Physics Research B 100 (1995) 378-382

Beam Interactions with Materials&Atoms

ELSEVIER

Simulation of fast electron emission from surfaces Carlos 0. Reinhold a-b,*, Joachim Burgdarfer

a,b, Kenji Kimura ‘, Michi-hiko

a Department of Physics and Astronomy, University of Tennessee, Knoxville TN 379961200,

Mannami ’

USA

b Oak Ridge National Laboratory, Oak Ridge, TN 37831-6377, USA ’ Department of Engineering Science, Kyoto University, Kyoto 606, Japan

Abstract We present a microscopic simulation of fast electron emission in glancing-angle ion-surface collisions. Our model accounts for both dynamic image interactions and multiple scattering near the surface and predicts a pronounced convoy electron peak for small emission angles. We find that convoy electrons principally originate from target core states which are excited via close collisions with the impinging ions. Polarization of core electrons during emission is found to play an important role. Very good agreement is found with experiments for fast Li+ ions interacting with SnTe(O,O,l) surfaces.

1. Introduction Electron emission in glancing-angle collisions has become a focus of ion-surface interactions. Electron spectra can provide detailed information about the neutralization dynamics of multiply charged ions, the electronic structure of the surface (surface density of states) and the long-ranged image interactions near the surface. From a fundamental point of view, the study of fast electrons emitted in ion-surface interactions provides an important link between atomic physics and condensed matter physics. Two decades ago a cusp-shaped peak was discovered in the spectrum of electrons arising from ion-atom [l] and ion-solid (transmission) collisions [2]. This cusp is observed for electrons ejected with velocities v, close to the projectile velocity up. In ion-solid collisions this structure is usually referred to as the convoy-electron peak (CEP). Cusp electrons consist of electrons in low-lying continuum states (i.e. near-threshold states) of the projectile. Because cusp electrons recede from the target in close spatial correlation with the projectile, the behavior of the cross sections in the limit 1v, - vp ] + 0 is governed by threshold laws characteristic of the two-body final state interaction between the electron and the projectile. Recent experiments concerning glancing-angle ionsurface interactions have revealed a prominent convoy peak. Compared to the peak for transmission conditions, however, the convoy peak for ion-surface interactions is dramatically broadened and shifted in energy. The first evidence for broadening of the CEP was found by de

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Ferrais and Baragiola [3] for scattering of protons at an Al surface. A similar broadening was observed for semiconductor surfaces [4,5]. Concurrently, a shift of the CEP to electron velocities larger than up was proposed [6] and independently measured [4] for projectile charges greater than 1. Subsequently, large shifts of up to 100 eV have been observed in several laboratories and a number of explanations have been proposed [7-111. It was readily understood that these effects were closely related to dynamic image interactions. At grazing angles of incidence the impinging ion remains near the target surface for a very long time and, therefore, the effective final-state interaction in which the excited electrons evolve is quite different from ion-atom collisions and foil transmission experiments. The energy shift was identified as “convoyelectron acceleration” and the underlying picture is that of emitted electrons repelled to larger energies by the negative image of the projectile ion travelling in close proximity. The theoretical description of fast electron emission in glancing-angle surface scattering is still in its infancy. Iitaka et al. [12] and Kimura et al. [9] have shown that a classical trajectory Monte Carlo (CTMC) simulation employing an initial ensemble of electrons distributed in a shell around the projectile yields a shifted CEP when the electrons propagate in the fields of the projectile and its image. As of yet, however, no simulation has been performed that employs realistic initial ensembles (“sources”) of electrons and describes the transport of fast electrons from their birth in a violent collision through a sequence of multiple scattering to their final exit from the surface. In this letter, we present the results of a comprehensive classical simulation of convoy electron emission. Based on our simulation, we have recently identified the peak as a

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result of a classical rainbow singularity for scattering of fast electrons at the induced dynamical screening potential

1131.

2. Model The present simulation is an extension of a model originally developed for fast electron emission from transmission of ions through solids [14]. Ensembles of initial coordinates were calculated for both target and projectile electrons employing the CTMC method as applied to atomic collisions [IS]. We decompose target electrons into outermost valence electrons and core electrons. Electrons in the outermost valence band of SnTe (i.e. Sp electrons) are treated as a free electron gas which is constrained to the z < 0 region by the surface barrier. Core electrons are assumed to be well localized in bound states of isolated Sn and Te atoms. The electronic evolution is described by a time-dependent effective one-electron Hamiltonian

~=$+v(r,r)-rCc k

Ap;S(t-t;),

(1)

a=e,i

where r and p (in a.u.> are the coordinate and momentum of the electron. This Hamiltonian describes the motion of an electron in the potential field V, perturbed by a stochastic force representing the collisional momentum transfers Apr due to the inelastic ((Y = i) and elastic ((Y = e) collisions with other electrons and ionic cores in the neighborhood of the surface. Elastic momentum transfers Api are calculated from the differential elastic cross section for the scattering of electrons at the Sn and Te cores. Inelastic momentum transfers are obtained from the imaginary part of a single-frequency plasmon-pole dielectric function 1161 including dispersion and single-particle single-hole excitations. The potential field V= VP + VP + V, + V, consists of: (i) the field of the projectile, VP, (ii) the dynamic image potential induced by the projectile, Vip, (iii) the surface barrier potential, V,, containing the interaction of the electron with its own image, and (iv) the field of the initial target core, V,. The time dependence of the potential results from the motion of the impinging ion which is assumed to follow a curvilinear trajectory for quasi-elastic scattering deduced from a planar averaged Moliere potential representing the interaction with the first layer of atoms and from the ionic self image interaction. In Fig. 1 we display the potential experienced by an electron near a proton moving parallel to a SnTe(001) surface. The wellknown wake pattern trailing the ion as well as the surface barrier potential are clearly visible. Dynamic image potentials have been obtained using a single-frequency classical dielectric function [16] (wpv = 15.1 eV, y= 8.54 eV). At the ion velocities up Z+ uF (u, being the Fermi velocity), our induced potential is found to be in good agreement

Fig. 1. Electronic potential V’ = VP + Vip + V, near a 0.3 MeV/u proton moving parallel to a SnTe(001) surface as a function of the position vector of the electron (x, 1 a.u., z). The surface plane corresponds to the (x, y) plane and the surface normal is oriented along the z-axis. The position vector the projectile is (0, 0, - 1.51, i.e. 1.5 a.u. above the top row of atoms. z = 0 corresponds to the jellium edge situated 3 a.“. above the first layer of atoms.

with the one calculated by Garcia de Abajo et al. [17] using the plasmon pole approximation for the dielectric function. We employ the parameterized potential of Jennings et al. [18] for the surface barrier.

3. Results After the incoming ion crosses the jellium edge (3 a.u. above the topmost layer), electron capture and loss probabilities become so large that the ionic charge state fluctuates very rapidly as a function of time [19]. For 0.3 MeV/u Lif ions interacting with a SnTe(001) surface the charge state fractions q = 2 and q = 3 become approximately equal (N 50%). Our simulation (Fig. 2a) consists therefore of an average of the spectra for Li’+ and Li3+ ions. Typically, 5 X 10’ trajectories were included to assure small statistical uncertainties. We compare our simulation with recent experimental data [19] for electron emission in coincidence with outgoing Liz+ ions. Remarkably, these data have indicated (see Ref. [19]) the independence of the convoy peak from the outgoing charge state in contradiction to the naive picture of convoy electron acceleration by the asymptotic image field of the projectile. The present simulation is consistent with this conclusion and provides insight into the mechanism that breaks the correlation between the asymptotic charge state and the convoy electron spectrum: convoy electrons are produced very close to the first layer of target atoms and leave the surface before the projectile completes its charge-changing cycle. This is seen in Fig. 3b where the yield of convoy electrons is plotted as a function of the distance between the ion and the first layer of target atoms at the moment of emission. Clearly, more than 50% of convoy electrons are

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emitted when the projectile is at a distance smaller than - 1 a.u. from the topmost layer. The lack of correlation between exit charge state and the shift of the convoy peak points to the local potential in close proximity to the surface as being responsible for convoy electron acceleration. We therefore include the polarization of core electrons in the dynamical screening potential. Pitarke et al. [20] have shown that core polarization gives a significant contribution to the anomalously large shift of the radiative electron capture (REC) peak observed by Vane et al. [21] for titanium ions channeled in a gold single crystal. Core polarization is accounted for in terms of an inhomogeneous electron gas with a local plasma frequency [20]

op( d)2= ci$”+

2.*3-

/I

2!2.K % l- _

; /

go-

j

(b)

C4V&)~ n,l

where p,,(d) denotes the planar-averaged number density of electrons in the state with quantum numbers n,Z and d is the distance between the ion and the first layer of atoms. At large distances (see Fig. 3a) the local plasma frequency in Eq. (2) tends to the volume plasma frequency pertaining to the displacement of 5s and 5p valence electrons: i.e.

0

-2

200

Electron

400

energy

600

(eV)

Fig. 2. Spectrum of electrons emitted at 100+50 mrad with respect to the surface resulting from the interaction of 0.3 MeV/u Li+ with SnTe(001). The angle of incidence of the impinging ions is 6 mrad. (a) comparison of the full simulations using the valence-band plasma frequency (w,,) and a distance dependent plasma frequency (w,(d)) with the coincidence data [19] (solid triangle). Theoretical and experimental results are normalized to each other at the peak. (b) Comparison of the total yield of electrons with the yield of outermost valence electrons.

0

1

2

3

Distanceto firstlayer (a.~) Fig. 3. (a) Local plasma frequency as a function of the distance from the topmost layer. (b) Yield of convoy electrons as a function of the distance between the ion and the first layer of target atoms at the moment of emission.

w&d > 2 a.u.> = wpv = 0.55 a.u. However, at the distance of closest approach w,(d) is about a factor of 4 larger than opv. Both simulations using the distance dependent plasma frequency and the volume plasma frequency yield significant convoy electron acceleration (see Fig. 2a). Inclusion of the core polarization increases the peak shift but contributes predominantly to the broadening of the peak which closely resembles the measured spectrum. This is due to the fact that the spectrum is an average over electrons emitted at different distances d, each of which suffers a different amount of image acceleration. It should be stressed that this comparison refers to a small subset of an exceedingly complex multi-electron process involving the emission of several hundred electrons per ion. After considering all sources of electrons, we find that the dominant contribution to the convoy electron spectrum originates from target core states (see Fig. 2b). This dominance is due to the large number of electrons in the N-shell of Sn and Te whose orbital velocities closely match the projectile velocity up. Thus, local processes such as electron capture to bound or low-lying continuum states of the projectile are strongly favored. Emission of outermost valence electrons at forward angles, on the other hand, plays a significant role only for electron energies above 400 eV where the yield of outermost valence electrons exhibits a peak (see Fig. 2b). This peak is the counterpart to the binary encounter peak known from ion-atom collisions and foil transmission experiments and it arises from head-on projectile-electron collisions. However, this is a marginal contribution to the total yield of electrons which exhibits only a weak shoulder in this region. Despite the

C.O. Reinhold et al. /Nucl. Imtr. and Meth. in Phys. Res. B 100 (1995) 378-382 Core

0.5

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electms

Valenceeledrons

0.5

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1.5

1

I

2.5

3.5

4.5

Electronenergy/ Ei Fig. 4. Theoretical densities of core and outermost valence electrons emitted from SnTe(001) surfaces after the interaction with 0.3 MeV/u Li+ ions. The points in the figure correspond to electrons emitted in the plane of the trajectory of the ions. The emission angle is measured with respect to the surface.

probability of electrons initially in the projectile is equal to unity, their contribution to the total yield is also found to be marginal (i.e. many more target electrons are emitted). At larger emission angles with respect to the surface, head-on projectile-electron collisions are expected to give rise to a “binary ridge” (also known from ion-atom collisions) at electron energies E, = 4Ei cos 0, 0 being the emission angle with respect to the local ion trajectory and E, = (“t/2) a.u. This ridge can be clearly seen in the density of outermost valence electrons emitted in the plane of the ion trajectory (see Fig. 4). For emission of core electrons under the current collision conditions, however, the binary ridge is completely swamped by the convoy electron peak clearly visible in the energy range Ei
Acknowledgements C.O.R. and J.B. acknowledge support by NSF and US DOE, Office of Basic Energy Sciences Division of Chemi-

cal Sciences contract no. DE-AC05-840R21400 with Martin Marietta. We also acknowledge the support of the Japan-US Cooperative Scientific Program sponsored by JSPS and NSF. K.K. and M.M. acknowledge support of the Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and Culture.

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