Reflection (e,2e) experiments: a novel surface spectroscopy

Journal of Electron Spectroscopy and Related Phenomena 76 (1995) 109-114

Reflection (e,2e) experiments: a novel surface spectroscopy S. Iacobucci #+, L. Marassi*, R. Camilloni#, B. Marzilli &, S. Nannarone* and G. Stefani & # Istituto di Metodologie Avanzate Inorganiche dei CNR, Area della Ricerca di Roma, CP 10 00016 Monterotondo Scalo, Italy & Dipartimento di Fisica "E. Amaldi" and Unita' INFM, III Universita' di Roma, P.le A. Moro 2, 00185 Roma, Italy +Laboratoire pour 1' Utilisation du Rayonnement Electromagnetique, Centre Universitaire Paris-Sud, 91405 Orsay CEDEX, France *Dipartimento di Fisica Universita' di Modena, via G. Campi 213 A, 41100 Modena, Italy The possibility of using the grazing angle (e,2e) technique as a binding energy and/or momentum spectroscopy of surface states rests on the accurate knowledge of the ionisation mechanism and on the capability of achieving a sufficiently good energy resolution. Two possible mechanisms are envisaged that can generate pairs of correlated electrons in the reflection geometry: a single inelastic collision at large momentum transfer or a double collision (elastic plus inelastic). In this paper are presented the results of new (e,2e) experiments that allow to elucidate the ionisation mechanism at intermediate energies (300 eV) and asymmetric kinematics. The measurements, performed on highly oriented pyrolitic graphite, also show that an overall energy resolution as good as 1.2 eV can be achieved. 1. INTRODUCTION In spite of the large number of spectroscopies currently used to characterise the electronic structure of surfaces [1], there are a few interesting physical quantities which are difficult, if not impossible, to measure. One of such quantities is the momentum distribution of bound electronic states. None of the surface spectroscopies applied up until now is capable of measuring the momentum distribution of a single bound state. The second quantity measured with some difficulty by the current spectroscopies, i.e. angle resolved photoelectron spectroscopy, is the binding energy for vanishing real momenta. This is specially true for disordered systems where because of the low symmetry it is not possible to reduce the real momenta to crystal momenta confined to the origin of the Brillouin zone. In photoionization experiments this difficulty originates from the evanescence of the photon momentum that implies real momenta of the initial state which are directly proportional to the photoelectron energy. In electron scattering experiments this constrain on 0368-2048/95 $09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0368- 2048 (95) 02508-1

the momentum is not any more present in as much as for each value of energy transferred in the ionising collision does exist a continuum of kinematically allowed transferred momenta. To take full advantage from the kinematical flexibility of the electron collision processes, both free electrons produced by the ionisation are detected coincident in time thus allowing a complete balance of energy and momentum. For such experiments the acronym (e,2e) is usually adopted~ they represent a unique tool for measuring the momentum distribution of an energy selected state as well as its dispersion in a zone of real momenta that extends all the way to zero value. These unique capabilities of the (e,2e) spectroscopy have been clearly established for the electronic structure of atoms and molecules [2] and more recently applied to investigate bulk properties of amorphous and crystalline solids [31. Even though the first application to surfaces was envisaged [4] shortly after the first (e,2e) experiment on a thin solid film [5[, it has been only recently that the feasibility of such an experiment has been demonstrated. Experiments performed in

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transmission mode and high energy asymmetric kinematics rely on the shortness of the mean free path of the low energy ejected electrons in order to achieve surface sensitivity for the technique which is not inherently surface sensitive[6]. Experiments performed in grazing angle reflection geometry are expected to be surface sensitive in as much as the penetration depth of the fast electrons, diffused and incoming, does not exceed the first two layers of the sample. The existence of pairs of correlated electrons ejected from the surface under electron collision has been demonstrated by Kirschner et al. [71 at normal incidence, while Iacobucci et al. [8] have shown the feasibility of a binding energy spectroscopy with quasi-momentum resolution performed in grazing angle geometry. Two main questions remain to be answered in order to fully exploit the potential capabilities of this latter spectroscopy: i) which is the limit for the overall energy resolution; ii) which is the dominant mechanism for production of the pair of ejected electrons. Both questions are addressed by this paper. It shows that energy resolution comparable to those characteristic of the best transmission (e,2e) experiments has been already achieved and that a mechanism of incoherent elastic reflection and inelastic ionising collision constitute the framework for the interpretation of these experiments.

2.REFLECTION (e,2e) The (e,2e) spectroscopy consists of measuring simultaneously the energy E o of the incident electron, the energies E e and E s of the two final electrons, and the probability of their being emitted into solid angles d_Qe and d_qs oriented along the directions 0 e and 0 s respectively (the five fold differential cross section) . A schematic of the kinematics is given in figure 1. Depending on the amount of momentum transfer = Ko - I(s, two approximations can be used to describe the (e,2e) process. In the dipolar limit, i.e. vanishing momentum transfer, the (e,2e) mechanism is equivalent to photoionization [9] and binding energy (e(Cl)) spectroscopy is possible. The dipolar (e,2e) differs from photoionization in as much as the momentum associate with the transition, Cl = K~ + Ks - Ko, is not uniquely

determined and can be changed by changing the geometry of the process while keeping fixed the energy balance e(C! )=Eo-Es-E e. In the impulsive (binary) limit (momentum transfer roughly equals the ejected electron momentum) the spectral momentum density of the electrons bound in the target can also be measured [10]. Several experiments performed on gaseous targets [11] and thin films have shown that the impulsive condition can be satisfied both in symmetric (Es=Ee) and asymmetric conditions; hence both kinematics permit measurement of the momentum distribution. The potentiality of (e,2e) spectroscopy on surfaces was theoretically investigated by D'Andrea and Del Sole [41 under symmetric reflection kinematics. The recent work by Iacobucci et al. [8] demonstrates the feasibility of such an experiment in asymmetric reflection kinematics and suggests that the ionisation mechanism amount to an incoherent elastic reflection plus an inelastic ionising collision rather than a single inelastic collision. Support to this double collision model comes from angle resolved electron energy loss (AREEL) experiments that have shown this mechanism to be the dominant one for valence [12] and core [13] ionisation. In the Plane Wave Impulse Approximation [141 and within the non interacting bound particle models, it is easily verified that the (e,2e) five fold differential cross section can be written (with implicit antisymmetrization ) [8] as: dS~ df2~d~edE

OC

K Ke Ko

j=l,j~t

.1-Ivq( ) /42 j=l

where E satisfies the energy balance, t and j are valence electron indexes and q~q (~j) is a one electron Bitch function with energy e(Cl) and crystal momentum Cl' = C t + G , G being a reciprocal lattice vector. The main features of the five fold differential cross section are readily understood when a simplified description of the bound states is adopted. In the quasi-free electron model, qJq (~j)can be written as linear combination of plane waves. Furthermore, in

I11

the frozen core assumption the cross section becomes dSo

K~K.

dO~df2~dE oc Ko

1 "K4 "~-o C~'-°

2

(1)

where the Ci, s are coefficients of the ground state wave function of the linear expansion. Therefore, the five fold differential cross section factorizes in a kinematical factor depending only upon the kinematics of the collision (first two terms of (1)), times a form factor which is solely determined by the target electronic structure. From equation (1) it can be also readily seen that the angular distribution of the scattered electrons is symmetric around the direction of the primary electron of the ionising inelastic collision.

FIG. 1 Kinematics of the (e,2e) experiment in grazing angle reflection geometry.

Furthermore, whenever the ion recoil momentum Cl is identifiable with the single-electron crystal momentum (impulse approximation), the (e,2e) process provides a momentum spectroscopy of the target. The symmetry of the coincidence scattered electron distribution is therefore expected to be a sensitive test of the ionisation mechanism. Namely, if the double scattering model is dominant, the distribution will be symmetric around the direction of the specularly reflected beam I~'o instead of the direction of the primary beam and in equation (1) the momentum transfer K will be replaced by the specular momentum transfer

3. EXPERIMENTAL

The apparatus permits to work at grazing incidence (®o= 0 ° - 170) and is based on an ultrahigh vacuum chamber containing an electron gun whose energy is automatically scanned during the experiment, a sample holder mounted on a temperature controlled manipulator with five degrees of freedom, and two electron analysers. The emitted electrons are analysed by a single-pass cylindrical mirror analyser (CMA) (resolving power 50, angular acceptance =0.23 sr) with the axis coincident with the surface normal c (see figure 1). The fast electrons are analysed by a hemispherical deflector (HDA) equipped with a three element electrostatic lens, rotatable in the scattering plane (®s = 0 ° - 12°) with an angular acceptance of +0.5 °. The HDA is operated at low-energy resolution (resolving power ~--102) in order to maximise the luminosity of the coincidence spectrometer. The best overall energy resolution achieved is 1.2 eV and mostly limited by the HDA resolution. The coincidence electronic chain is a conventional one [ 15]. The time resolution of the spectrometer is about 12ns and largely due to the time spread of the trajectories in the two analysers. The true coincidence rate It must be discriminate from the nearly fiat background of the uncorrelated events (accidental coincidence) which occurs at a rate Ia. The optimal acquisition time is achieved when the ratio It / Ia, which depends on the incident current Io, is about one [15]. In the best case we measured It~0.05Hz with a ratio It / Ia~0.5 for I o ~ l n A . For the measurements of this paper, a highly oriented pyrolitic graphite (HOPG) sample has been used. It was prepared according to UHV standard procedures [16] by peeling in air and annealing at about 700°C at residual pressure of 1.10 "10 mbar. Cleanliness and orientation of the surface were checked by Auger electron spectroscopy and AREEL measurements. The best monitor for surface cleanliness was the persistence of the sharp n--~n* transition at 6.2 eV in the AREEL spectrum and the presence of a narrow angular distribution (FWHM=2.3 °) of the peak of specularly reflected elastic electrons. Reproducibility of these measurements over a period of six weeks has been assumed as a guarantee for the stability of the surface conditions and of the energy calibration

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during the long acquisition time needed for coincidence measurements.

4. RESULTS Two sets of measurements have been performed at two different grazing angles (®o= 6.7 ° and 4.7 ° ) always detecting 300 eV scattered electrons correlated in time with 8eV ejected electrons. The measurements performed under strict reflection geometry (Oo=Os) were aimed at measuring the binding energy spectrum, while those performed at fixed binding energy and variable ®s were aimed at measuring the symmetry of the five fold differential cross section. In figure 2 is reported the HOPG binding energy spectrum as measured at ®o=®s= 6.70 . The vacuum level is the origin for the binding energy scale which has been derived from the energy conservation law.

0.06 HOPC

Ee = 8eV Es = 300eV

N SE

es=8o=6.7o

0.04

(1) e5 k--

@ 0.02 (D C @ -(:3 C)

c

0

O C)

-0.02 -t0

I

0

I

10

binding

i

I

20

3O

energy

(eV)

40

Figure 2. Coincidence spectrum from HOPG surface. Error bars represent one standard deviation for raw data. The continuous line is the best fit to the spectrum, see text for details.

Under the assumptions used to derive the cross section in equation (1), the features in the binding energy spectrum are to be interpreted on the basis

of the band structure of graphite. The momentum reconstructed by the chosen kinematics has non vanishing component both in the parallel and perpendicular directions to the HOPG ~ axis (qp and qn). Taking into account the finite analyser angular acceptances, the spectrometer work function and the surface potential barrier of the sample [81, the reconstructed values of qn range from nearly the middle to the boundaries of the first Brillouin zone in the FMK plane (from 0.65 to 1.53 A'I). The qla component ranges between 1.67 and 2.08 A "l, i.~. from bottom to middle of the third Brillouin zone along the FA direction. Stemming from valence band calculation 117] and on the basis of the volume of momentum space sampled by the experiment, four individual contributions from valence states are to be expected in the range of binding energies investigated. Consequently, the measured spectrum has been fitted by a least-square method, simulating the expected individual transitions by means of Gaussian functions of variable height, width and position. Experimental data for (e,2e) on solid samples are affected by multiple losses that result in enhanced transition intensities at larger binding energies. A previous work [81 has already shown that in grazing angle reflection geometry binding energy and width of the individual transitions are essentially unchanged by multiple scattering effects that will only affect by a few percent the observed (e,2e) intensity. Being the present work mainly concerned with determining the limiting energy resolution of the experiment, it was not felt necessary to correct for multiple loss effects. The improved energy resolution of this experiment (1.2 eV instead of 3eV of our previous work [81) allows to resolve, in the binding energy region from 5 to 11 eV, the ionisation of the n band from the G3 one. According to the HOPG momentum density 118], in the volume of real momenta sampled by the present experiment the four main bands display similar values of the momentum probability; hence they should yield similar amplitude for the (e,2e) cross section. Consequently, based on the calculated dispersion band [17], four main components to the (e,2e) binding energy spectrum are to be expected roughly centred at 3.7, 6, 10 and 19.3 eV respectively for the n, cr3, c~2, and cr I bands. The best fit to the energy spectrum (continuous line of figure 2) locates the position of the individually contributing peaks very close to the expected

113

binding energy value. Furthermore, the a 2 peak is broader than the others, which is to be expected this being the band affected by the largest energy dispersion in the momentum region investigated. The peak corresponding to band g l is deeper than expected by about 1 eV. This discrepancy is overcome if we assume, for its dispersion curve the one measured in a transmission (e,2e) experiment [ 18] instead of the calculated one [ 17].

0.3

t a k e - o f f angle (deg) 2.3 4.3 6.3 8.3 x

grazing

angle

:

4.7

10.3 deg

\ \ N \

C

N

c~ 10 2

.//

© od k_

© (P C q) -0 "~

--

101

reflection. The measure at the smaller grazing angle is shown in figure 3 and it is evident the symmetry of the five fold differential cross section around the specular reflection direction. Similar measurements at 6.7 ° grazing angle, not shown in the figure, display similar symmetry around the elastically reflected beam.. Regardless of the collisional model adopted, because of the CMA large accepted solid angle, the form factor of (1) doesn't depend upon ®s. On the other hand, the ®s dependence of the kinematical factor drastically changes if a single or a double collision model is adopted. The relative cross section, as predicted by the two collisional models under the assumption of constant form factor is shown in figure 3. The shape of the measured cross section clearly supports the double collision hypothesis. It is to be noted that the experimental cross section is broader than the shape of the simple kinematical factor shape because of the variation of the form factor not taken into account by this calculation. It is finally to be mentioned that the measured coincidence angular distribution is very close to the correspondent non coincident energy loss distribution. This is good evidence for a single dominant mechanism for all of the inelastic processes at glancing angle, i.e. the double collision one.

c 0 ©

5. CONCLUSIONS I

5

L

7 9 scattering

k

,

I

11 19 angle (deg)

15

Figure 3. Angular distribution of the (e,2e) cross section at a grazing angle of 4.7 °. The take off angle is O s while the scattering angle is Oo+® s. Continuous and dashed lines are the kinematical factors for the double and single collision models respectively.

The angular distribution of the scattered electron has been measured tuning the spectrometer at the peak of the n band feature of the (e,2e) spectrum. The measurement has been done at two grazing angles' Oo= 4.7 0 and 6.7 °, and for the scattered angle variable around the specular

By the present investigation it has been confirmed the possibility to use grazing angle reflection (e,2e) events to build up a binding energy spectroscopy with partial momentum resolution. Furthermore it has been demonstrated that the energy resolution achieved in this geometry is at least as good as the one obtained by the transmission (e,2e) experiments on thin films, i.e. an overall resolution on binding energy of 1.2 eV. The first necessary, (even though not sufficient) condition for realising a bound state momentum spectroscopy based on grazing (e,2e) experiments is the accurate knowledge of the mechanism that generates the pairs of coincident electrons detected by this spectroscopy. The present investigation clearly demonstrates that, at least under the kinematics investigated, the double collision mechanism prevails over the single inelastic collision one.

114

We are grateful to EEC Human Capital and Mobility, Contract No. ERBCI-IRXCT930359 and to Progetto Finalizzato Chimica Fine CNR for partial support of the work, and to P. Luches for taking part at some of the measurements reported.

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7 8.

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