PHYSICAL REVIEW B
VOLUME 61, NUMBER 20
15 MAY 2000-II
Excitation of volume plasmons in glancing collisions of protons with Al„111… surfaces
E. A. Sánchez, J. E. Gayone, M. L. Martiarena, and O. Grizzi
Centro Atómico Bariloche, Instituto Balseiro, Comisión Naeional de Energı́a Atómica and Consejo Nacional de Investigaciones
Cientı́ficas y Técnicas, 8400 S.C. de Bariloche, Rı́o Negro, Argentina
R. A. Baragiola
University of Virginia, Engineering Physics, Thornton Hall, Charlottesville, Virginia 22901
共Received 30 November 1999兲
We studied electron emission from Al共111兲 surfaces induced by 4–100 keV protons at glancing incidence.
The electron energy distributions show a structure due to the decay of volume plasmons. The intensity of the
plasmon structure was measured as a function of angle of incidence to the surface. We found that volume
plasmons are excited even under conditions where protons do not enter in the solid. The results are consistent
with an indirect excitation mechanism by fast secondary electrons produced in binary ion-electron collisions.
This mechanism is more important than direct excitations by ions and excitations produced by Auger electrons.
INTRODUCTION
Fast charged particles moving inside solids can directly
excite collective density oscillations of valence electrons
共plasmons兲.1,2 Due to the finite response time of the valence
electrons to the fast charge, plasmon excitations requires that
the collision time, 1/␷ n 1/3, be shorter than the screening time,
where n is the valence electron density. This means ion velocities ␷ in excess of ␷ F , the Fermi velocity of valence
electrons. The density oscillations form an oscillatory wake
trailing the ion motion, with a characteristic wavelength
␷ / ␻ p . The wake field can be felt by nearby projectile ions
when aggregates of charges travel inside the solid.3 The excitation of plasmons is often a predominant energy-loss
mechanism for fast electrons and protons.4 In addition to
these bulk excitations, or volume plasmons, fast charges can
also excite lower-energy surface plasmons, which are density oscillations confined to the surface region.
Plasmons have a short life, spanning at most a few oscillations, and then decay mainly by transferring the energy to a
single electron in an interband transition.5 In this process, the
atoms in the solid absorb most of the momentum of the
emitted electron since plasmons have wavelengths 共and
therefore momentum q兲 limited by interelectron spacing. The
excited electron resulting from plasmon decay may be emitted outside the solid, where it has been observed to produce
a distinct structure in the energy distribution of electrons
emitted in ion-solid interactions.6–11 Plasmon decay constitutes an important fraction of the total electron emission.11,12
Because of the strong inelastic electron-electron interactions
in solids, electrons from plasmon decay are attenuated exponentially with depth; those observed originate from shallow
depths of the order or smaller than the electron escape depth
of about 1 nm.
In addition to the few experimental studies of plasmon
excitation of metals by fast ions, several theoretical studies
have been made to obtain excitation rates vs ␷ and energy
distributions of electrons from plasmon decay.13–18 The
usual electron gas description of valence electrons leads to a
0163-1829/2000/61共20兲/14209共6兲/$15.00
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minimum or threshold velocity ␷ th for plasmon excitations
by a moving charge, determined by conservation of energy
and momentum.13 For ions with mass much higher than the
electron mass, the threshold velocity for exciting a narrow
plasmon resonance is ␷ th⬇1.3␷ F . 13 A slightly lower threshold results from the small plasmon width in a metal like Al.
However, recent experiments have shown that plasmons can
be excited by ions moving with velocities significantly lower
than ␷ th . 11,19–22 Several mechanisms that can excite plasmons at ␷ ⬍ ␷ th have been identified. If the ions carry a high
potential energy, like He⫹, Ne⫹ or multiply charged ions,
potential plasmon excitation can occur by an Auger capture
process.19 Indirect plasmon excitation can occur by fast electrons excited by the projectile, if they are excited with energies ⲏ 23 eV with respect to the Fermi level.11 Electrons
with such high energies can be produced in binary ionelectron collisions and also result from the Auger decay of
inner-shell vacancies.23 A third mechanism for plasmon excitation below ␷ th is shakeup during the capture of an electron. If the ion velocity is sufficiently high, the energy release in electron capture can reach the plasmon energy even
for ions like protons, whose neutralization energy is too low
to allow for potential plasmon excitation.11
The identification of a particular excitation process is
made difficult if all processes are present in an experiment:
direct excitation, excitation by fast secondary electrons, and
plasmon shakeup in electron capture. For this reason, we
have chosen to study plasmon excitation by fast protons incident at very small glancing angles to the surface, in conditions where the protons do not traverse the first atomic layer.
In this case, the excitation of volume plasmons, both direct
and by electron capture should be suppressed in favor of
surface plasmons 共the begrenzung effect兲.24,25 This implies,
within existing models, that volume plasmons may be excited only by fast secondary electrons penetrating into the
bulk.
EXPERIMENTS
Our experiments are made in ultrahigh vacuum using a
cylindrical mirror electron spectrometer, in a setup that has
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©2000 The American Physical Society
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E. A. SÁNCHEZ et al.
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FIG. 1. Typical spectrum for 60 keV H⫹-Al共111兲 at 1° incidence. The inset shows how the angles are defined.
been described in detail before.26 Proton beams in the range
4–100 keV were produced by an ion accelerator and collimated to ⫾0.1° and a 0.4⫻1 mm size, determined by variable slits. The sample was a mechanically polished Al single
crystal with a 共111兲 surface. The surface of the Al共111兲
sample was prepared by repeated cycles of 20-keV grazing
Ar bombardment 共0.5–2° incidence angle兲 and annealing at
450 °C. The azimuthal orientation of the surface was continuously changed during the Ar bombardment. This method
produces a very flat Al surface, as has been carefully
checked at other laboratories.27 In our case, the characterization of the surface roughness was performed by measuring
the convoy electron emission produced by 60 keV H⫹ at 1°
incidence,28 and the Al Auger electron peak produced by 20
keV Ne⫹ as a function of the incident angle.29 Both measurements show that the vast majority of the incident ions
共⬎95%兲 interact with flat surface regions 共i.e., without hitting a step during their trajectory兲. The surface cleanliness,
achieved with the repeated sputtering-annealing cycles, was
verified with Auger electron spectroscopy before and after
performing the measurements.
The geometry of the experiment is shown in Fig. 1, as a
projection on both the surface plane and on the plane that
contains specular scattering trajectories. ␪ e is the elevation
angle with respect to the surface; ␪ e ⫽30° shown corresponds to 1° projectile incidence. For the geometry of the
spectrometer, increasing the incidence angle decreases the
elevation angle. ␾ e is the angle between the direction of
observation and the scattering plane, measured on the surface
plane. The ion beam irradiates a narrow stripe whose length
measured along the sample surface depends on the incident
angle. At the smallest grazing angles, the stripe extends the
whole length of the sample, with part of it outside the region
seen by the analyzer 共a circle of 1.3-mm diameter measured
in a plane normal to the observation angle兲. At incident
angles ␣ ⭓7°, the irradiated stripe is entirely within the zone
seen by the analyzer and all the emitted electrons are analyzed in energy and angle. In order to compare the electron
intensity measured at different incident angles, a correction
FIG. 2. Typical spectrum for 70 keV H⫹-Al共111兲 at 1° incidence. We show the three methods used to estimate the plasmon
intensity. The background in the N(E) spectrum is a calculation,
normalized at 22.5 eV that considers screened-Coulomb interactions between the projectile and free valence band electrons.
function for ␣ ⭐7° has been applied to account for the electrons not collected due to the mismatch between the irradiated and observed regions.
Figure 1 shows a representative electron energy distribution for 60-keV protons at 1° incidence, where we indicate
the main spectral features. All the electron spectra shown in
this paper were corrected for the transmission function of the
analyzer. Electrons from plasmon decay are identified because of their distinct energy distribution, with a maximum
electron energy E m ⫽E p ⫺ ␾ ⬇10.7 eV, where E p ⬇15 eV is
the volume plasmon energy and ␾ ⫽4.3 eV the work function of the Al共111兲 surface. The plasmon feature has an expected width of ⬃E Fermi since the energy released in plasmon decay can be absorbed by any electron in the valence
band. The high-energy edge of the plasmon decay distribution is abrupt, due to the discontinuity of filled electron states
near the Fermi level, but it is broadened by the finite width of
the plasmon resonance. The relative sharpness of this highenergy edge results in a dip in the derivative of the electron
energy spectrum N(E), with a minimum at E m 共Fig. 2兲. The
derivative enhances the visibility of the plasmon decay structure because other processes like direct excitations in binary
ion-electron collisions and Auger neutralization at the
surface30 contribute to a slowly varying ‘‘background’’ in
N(E). The spectrum of Fig. 2 shows also the presence of
surface plasmons 共dip around 7 eV in dN/dE兲. Surface plasmons are hard to see in most cases due to the overlap with
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EXCITATION OF VOLUME PLASMONS IN GLANCING . . .
the intense low-energy peak of secondary electrons and for
this reason this work concentrates on volume plasmon excitations. We have found that the surface plasmon structure is
more noticeable at the higher incident energies, consistent
with previous observations.8
To quantify the number of electrons emitted due to volume plasmon decay, we must extract them from the total
energy distribution N(E), which includes electrons from
other processes. The methods we used are illustrated graphically in Fig. 2. The top panel shows the method given by
Ritzau, Baragiola, and Monreal.11 The high-energy continuum tail N t (E) is fitted by a smooth function, which is
extrapolated slightly to E m ⫽E pl⫺ ␾ . The figure shows also a
tail calculated for electron excitations in binary collisions of
protons with the valence electrons of Al,31 normalized at
22.5 eV to experiment. Details of the calculation are discussed below. A measure of the number of electrons from
plasmon decay is obtained integrating N(E)⫺N t (E) over a
2-eV region around the plasmon edge. The middle panel
shows how we obtain a measure of plasmon decay intensity
from the derivative, after subtracting a background; in this
case, the derivative of the theoretical N t (E) is also shown in
the middle panel. This method is the usual procedure for
obtaining intensities in Auger electron spectroscopy, and has
been justified recently for the case of plasmon decay.32 Finally, the bottom panel contains the second derivative; a
measure of plasmon intensity in this case is given by the size
of the positive and negative excursions, h 1 ⫹h 2 , measured
from the second derivative of N t (E).
Of the three methods shown, we find that the less ambiguous is the one using the intensity of the dip in the first derivative, which is also in good agreement with the method
using the second derivative. Subtraction of the background in
N(E) has more uncertainties at low proton energies, where it
is difficult to fit the background with a simple function.
When presenting plasmon intensities in the following figures, we give the uncertainty caused by the use of different
methods as an error bar 共which does not represent the statistical error of a given procedure兲.
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FIG. 3. Plasmon intensity versus projectile energy for two incident angles. At 1° incidence, the extrapolated threshold is at (5
⫾2) keV. The curves are normalized according to the results of
Fig. 4.
mon excitation requires a threshold velocity, ␷ ths . For protons in Al, ␷ ths⫽7.4⫻107 cm/s, substantially smaller than
␷ th , the value for direct excitations. The proton energy corresponding to ␷ ths is 2.9 keV, close to observations.
To test the role of secondary electrons we plot in Fig. 5共a兲
the plasmon intensity vs I SE the differential yield of secondary electrons with energy between 25 and 75 eV, measured
at ( ␪ , ␾ )⫽(30°,72°). We have chosen an emission angle far
from the forward direction to avoid the strong angular anisotropy caused by direct electron emission at forward
angles, and by electron capture to the continuum of the projectile, that dominates the spectrum up to 15–20° from the
RESULTS AND DISCUSSION
Figure 3 depicts plasmon intensities as a function of proton energy E 0 for incidence at 1 and 10°. In both cases we
see that plasmon excitations occur below the threshold predicted for direct excitations 共E 0 ⬇40 keV for protons in Al兲,
in good agreement with the results of Ritzau, Baragiola, and
Monreal11 for 20–100-keV protons at 30° incidence to the
surface. Since we are able to go to lower incident energies
we can extract an extrapolated threshold of (5⫾2) keV. We
note in Fig. 3 that the plasmon intensity is much enhanced
for the glancing geometry. A study of the dependence of
plasmon intensity on incidence angle was then undertaken.
The results in Fig. 4 show that the maximum intensity moves
towards higher angles for decreasing projectile energy. Using
a planar model for the surface potential,33 we find that the
angles at the maximum correspond roughly to the critical
angles required to penetrate the surface: 2.1, 1.7, and 1.0° for
proton energies of 20, 30, and 90 keV, respectively.
Since the maximum electron energy for binary ionelectron collisions depends on ion velocity, secondary plas-
FIG. 4. Plasmon intensity versus incident angle for three projectile energies. The maximum intensity moves towards higher angles
for decreasing projectile energy.
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E. A. SÁNCHEZ et al.
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FIG. 6. Electron energy spectra taken at 1° incidence showing
the high-energy tail of the electron distribution, which includes the
Al LVV Auger electrons. The spectra are normalized to the primary
beam current.
FIG. 5. 共a兲 Plasmon intensity versus the integral of the electron
energy distribution between 25 and 75 eV, measured at ( ␪ e , ␾ e )
⫽(30,72°). 共b兲 same as 共a兲 but using the total secondary electron
intensity 共0–75 eV兲 in the ordinate axis.
ion specular direction.34 Since the observation of fast electrons at large angles from the trajectory require elastic collisions with target atoms, the intensity of fast electrons measured at this specific direction is likely to be representative of
those that may excite plasmons. The linear behavior shown
in Fig. 5共a兲 suggests that plasmon excitations by secondary
electrons are much more likely than direct H⫹ excitations;
otherwise, a departure from the linear behavior should appear around 35 keV. In Fig. 5共b兲 we test for correlation between the plasmon intensity and all secondary electrons. The
linear dependence remains, showing that electrons below 35
eV are correlated to the fast electrons. This is expected at
high proton energies E 0 , when a large fraction of slow secondary electrons results from collision cascades,12 but not at
low E 0 , where the electron cascade is relatively unimportant.
To test the role of secondary excitations by energetic Auger electrons from the decay of Al-2p vacancies 共LVV
electrons兲,30 we plot in Fig. 6 normalized electron energy
spectra taken at different proton energies. It can be seen that
the intensity of Auger electrons is very low compared to the
integral of N(E) between 35 and 75 eV. For example, for
20-keV protons at 6° incidence, the Auger contribution is
only 0.3% of the total electron emission. Thus we conclude
that Auger electrons do not play a significant role in plasmon
excitations at low projectile energies.
To better understand the relation between plasmon excitation and the emission of fast secondaries we need to know
how the measured secondary electron intensity I SE is correlated to the flux of energetic electrons inside the solid, those
with energies higher than ⬃25 eV, that can excite plasmons.
This correlation will depend on the distance of closest approach of the ion to the surface, i.e., on the glancing angle.
Thus we have performed a calculation of the single electron
excitation produced by the screened Coulomb interaction between projectile and surface electrons. The details of the calculation have been published.31 Basically, we consider projectiles moving parallel to the surface at the distance of
closest approach, evaluated for each energy and glancing
angle, following Ref. 33. The screened Coulomb interaction
is approximated by a Yukawa-type potential and the solid is
described within the jellium model. Multiple collisions dur-
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EXCITATION OF VOLUME PLASMONS IN GLANCING . . .
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FIG. 7. Calculated intensity of electrons excited inside the solid
to all angles and with energies ⬎25 eV (I SE,in) versus the calculated
intensity of the electrons emitted outwards, in the direction of the
electron analyzer with energies ⬎25 eV (I SE, o ).
ing the emission process and higher-order electrons resulting
from cascades are not included. This model has been applied
previously to study electron emission in proton-aluminum
collisions at grazing angles,31 and found to give a good description of the experimental high-energy tails. However, the
model cannot reproduce the electron distribution at low energies, mainly because of the neglect of the electron cascade
and plasmon decay. We evaluate numerically the intensity
I SE,in of electrons excited inside the solid to all final angles
and with energies above 25 eV, and the intensity I SE,o of
electrons emitted in the direction of the electron analyzer,
with energies above 25 eV. Figure 7 shows the calculated
I SE,in versus I SE,o for H⫹ energies ranging from 20 to 100
keV. The almost linear correlation observed in the figure
justifies the use of the experimental I SE as representative of
the electrons excited inside the solid.
Further information on the effect of energetic secondary
electrons can be obtained from the comparison of the
incident-angle dependence of the intensity of electrons from
plasmon decay and the intensity of fast secondary electrons.
This is shown in Fig. 8共a兲. We note that the dependencies are
different; this is clearer in the intensity ratio shown in Fig.
8共b兲. The reason for the different angular dependence of the
two intensities is the change in the ion trajectories with a
change in incidence angle. For small angles, below the critical angle for proton penetration in the bulk, roughly half of
the secondary electrons are emitted directly into vacuum and
half are directed towards the interior. Only these inward
moving electrons are able to excite volume plasmons. When
the incidence angle is increased, a larger fraction of excited
electrons are able to enter the solid. At large incidence
angles, essentially all secondary electrons are produced inside the solid. This explains qualitatively the factor of 2 in
FIG. 8. 共a兲 Intensity of plasmon decay electrons and fast secondary electrons 共25–75 eV兲 versus incident angle. 共b兲 Ratio of the
plasmon intensity to that of fast secondaries shown in 共a兲.
the efficiency of plasmon excitation by secondary electrons,
when comparing results for large and small angles of incidence. We note that even at small glancing angles the protons penetrate the jellium edge, although they do not go
through the first atomic layer. The electrons that escape directly from this first layer may excite plasmons but, because
of the begrenzung effect, the plasmons will be surface modes
and will not be counted in the intensity shown in Fig. 8.
In summary, the observations of electrons from the decay
of volume plasmons in Al共111兲 induced by protons over a
wide range of incident energies and incidence angles are
consistent with an indirect excitation mechanism by fast secondary electrons produced in binary ion-electron collisions.
This contribution to plasmon excitation is dominant over the
contributions coming from Auger electrons and from direct
proton excitation.
ACKNOWLEDGMENTS
We acknowledge support from a cooperative research
grant from the National Science Foundation and the Consejo
Nacional de Investigaciones Cientı́ficas y Técnicas of Argentina 共NSF INT-9724820, and PIP 0423/98兲, and from the
Secretaria de Ciencia y Technologı́a 共PICTs 3-4-110/97 and
3-4220/98兲.
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