Nuclear Instruments and Methods in Physics Research B 164±165 (2000) 879±885
www.elsevier.nl/locate/nimb
Probing inelastic interactions of ions moving in solids by electron
spectroscopy
R.A. Baragiola
b
a,*
, S.M. Ritzau a, R.C. Monreal
b
a
Laboratory for Atomic and Surface Physics, Engineering Physics, University of Virginia, Charlottesville, VA 22901, USA
Universidad Aut
onoma de Madrid, Departmento Fõsica Te
orica de la Materia Condensada, C-V, Cantoblanco, 28049 Madrid, Spain
Abstract
We have measured energy distributions of electrons emitted from clean aluminum surfaces by 20 keV/amu H‡ , He‡
and He0 projectiles. Ratios of energy distributions obtained from two types of projectiles carry information on differences in the electron excitation collisions. We discuss these di€erences in terms of screening of the projectile by
valence electrons, Auger capture and projectile ionization, with the aid of linear response theory. We ®nd the shapes of
secondary electron energy spectra are dominated by the energy dependence of the electron escape depth and of the
binary ion±electron interaction. The latter must be determined by considering the screened potential of the projectile
and its changing charge state as it penetrates the solid. Ó 2000 Elsevier Science B.V. All rights reserved.
PACS: 79.20.-m; 34.50.Dy; 34.70.+e; 79.20.Ap
Keywords: Electron emission; Electron capture; Electron loss; Charge fractions; E€ective charge
1. Introduction
The study of collision processes of atomic
particles in condensed matter is hindered by the
diculty of extracting information about individual events from observations made outside the
solid. The usual method of probing inelastic interactions of ions moving in solids is by measuring
an integral quantity, the energy loss of projectiles
traversing a thin section of material, from which
the stopping power is derived. Another view of
*
Corresponding author. Tel.: +1-804-982-2907; fax: +1-804924-1353.
E-mail address: [email protected] (R.A. Baragiola).
electronic excitations can be achieved by studying
the ejection of electrons from the solid. This approach has the added complexity that other
properties such as the surface potential barrier and
electron escape depths intervene, but useful information can be derived from the dependence of the
electron yield c on the type and energy of the
projectile, the type of material, surface properties,
and other variables [1±5]. Two energy transfer
mechanisms can energize electrons so they can be
ejected from the solid. In potential electron emission, the excitation energy is provided by the potential energy of the projectile that is released, for
instance, upon the capture of electrons from the
solid. A di€erent process, dominant at high-projectile velocities, is kinetic electron emission, which
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 0 1 3 - 7
880
R.A. Baragiola et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 879±885
results from energy transfers enabled by the momentum of the projectile. The underlying mechanisms for kinetic emission have been the subject of
several recent theoretical studies [6±12].
Compared with energy loss measurements, the
study of electron emission has the advantage of
being capable of providing information on di€erential energy transfers above a few electron volts
by measuring the energy distribution of emitted
electrons. This method has been applied to the
study of collisions in the gas phase for decades
[13], which bene®t from the simplicity of not
having to consider (usually) multiple collision
events. In dense gases and solids, especially at
high-projectile velocities, one also has to consider
the cascade of electron collisions initiated by energetic electrons. These types of studies have not
been common; the vast majority of previous experimental and theoretical research have focused
on describing total electron yields. Here, we explore the use of energy distributions of electrons
emitted from solids by energetic ions to obtain
information about electronic excitation mechanisms. Our study involves experiments and a theory that considers multiple charge-exchange
collisions by the projectiles and the transport of
excited electrons in the solid. We focus this paper
on the comparison of electron emission by H‡ and
He‡ (the so-called Z1 dependence) and by He‡ and
He0 (the charge state dependence).
2. Experiments
The experiments were performed in an ultrahigh
vacuum chamber attached to a 120 kV ion accelerator (Fig. 1), using procedures described previously [12]. Projectiles were incident at 60° to the
sample normal and electrons ejected in the direction
perpendicular to the surface were energy analyzed
with a hemispherical sector electrostatic spectrometer, operating at a resolution of 0.2 eV. Clean,
polycrystalline surfaces were produced by in situ
vapor deposition of 99.999% pure aluminum, and
the cleanliness was monitored by Auger electron
spectroscopy. For the results reported in this work,
we used 20 keV H‡ and 80 keV He‡ and He0 to
compare projectiles at the same velocity (20 keV/
Fig. 1. Schematic drawing of the experimental setup.
amu or m ˆ 0:89 a.u., close to the Fermi velocity of
Al). The ion current was measured with a Faraday
cup. The energy distributions for
R ion impact are
normalized so that the total area N …E† dE equals
the known electron yields (c ˆ 2:0 for H‡ and 3.85
for He‡ at 60° incidence [14,15]). In the case of
neutrals, where the current could not be measured,
we normalized the energy distributions to the case
of ion impact, so that c0 =c‡ ˆ 0:9 0:1, consistent
with previous measurements of these ratios in carbon [16] and gold [17] targets.
Fig. 2 compares electron energy spectra N(E)
obtained with 20 keV/amu He‡ and H‡ projectiles.
It is seen that He‡ excites more electrons than H‡
over the whole electron energy range measured.
Although He‡ gives much more potential emission
than H‡ at very low impact velocities because of
its larger potential energy, we do not expect this
mechanism to be important at 20 keV/amu. This
is because the Auger capture cross -section for
80 keV He‡ is 2:5 10ÿ17 cm2 [18], which implies
at 60° incidence,
a mean depth for capture of 34 A
much larger than typical escape depths of lowenergy electrons. On the other hand, enhanced
kinetic excitation by He‡ compared with H‡ is
expected since a larger nuclear charge produces
larger ion±electron scattering cross sections. The
shape of N(E) for kinetic emission is determined
mainly by three factors. (1) The energy distribution of electrons from excitation collisions in the
bulk decreases with E, a property of the screened
Coulomb interaction. (2) The escape depth of
electrons, determined by electron±electron and
R.A. Baragiola et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 879±885
Fig. 2. Electron emission from H‡ and He‡ impact on Al at the
same velocity corresponding to 20 keV/amu. Top: energy distributions N(E). Bottom: ratio of energy distributions,
‡
R…E† ˆ N …E†‡
He =N …E†H . The points are the experimental data.
The lines are the results of theory for the following cases: (±±±±)
charge of the ion frozen to singly ionized and no elastic scattering of electrons, (- - -) charge of the projectile evolves with
depth, no elastic scattering of electrons. (±±+±±+) charge of the
projectile evolves with depth, elastic scattering included.
elastic electron±atom collisions decreases with E.
(3) The probability that an excited electron escapes
from the surface increases from zero at E ˆ 0 and
tends asymptotically to 1 at high E.
Also shown in Fig. 2 is the ratio
‡
…E†=NH‡ …E†. It reveals more clearly the
R…E† ˆ NHe
di€erences between the two projectiles and is more
accurate than the individual N(E), because the
ratio removes the energy dependence of the eciency of the spectrometer. The ratio R(E) increases with energy. In general terms, this was
expected because higher electron energies require
collisions closer to the nucleus of the projectile (for
unscreened charges, the Rutherford cross-section
is proportional to the square of the charge, and the
ratio should be 4).
881
Fig. 3. Electron emission from He‡ and He0 impact on Al. Top:
experimental energy distributions normalized so that the ratio
of the total electron yield is c0 =c‡ ˆ 0:9. Bottom: ratio of energy distributions, R…E† ˆ N …E†0He =N …E†‡
He . The points are the
experimental data. The line is the result of theory, considering
the evolution of projectile charge with depth and elastic scattering of electrons.
Fig. 3 compares energy distributions of helium
ions and neutrals. The ratio R…E† ˆ NHe …E†=
‡
NHe
…E† is seen to fall monotonically with energy.
At high E, R(E) is below 1, as expected from the
larger screening in He than in He‡ . However, the
ratio increases at low E, which is not consistent
with a purely screening mechanism in projectileelectron scattering. In fact, at low-electron energies, neutral atoms eject more electrons than ions.
3. Theory
As the projectile penetrates the metal, electron
transfer processes become operative and the
charge state of the projectile evolves in time until
equilibrium is reached deep in the solid [18]
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R.A. Baragiola et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 879±885
Fig. 4. Top: attenuation function for electrons of 2 and 20 eV,
as a function of depth z. Middle: charge fractions for initial He‡
beams as a function of depth. Bottom: charge fractions for an
initial H‡ beam as a function of depth. The graphs illustrate the
change in the weighting of di€erent charge states with electron
energy, due to the energy dependence of the attenuation length.
(Fig. 4). There are several mechanisms by which
the particle can excite electrons. (1) Binary collisions between the projectile, either in a neutral or
charged state, and conduction electrons. (2)
Charge transfer processes such as Auger capture
and loss and resonant electron loss accompanied
by excitation of the metal and/or projectile electrons. (3) Close collisions between the projectile
and core electrons of the target can lead, by electron promotion, to the formation of core-holes
that will be ®lled with the emission of Auger
electrons. In the list of mechanisms we do not include direct Coulomb excitation of plasmons since
the projectile velocity in this work is below the
threshold for this process [12].
Electrons from these types of excitation events
can escape from the metal if they have enough
energy to surmount the surface barrier and are
excited at depths comparable or smaller than the
mean escape depth. These electrons can in turn
excite other metal valence electrons or plasmons.
These processes give rise to a cascade of secondary
electrons and electrons resulting from plasmon
decay which tend to pile-up at low-electron energies. Excitation of cascade electrons above the
vacuum level is only possible when the energy of
the electron from the primary excitation is E > u
(energy larger than 2u with respect to the Fermi
level), where u is the work function of the surface
( 4:3 eV for Al).
In this work, we will be concerned with the
excitation of primary electrons by incident He‡ ,
He0 and H‡ on Al; analysis of the electron collision cascade will be the subject of a future paper.
Its contribution is important at the lowest electron
energies, where they cannot be disentangled from
other processes such as Auger capture and electron
loss from the projectile. As we will discuss, we do
not ®nd that the e€ect of cascades is important in
our analysis. The possible charge states of He
considered are neutral (0), singly ionized (1) and
double ionized (2). For H on Al, the negative ion
()1) is possible together with the neutral and the
bare proton. The time evolution of each charge
state is obtained from a set of coupled rate equations which, for the case of He, reads
d/2
ˆ C12 /1 …t† ÿ C21 /2 …t†;
dt
d/0
ˆ C10 /1 …t† ÿ C01 /0 …t†;
dt
d/1
ˆ C21 /2 …t† ‡ C01 /0 …t† ÿ …C10 ‡ C12 †/1 …t†:
dt
…1†
Here Cif denotes the rates for electron transfer
from the initial charge state i to ®nal charge state f,
and /i the fraction of He in charge state i (0, 1, 2).
These are standard expressions, except that they
do not include, for clarity, the unlikely doubleelectron transfer processes. Eq. (1) is solved with
the initial conditions /1 …t ˆ 0† ˆ 1, for incident
ions and /0 …t ˆ 0† ˆ 1 for incident neutrals. Similar equations are solved for H on Al. The solutions of Eq. (1) are of the form
/i …t† ˆ /1
i ‡ Ai …t †;
…2†
R.A. Baragiola et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 879±885
where /1
i is the stationary (equilibrium) solution
and Ai (t) is the transient solution (see Fig. 4). The
probability per unit time that a particle in a charge
state i excites electrons of energy E in an energy
interval dE, within linear response theory and the
Random Phase Approximation, is easily derived
from Section 7 of [18]. It reads
Z
Z
X 4p 2 q …q† 2
dPi
1 p
i
ˆ
2E
dX
dx
dE 2p2
q2 eL …q; x† k 0 <kF
ÿ
d E ÿ Ek0 0 ÿ x d…x ÿ qm†;
…3†
with the restriction of momentum conservation
k ÿ k 0 ˆ q. In Eq. (3), where atomic units are used,
k 0 and k are the initial and ®nal electron momentum. The electron excited with energy transfer x is
described by its energy E and its angle X. qi (q) is
the Fourier transform of the electric charge density
given by the projectile nucleus and the electronic
charge distribution of the projectile in charge state
i, and eL (x, q) is the Lindhard dielectric function.
The spatial distribution of excited electrons is, in
general, anisotropic but elastic scattering randomizes this distribution eciently, since mean
for
free paths for elastic collisions are less than 6 A
E < 30 eV [1]. Then, for the number of electrons
emitted in process 1 above, we write
XZ 1
dN
dPi 1 ÿz=L…E†
ˆ T …E†
e
dt/i …t†
;
dE 2
dE
0
i
…4†
where z ˆ mt cos h; m being the projectile velocity
and h its incidence angle. In Eq. (4), T(E) is the
probability of transmission of an electron over the
surface barrier potential, and L(E) is the electron
attenuation length. The factor of 1/2 takes care of
the fact that, on the average, only one half of the
excited electrons travel towards the surface. The
attenuation factor exp()z/L(E)) is the probability
that an electron of energy E, excited at a depth z,
reaches the surface without energy degradation, an
average over initial emission directions and paths
to the surface. The concept of attenuation is valid
in the case of low-energy electrons since the
probability that they lose only a small fraction of
their energy in an inelastic collision is small. One
can see that L(E) a€ects the shape of not only N(E)
883
but also of R(E), because it determines how much
``memory'' of the initial charge state of the projectile is carried by the emitted electron.
Eq. (1) was solved for He and H, using theoretical cross-sections given in [18]. The time scale over
which the transient solution Ai (t) of Eq. (2) dies out
can be obtained approximately by neglecting /2 for
the case of He, and /ÿ1 for the case of H. This is a
good approximation for the velocities of the present
work since the equilibrium fractions of He2‡ and
Hÿ are both only about 10%. Calling C the sum of
the electron capture and loss rates we obtain
Ai …t† ˆ Ai …0† eÿCt . Then, charge equilibrium will be
reached with a characteristic depth scale
Only those electrons excited within
D ˆ mC 8 A.
a depth of the order of L(E) will be detected outside.
Therefore, very low-energy electrons, for which
L…E† > D, may originate deep in the solid under
conditions close to equilibrium while high-energy
electrons, for which L(E) [ D retain some memory
of the initial charge of the projectile. This e€ect is
illustrated in Fig. 4, where we plot the charge states
for incident H‡ and He‡ , and the attenuation factor
exp …ÿz=L…E†) for E ˆ 2 and 20 eV.
4. Discussion
The ratio R(E) for He‡ /H‡ increases with
electron energy. This is expected since larger energy transfers imply closer ion±electron collisions
so that the e€ect of screening is lower. At our velocities, the limit of R ˆ 4 for Rutherford scattering, which is the ratio of the square of the nuclear
charge, is not achieved since even the head-on
collisions are a€ected by screening. The ratio of
the total electron yields (ratio of areas under the
N(E) curves) is 1.93 and close to the ratio of
electronic stopping powers [19]. Our theory, which
considers only electrons excited in binary collisions, gives already the overall shape and magnitude of the experimental results.
The importance of attenuation length and the
depth evolution of the projectile charge are shown
in Fig. 2, where we give the results of calculations
performed using the inelastic mean free path for
L(E) (dashed line) and an improved description of
electron transport by adding elastic scattering as
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R.A. Baragiola et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 879±885
well (crosses). In the calculation where the projectile charge is kept frozen at the incident value, the
e€ect of attenuation lengths is cancelled out when
taking the ratios. In this case, R(E) gives directly
the ratio of probabilities of producing an electron
of energy E by He‡ and by H‡ . However, in the
case where the projectile charge is allowed to evolve
with depth, the theoretical R(E) changes its behavior at low E while retaining its shape in the highenergy region. This is because, as stated above,
high-energy electrons are emitted near the surface
and therefore retain memory of the charge of the
projectile, while low-energy electrons are emitted
from depths where charge equilibrium is attained.
These low-energy electrons are therefore more
sensitive to the values of the attenuation lengths
than high-energy electrons, as can be seen by
comparing the results with both choices of L(E).
Improvements in theory may be attempted using a non-linear approach, since recent results for
the stopping power of protons on Al [20] using a
Density Functional approach show that the nonlinear stopping power is two times larger than the
linear stopping power at m ˆ 0:9 a:u. For balance,
this may also require treating electron transfer
processes and electron attenuation using a nonlinear theory.
One can notice in Fig. 2 that the ratios grow
fast with E J 20 eV, unlike the theoretical results.
The reason is that, at these energies, the electron
spectra contain Al-2p Auger electrons degraded in
energy, which are excited more eciently by He
than by H projectiles at 20 keV/amu [21,22]. Al-2p
Auger electrons and other high-energy electrons
excited in close collisions can have a high probability of producing secondary electrons of lower
energies, which we have not included in the calculation. However, those cascade electrons will be
produced with high ratios R (those relevant to the
high energy of the electrons that can initiate
the cascade), whereas low values of R are found
at the low-energies characteristic of cascade electrons. This shows that the cascade produced by the
Al-2p Auger and other high-energy electrons is
relatively unimportant in R(E). On the other hand,
fast electrons can eciently excite plasmons,
whose decay contributes to the electron spectrum
below 11 eV [12]. Since R is large for fast elec-
trons, the plasmon contribution will also have a
high R value compared with electrons at the same
energy originating directly from ion±electron
scattering.
At low-electron energies, the calculated ratios
are higher than experiment. A possible reason is the
contribution of electrons excited in the charge exchange processes (2) above. These electrons are not
accounted for in this work; they are fewer than the
electrons excited in binary collisions, as found in
[7]. Auger capture, which will be more important
for H‡ than for He‡ projectiles, produces electrons
in the low-energy region. Another contribution to
the low-energy part of N(E) is electron loss (projectile ionization) from the neutralized projectiles
which is more likely for H than for He‡ . In gasphase collisions, most projectile ionization produces electrons with near-zero energy in the projectile frame. In the laboratory frame, they appear
as a broad peak centered at the velocity of the
projectile. In the case of ions moving inside solids
we need to take into account that the ®nal state of
the electron needs to be above the Fermi level. An
electron cannot move inside the solid with the velocity of the projectiles, because it is below mFermi , in
the occupied part of the band. We thus expect that
most of the electrons from projectile ionization will
remain inside the solid near the Fermi level, with a
tail extending above the vacuum level populating
low E. These electrons are possibly the ones that
give the enhancement of the ratio R above the
theoretical values for binary ion±electron collisions. Suppression of electron loss by the unavailability of ®nal electron states explains the drop of
the electron loss cross sections in solids compared
with gases at low velocities reported in [18].
In comparison between He0 and He‡ projectiles,
we note that binary collisions calculated by theory
can account for the reduced N(E) at intermediate
and high-electron energies (Fig. 3). However, R(E)
is again above theory for low-electron energies,
which could also be explained by electron loss.
5. Conclusions
Measurements of energy distributions of electrons emitted in ion±solid interactions carry in-
R.A. Baragiola et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 879±885
formation about di€erent electronic excitation
processes. We have identi®ed several factors that
are important in understanding energy distributions. Ratios of energy distributions for di€erent
projectiles at the same velocity give information of
the screening of the projectile nuclear potential by
target electrons. The screened potential determines
the strength of the binary ion±electron interaction,
which is the main mechanism of electron excitation
for light ions at our impact velocity. Another important factor is the evolution of the charge state
distribution and screening with depth in the solid,
due to charge-changing collisions. Here, the important parameter is the characteristic distance for
charge equilibrium D compared with the electron
escape depth L. At high-electron energies (e.g., 30
eV), L is smaller than D, so the energy distribution
is strongly a€ected by the initial charge state. For
electron energies of a few eV, L is of the order or
larger than D and therefore we expected that incident neutrals and ions would give similar energy
distributions. However, we see a strong enhancement in the emission of low-energy electrons for
He0 compared to He‡ that we hypothesize is due
to projectile ionization. A similar argument is applied to explain the enhancement in the electron
yield for H‡ with respect to He‡ at low E. The
comparison of distributions of high-energy electrons needs to consider the emission of Auger
electrons from the decay of core holes excited in
close collisions. Finally, we point to research avenues that can be taken to improve theory to
achieve a better understanding of these phenomena. These include the consideration of non-linear
e€ects in ion±electron interactions and the inclusion of the electronic cascade in the solid.
Acknowledgements
This work was partially funded by the Southwest Research Institute, the National Science
885
Foundation, and the Spanish Comisi
on Interministerial de Ciencia y Tecnologõa (contract PB970044).
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