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Section V
Electron emission
NOMB
Nuclear Instruments and Methods in Physics Research B78 (1993) 223-238
North-Holland
Beam Interactions
with Materials&Atoms
Principles and mechanisms of ion induced electron emission
Rafd A. BaragioIa
The mechanisms responsible for emission of electron from solids are described, separating them, when possible, into electron
excitation, electron transport and cascade multiplication, and transmission through the surface barrier. Discussions include
important energy quantities and quantum mechanicai effects in the transport of slow electrons in the solid and through the surface
barrier. Some new aspects not previousiy described are explored, such as how much information can be obtained by treating
insulators as dense gases, electron loss from the projectile, differences between prompt and delayed excitation processes and final
state effects in multiple electron emission.
1. rntroductio~
Electron
emission
(EE) is one of the most conspicu-
consequences of inelastic ion-surface
collisions
and, in general, of interactions of any ionizing radiation with condensed matter. It is basically understood
as follows: the primary particle, the ionizing projectile,
frees secondary electrons in collision events. These
electrons then undergo a cascade of collisions in the
solid, which can produce additional ionization, until
their energy is degraded into heat or stored in long-lived
excited states. Those excited electrons which are directed outwards can cross the surface of the solid and
escape before being thermalized, giving rise to secondary EE. The main observable in EE is the average
electron yield y (number of electrons ejected per primary particle), either as an integral quantity or in the
form of distributions of electrons according to their
energies, angles of emission, and spin state. EE events
are statistically distributed; that is, the yield flue&rates
around the mean value y and is described by probabilities of emission of n electrons per projectile.
Experiments involve measuring the dependence of
EE on different factors. These include the type of
projectile and the target and the experimental geometry. The most important projectiIe properties are the
type (heavy particle, electron, photon, etc.) and the
energy. For heavy particles, additional important properties are also their excitation and ionization state,
their mass, and whether they come as single atoms,
molecules or clusters of molecules. Relevant target
properties are the elemental composition and atomic
and electronic structure in the surface region, the
magnitude of surface electrostatic fields (for insulators
and semiconductors), the temperature, and, for magnetic materials, the degree of magnetization. The rele-
ous
0168-583X/93/$06.00
vant geometrical factors in the experiment include the
angle of incidence with respect to the surface and to
possible preferred crystallographic planes. The achievable reproducibility of EE yields from clear surfaces
shown in fig. 1 is quite high compared with data from
other ion-surface collision experiments.
The topic of ion induced EE has been surveyed
recently with emphasis on obse~ations [l-3] and theory [4-G] and discussed at a specialized conference [7].
Here, I will describe the main physical processes in
kinetic electron emission (KEE) from solids, that is,
EE induced by the motion of heavy atomic and molecular projectiles. Potential EE (PEE) which results from
conversion of the potential energy of the projectile
without need for atomic motion will not be described
in detail; the topic has been covered in another set of
recent reviews [8-121. I will describe KEE from a
different perspective, touching some aspects not previously considered. The starting point of this work will
be a discussion of individual scattering events in gases
and what can be expected by ~nsidering the solid as a
dense gas, emphasizing similarities and differences,
2. Gas-phase versus ion-surface
collisions
EE from surfaces is the contempt
of ion~ation in
gas-phase collisions (although not all processes which
produce ions liberate free electrons). Much insight can
be gained by studying ionization in the gas phase, since
the mechanisms occur directly, or in a modified form,
in ion-surface collisions. Similar considerations should
also apply to collisions with large molecules and with
clusters. Ionization collisions take the form of target
ionization, projectile ionization (electron loss or detachment), and combined processes. Ionization by
0 1993 - Elsevier Science Publishers B.V. All rights reserved
V. ELECTRON EMISSION
224
R.A. Baragioh / Ion induced EE
I
3.0 -
Hf
I
-
2.1. Gas targets
2
Let us consider first a particle of energy E, passing
through a chamber containing gas at density N where
electrically biased electrodes are used to separate and
collect ions and electrons. One can distinguish between
experiments done at low pressures (thin targets in
single-collision conditions) and at high pressures (thick
or dense targets). For thin targets, the probability of
double collisions is small; i.e., there is no significant
change in the state of the projectile or scattering of the
ejected electrons on their way to the collector. The
number of ionization events per unit path length dx in
the gas, and per projectile is:
Ag
Au
v
2.5 r
dv( E,)/dx
I
100
10’
PROTON
102
ENERGY
1
I
I03
104
/ keV
Fig. 1. Total electron yield y for H’ impact on clean metals
as a function of ion energy. The data has been obtained at
five different laboratories: o - Baragiola et al. [29], l Hasselkamp et al. [141], x - Veje [142],
-Holmin et al.
[143,144], 0 - Koyama [145], --interpolation between
data sets (from Hasselkarnp 11461).
heavy particles can also accompany other processes,
such as charge exchange, excitation, and dissociation.
Ionization can occur during the collision, or after delayed relaxation of excited atomic states, such as in
autoionization or Auger processes.
In dense gases and solids, energetic electrons released in the primary ionization events can produce
additional ionizations by colliding with other atoms,
generating a collision cascade which dilutes the energy
initially concentrated in the projectile into a large
number of particles. The observation of EE events in
gases and solids implies the collection of part of the
electrons in the cascade before they recombine with
positive ions. In targets with an excitation gap (gases
and nonmetallic solids) this can be done with collectors
inside or outside the target material. In metals, the
observation of ionizations has been restricted to electron ejection from the surface.
AI1 collision processes will be different in gases than
in condensed matter, due to differences in the initial
and final electronic states. However, some of these
differences are small and so one can draw general
analogies as a heuristic approach to understand EE in
solids. From there one can then discuss specific condensed matter effects and evaluate their importance.
= C( E,)N,
(1)
where u is the ionization cross section.
By increasing the gas pressure sufficiently, one can
already discern several specific molecular and condensed matter effects. Projectiles will suffer multiple
collisions some of which may produce several sequential and, possibly, simultaneous ionizations. Furthermore, the projectile will lose energy and may change its
electronic structure, be deflected and set target atoms
in motion. These target recoils can produce additional
ionization by conversion of their potential or kinetic
energy.
The electrons ejected in primary ionizations, the
first-generation (1G) electrons will undergo a variety of
collision events after being ejected. They will scatter
and lose energy in collisions with target molecules;
some of these collisions can produce additional ionization if the electron energy is above the ionization
potential of the target. When the energy of the electrons degrades to a few eV or less, they can be lost by
recombination with ions or by attachment to target
species to produce negative ions.
By applying an electric field to the gas, the charges
can be separated before significant recombination occurs, collected, and counted. An important empirical
finding is that dv/Ndx
is equal to the electronic
stopping cross section S, = (dE/N dx), divided by a
constant, w:
dv(E)/dx
=&N/w.
(2)
If the particle stops completely in the gas, the number
of ion pairs produced is:
E,
‘= / o
S(E), 1
----dE,
S(E),,,
w
(3)
where S,,, is the sum of the electronic and the nuclear
(elastic) stopping cross sections. If E, is sufficiently
large, S,,, - S, over most of the path and one can use
the asymptotic expression:
v = E,/W.
(4)
R.A. Baragiola / Ion induced EE
The average energy required to produce an ion pair,
the “W-value” depends very little on the type and
energy of the ionizing radiation and relatively little on
the nature of the gas [13,14]. This property is very
important in the operation of the gas-filled proportional counter [15], a radiation detector used to analyze
the energy of the incident radiation by counting the
number of ion pairs produced.
At low impact velocities, v is no longer proportional
to projectile energy [16,17] since the fraction of the
projectile energy available for electronic excitations
decreases due to the generation of energetic target
recoils and atomic vibrations in elastic collisions with
target nuclei. Some of the energy transferred to the
recoils will still be delivered to the electronic system in
additional ionization collisions [l&19]. The relative
contribution of recoils increases with increasing ratio
of the mass of the projectile to target atoms. This
recoil effect has important implications in KEE at low
energies. An additional effect occurring as the excitation energy approaches the ionization threshold, is a
fall of the average energy of the excited electrons, so
that fewer can produce secondary ionizations.
The number of ion pairs produced is statistically
distributed, since there is a fluctuation of energy transfers in individual collisions. The fluctuations in v are
important because they determine the energy resolution of proportional counters (and solid state radiation
detectors). It has been found that fluctuations are not
those corresponding to a Poisson distribution. Rather,
the variance is s2 = Fv, where F is the Fano factor
[20]. Table 1 gives values of W and F for some gases
and also some liquids and semiconductors [15]. F
should increase near the ionization threshold to the
value F = 1 resulting from a Poisson distribution
[21,22].
2.2. Solids
The concept of mean energy to create an ion pair is
well defined in semiconductors and insulating solids,
where one usually speaks in terms of electron-hole
Table 1
W-values and Fano factors for different materials under irradiation by fast ions [15]
Target
W leV1
F
He (gas)
Ar (gas)
42.7
26.2
23.6
20.3
21.5
15.6
3.8
3.0
_
0.17
0.116
< 0.09
< 0.17
0.059
0.084-0.14
0.057-0.13
Ar (liquid)
Ar+O.5% C,H,
Xe (gas)
Xe (liquid)
Si
Ge
225
timeFig. 2. Number of excited electrons with energy E * above the
valence band edge vs time. In the case where E * > E,, but
less than ZEa, a typical band gap energy in an insulator, the
electron cools fast in a metal but can only lose energy slowly
to phonons in the insulator. When the electron energy is
E * > ZE,, fast cooling by electron-electron
interactions is
also allowed in the insulator. An appropriate time scale for
this graph is in the range offs.
pairs. Like in gases, W can be measured by separating
the charges in an electric field, and collecting them in
electrodes, before significant recombination
occurs.
Some loss of charges occurs when the density of ionizations is very high (e.g., for fast, heavy projectiles such
as fission fragments).
Ionization of semiconductors
is usually studied
through induced electrical conductivity in the bulk
[23-251 and at surfaces [26,27]. It has important application in radiation detectors and in the behavior of
electronic components in space. Studies in insulators
and more complicated due to, in general, a low mobility and high trapping rates for electrons and holes.
Slow or trapped charges will help set up high internal
electric fields which will hinder or impede charge collection. In the case of high mobility insulators, such as
diamond or liquid Xe, the collection of induced charge
is more feasible and has led to the development of
practical radiation detectors. In the case of metals,
charge separation is not possible, and the “number of
excited electrons” is not a clearly defined quantity due
to the possibility of fast and continuous energy degradation. Such behavior is understood diagramatically in
fig. 2.
Some condensed matter effects, already found in
molecular targets, occur when the distance between
target atoms becomes very small. A small distance
between ions at high ionization densities will cause
considerable repulsive forces. They can dissociate free
molecules and dislodge the lattice in solids, creating a
damage track along the path of the projectile [28]. The
high ion concentration will also set up a high electric
field which will affect the motion of the electrons and
holes. The creation of high ionization densities has not
been studied; one can expect saturation effects in the
region close to the maximum of the stopping cross
V. ELECTRON EMISSION
226
R.A. Baragiola / Ion inducedEE
section, especially for highly charged projectiles. One
of the important unsolved questions is the probability
of exciting plasmons in the presence of a plasmon field
previously excited by the same projectile.
Quantum effects appear in the ionization cascade
when the distance between atoms is small. The associated de Broglie wavelength h = h/mu = 12.25 w E-l12
(eV) for low energy cascade electrons is of the order of
or larger than the nearest neighbor distance between
atoms in molecules and condensed matter. Coherent
scattering and interference of scattered waves will occur which, in the case of an ordered array of target
atoms, will result in diffraction patterns.
The other important aspect of the solid is the abrupt
discontinuity of the surface. This interrupts the full
development of the cascade, a fact not considered or
described in many transport theories. This interruption
allows EE which would not be observable otherwise.
The surface barrier hinders ejection of those electrons
that have fallen below the vacuum level due to energy
loss collisions. Those electrons will be attenuated in
number with a probability that depends on the distance
between the point of excitation and the surface. Thus,
both the existence of a surface barrier and inelastic
collisions of cascade electrons serve to determine a
mean escape depth, L, from which electrons can originate.
By analogy to the situation in gases, one can thus
expect a proportionality between the electron yield y
and E, the energy deposited in electronic excitations
within the escape depth. Experiments have shown that
this proportionality holds over a wide range of conditions. In many cases involving fast projectiles, E a
S,NL/cos(cu), where LYis the angle of incidence of the
projectile with respect to the surface normal. We have
found [29] a fairly universal proportionality of electron
yields with the electronic stopping power, dE/dx,
rather than with the stopping cross section dE/N dx,
a quantity usually preferred due to its insensitivity to
target density:
y =B(dE/dx),/cos(a).
Deviations from this formula are expected, and observed, at low energies, at large angles of incidence, in
conditions of strong ionization by recoils and when the
electronic cascade is highly anisotropic. I prefer not to
consider B as a “material parameter” in the sense of
Schou’s A [30], since the properties of the cascade and
the probability of escape depend, in principle, also on
the projectile through the angular and energy distribution of 1G electrons. In practice, it is observed that in
some cases, B seems to be relatively independent of
the target material and in others to depend on the type
of projectile. We found that B falls in the narrow
band: B = 0.10 + 0.03 A/eV for different clean metal
targets under 5-50 keV HC bombardment [29] and
about 20% lower for heavier ions (He through Ne) [31].
Hasselkamp et al. [32] found that these values of B
also hold up to 800 keV and extended the observations
to 27 metals and semiconductors. They found that the
band included most materials with the exception of
Mg, Cd and In which fall above and Cr and Nb which
fall below the band. They also found that B for Ar
impact is about 20% lower and does not show the
general constancy with velocity tound for incident H+
[33]. B values around 0.31 eV/A have been found for
the total yields from C foils bombarded by fast ions
ranging from hydrogen to uranium [34-361.
3. The primary processes
The EE process is conveniently divided into three
steps, (1) primary ionization, (2) electron transport,
and (3) escape through the surface, except when excitations occur just at the surface, when the three events
are inextricably coupled.
3.1. Electron excitation
The most important step in EE is the primary
ionization. The effect of the electron cascade and the
surface barrier may be minimal for excitations outside
surfaces, but the ionization event must always occur in
EE. There are several ways in which the projectile can
transfer energy to target electrons. Direct, “prompt”
processes occur during the collision, in a short time
scale 0.01-2 fs. Indirect, “delayed” processes result
from the relaxation of electronic energy stored during
the collision. The time scale of these processes is 0.1-l
fs for plasmon decay, l-100 fs for Auger decay [37,38]
to seconds or longer for exoelectron emission after
particle impact [39].
3.1.1. Direct processes
The minimum or threshold energy required to liberate an electron from a perfect solid, U, is the energy
difference between the top of the valence band and the
vacuum level. This is the work function in metals, 4,
and the electron affinity x plus the band gap E, in
insulators and semiconductors. Thus, U is equal to the
photoelectric threshold of the surface. Af finite temperatures, EE can occur below this threshold, from
occupied states lying above the valence band maximum. Threshold energies range from 2.1 eV for Cs to
more than 20 eV for condensed He. I introduce here a
measure of the efficiency of the EE process, the quantity Q = E,/y, the average energy spent to emit an
electron, where E, is the electronic energy lost by the
projectile in the escape region. Q can be delivered by
the projectile in different ways. If the projectile is
excited or ionized, it carries an internal potential en-
227
RA. Baragiola / Ion induced EE
ergy Ei that can be released by multiple electron
interactions, like in the Auger process. If Ei > ZU,
potential EE can occur. In this case, values of Q range
from - 30 eV at low excitation energies [40] to 90 eV
and more for multiply-charged projectiles [41,42]. In
the case of KEE, Q - 300 eV for clean metals and
semiconductors [29,31,32] and approximately the Wvalue for thin Ar films [43].
The contribution of PEE yields yp to KEE can be
deduced in different ways. Comparison of EE by ground
state neutrals and ions show that the difference in the
yields remain approximately constant in the keV energy range, suggesting a constancy in y, with ion
velocity v. [44]. On the other hand, Hagstrum [45] has
shown that in many cases PEE depends on u0 due to
competition of different PEE processes depending on
the interaction time of the ion at the surface or on the
normal component of v,,. A strong energy dependence
is found for molecular ion impact on surfaces, where
the internal energy might be dissipated in molecular
breakup, depending on the ratio between the transition
rates for Auger processes and dissociation [46]. A
method has been proposed that uses emission statistics
to separate PEE from KEE by assuming that PEE
cannot produce more than one electron [47], i.e. for
Ei > 3U, when the excited electron cannot produce
additional EE. However, the situation is not clearly
defined since the KJZE threshold for emission of one
electron is probably different from that for emission of
two electrons.
3.1.1.1. Kinetic electron emission There are several ways
in which moving projectiles can excite electrons at the
expense of their kinetic energy. At high velocities, the
energy transfer can be a result of a close collision with
a target electron, and is described by the Rutherford
cross section. It can also result from distant collisions,
where the transient electric field produced by a passing
charged projectile induces a dipole excitation. The
perturbation can be described as a source of virtual
photons with excitation rates related to photoabsorption cross sections [48]. At lower velocities, it is also
necessary to take into account electron-electron
interactions. When the velocity is very low, the electrons
can follow the perturbing effect of the ion adiabatically, and excitations are very unlikely. The angular
distribution of electrons ejected in gas-phase collisions
is usually forward peaked, especially for the more
energetic electrons which result from direct binary
collisions with the projectile.
In the treatment of EE from metals under slow ion
impact problems arise when using the free-electron
model to describe the solid. This model is often a good
first-order approximation of the valence band; for instance, stopping power calculations using electron gas
models provide generally good agreement with experiment. The free-electron model was first tested by the
author and co-workers for Al bombarded with ion of
velocities u lower than the Fermi velocity uF (fig. 3)
[31]. For free electron targets, KEE is limited by momentum conservation due to the strong mismatch between the masses of the electron, m, and of the heavy
projectile, MB m. The maximum energy transfer to
an electron occurs when an electron at the Fermi
surface, with momentum antiparallel to the projectile
scatters into a final state with momentum parallel to
the projectile. It is given by:
E max= 2mu(v
+ vF).
(f-9
The excited electron
is directed inwards but can be
Y
1.0
0
CI
v Ar
Q Kr
Q Xe
0.5
VELOCITY
(107cm/sec)
Fig. 3. Total electron yields for ion impact on clear Al as a function of projectile velocity (from Alonso et al. [31]).
V. ELECTRON EMISSION
228
R.A. Burugiola
/ km induced EE
observed outside due to the strong elastic scattering
with the target atomic cores [4Y]. This free-electron
model then predicts
a threshold
velocity u,,, below
which no emission can occur, where E,, =c$, the
work function of the metal surface:
ing statistical atomic models, and has not yet been fully
justified. It has been applied with limited success to
describe stopping powers [52]. We recognized that this
would allow the description
of KEE induced by slow
heavy ions, and applied it to describe experimental
data at low energies and to establish quantitatively
the
contribution
of ionizations due to recoiling target atoms
[31,53]. That KEE requires close collisions with target
atoms has been recently demonstrated
by Rabalais et
al. [54], who studied the impact parameter dependence
of Ar ’ induced KEE from Ni(ll0)
at 4 keV. They
observed essentially no emission at grazing incidence
and emission
started
abruptly when the decreased
shadowing of atomic planes allowed the minimum impact parameter
in a collision to be below 0.3 A, or
about the sum of the maximum radial charge density of
the L-shells of Ar and Ni.
The experimental
data show that the yield curves extrapolate to zero for velocities close to this value for
light ion impact, if one subtracts the contribution
of
PEE. Lower thresholds
can be obtained if one takes
into account phonon exchange with the lattice, e.g.,
unklapp processes,
or if the collision occurs in the
proximity of ion cores in the solid [50] where the
valence electrons have higher velocities.
However, heavy ions arc found to produce KEE at
much smaller impact velocities. This situation reminds
us of the problem
of the photoelectric
effect from
metals, where emission occurs even though a photon
cannot be absorbed by a free electron. The conscrvation laws arc fulfilled by the participation
of a target
atom in the exchange of momentum. Thus, WC inferred
that KEE at low velocities requires a relatively close
atomic collision.
This implies the same excitation
mechanism
for metals and nonmetals
and makes it
unnecessary to invoke inner-shell excitations [5 11.
The need for close atomic collisions suggests that
the ground state band structure
of the solid is not
important during excitation. This would then allow us
to USC atomic excitation models, such as Firsov’s friction model of energy transfer in slow collisions [52]. In
this model, excitation occurs when electrons flow between the two atoms during encounter,
changing their
net avcragc momentum.
This builds up excitation energy which can cause ionization when it exceeds the
ionization potential. Firsov’s theory was developed us-
0.35,
,
,
,
I
3.1.1.2. Electron emission from the projectile In an
atomic collision, the excited electron may originate not
only from the target atom but also from the projectile.
To estimate the contribution
of electron loss to KEE, I
have used gas-phase cross sections, which are similar to
those for target ionization (electron loss is target ionization in the projectile refercncc frame). If the projectile beam is charge equilibrated,
the number of electron lost by the projectile is given by vi = oCcNx, where
a, is the cross section for a charge exchange cycle [55].
For a beam consisting of singly charged ions and neutrals, rr, = ~,,,u,~~/(u,~ + era,), where u,,,,, is the cross
section for a collision that changes the charge of the
projectile from II to m. If the projectile beam is initially neutral or if it becomes neutralized
immediately
upon entering the solids, v, = wO,Nx. Electron rccapturc by the ionized projectile usually occurs too deep in
the target to bc a source of electrons
in a further
electron loss event, except in insulators or in the case
I
I
I
I
I
12.5
Energy (kev)
Fig. 4. Fraction of electrons originating in electron loss from the projectile and electron multiplication factor for collisions of charge
equilibrated El beams with Ar.
229
RA. Baragiola / Ion induced EE
of the downstream side of foils. If the electran is
emitted isotropically in the projectile frame, it will
have an average energy Eeq = (~/~~~*
in the laboratory system. This will produce a forward peaking which
is noticeable if E,,, is more than a few eV. During the
collision, a loosely bound projectile electron, like in
negative ion or in Rydberg states, will have a stronger
interaction with the target atom than with its parent
core. It will then scatter approximately as a free clec&on and ionize easily for Eeq larger than its binding
energy.
I have estimated the contribution of electron loss to
KEE for proton impact on Ar films by using gas-phase
cross sections [56-581. In thick films, we can assume
that the ion beam is charge equiIibrated through many
charge exchange cycles over most of its path, IIn this
case, we show in fig. 4 a N 30% contribution of electron loss at low energies falling rapidly with energy
after the maximum in the electron capture cross section. In the case of neutral H impact on thin films,
where charge exchange cycles are not important, the
contribution of electron loss is larger; it grows with
energy from 35% at 10 keV to 42% at 1 MeV.
3.1.1.3. Molecular effects in IBE An interesting question is how the EE yield produced by molecular ions
compares to the yields produced by its constituent
atoms. It is found that for hydrogen projectiles, the
ratio of yields R, = r(Hi, u)/Zy(H+, U) at equal velocity is R, < 1 at low energies and R, > 1 at energies
higher than about 100 keV/proton [3,59-621. The reduction at low energies occurs even taking into account
a smaller PEE by molecular ions [Xl. The origin of this
molecufar effect has been a matter of controversy. We
have argued for an interference effect, which has been
demonstrated for stopping powers: molecular ions lose
less energy than protons at IQWvelocities and more at
high velocities. This is due to an interference in the
scattering of the target electrons in the molecuiar
centers f63f. At high velocities where the dynamic
screening is weakened> tire two protons act like a He’+
ion in distant collisions and give a higher yield due to
the z2 dependence of the energy losses. Additional
emission will also result from loss of the Hz electron.
An alternative view 1641 proposed that the molecular
fragments act totally independent
of each other:
?@I,‘) = r(H+) + rfHO) <i.e., interference effects are
ignored) and explains R, < I at low velocities by assuming that y(H) < y(H’). This assumption is based
on the lower stapping power far Ho compared to HC,
caused by screening of the proton charge in Ho, However, screening affects prin~ipall~ the low energy loss
~ontr~but~ons to the stopping power, which are relatively unimportant in exciting electrons above the vatuum Ievel. Furthermore, ionization cross sections at
keV energies may be larger for II than for HC impact
a i
2
10
20
30
4a
50
Electron Energy (ev)
Fig. 5.
Electron energy spectrum from impact of 2 keV Ne”
1651. A complete description of the molecular effect
must necessarily include the (velocity dependent) contributions of interference during excitation, eIectron
Ioss, and screening effects in ionization rates.
3. I, 2. Relayed procesm
Energy
stored temporarily in inner-shell holes or
plasmons can be later released in energetic electrons
which can produce additional ionizations. One of the
main properties of these temporary energy stores is
that the energetic electrons produced from them will
tend to have an isotropic angular distribution, unlike
electrons from direct energy transfers, which tend to
peak in the forward direction. The different angular
distributions will affect the eIectron transport and thus
the KEE yields.
3.1.2.1. E~~~~~~ from Auger decay Hofes in shallow
inner (core) atomic levels usually decay by the emission
of Auger electrons, easily identified in the high energy
tail of the energy distribution of ejected electrons (fig.
5 [66]). The emission is delayed with respect to excitation, by the Iifetime of the core hole (typically l-10 fs).
The subject of ion induced electron emission is covered
in several reviews [8,67-691. Core excitations can occur
in the projectile and in the target atom, as a result of
small impact parameter collisions. The Auger decay
can occur in the bulk or in vacuum for reflected
projectiles or sputtered atoms. Auger energies will be
different in both cases, and reflect the different distribution of valence electrons at the location of the core
hole. There are several instances of misconceptions in
the literature regarding the ejection of core-excited
atoms. AIthough the violent collisions often produce
sputtering as well, the inverse is not true; that is, most
sputtering events are not accompanied by inner-shell
excitations. Therefore no direct correlation should be
expected between Auger and sputtering yields. The
Auger decay of excited heavy projectiles in vacuum can
V. E3LFZTRON EMKSSIUN
230
R.A. Baragiola / Ion induced EE
produce high mean charges of projectiles that have
traversed thin foils 170-721, or backscattered from the
solid [66,73]. Auger emission from target atoms can
produce high ion yields in secondary ion mass spectrometry.
Auger energy distributions consist of a broad structure, readily associated to Auger transitions in the
bulk, and sharp (1 eV wide or narrower) atomic-like
peaks. Analysis of Doppler shifts and broadenings of
the sharp lines [74,75], and the observation of energy
shifts which accompany work function changes induced
by alkali adsorption [76] have shown that they correspond to transitions in core-excited sputtered atoms
decaying in vacuum. To first order, Auger emission in
vacuum is isotropic while that from the bulk follows a
cosine law. This causes the ratio of intensity of atomic
Auger lines to bulk lines to be strongly enhanced for
emission close to the surface [77]. Very detailed studies
of the dependence of ion-induced Auger spectra on
angles of incidence and emission have just been published [78].
A topic still subject to controversy is the relative
role of core excitations in collisions between the projectile and a target atomic (pt) to those between two
target atoms (tt). Here the evidence is indirect, and
comes from comparison of experiments to computer
simulations, which have reached a high degree of development. Our Monte Carlo analysis of Be K emission
[79] showed an excellent agreement with the experimental energy dependence of the Auger yield. This
provided firm grounds to determine the relative importance of pt and tt processes in X-ray emission yields,
more accurately than possible using analytical theory.
The results show that tt collisions dominate EE by
Auger processes at the lower energies. Recent simulations of L-shell excitations in bombardment of solid Al
targets with Ar ions [80] conclude that pt collisions are
largely responsible for Auger yields even at energies
close to the threshold. This is in striking contrast with
other recent theoretical studies [81-831 and is also
contradicted by the observation that Auger yields in Al
[84] and Si [85] compounds vary with the square of the
concentration of the light element which is excited.
Detailed measurements by Bonanno et al. [86] have
recently confirmed that the ratio of pt to tt contributions increases with increasing energy and also varies
with incidence angle.
The origin of the continuum tails extending below
the Auger peaks in the region of very high electron
energies is still obscure. At high impact velocities, they
have been explained to arise from binary collisions
between the projectile and a target electron. At low
velocities, the explanation is still a matter of debate
[87]; models proposed include direct coupling to the
continuum and emission of Auger electrons during the
collision. Our measurements for very low energy (OS-6
105
I
I
I
I
I
-Ar+--+Au
. . . .. . . . He+.-+A”
100
I
0
500
I
I
I
1000
1500
2000
Electron Energy (eV)
I
2500
3000
Fig. 6. Electron energy spectra of Au under He+ and Ar+ as
a function of projectile energy (from Baragiola et al. [SS]).
keV) ions in solids have shown that the continuum
electron energy distributions extend up to a surprisingly large fraction of the center-of-mass energy (fig. 6)
[88]. This shows that the extremely high electron energies result from nearly head-on collisions between the
projectile and a target atoms. The high energy tails are
strongly dependent on the type of target, they decay
generally slower with electron energy the higher the
atomic number of the target.
3.1.2.2. Plasmons Plasmons are collective excitations of
the electrons in the form of charge density fluctuations
with frequency w,,. They can be excited in surface and
bulk modes by particles with velocities larger than
about vF or by the sudden creation or annihilation of a
core hole. Plasmons can also be generated by the
energetic electrons in the cascade created by ions
slower than vF [89].
The delocalized plasmon oscillations can decay by
localizing into a single electron-hole pair. It has been
found that this localization occurs at a very short
distance from the point of excitation [90,91]. The electron resulting from plasmon decay can be detected in
the energy distribution of ejected electrons as a broad
bump. This results in a maximum electron energy of
hw, - U outside the solid, plus a broadening resulting
from the finite plasmon lifetime. This lifetime cannot
be explained within free-electron gas models, but is
related to the real band structure of the solid. Plasmons have been found to contribute more to EE than
the direct transfer of the same amount of energy into
electron-hole pairs [92,93], under excitation with high
energy electrons. Similar behaviour is expected for
high velocity ions. This effect has not been taken into
account in current EE models.
R.A. Baragiola / Ion induced EE
3.2. Electron transport
A proper description of the cascade requires knowledge of the probability that a 1G electron loses energy
and eventually generates new excited electrons. This
problem has been studied by using an electron gas
model to describe inelastic electron-electron
scattering. In some cases, simulations have included classical
electron trajectories using Monte Carlo methods between elastic scattering events with single atoms [94].
The justification for doing this has not been given. The
problem is that the majority of the electrons in the
cascade have wavelengths of the order or larger than
the mean atomic spacing, a. The electrons will not,
therefore, interact in a binary fashion with a single
atom at a time, and the concept of cross section cannot
be applied as is done in classical transport theory or
simulations. Diffraction and interference of very low
energy electrons is observed for instance in extended
X-ray absorption fine structures (EXAFS) [95].
A different question is whether the trajectory of an
electron can be defined between elastic scattering
events. A classical description is valid if the uncertainty
in the momentum h/a due to localization within a
region of size a is much less than the electron momentum p. This implies the often fulfilled condition E’ x=0.5 eV far from the Brillouin zone boundaries, where
E’ is the electron energy inside the solid.
An important consideration in understanding electron transport is that the probability of a small inelastic
energy loss is very small for low energy electrons [96].
This is because all the states of the valence band are
occupied so that only the top of the band can absorb
small energy transfers. Fig. 7 shows the probability that
an electron loses energy above a given value in carbon
1 .o
0.8
I
I
I
I
I
E=lOOeV
ELECTRONS
IN CARBON
o E = 4000 eV
0
10
20
30
50
40
fio
60
70
80
[97]; it can be seen that the most probable energy loss
is slightly larger than the energy of a bulk plasmon
(N 25 eV). A large average energy loss means that an
inelastic interaction will most likely attenuate secondary electrons (drop their energy below the vacuum
level). This in turn means that secondaries suffer very
few inelastic collisions before they escape. Therefore,
the randomization of their motion in the cascade should
occur mainly be elastic scattering or quasi-elastic scattering with phonons. In nonmetals low energy losses
are more strongly suppressed; only losses larger than
the band gap are allowed, neglecting excitons and
other gap states.
At intermediate and high energies, a substantial
fraction of the secondaries will have enough energy to
produce additional EE by cascade multiplication. The
extent of the cascade will be determined mainly by the
range R(E’) of the 1G electron, which is a function of
its energy E’. R is defined here as the mean distance it
travels from the excitation site before its energy falls
below the vacuum level. The shape of the cascade will
be mainly determined by the angular distribution of
the 1G secondaries. For fast light projectiles, this distribution of the secondaries is strongly peaked forward,
the more so the faster the projectile and the faster the
ejected electron [98]. The anisotropy of the primary
event will tend to be washed out by elastic collisions.
Cascade multiplication depends on the electron energy and can be described by a factor y equal to the
total number of electrons divided by the number of 1G
electrons. The probability that a 1G electron produces
at least one more electron above the vacuum level is
zero if the energy above the vacuum level is less than
twice the threshold energy, i.e., E < 2U. Based on pair
production in gases, an approximate multiplication factor for electrons will be given by p(E) = 1 + (E U)/U. Thus the transition from the single excitation to
cascade multiplication regime will depend on the energy distribution of the excited electrons. One can get
information about this in the case of gases, where one
knows the primary ionization rate, ciiN dx and total
ionization rate S,N dx/W. The multiplication factor is
then given by:
/_l =
90
100
(eV)
Fig. 7. Probability that an energy loss is larger than a given
value, hw, for electrons of several energies in carbon (from
Ashley [97]).
231
S,/UiW.
(8)
Fig. 4 shows the multiplication factor p for protons in
Ar, taking into account also charge changing collisions,
calculated using gas-phase data from the literature
[99]. One can see that at 10 keV a small fraction of the
ionizations is caused by secondary electrons, whereas
at high energy, more than half of the excited electrons
are produced in the cascade.
The diffusion of the deposited energy away from
the collision site causes the number of excited electrons to vary with the distance to the surface, even if
the scattering and energy loss of the projectile can be
V. ELECTRON EMISSION
232
R.A. Baragiola / Ion induced EE
neglected [6,100,101]. This is because at depth z > R
(the electron range) there are contributions from the
region extending from z -R to z + R, whereas at the
surface, there is only a contribution from the region
extending from z = 0 to z = R.
A depth dependence of the deposited energy can be
caused by a change in the charge of the projectile as it
enters the solid [102], which will also result in a dependence of KEE on the charge of the ion. At low velocities, energy degradation of the projectile in the electron escape region becomes important. This, by itself,
causes a decrease in the primary ionization density
with depth which may be compensated by the increase
due to larger path lengths produced by angular scattering and ionization by recoils. This latter contribution
may increase or decrease with energy, depending on
the projectile-target
combination [30].
To calculate how many electrons reach the surface,
we recall that when an inelastic energy loss occurs, it is
usually a substantial fraction of the electron energy.
The flux of electrons which reaches the surface with
final electron energy E’ > U can then be approximated
by the flux of electrons which have not undergone an
inelastic event. The probability of attenuation is described by the inverse of the inelastic mean free path
A,. If the probability for elastic scattering is small,
such as at high electron energies or for low Z targets,
the electrons are attenuated in straight paths to the
surface, according to the attenuation length [103]:
L = A,/COS
et,
(9)
where 0’ is the angle of the internal path with respect
to the surface normal. The formula should hold in only
few cases. For instance, Monte Carlo calculations by
Dehaes et al. [104] for proton impact on Al above 10
keV show than an electron suffers, between birth and
escape, an average of about 7 elastic and 0.4 inelastic
collisions. In the more usual case where elastic scattering dominates, the diffusion process will be described
by an attenuation length [loo]:
L = (Ai,htr/3)1’2,
(10)
where At, is the transport mean free path for elastic
scattering. Monte Carlo simulations have shown that
the actual attenuation as a function of depth can be
more complicated than described above [105-1071.
Values of L averaged over the energy spectrum of
the emitted electrons are 5-15 A for metals [108-1101
to hundreds and even thousands of A for wide band
gap insulators, such as the noble gas solids [111,112].
3.3. Transmission through the surface barrier
The surface electrostatic potential is corrugated on
the atomic scale, small compared with the scale of the
wavelength of electrons of a few eV, suggesting that it
is a good approximation to consider the surface as
planar. In fact, photoemission experiments in single
crystals which show that the momentum of the electron
parallel to the surface, hk,, is conserved during emission [113]. The effect of the planar barrier of height Z
is to refract the electrons, changing their energy from
E’ inside to E = E’ -Z outside, and changing the
momentum perpendicular to the surface, fik I. Thus,
the angle of incidence and emergence with respect to
the surface normal are related by: k sin 0 = k’ sin 8’.
Refraction causes total internal reflection for angles
larger than
8’ma
=
arcos( Z/E’)l”.
(11)
The probability of transmission through the barrier T
can then be calculated by assuming that all electrons in
the cone with 0’ < 0&, can escape. Therefore T depends on the shape of the angular distribution of the
electrons reaching the surface. When elastic scattering
can be neglected 11031,electrons can be considered to
travel in a straight line to the surface attenuating in
number according to exp( - z/L exp( - 2/L)). Then
1
T(E)=:=.
E
(12)
On the other hand, when elastic scattering is important, the transmission through the barrier can be calculated assuming that electrons arrive at the surface
isotropically in the half space inside the solid. In this
case,
T(E)=f(l-/&).
(13)
These escape probabilities are classical. Quantum mechanically, not all electrons with the escape condition
can escape. Reflection can occur even if E’ > I, when
the uncertainty in the energy of the electron introduced by the finite interaction time r with the surface
is of the order or larger than E’. This uncertainty is
SE’ = h/r, where r = b/v = b(m/2E’>1/2
and b is the
width of the barrier. This means reflection can occur
for h(m/2E’>1/2/b
> E’. Thus quantum barrier effects will be Oimportant for E < 0.5 eV for a barrier
width b = 2 A. The quantum mechanical reduction in
the transmission above the barrier is very strong in
thermoionic emission, where electron energies are very
small: it reduces the thermoionic “A-factor,” and hence
the emission current, by 25-50% 11141. Hence, one
should also expect important reductions in KEE near
threshold.
The value of the inner potential Z that influences
electron escape, is found to be of the order of 11-15
eV in metals from LEED measurements [115]. It is
remarkable that these are close to the values expected
from a free-electron model, E, + 4, as if band struc-
R.A. Baragiola
ture effects were not important. This is possibly related
to the short lifetime of excited electrons in metals,
which broaden significantly the states in the conduction band. Recent inverse-photoemission
experiments
[116] have revealed that the width of s and p conduction band states for metals seem to follow a universal
curve T&E’) = O.l3(E’ -E,),
or typically N 0.5 eV at
the vacuum level. For d-like bands, the widths are even
larger, - 0.6(E’ -E,).
As mentioned above, the barrier I for insulators is
the electron affinity x, which can be as low as a
fraction of an eV or even negative, such as in the (111)
face of diamond, in solid Ar or in semiconductors with
special surface coatings [117]. This reduced barrier is
one of the main reasons for the larger EE yields of
insulators as compared with metals.
An interesting case is that of PEE, where the
three-step model does not hold in a strict sense. The
wave function of the intervening electrons extend over
the barrier which is modified by the presence of the
projectile. This complexity has not yet been treated in
the literature. This problem should be circumvented by
considering a final state wave function which already
has the correct asymptotic solution outside the solid,
avoiding the artificial introduction of a surface barrier.
4. Final state effects
So far, the description of the final state has been an
electron moving away from the solid in the presence of
the surface; that is, in the field of its image. In some
cases, this is not a good representation because of the
presence of other fields which appear when the electron leaves the solid, due to presence of other charged
particles in vacuum in the vicinity of the electron. I call
these effects final state interactions; they appear because of an incomplete description of the final state
wave functions. The discussion below excludes the effect of macroscopic sample charging or electric path
fields near rough surfaces.
4.1. Effect of ion fields
It has been observed in the gas-phase and for fast
ions traversing thin foils that the energy and angular
distributions of electrons are distorted by the field of
the ionized projectile. When the velocity of the electron is very similar to the velocity of the ion in magnitude and direction, a large increase is observed in the
laboratory cross section, producing a cusp-shaped peak
in the doubly differential distributions (d’n/(dE
da)).
This is due to the focusing of the electron trajectories
by the long range Coulomb field of the ion. Since these
electrons accompany the projectile, they have been
termed “convoy” electrons [118]. The effect of the
/ Ion induced EE
233
projectile field is not limited to a single ion. Other
interesting and complex effects result from EE from
foils traversed by molecules or clusters of ions. FOCUSing of electron trajectories also occurs where the projectile backscatters as an ion, as in grazing angle collisions [119,120].
A prediction that follows from the above discussion
is that in PEE with slow multiply-charged ions (MCI),
the trajectories of the electrons will be even more
severely affected by the strong Coulomb field of the
positive ion and its negative image. The electric fields
in this case are different from the counterpart in
gas-phase collisions, where partial neutralization of the
MCI produces a positively charged target atom.
4.2. Multiple EE
In many instances, projectiles can produce the emission of multiple electrons within a very narrow time
interval. The electron-electron
interactions or correlations will alter the energy and angular distribution of
the emitted electrons, as already seen in double ionization in the gas-phase [121]. The effect will be present
in measurements
of EE statistics in solids even at
relatively small value of y but should of course be
more pronounced in situations which render large average electron yields [122,123]. In these cases, the
ejected electrons will move in the field of the other
electrons and their images; their trajectories will be
deflected, compared to those of electrons emitted
alone. The ejected charge cloud will evolve in time
according to the internal fields and the applied external extraction field. Electrons in the front of the charge
cloud will receive extra energy while those at the
trailing side will be slowed down, even pushed back to
the solid (depending on the extraction field), as observed in pulsed-laser induced photoemission [124,125].
The amount of energy that can be gained can be of the
order of U = ye’/P,, where r,, is the initial radius of
the electron cloud (U - 20 eV for rO= 15 A and y =
20). Then, this space charge should act to decrease the
yields, flatten the angular distribution, broaden the
energy distribution of the electrons and affect the I-V
characteristics of the target-collector diode. The effects
should be sought after particularly in cases where y is
very high. Electron yields in the hundreds have been
seen for PEE of very highly charged ions [42]. In KEE
from solid Ar, we have observed y of several thousands [126]; similar values are expected in other materials with negative electron affinity. Even higher yields
should be possible using fast heavy ions and conditions
of oblique incidence.
Large electron yields also result from energetic
ion-surface
collisions at grazing incidence. For instance, collisions of OS-2 MeV He+ on SnTe(OO1)
surfaces, produce electron yields larger than 200 for
V. ELECTRON EMISSION
234
R.A. Baragiola
.
.
.
.
.
Grazing
ion
.
*
.
.
.
.
l
.
.
.
.
. .
*
.
._-.
. *a _ 0.
.
_
.._-a..
l
l
/ .
.
.
Solid
Fig. 8. Schematic drawing showing electron could originating
from multiple-electron emission by a fast ion at grazing incidence on a surface.
of less than 1” to the surface [127]. One
should expect even higher yields at lower energies,
close to the stopping power maximum. One can visualize that the trajectory of the ion is accompanied by a
cloud of ejected electrons (fig. 8). A convoy electron
which would normally be ejected along the ion path
with a velocity close to that of the ion, would be
pushed to higher energies. It is proposed here that this
is the case for energy shifts observed [128-1321 in
ion incidence
convoy EE at grazing incidence which has been attributed to acceleration
by the image charge induced
by the projectile [133,134].
5. Yields
To calculate differential and total yields one has to
develop quantitative descriptions of the mechanisms
shown above and assemble them to derive observable
quantities. No complete theory exists at this time although some special cases have been derived where
simplifications are possible. For instance, at high velocities, one can neglect recoil effects and consider that
the projectile does not lose much energy over the
escape depth. In this case, the number of primary
events is independent
of depth z. One then needs
energy and angular distributions of these 1G electrons
as input to a calculation of the electron transport and
multiplication in the cascade. These can be obtained
from atomic physics calculations or experiments, and
one can use electron gas models for the valence band,
which gives the most important contribution at low
impact velocities. At high velocities, most inner shells
can be excited, each contributing approximately in
proportion to its number of electrons, and so it is
/ Ion induced EE
important to describe well inner-shell excitations and
the subsequent Auger decay.
Once the excited electron sources are obtained,
calculation of the electron cascade can proceed using
transport theory or Monte Carlo simulations starting
with electron scattering data from gas-phase collisions
or free-electron models, as appropriate to the type of
solid. Here the main difficulty is the lack of an adequate description of elastic scattering at the lower
electron energies where quantum effects are important. Once the flow of the electrons at the surface is
obtained one can calculate the transport through the
barrier. In this case, the main difficulty is the estimation of the inner potential and quantum reflection
effects.
Calculations at low velocities need to take into
account excitations by fast target recoils, which require
an evaluation of the atomic cascade. Scattering of the
projectile near the surface makes the ionization path
longer inside the escape region. If the scattering is very
strong, the projectile can backscatter producing additional excitation. The maximum excitation is caused by
a projectile which scatters and follows a trajectory
parallel to the surface, just below it. This process is
unlikely and will not contribute to any significant extent to the total yield. It can, nevertheless, be observed
as a finite probability of ejecting a very large number of
electrons n (n >> 7).
A good description of valence excitations by projectiles and recoils becomes more important since innershell contributions are small. To calculate the distribution of 1G electrons one has to follow the trajectories
of projectile and target atoms (e.g., by using Monte
Carlo or molecular dynamics simulations). For each
collision one calculates the inelastic energy transfer by
using, for instance, Firsov’s formula or improved versions [135,136]. If this calculated energy transfer is
larger than U, one counts an excited electron from
which one builds a distribution of ionization events,
n(z) as a function of distance z to the surface. At low
enough energies, cascade multiplication can be neglected, and one can equate n(z) to the depth distribution of 1G electrons. If one neglects inelastic electron
collisions that do not attenuate the electron flux, one
can calculate the energy distribution of ejected electrons from
g
= T(E’)/n(z,
E’) exp(-z/L(E’))
dz,
(14)
where E = E’ - I, from which one can deduce the total
yield by integration.
Another simple case is that of KEE near threshold.
When the mass of the projectile is larger than that of
the target atoms, the threshold behavior of KEE will
be dominated by recoil effects, since the recoils can be
faster than the projectile [53]. When the projectiles are
R.A. Baragiola / Ion induced EE
lighter than the target atoms, KEE at threshold is
produced by inelastic ion-surface collisions with surface atoms. One can disregard electron transport in
first approximation and assume that all electrons in the
escape cone (eq. (11)) will go into vacuum. Then the
energy distribution of emitted electrons is given by
(15)
where (T is the ionization cross section and Na is the
surface density of target atoms. The use of the stopping power is not justified here because the excitation
of electrons above the vacuum level is dominated by
rare events rather than by average energy loss collisions [137]. Another important consideration is that the
accuracy of the description of the escape function
T(E’) is more important at threshold where most of
the electrons have very small energy. Integration of eq.
(14) and comparison with eq. (1) show the parallelism
between gas-phase ionization and EE from gas-covered
surfaces first demonstrated by Amme [138].
235
electronic configuration in the oxygen in both cases,
the reason for the large differences in the two materials is not likely to result from (1) above. This is further
supported by the observation that the change in the
yields is not proportional to the oxygen concentration.
The change in the surface barrier appears to be the
main factor affecting the yields, but it is not necessarily
related to changes in the work function. Adsorbed gas
generally (but not always) causes an increase in the
electron yields [139]; the relative change in the yields is
larger than the lower incident energy [140].
EE from thick insulators is an intriguing problem
which is difficult to study due to surface charging. We
have recently reported [126] measurements of KEE
from thin Ar films. Argon is an interesting material for
EE studies because it has a large band gap, an extremely large mean electron escape depth (of the order
of a micron), and a negative electron affinity (conduction band above the vacuum level). We have observed
nearly complete extraction of electrons from thin films
and, under some conditions, dielectric breakdown during and after ion bombardment in the presence of a
weak external electric field.
6. Adsorbed layers and insulators
It has been known for a long time that EE from
insulators is larger than from metals or semiconductors. In most of the literature this is attributed to result
from a larger mean electron escape depth due to the
reduced electron scattering for ejected electron energies lower than the band gap. Another factor, often
more important, is that excited electrons escape more
easily from insulators due to a reduced surface barrier.
The relative importance of these two factors can be
discerned by analyzing the effect of the thickness of
the insulating layer.
Adsorbed layers already have a very strong influence on electron yields. The lack of specification of the
surface for targets exposed to air hinder the possibility
to extract information about mechanisms from electron
yields. This is true for almost all the work done previous to 1950, but occasionally one finds this shortcoming in current publications. An exception seems to be
the case of measurements on carbon foils, where at
least good reproducibility is often (but not always)
found between different laboratories.
The adsorption of small quantities of gas (of the
order of a monolayer or less) can change EE for many
reasons. The most important seem to be (1) a different
electron excitation probability for the adsorbed species
as compared to the bulk, and (2) a change in the
surface barrier. The change in the electron attenuation
length is a second order &ect for the thinner layers.
Comparative experiments on the adsorption of oxygen
on clean Al and MO surfaces showed very large effects
on the yields [139]. Since one can expect a similar
7. Conclusions
Electron emission under ion impact results from
direct ionization of the projectile or target atoms plus
additional ionizations produced by energetic secondary
electrons. The study of EE provides some of the most
detailed pictures of inelastic ion-surface collisions, giving insight on mechanisms which can be applied to
study other processes, such as energy loss, charge
transfer, ionization damage and desorption. These
mechanisms can be described conceptually but calculations are still far from the level of accuracy possible,
for instance in the emission of atoms (sputtering).
Besides the lack of general theories there are still
many unsolved problems in the understanding of high
ionization densities, excitations by slow projectiles and
by molecules or clusters, the threshold behavior of
KEE, quantum effects in the motion of excited electrons, final state interactions,
and ionization and
breakdown in insulators.
Acknowledgements
This work was partially supported by National Science Foundation, through grant DMR-9121272 and by
NATO through grant CRG 901013. The author thanks
D.E. Grosjean and R.E. Johnson for critical reading of
the manuscript and the M. Riisler for useful comments
and for bringing ref. [93] to his attention.
V. ELECTRON EMISSION
236
R.A. Baragiola / Ion induced EE
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