International Journal of Mass Spectrometry and Zon Processes, 78 (1987) 357-392
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MECHANISMS
MOLECULES
FOR THE DESORPTION
357
OF LARGE ORGANIC
R.E. JOHNSON
Department of Nuclear Engineering and Engineering Physics, University of Virginia,
Charlottesville, VA 22901 (U.S.A.)
(Received 15 January 1987)
ABSTRACT
Energizing mechanisms and models for the ejection of biomolecules due to electronic
excitations by fast ions are compared and discussed. The energizing processes are also
compared with those induced by UV photons in organic solids and by electronic sputtering of
low-temperature condensed-gas solids by fast ions. The calculation of a yield for an ejected
species is roughly divided into the determination of the probability of creation/survival
of
the species, an effective area, and an effective depth, which is determined by the radial
dissipation of energy when ions are at normal incidence. Aspects of this calculation can be
tested separately by experiment and the various models proposed in the literature often only
address a part of the yield calculation. The measured low-temperature, condensed-gas
sputtering yields for H,O indicate that a much larger material volume is removed than that
suggested by the recent neutral yields for the ejection of whole leucine molecules. It is seen
that significant radial energy transport determines the yields for water ice sputtering at high
excitation densities but probably not the leucine yields. The general nature of a model for the
total yield is discussed and differences between this and the observed energy density
dependence for neutral leucine yields are considered. A rough estimate of the neutral leucine
yields is given based on the initial track parameters for the energy deposited and assuming
the incident ion induces a local expansion of the solid. Further, differences in the dependencies of the biomolecular ion yields and neutral yields on energy density deposited suggest that
the ions do not come uniformly from the ejected volume.
1. INTRODUCTION
Following the studies by Brown et al. [l] of electronically stimulated
sputtering of low-temperature condensed gases and the discovery by Macfat-lane and Torgerson [2] of the electronically stimulated ejection of organic
molecules, there has been a number of ideas put forward on the nature of
those processes that follow the passage of a fast ion through such solids.
These processes have been of long-standing interest for defect and track
formation in solids and the early ideas on sputtering of condensed gases
0168-1176/87/$03.50
0 1987 Elsevier Science Publishers B.V.
358
showed a strong correlation with models from that literature. Electronically
stimulated ejection has also generated considerable interest because of its
importance in planetary science [3] and as a practical means of performing
mass spectroscopy on thermally labile molecules. However, it is not clear
that there is much agreement on the description of those processes that
control the ejection of matter from condensed gases or organic layers. This is
due, in part, to the nature of the experiments initially performed and is
therefore improving rapidly as important parameters are being controlled
and/or varied sensibly.
Earlier, Johnson and Brown [4] reviewed the energizing processes that
could lead to the ejection of small molecules from condensed-gas solids.
Since that time, a number of clear examples have been found of materials in
which specific ejection mechanisms dominate. Indeed, the important
processes can differ between materials and can be different at different
excitation densities [5,6].
In this paper, I will briefly review aspects of certain energizing processes
and transport processes that are thought to apply to the desorption of large
organic molecules from organic solids. This will not be a comprehensive
review. I will consider a few of the processes most frequently discussed and
describe the corresponding models for determining the ejection parameters.
I will try to point out which aspects of the several models are common and
which exhibit differences that might be tested experimentally. As the organic
molecule ejection experiments have concentrated on ion yield measurements,
I will borrow from the literature on electronic sputtering of small molecules
from low-temperature condensed-gas [5,6] solids, particularly when these
yields are large. Only recently have Sundqvist and co-workers obtained
neutral yields 171,whereas neutral yields have been extensively measured for
the low-temperature condensed gases, e.g. H,O [8]. The importance of these
neutral yields for understanding the electronic relaxation processes occurring in the solid has been demonstrated for the condensed-gas solids [5,6].
That is, there existed a large body of data on ion desorption from condensed
gases in which the neutralization of the ejecta masked many aspects of the
energizing processes.
In this paper, I will only discuss electronically stimulated ejection of
material. This is the mechanism of interest for fast ions as indicated in Fig. 1
where the total neutral yield of H,O ejected by incident H+ and incident
ions with 6 I 2 I 10 (C, N, 0, F, Ne) are given [9]. Two distinct sputtering
regimes are seen. The maximum at high energies is due to electronic energy
deposition and the enhancement at low energies is due to direct collisions
with the atomic centers. The latter region can also lead to the desorption of
whole biomolecules, although the relative efficiency may be lower [lo]. The
description of electronically stimulated ejection begins with a general de-
359
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tC+,N+,O+,F+,Ne+l
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E/Ml
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1011
I05
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Fig. 1. Yield of net material removed, primarily as H,O, vs. ion energy [9]. Lower curve and
right-hand axis, incident H+. Upper curve and left hand axis, incident (C’, Nf, O+, F+,
Ne+ ). Data described in ref. 9. 0, Three new points added since, measured by D.B. Chrisey,
for lo-50 keV Ne+. Yields at higher energies determined by electronic energy deposition;
yields at smaller energies by collisional energy deposition.
scription of the energizing mechanisms in Sect. 2. This will be followed by a
discussion of related photon-induced desorption processes. The various
models which employ these mechanisms will then be reviewed in Sect. 4 and
finally, the nature of a general model for calculating ion and neutral yields
will be discussed in Sect. 5. Many of the important details for these
discussions are contained in the Appendix. As Sect. 5 contains the new
material presented, readers familiar with the various models and energizing
mechanisms may wish to turn directly to that section.
2. ENERGIZING MECHANISMS
The excitation resulting from photon absorption in a solid will migrate
until localized at some special site (e.g. defect, surface, particular bond, etc.).
The energy can then be re-emitted or can decay non-radiatively producing,
eventually, lattice motion (heat). If this decay occurs near the surface and
the unit of energy deposited is larger than the binding energy, material can
be ejected from the solid (desorbed) [ll]. This is the case for the desorption
of, for example, oxygen atoms or ions from an oxide layer on a surface. Such
an effect can be stimulated by absorption of a UV photon producing an
electronically excited or ionized state at the surface. The subsequent decay
process is generally described using a localized repulsive state in which the
excited electron no longer fully screens the repulsive (coulomb) interaction
360
between neighboring atomic nuclei. If the excited state “decays” (e.g. emits
a photon) during the ejection or the nuclei captures a charge on exiting, the
ejection can be limited or the species escapes as a neutral.
In condensed-gas solids or overlayers, IR photons can also be absorbed
into states with energies above the surface binding energy. In ref. 4, it was
noted, for example, that the energies of the vibrational states of molecules
like CO (0.2 eV) are larger than the surface sublimation energy = 0.08 eV.
Therefore, it is energetically possible that CO can desorb by a multiphonon
process. However, because of the poor coupling between these modes, this
does not occur with any significant efficiency. Therefore, the state of the
energy deposited near the surface is very important and not simply the
amount deposited relative to the size of the surface barrier.
Following the passage of a fast ion through a non-metallic solid, a
“track” is formed which consists of a distribution of excited and “ionized”
states that might have been produced by photons, as recently reviewed by
Inokuti [12]. These states are generally described as being distributed radially about the path of a very fast ion. The incident ion predominantly
produces electron-hole pairs (ionized sites), whereas excited states are
produced at the = 10% level [13,14]. The electrons produced (secondary
electrons) have a mean energy = 50 eV and travel, on the average, = 5 nm
from the point of production with a bias in the direction along the ion’s path
[15]. Some of these electrons can be ejected from the entrance surface, or (in
a thin sample) the exit surface, resulting in a temporary local charging of the
sample. The above processes can also be induced by incident energetic
electrons. However, as these particles have a much lower momentum and are
scattered easily, the concept of a radial track of excitations disappears [15],
except for the very fast electrons which do not produce ionization with any
efficiency. Incident ions have a further advantage since varying the ion type
can produce significant changes in the excitation density, a fact used to good
effect by Sundqvist and co-workers [16,17]. Compared with the photon
stimulation of solids, an incident ion creates its excitation track in times of
the order of lo-l5 s [4], which is much faster than typical photon pulses [18].
As the secondary electrons have excess energies larger than the typical
band gap energies, they produce additional ionization as well as vibrational
excitations and phonons as discussed in ref. 4. In a molecular solid, on the
average about half the net energy deposited by the ion results in electron-hole
pairs and half in vibrational and phonon excitation, with a small fraction in
excitations [12-141. Of the fraction going into vibrations and phonons, more
of the energy goes into the internal modes due to the more efficient coupling
of the secondary electrons with these modes and the fact that they can be
excited concomitantly with ionization of molecular species.
For fast incident ions entering a solid, there can be a deficit in the net
361
rm
I
I
rb
‘b
br
‘m
Fig. 2. Schematic diagram of energy deposited per unit volume in the solid, e&r, z) (see
Appendix). (a) ~(0, z), energy vs. depth exhibiting surface deficit (ref. 19). Location of
characteristic depth, z, vs. the ejection depth, zS, determines whether deficit plays a role. (b)
c,,( r, z > E), energy vs. radius at depths greater than 1. Exhibits r-’ dependence beyond the
so-called Bohr radius, q,, for primary excitation (which is proportional to ui for large oi) and
at a radius less than some maximum secondary electron radius, r,, (which is proportional to
0: for large ui, e.g. ref. 22).
energy deposition in the entrance surface region of the target [19]. This
occurs when the incident ion is in an initial charge state which differs from
the mean charge state in the solid [4,20], but is also due to the fact that the
secondary electrons are forward-directed and there is some loss of secondaries from the entrance surface [21]. In describing this, it is important to
remember that, although the average distance traveled by the secondaries is
not large, it is the fastest secondaries that produce most of the subsequent
ionization and these can have relatively long path lengths (= tens of nm)
and are more strongly forward-directed. In Fig. 2 is given a schematic
diagram of the deposited energy density vs.‘depth and the radial distribution
of energy deposition. The difference in the energy deposition at the entrance
vs. the exit surfaces in Fig. 2 can be an important test of the role of the
secondary electrons in the desorption process [19]. The radial dependence
exhibits a characteristic - rm2 behavior from an inner radius, T,,, the Bohr
362
adiabatic radius, out to an outer radius, r,, both of which depend only on
the track material and the ion speed [22].
The energy that leads to the ejection of molecules follows from the initial
state described above. The distribution of this energy varies from ion to ion
in the radial extent, the surface deficit (controlled primarily by the ion speed
and incident charge state), and the energy density deposited (controlled by
the nuclear charge and the speed). The subsequent decay of the energy, as
described in ref. 4, can lead to ejection due to a number of exothermic
effects. Initially, there is a “charge separation” in the solid due to the fact
that the “hot” secondary electrons produced by the incident ion do not
completely shield the holes (ionized sites) which lie close to the incident
ion’s path, or these electrons may temporarily be trapped. Because of this,
the nuclei close to the ion’s path can repel each other providing, in principle,
an expansion force for the solid [23]. This is simply an extension to a large
number of sites of the repulsive force for surface desorption discussed
above. The efficiency of this expansion force for ejecting material depends
on the length of time it takes for the electrons to “cool” and return fully
screening the ions. Since the electrons “cool” most effectively by vibrational
and phonon excitation, this cooling process itself can contribute to the
expansion [24].
After the electrons cool to the band gap, they reach the ground state of a
small molecule by a series of exothermic processes [4,25] (e.g. repulsive
decays) and only occasionally emit a photon in such solids (in rare-gas solids
and N,, the photon emission is actually very efficient [25,26]). These decays
further energize the atoms and molecules in the solid and also cause
intramolecular bond rupture [22]. In a solid composed of large molecules
with many internal degrees of freedom alternate decay routes are available,
as will be discussed later. Finally, additional exothermic energy release is
available from the reaction of the radicals produced [27]. With the exception
of the last process, which may be controlled by diffusion and/or energy
barriers, the energy deposition processes occur rapidly on the time scale for
ejecting large molecules. Along these lines the ejection of small ions,
primarily protons, has been shown to be extremely fast 1281, respon~ng only
to “early” charge separation [29].
In the above, a fairly arbitrary distinction was made between the repulsion that occurred when the electrons were “hot” and that repulsion which
occurred after the electrons cooled to the band gap. As pointed out earlier,
coulomb repulsion does not require two holes (ions), it simply requires a
deficiency in the screening between neighbors [4] (e.g. as in the repulsive
dissociation of H, to two H [30]). Therefore, from the initial excitation of
the electrons until they return to the ground state, neighbors are not
completely screened and an effective repulsive expansion of the lattice
363
occurs. Of course, the energy deposited in the other modes (e.g. ~bration~
excitation) also contributes to this expansion f24] and must be included in
the whole. The relative importance of these modes is one of the primary
differences between many models.
As the ion’s energy is deposited in a radial region which is very narrow
macroscopically, but many molecular radii wide, and as this energy is
rapidly converted to an expansion energy, it is not surprising, in retrospect,
that a solid composed of weakly attached units can experience desorption. It
is possibly surprising that large species (e.g. insulin) can be ejected as whole
molecules, but this is, primarily, a matter of scale [16,17] (track scale vs.
molecular scale) and relative times [4,31] (ejection time vs. molecular survival
time [32]). Since the lattice is energized rapidly ( = lo-i3 s) with steep energy
gradients, the ejected surface molecules do not equilibrate with the bulk,
hence, thermally labile molecules can survive, as pointed out by Macfarlane
[31]. Therefore, the non-equilibrium nature of the ejection process is agreed
upon as being crucial for the ejection of whole thermally labile molecules.
What is not agreed upon is the method for c~culat~g the mount of and the
state of the ejecta, which requires that the ejection mechanisms are understood. This is important as it restricts our ability to extrapolate our present
capabilities for desorption to larger molecular species.
3. PHOTONS
VS. IONS
Before considering the models for desorption, a comparison is made
between photon ablation of polymers and ion sputtering of organic solids.
At wavelengths of the order of 500 nm (= 2.4 eV) and less, short pulses
(= 10 ns) of photons tend to melt the solid in the absorbing region and its
et al.
s~roundings [33]. For = 10 ns pulse at = 133 nm (6.24 eV), S~vas~
[18] have shown that a relatively clean etch is produced, which they describe
as resulting from an explosive expansion of the energized region. This
“expansion” has been qualitatively simulated by a chemical dynamics calculation [34] (Fig. 3) in which units of an organic polymer are presumed to
interact repulsively with neighbors due to excitation by UV light.
Based on the above, if the energy is deposited in vibrational excitations in
times of the order of lOns, then heating and melting occur. Infrared pulses
can desorb thermally labile molecules provided the power density is high
enough (;t lo8 W cmv2) [33]. Derrick and co-workers [35] showed that, in
field ion desorption, putting IR photons directly into molecular vibrations
was equivalent, with regard to desorption, to gently heating the whole
sample. On the other hand, if electronic excitations are produced, as with
UV photons, then ejection of organics occurs without significant melting
[18]. Therefore, in examining the incident ion-induced ejection process, the
364
0.8 ps
23ps
Q go8 Q
00 Q 00
@t&g@
Q800
5.4ps
66 ps
Fig. 3. Partial sequence of events in the loss of molecular groups from a region of an excited
solid [34]. The “excited” molecular units consisting of a number of atoms are assumed to
have switched from having cohesive forces with neighbors to having repulsive forces. This
indicates typical time (hence velocities) for track expansion (ejection) and shows that the
interaction with the “walls” of the hypothetical track near the surface is violent. It is more
realistic for ion tracks than for photon ablation by incident laser beams as the latter has a
scale which is huge compared with the molecular scale shown here. It is also unrealistic as the
fixed repulsive interaction inhibits condensation. However, it shows characteristic times and
the behavior of the walls and the layers.
“quality” of the energy deposited is important [4]. This was discussed earlier
when we described the inefficiency of individual vibrational excitations for
desorbing small condensed-gas molecules.
For our present considerations, it is useful to compare parameters of the
ion and photon experiments. A “threshold” was observed for ablation
at = 1OmJ cm-* of 193 nm light, following which the yield varied as the log
of the fluence [18]. After = 250mJ cm-*, the yield remained constant, most
likely limited by the pulse length and the ejection time. The extinction length
for these photons is = 100 run and at 1OOmJ cm-*, approximately 100 nm
are removed. This corresponds to a deposition dose of = 60eV nmm3 and the
threshold value is about one tenth this. By comparison, the track expression
365
used by Hedin et al. [17] indicates that the energy density is = 60eV nrnm3 at
0.6nm from the track of a 16 MeV charge state equilibrated oxygen ion
incident on condensed valine. (They generally use ions delivering even
higher doses [16].) This energy is deposited as energetic electronic excitations
[12] and this density is above the binding energy density of valine, which has
a size of - 0.5 nm. Therefore, it is not surprising that material ejection
occurs due to such incident ions. However, it is remarkable that the 100 nm
of polymer removed in the UV experiments corresponds to = 1 photon per
10 carbon atoms removed. Therefore, in the photon experiment, each
absorption affects a number of layers and any cooperative effects must have
long time scales, = 10m8 s. When interpreting these data, care must be taken
with regard to “late effects”, as Brown and co-workers [36] have shown that
low-density excitations, produced by fast protons, converts 2: 10K CH4 into
a predominantly carbon material with almost no sputtering of carbon-containing species, producing primarily H,. Therefore, the background temperature may be important in the photon experiment which does show ejection
of significant amounts of carbon at low excitation densities.
The incident ions have an advantage for sputtering in that they create the
excitation densities described above in times which are orders of magnitude
faster than the photon pulse producing excitation events which are closely
spaced in time relative to the ejection times. Therefore, unlike the photon
yield results, the size of the yield of material sputtered from these solids
increases faster than linearly with increasing energy density deposited [4,7].
As the net amount of material ejected per incident ion increases, the
possibility of large unfragmented pieces being ejected increases. Finally, in
describing the ablation due to photon absorption, whether one uses the
words local expansion of the solid or activation and ejection of a surface
species does not really matter because of the long times involved. In
describing material ejection from the densely excited track produced by a
single ion, the opposite is the case.
Photon-induced dissociation of clusters can also give some insight into the
energy relaxation processes [37]. The fragment spectra exhibit two distinct
features. First there is an energetic component which is clearly due to a
repulsive decay, as in the photodissociation of or in dissociative recombination in diatomics and other small molecules [30]. This occurs as if the
excitation rapidly became localized at a specific bond. Second, there are low
energy fragments that are thought to be produced after the energy deposited
has been “randomized” and shared among a large number of lower energy
modes of the system. Because of the energy sharing, this is a slower process,
therefore excited clusters (e.g. ablated from a surface) can be stabilized by
transport through a non-reacting (e.g. He, Ar) gas [38]. That is, there is often
sufficient time that inefficient collisions with slow neutrals can result in
366
vibrational relaxation of the cluster. The production of the low-energy
fragments suggests that the electronic excitation can be manifested, for
instance, as a large number of lower-energy vibrational excitations. Therefore, when the UV photons are absorbed in the ablation experiment described above, it is not clear whether a local repulsive force is established
with neighbors, as suggested by the authors, or whether a general expansion
is induced due to the excitation of many vibrational modes, as in the
ion-induced desorption model of Williams and Sundqvist [24]. If the latter is
correct, then the absorption of a large energy quanta is simply a way of
producing multiple vibrational excitations rapidly in a solid composed of
large molecules.
Presumably, when the electrons decay to the band gap in the molecular
insulators, recombination can also take place by the two processes described
above, producing repulsive ejection (e.g. H from an O-H bond, which is a
process invoked for sputtering of H,O; see, for example, ref. 4) or by
lower-energy processes after the excess energy has been shared in the large
molecules. Because of the presence of neighbors, the phonon spectrum can
also be populated. This is opposite to the “normal” heating process in which
phonons and vibrations are excited concomitantly [33,35] and also differs
from the IR excitation of vibrations in which the photon pulses, hence the
times for absorption, are long.
Based on this discussion, and that earlier, it is clear that a large fraction
of the (dE/dx).
deposited by an incident ion in a solid composed of large
molecules rapidly ends up in vibrations and phonons (via repulsions, recombinations, etc.). The other major fraction is manifested in a related process,
covalent bond breaking, with very small amounts in luminescence, secondary electron ejection, etc. Therefore, as a first approximation in calculating the large-molecule yield, the deposited electronic energy could be divided between energy leading to expansion and that stored in “permanent”
bond alterations. Before considering this further, certain models are discussed.
4. MODELS
Models can be divided according to two aspects. The first relates to the
principle energizing mechanism and the second to the description of the
“expansion” process. Some models are not specific about the first aspect
and other models do not describe the “expansion” in any detail. They may
therefore be complimentary to each other.
367
RRKM
(QET)
In these models, the energy deposited by the ion excites the molecular
system (solid) to a relatively long-lived but unstable intermediate state which
decays and distributes its energy statistically, populating the available exothermic final states of the system [32,39]. In this model, no attempt is made
to describe the ejection process in detail and therefore it is not generally
used to describe the amount of material removed (yield). Ejection is one of
the possible final states and the model gives relative final-state (fragment
size, internal energy, translational energy, etc.) populations for this ejecta.
The argument is made that the final-state populations are independent of
the nature of the energizing mechanism, to a first order approximation, and
they depend, primarily, on the energy of the excited intermediate “state” of
the system. This, of course, requires that this state lives long enough to
“activate” all of the exothermically available modes of the system. As
vibrational periods are of the order of lo-l3 s, then for systems involving
hundreds of modes, times greater than = lo-l1 s are required. For very large
systems, such times can be longer than typical times for the ejection of
surface species (see Fig. 3) and therefore the model may not be appropriate
for the ejection process. In such a case, the internal energy carried off by the
ejected molecule will continue to be redistributed among internal modes, as
in the excited cluster example discussed. The model is most successful when
there are a large number of modes closely spaced in energy and should be
useful in describing the general fragmentation pattern and the exit energy
spectrum of the fragments of large ejecta. It is generally less appropriate for
describing relative amounts of very specific end products. However, it is
based on the premise that many of the apparently different processes for
decomposing materials energetically have common end products [39,40].
Coulomb explosion
In such models, the nature of the final-state products is generally not
considered and the total amount of the ejecta is estimated from the energy
of charge separation in the track core. The repulsion energy presumably
carries off whole neutrals as well as ionized species, possibly as clusters
which decay in much the manner discussed for field ion desorption [41],
although the manner in which the materials exits is generally not described.
Johnson and Brown [4] consider the energy input to the expansion (explosion) as a function of the mean screening radius of the ions by the electrons
but do not calculate a yield. Seiberling et al. [42] use this explosion to heat
the solid and then calculate the yield as a thermally activated desorption.
(Thermal models will be discussed shortly.)
368
Ritchie and Claussen [43] also use the energy stored in the charge
separation to “heat” the lattice. This heating is not by nuclear repulsion, but
rather the energy of charge separation is dissipated by electron-ion collisions in the core plasma. The heating is further sustained by the “excited”
states produced as the electrons cool to the band gap. Therefore, the
electron-electron (Auger) processes add this band gap energy to the total
heating energy. The lattice so energized is then described as expanding into
the vacuum while it cools radially. They ignore the electron cooling to the
internal vibrational states of the system, assuming that it only excites the
phonons, as this model was designed to describe the sputtering of atomic
condensed gas solids. Although Ritchie [43] gives the “expansion” equations,
they are not solved in any detail. They include no mass flow but only
diffusive transport.
Watson and Tombrello [44] treated the excited electrons as dynamically
screening the nuclei in the track region. This screening is also sustained by
the band gap energy with the electrons cooling via electron-electron
processes. They describe the subsequent expansion of the lattice as due to
the pressure of the excited electrons, but it would be better described as a
repulsive expansion due to the reduction in screening of the repulsive forces.
That is, the increase in the local electron “temperature”, which they calculate from the initial energy deposition, changes the lattice forces in the track
from binding to repulsive, as discussed earlier. The behavior of the electrons
in this model is equivalent to that described by Ritchie and Claussen [43],
giving a time dependence to the screening used in ref. 4. This model is very
attractive, however, in that they directly calculate a yield associated with the
resulting lattice expansion. In this calculation, they do not include any
thermal transport of the lattice energy. The dynamic screening time which
limits the yield is determined by the electron cooling described above. This
implies that, even if the cylindrical region is highly energized, no additional
material escapes after the lattice returns to a binding state.
Thermal spike models
Such models differ from the above in that they primarily describe the
radial cooling of the track energy according to the “thermal” diffusivity of
the material (Appendix). These models may [42] or may not describe the
energizing process. In the latter case, a fraction of the electronic energy
deposited is often used as a fitting parameter to measured yields as in ref. 4.
In the standard form, ejection occurs not as an expansion of the activated
region, but as the activation and ejection from the surface [45] on a
molecule-by-molecule basis, due to the local energy density, often given as a
temperature [31]. This has been applied [46] to collisionally energized
369
regions, having high densities of collision cascades, for room-temperature
atomic solids and condensed-gas solids with very limited success (e.g. the
onset is predicted roughly but the dE/dx dependence is not). It is attractive
as the yields can be directly calculated from the initial energy distribution
(parametrized by a mean width), the material sublimation energy, and the
thermal diffusivity. The latter is often the least well known parameter
because of the high energy densities of the solid in the track region,
generally well above the boiling point when there is significant sputtering.
There is considerable confusion in the literature on the use of the word
temperature in these models. The model as generally applied to the ejection
of atoms and small molecules describes a spike in which local thermal
equilibrium of the center-of-mass motion occurs. It may also be used when
some particular set of modes is equilibrated [31,47] (e.g. vibrations). However, as the spike gradients occur over molecular dimensions in an ion track,
local equilibration does not occur. In describing the sputtering of low-temperature condensed N, Johnson and Brown [48] suggest that use of a
diffusion equation to describe the radial dispersal of energy is reasonably
general. The caveat comes when converting the calculated energy densities
into, for example, molecular motion producing ejection. It is probably
appropriate simply to use this energy density to describe the activated yield
without reference to molecular motion [45], parametrizing the activation rate
constant for escape as suggested for biomolecules by Macfarlane [31] and
recently estimated by Lucchese [47] (see Appendix). Such a model is
intended to describe the ejection of molecules from a substrate heated by the
incident ion and becomes very similar to QET theories. It has the advantage
that spatial and temporal energy distributions can also be calculated. As
spike models have a long history, there are many and varied applications to
surface physics which will not be considered here.
Expansion models
Because of the high energy densities deposited, an expansion of the track
region will occur. This is limited radially by the surrounding material, but
outwardly the expansion is into the vacuum, when describing perpendicular
incidence. Occasionally, the expansion mechanism is described and these
mechanistic models are discussed first. Presumably, in the expansion whole
molecules and molecular ion clusters can be ejected [40].
When the charge separation energizes the expansion, we have already
described the model of Watson and Tombrello [44]. Williams and Sundqvist
[24] recently proposed a related idea. They noted that, in a molecular solid,
the dominant low-energy secondary electrons cool more effectively to vibrational excitations than to plasma heating in the core or to band gap
370
excitations. This was indicated in the earlier discussion. The vibrational
excitation of many modes of a large molecule can cause a direct expansion
of the molecular volume. Such an expansion is also a manifestation of the
overall excitation of the track region. This expansion might respond as in the
simulation in Fig. 3, but with the binding forces not turned off. If the
expansion is rapid, then molecules are ejected at the surface at a velocity
related to the velocity of sound in the material [24,49]. A calculational
procedure has not yet been developed for this model. According to the
authors, the model predicts that, when the yield is large, those materials
made up of larger organic molecules will have larger yields as the number of
internal to external bonds is larger.
For small molecule ejection at large yields and for highly energized
atomic solids, hydrodynamic expansion [49] in response to the kinetic energy
density has been proposed as a means of calculating the yields when large
amounts of material are removed [50]. Such a kinetically driven expansion
clearly cannot describe the large molecule, electronically energized case
discussed here. However, the general principles are applicable to a local
expansion in an organic solid once the energizing mechanism is defined. At
high energy densities, the surface layer leaves at roughly the same rate as
energy is transported away radially. Therefore, the top layers leave as a free
expansion while the subsequent ejection from greater depths is suppressed
by radial energy transfer and condensation [50]. For example, in Fig. 3, if
the attractive forces are restored, then the lower layers, which have dissipated some of their energy to the walls, are less likely to leave. Therefore,
in expansion models, the key time is the time for radial dissipation of the
energy, which might be described roughly as a diffusive transport, as in the
spike models (see Appendix).
Free expansion of molecules into the vacuum has been extensively studied
via nozzle beam experiments. It is noteworthy that, when large molecules are
involved, the expansion energy is derived, primarily, from the internal
vibrational energy of the molecules due to the preponderance of such modes.
In an expansion of UF,, for instance, depending on the length of the
collisional interaction region, - 90% of the internal energy can be converted
to center-of-mass motion [51]. Therefore, such a vibrationally enhanced
expansion cools the molecules by an amount determined by the expansion
energy achieved. For the bimolecular case, the ejection energy is small
compared with those estimated internal energies of molecular ions [52]
ejected from near the track core so that significant energy conversion is not
achieved for these species. However, this process may be important for
stabilizing those neutrals which are ejected at large distances from the ion
path. The vibrationally enhanced nozzle expansion of a gas is, of course,
very different from the physical vibrational expansion proposed by Williams
371
and Sundqvist [24]. The former requires considerable “contact” time for
vibrational to translation energy exchange to occur. The latter involves a
change in effective size of a confined material, which, of course, results in
some vibrational to translational energy exchange.
“Shock” models have also been proposed [53]. These are hydrodynamic
models for which the effective pressure gradient is very large. For a
cylindrically energized track at perpendicular incidence, the primary expansion is into the vacuum as described above. The creation of a radial shock
which interacts with this surface could be important for producing ejection.
However, at glancing incidence, the fo~ation
of a shock might be quite
important in determining the yields, causing significant deviations from the
predicted angular dependence of the yield. The craters produced by energetic ions depositing large amounts of energies at the surface have been
studied experimentally and show some agreement with such models to first
order [54].
Excitation models
Repulsive decay of states, as described in ref. 4, has successfully been
used to calculate the ejection of atoms and small molecules from condensedgas solids at low excitation densities IS&]. At these densities, the yields may
be linear in (dE/dx),
as indicated in Fig. 4 for sputtering of low-temperature condensed N, by MeV protons and helium ions [48,55]. These yields,
like those for E-I,0 in Fig. 1, are measured at very low sample temperatures,
where the yields are found to be temperature-independent,
and at low
currents, where they are also beam current-independent.
The observed
linearity of the yield with excitation density considerably simplifies the
interpretation of the ejection mechanism, indicating that ejection occurs on
an excitation-by-excitation
basis via a repulsive decay [4-61. It is seen,
however, that, as the excitation density deposited increases, the yield eventually becomes non-linear, nearly quadratic in excitation density, ~dicat~g
that cooperation between excitation events determines the ejection process
[4,483. The yield for water ice similarly sputtered only shows a quadratic
dependence at the same excitation densities [8] (Fig. 5) but increases more
rapidly with (dE/dx),
at even higher excitation densities [42]. A very
non-linear (dE/dx)z dependence has been found for the ejection of neutral
whole leucine molecules [7], as seen in Fig. 6.
Johnson and Sundqvist 1561suggested that the repulsive decay processes
used to describe small molecule ejection at lower excitation densities might
also energize the ejection of large organics when the excitation densities are
high, as in Fig. 6 for leucine. That is, as the excitations in the ion track decay
r~~sively in times short compared with the ejection time, large amounts of
10 -
F
._
\
z
-
E
>
l-
1
.l
L
I
I
10'
100
n $dE/dx
Ia (10”’
I
102
aV cm2/N2 )
Fig. 4. Sputtering of neutral N, at 10 K by protons (O), He+ (A), and charge state
equilibrated He+ (0) (roughly He2+ at these energies) [5]. These are plotted vs. the
equilibrium stopping cross-section, nG’(dE/dx),.
Lines drawn through data as guides. The
differences between He+ and equilibrated He+ suggest that the surface energy deficit in Fig.
(2) is not fully eradicated by energy transport processes. The difference indicates transport
over - 6-12 monolayers of N, [48]. Yields are mass loss measurements requiring, therefore,
larger fluences than in Fig. 6.
material and large fragments can be ejected if the initial excitation density is
high.
This was also the initial concept behind the ion track model [17,57] in
which the secondary electron shower created a distribution of excitations
(“hits”) over a well-defined radial distribution (see Appendix). As the
repulsive decays so produced can also fragment the molecules of the solid,
there is a region of the track in which a sufficient number of decays occur
(Poisson distributed according to the track excitation density) such that a
large molecule can be ejected but the number is not so large that fragmentation is inevitable. This model was used to describe the threshold and
saturation regions vs. (dE/dx),
for whole ion ejection found by H&ansson
et al. [16]. In this model, the number of hits required for whole-molecule
373
0
IO00 0
0
0
0
IOO-
B
/
f
IO-
a
< 8 -
l
.
‘97
l
‘0
.
.
/
0.1 /
/
/
0.01’
,
1l‘I
I
1
nM’(dE/dx),
#
111
‘
too
lo
(10-‘5eV
f
1,’
loo0
cm2/H20)
Fig. 5. Neutral sputtering yield (81 of Hz0 at 10 K by incident protons, He+ and F”” vs. the
eq~b~~
stopping cross-section. These are the electronic ~~~butio~
from Fig. 1.
Quadratic line drawn as guide only. He+ data at same ni’(dE/dx),
on either side of line
indicate that track widths are important. Yields are mass loss rn~~~~~
requiring larger
fluences than those in Fig. 6 for leucine. 0, H; Cl, n, He; A, C; v 0; 0, F.
desorption is related to the amount of bonding between the unit molecules
and therefore grows with the molecular size. The model has been shown to
be very usefulfor interpretingand organizing the ion yield data independent
of a specific description of the nature of the hit. And it is also useful for
374
106
1
I
I
105
104
T
2
\
i
103
z
!i
lo2
10'
0
I
100
10“
100
r-t,,,,-‘(dE/dx),
I
10'
I
102
103
(MeV/(mg/cm2))
Fig. 6. Yield of whole leucine molecules ejected at the same incidence ion velocity and for
equilibrium charge state ions [7]. Yields are expressed as a mass ejected (u/ion) vs. (dE/dx)z
line drawn through data. 0, Data for total mass yield from H,O at c: 77 K for incident
fluorine (corrected to perpendicular incidence), helium, and hydrogen at the same ui as in the
leucine data. Arrow indicates He+ is not equilibrated and therefore yield is a lower limit.
estimating the excitation densities and spatial distributions of this energy
which are required for ejecting even larger molecules. It does not rely on
repulsive recombination of ionized sites. The secondary electrons passing
through the molecular region produce the energizing excitations and the
fragmentation, so that the yield scales according to the molecular size
[17,57]. As the scaling in such a model depends on local energy density
deposited, a “temperature” can be invoked [17,31]. Therefore, Lucchese [47]
has recently described many of the features of the track model using a
thermal activation model, as discussed earlier.
The local repulsive decay following electron recombination is, of course,
closely related to the coulomb explosion models for small molecules as
described earlier. However, the concept can change when considering large
molecules with large numbers of internal degrees of freedom. In such a
375
system, electron ion recombination occurs via an intermediate quasi-stable
state [58]. Given sufficient time, this will eventually result in the ejection of
fragments as in the photon absorption experiments [37]. As the excitation
energy can be shared among the large number of internal modes of the
system, the state can survive for long times during which energy can be
dissipated to the surroundings. Therefore, electronic recombination of ionized
sites (hits) can also produce internal vibrational excitations with concomitant lattice expansion and dissipation to phonons. (This occurs in addition
to any direct vibrational excitation by the lower-energy electrons described
earlier.) Hence, excitation models may be very different for materials
composed of large and small molecules. Therefore, the ion track model for
desorption, which is not specific about the ejection process, can, in principle,
be related to the expansion models.
5. YIELDS
In this section, the parameters of a reasonable model for the yields are
described and evaluated. An expression for a yield for a given species can be
written quite generally based on the ideas described above and in a form
generally used in thermal spike models (see Appendix). Normal incidence is
assumed throughout so that
yI= fd2rfdt@,(r,
J
t)Pi(r,
t)
J
04
Here QM is the mass flux outward across the surface of the target expressed
in terms of equivalent whole molecules ejected, t is the time after passage of
the ion, and r is the radial variable about the track. This may be an
activated flux, as in a thermal spike model, or a flux associated with an
expansion (e.g. hydrodynamic flow). To first order, we ignore fragmentation
after ejection. The Pi then is the probability that, in the expansion, a species
i can exist or be created and survive the ejection. This includes ion
formation, whole molecules, fragments, etc. If a statistical model (e.g.
RRKM) has any validity, it can be used to describe this quantity in the exit
region. Therefore, in the above we have separated the overall material
ejection (sputtering, expressed via QM) from the processes that determine
whether or not a whole molecule can survive.
As the molecules are closely packed in the solid, they must exit layer by
layer. Therefore, we can, in principle, write E!q. (la) as
q = [d2r(n,L)~Pi(r,
J
zj, At,)
(lb)
j
where zj is the initial depth of the jth layer of thickness L ( nG113),nM is
the molecular number density, and Atj is the time it takes to exit. Clearly,
376
Atj and zj are related [see Eq. (la) and Appendix]. Based on our previous
discussion, Atj is an important quantity for determining the state of the
material escaping. That is, the time for survival of a thermally labile
molecule should be longer than Atj in order for a significant number of
whole species to be ejected from layer j. Alternatively, neutralization should
be slow compared with Atj for ions to come from that layer [28].
Desorption
The form in Eq. (lb) immediately allows us to discuss surface desorption
processes. The desorption yield can be written, quite generally, in the form
of Hedin et al. [17]
Yoi = Nn,L
J
d*rPi(r,
At)
(24
where N is the number of layers involved (N is often assumed to be one
[17,47,59]; however, Save et al. [60] have shown recently that ion desorption
comes from a number of layers with N a slow function of (dE/dx,),).
This
yield is determined by the radial scale of the ejecta and the probability of
ion formation. The ejection mechanism is contained in the radial scale and
At. The ion track model [17,57] and the “thermal” desorption model [31,47]
determine the ejection probabilities from that energy density in the surface
region which is sufficient to overcome the molecular binding (i.e. sufficient
density of events [57] initiated in the track model; sufficient kT in the
“thermal model”). Useful analytic expressions for these models using Eq.
(2a) are given in the Appendix.
We can write the above approximately as
Yoi = Nn,L(vr2)Pi
(2b)
where the effective area, m*, is the larger of the molecular cross-sectional
area, L*, and the track area at that minimum energy density required to
overcome the surface binding. Pi is an averaged production (survival)
probability and is discussed in more detail in the Appendix. In the ion track
model [17,56], only the initial energy density is considered, whereas the
“thermal” desorption model [45,57] allows radial transport of this energy. It
is interesting that the radial scale in both cases is proportional to (dE/dx),
at high (dE/dx),
(see Appendix) and differs only by a constant. In both
models, the effective Pi becomes approximately constant as (dE/dx),
increases for fixed initial track width, in rough agreement with experiment.
More precisely, an inner effective radius, rti, can be defined inside which
the fragmentation probability is high and an outer radius, rmax, can be
defined beyond which ejection is unlikely. Because the energy density decays
as - r-* in the ion track and the maximum energy density achieved by
377
thermal diffusion at any r (see Appendix) is a function of r2, then the area
at high (dE/dx),
between r_ and r,, becomes proportional to (dE/dx),
(see Appendix).
vr2 + L2 for large molecules and Pi --) 0, giving a
At small (dE/dx),,
“threshold” region [AS]. (When m2 < L2, only damage occurs [17,47] for
large molecules so that the yield goes rapidly to zero.) These models differ
significantly in the “threshold” dependence with the ion track model exhibiting a power law dependence corresponding to the number of secondary
electron events and the “thermal” activation model exhibiting exponential
decay characteristic of thermally activated processes (see Appendix). They
also differ in that ejection from the outermost regions of the track can lead
to fragmentation of thermally labile molecules in the “thermal” model due
to the slow “heating” rates [47] but not in the ion track model. This is an
important difference for calculating yields. In this sense, the thermal desorption model for ions appears contrary to the observation of large yields of
whole neutrals which must come from this outer track region [7] (see next
section). Neither model is specific about the ejection process, describing only
the critical energy densities required based on the experiments. Expansion
from below may or may not occur in the track model. In contrast, hydrodynamic models, for example, can only give expressions for m2 above and
additional information is needed for Pi, such as that obtained from the track
model, “thermal” activation model, RRKM, etc.
Sputtering
In order to describe the total loss of material, a limit needs to be
determined for the expansion. Inevitably this involves consideration of the
radial transport of energy or momentum for the case of normal incidence
which we are considering. We can use either form [Eqs. (la) or (lb)] for the
yield. Here, we adopt the general form [44,50] for yield in equivalent whole
molecules ejected
Y= (m-‘)(At
aM) = (vr’)(At
nM(u))
(14
In this, m2 is determined in a manner similar to that for ion desorption.
However, the required ejection energy for the predominantly neutral bulk
yield is thought to be less [7] than it is for ion desorption. That is, the
effective m2 is larger. At@,, gives a depth as a column density of material
removed. In an expansion or flow model Q)M= nM( u) where n M is the
whole molecular number density and (u) is the mean expansion speed.
The yield in Eq. (lc), though expressed in terms of the equivalent number
of whole molecules ejected, describes the total mass removed. This is what is
measured to obtain Figs. 1,4, and 5. For the leucine data in Fig. 6, however,
the yield is the number of whole molecules ejected. In which case the yield
378
in Eq. (lc) should be multiplied
probability, P,
Y, = YP,
by an average whole molecule
survival
(14
Because whole molecules have a lower removal energy per unit mass than
fragments, one might expect that, when the yields ure large, the mass ejected
is dominated by whole neutrals, as indeed is the case for the ejection of H,O
[8]. This has yet to be demonstrated for biomolecules, which fragment more
readily than H,O, and therefore, the leucine yields in Fig. 6 are lower limits
on Y, an important point to keep in mind in the following. Ions, of course,
have an even higher removal energy and constitute only a small fraction
(- 10e3) of the yield.
In the subsequent discussion, we will not describe the very interesting
“threshold” region for the neutral whole molecule yields (see Appendix). In
this region, the yields can display varied dependencies with excitation
density, as in the N, and H,O yields at low (dE/dx),
in Figs. 4 and 5. The
“threshold” region for ion ejection was also found to exhibit variations in
the (dE/dx),
dependencies for different bimolecular ions. These were
related, roughly, to the molecular ion size (amount of binding, Appendix)
[16,17,47,57]. It is clear that, for desorption of neutral biomolecules, there
will also be a “threshold” region in which the yields exhibit varied dependencies on (dE/dx),,
as the track scale approaches the molecular scale. The
region above threshold can be estimated for large molecules by requiring
n,U -CC(L) where c(r) is the radial energy density (Appendix), U is the
material cohesive energy, and L is the molecular dimension [(dE/dx),
> 3
MeV mg-’ cmm2 ] for leucine in Fig. 6. [Note: if a minimum excitation
energy is required, then that energy (e.g. W in the Appendix) replaces U in
determining a threshold.] The value of (dE/dx),
estimated here is lower
than the energy “densities” for which leucine ejection was measured, as seen
in Fig. 6. Therefore, large numbers of neutral leucine molecules are removed
[7] over the same range of values of (dE/dx),
at which the ejected
molecular ion yield changes from a “threshold” behavior [16] to being
proportioned to (dE/dx),.
This is consistent with the removal of neutrals
coming from a much larger area, rr2, (lower excitation density than that
associated with ion yields [7]) and/or greater depths (larger At). This is an
extremely important result but at present it relies on very few data points. If
it holds true for leucine and for other molecules, it implies that ions do not
uniformly come from the whole volume ejected. Rather, they are produced
in the ejection process coming, on the average, from a region closer to the
incident ion’s path [17] and, possibly, closer to the surface.
The radial dissipation of local energy density giving At in Eq. (lc) can be
estimated quite generally, as in a diffusion process [48,50]. This decay is
379
described in the Appendix where it is seen that the time and the square of
the radial variable always appear together. The effective track area, rrr2,
scales with (dE/dx).,
as described above, and the energy diffusivity, K, can
be used to write
In this “non-threshold”
region, (0) is determined only by the material
properties (e.g. surface activation energy in a thermal model, see Appendix).
Now the yield in Eq. (lc) can be written [4] quite generally as
Y = C(dE/dx):
(3a)
where C is a constant which depends only on the material properties when
the track shape is fixed.
The quadratic dependence in Eq. (3a) has been observed in many lowtemperature, condensed-gas sputtering experiments as indicated in Figs. 4
and 5. In stating that the yields are quadratic in (dE/dx).,
it is meant that,
in the sputter layer, they are quadratic in excitation density, e in Fig. 2. This
quantity is, of course proportional to (dE/dx),
but also depends on the
charge state and track width, therefore C in Eq. (2) also depends slowly on
the ion’s speed, ui. Using the spike model for the condensed gas data
[30,46,4g], we have found it convenient to express Eq. (3a) in the form used
in refs. 4 and 25
y_
()
o2
* i
1
fwvdx)e~,‘2 2
u
where U is the material cohesive energy and ad is the interaction cross-section between molecules in the solid, roughly the molecular size (u, - L2 nk*“). From this equation, the fraction, f, of deposited electronic energy
which goes into the ejection process for incident light ions is found, by
comparing with experiment, to be - 0.15 at high ui and - 0.5 at low ui for a
number of condensed-gas molecules [4].
Watson and Tombrello [44&l] noted the similar velocity dependencies of
the yields for light ions. For example, the yields for the ions hydrogen
through fluorine (converted to normal incidence), incident on H,O and SO,
can fit, to within about a factor of 2, an expression like Y - [cZ~‘~A/Z.J( A2.5
+ 1)12. In this A = ( u~/Z~/~U,), c - 1.7, 2 is the nuclear charge, and u,, is
the speed of an electron in the hydrogen ground state. This expression gives
the appro~ately
correct (dE/dx).
dependence at high and low ui and
accounts for track size changes (see Fig. 2). However, the complications of
track width and incident charge state considerably obscure the discussion of
mechanisms. Therefore, it is more useful to compare data at fixed track
380
parameters [16] which we will assume to be the case in the following. [Before
proceeding, we note that, whereas Nl + e + N + N can efficiently eject N,
molecules, processes such as H,O+ + e + H + OH do not efficiently eject
H,O as the energy is carried primarily by the H [30]. Therefore, H,O does
not exhibit a linear region in the same (dE/dx),
range.]
Although the quadratic dependence on the excitation density is clearly
seen for the condensed gases, it is interesting that the water ice yields at
higher excitation density in Fig. 5 may vary somewhat faster than this [42],
as does the neutral leucine yields which vary as (dE/dx)3 for fixed vi (Fig.
6). Further, the high energy density yields for collisional sputtering of
atomic solids also appear to vary faster than the energy density squared [62].
This possibility, that the observed neutral yields for fixed vi vary faster than
in eq. (3a), is briefly examined below, even though it is far from being
confirmed as a general result for organic molecules or for condensed gases,
and this trend cannot, in any case, continue indefinitely with increasing
(dE/dx).
due to energy limitations [4].
Since any expansion energy must be dissipated from the core of the track
outward according to some transport process, the result in Eq. (3) is quite
general. Sieberling et al. [42] attempted to describe the possibility of stronger
non-linearities at high (dE/dx),
by noting that, if the coulomb repulsion
energy “heated” the lattice, the energy per unit path length that should be
used in Eq. (3a) is itself proportional to the square of (dE/dx).
(within
some limits [4]). In that case, a yield that is proportional to the fourth power
of this quantity results, implying that the deposited energy contributes more
efficiently to ejection. Although, the concept of a more efficient use of the
energy deposited may be valid, there is an upper limit to rr2 of
(dE/dx),/(
n,U). Further, the ion desorption measurements indicate a
saturation region in the track in which vr2 for ion ejection varies roughly as
(dE/dx),.
As one might expect the ion yields to be most closely related to
the coulomb explosion, such a model does not appear to explain bimolecular
desorption.
In expansion models, the speed of expansion can depend on the effective
pressure differential [49] created in the material by the incident ion, hence,
this speed varies with the energy density deposited [44,50]. Similarly, Wilhams and Sundqvist [24] point out that the vibrationally excited molecules
expand in times comparable with the principal vibrational breathing period,
with the amount of expansion determined by Young’s modulus and the level
of vibrational excitation. This also implies that the surface molecules will
initially expand at a rate determined by the local excitation density. Therefore, in such expansion models, (v) has a roughly (dE/dx)1,/2 dependence,
which, when included in Eq. (lc), could give a yield varying as (dE/dx)z12
if K is constant. This also implies that there will be a roughly M-‘j2
381
dependence on the molecular mass, which can be tested experimentally.
Care must be taken with the result in Eq. (3a) and the above discussion as
the depth At@,, given in these models increases with increasing energy
density at a rate faster than the mean radius of ejection. This would require,
eventually, deep narrow craters. Allowing (u) to have a (dE/dx),
dependence would enhance this effect. From the simulation in Fig. 3, it is clear
that the sides of the excitation region are considerably agitated by the
expansion. Therefore, the radius and the depth must eventually increase with
increasing expansion energy at roughly the same rate, giving a fixed crater
shape. This is the case in the shock models [53], but the area dependence
remains proportional to (dE/dx),
so that AtQM varies as (dE/dx)‘,/2 and
the yield varies only as (dE/dx) zj2, which is not similar to the neutral yield
experiments described. [Recently, Save et al. [60] have shown that the whole
ion yields exhibit crater depths which vary slowly with (dE/dx),,
giving a
lower limit to the full crater depth. Also, Wien et al. [63] note that the depth
from which energy contributes to ejection is large.]
Biomolecule yields
The simplest “explanation” for the difference between the (dE/dx),
dependence of the leucine yields in Fig. 6 and the yield predicted by Eq. (3a)
is that P, in Eq. (Id) varies as (dE/dx),
over the region of (dE/dx),
studied. That is, the survival probability of whole neutrals in the ejection
process might also increase with increasing vrr2. Alternatively, the expansion
ejects a volume for which the dimensions have a different variation with
(dE/dx),
from that assumed in obtaining Eq. (3a), as discussed above.
Such variations in the effective area can clearly be tested experimentally as
suggested by the data of Save et al. [60] and by the measured damage
cross-sections [7]. Below, we examine other aspects of the leucine data in
Fig. 6.
In order to investigate whether the effective radius, r, for the neutral
yields for leucine [7] correspond to the initial critical energy density or to a
transport radius (see Appendix), we estimate r from the yield. Assuming a
hemispherical volume is removed, the largest neutral leucine yield measured
corresponds to r = 5 nm. An effective “damage” radius for the same
incident ion and energy is found to be of the order of 4.4 run [64], in
reasonable agreement. Such radii correspond to an energy density in the ion
track = 5 eV nmm3 which should be compared with the binding (cohesive)
energy per unit volume = 10 eV nrnm3 for leucine [65]. This would suggest
that some radial energy transport is required to produce the neutral yields.
On the other hand, SZve et al. [60] and Salehpour et al. [64] find a thickness
dependence for the ion yield - 15 nm for the highest energies. Assuming this
382
is a lower limit to the average removal depth [60], then the neutral whole
molecule volume gives r - 3 nm, corresponding to an energy density of 11
eV nme3 which is close to the binding energy per unit volume, requiring
almost no energy transport and PM - 1. However, this radius is less than the
damage radius. Therefore, experiment does not yet clearly indicate whether
or not the neutral yield requires radial energy transport. In the Appendix, it
is shown that, choosing track parameters, such a test can be made.
The analysis of the H,O data using Eq. (3b) suggested that only a fraction
of the (dE/dx),
contributed to the activated ejection. Such a result indicates some dissipation of energy by low-energy phonons which do not
contribute to ejection. Therefore, it is striking that, extrapolating the ice
yields in Fig. 6, the net mass of whole leucine molecules removed is much
lower, even though the binding per unit volume is lower in leucine. (This
comparison depends on the samples sputtered both being compact and
having their “normal” densities.) As the compressibilities are also similar,
this result implies one of the following: that P, +z 1 for leucine, that larger
amounts of energy dissipation occur in the organic molecule layers, or that
the ejection of H,O is predominantly different from that for leucine. Two
principal effects might account for the latter possibility. First, cross-linking
can occur in organics [36], thereby inhibiting ejection. Secondly, roughly
extrapolating the H,O yields in Fig. 6 to that for the largest (dE/dx),
and
assuming that a hemispherical volume is excavated, a radius of the order of
9 nm is indicated. This corresponds to an initial energy density of - 1 eV
nme3 vs. the cohesive energy of - 19 eV nm-3. (Allowing a deeper hole
does not change this enormously.) Therefore, it would appear that radial
energy transport is required to account for the larger effect area w2. That is,
small molecules, which are not thermally labile and which have a lower
binding energy per molecule, are ejected by the radially diffusing energy,
whereas the larger organic molecules are not. (This transport is, however,
not necessarily “thermal”, as stated earlier.)
Finally, a simple estimate of the yield is made for leucine. If we assume
the initial rudiaZ expansion speed, u(r), is proportional to the outward
expansion speed, (u), then u(r) = a( u)L/r. Here, a is a proportionality
constant and the radial expansion speed decreases as r-l, which is scaled to
L for convenience. Allowing the expansion to proceed out to that value of r
at which the initial excitation density is equal to the cohesive energy density
[i.e. (a~~),], then At = r2/2a(u)L.
Evaluating this for parameters for
incident I in Fig. 6, we obtain m2 - 25 nm2, (u)At - 8 nm if a = 1, giving
a yield in Eq. (lc) of Y = 1600. This is fortuitously close to the measured
and
yield of - 1200. In this rough description, of course, Y a (dE/dx)z
vr2 is less than the measured damage cross-section. However, this estimate
suggests that the scale of the yields is understandable based on the initial
track parameters.
383
6. CONCLUSIONS
In this paper, energizing mechanisms and aspects of models for describing
desorption yields in weakly bonded molecular insulators have been discussed. This is done in order to compare ideas developed for small molecule
desorption to the desorption of biomolecules and also to describe those
aspects of the desorption process which are common to a number of models.
As the calculation of the yield can be roughly divided into the probability of
production and/or survival of the ejected species and the volume (or area)
removed, the models generally deal primarily with one or the other of these
aspects. Since the amount of material removed is critical to understanding
the bimolecular desorption process, it was considered in more detail at the
end of this paper.
In the discussion of mechanisms, it was clear that energetic excitations are
desirable. For small molecules, this can lead to repulsive decay and ejection
whereas, for large molecules, this may simply be a means of exciting many
internal modes concomitantly. Rapid multiple excitations are also produced
in large molecules in the shower of secondary electrons initiated by the
incident ion [17,24,28]. Because the energetic excitations (e.g. ionizations)
can lead to either multiple energetic excitations or bond rupture, the
lower-energy secondary electrons may be of special importance in whole
biomolecule desorption [24]. Any special role of secondary electrons can
probably be established by comparing, for instance, ejection yields on the
entrance to and exit from a sample [19] (e.g. Fig. 2).
The total energy deposited in a molecular solid, therefore, rapidly goes
into expansion with a fraction “lost” to permanent bond alterations. The
spatial distribution of this expansion energy (determined by the track width,
hence, the incident ion speed, Ui) determines its efficiency in producing
molecular ejection, as is observed in the water ice sputtering data at high
and low vi. With this in mind, it is useful to look for trends in the data for
fixed track parameters [7,16] varying only (dE/dx),,
for the same (dE/dx).
varying the track width (i.e. vi), or for molecules of different sizes (binding)
at the same energy densities. Such measurements are especially important
for neutral yields.
In trying to calculate the volume of material removed, it is useful to
consider the area and depth of removal due to an expansion or activated
desorption. Comparing descriptions of the data on bimolecular ion desorption [17,47] with that for bimolecular neutral ejection yields, it appears that
the former are derived from a higher-energy density region of the track [7].
That is, the average areal region for desorption, rr2, is thought to be much
larger for the neutrals than the ions. It is also striking that the leucine yields
exhibit a fixed dependence on (dE/dx).
over a region in which the
384
dependence of the ion yields alter [7], becoming “saturated” with a linear
dependence on (dE/dx),
[16,17]. If this is found to be a general result, it
emphasizes that ions are not uniformly derived from the volume of neutral
ejecta. This would seem to imply that “preformed” ions are not essential for
understanding the biomolecule ejection data. However, it also suggests that,
if such ions can be created in the material, larger ion yields may be possible.
It is also striking that the neutral volume of predo~nantly
whole water
molecules removed from a very-low-temperature
sample at a comparable
(dE/dx),
is considerably larger than the neutral whole leucine molecule
volume removed when extrapolating the leucine yields to the (dE/dx),
for
fluorine on f-f,0 in Fig. 6. This is true in spite of the fact that the cohesive
energy per unit volume of the former is larger. Whereas no si~ifi~ant radial
energy transport appeared to be required in order to understand the effective rr2 for leucine, this is not the case for water molecule ejection. That is,
energy transported beyond the initially critical deposited energy density,
( mr2)o (see Appendix), by some means, contributes significantly to the
ejection of small water molecules but not to the ejection of whole leucine
molecules. In this regard, it is noteworthy that the effective vrr* for water
exceeds the measured “damage” cross-section from leucine (although this
conclusion depends somewhat on the assumed crater shape).
The picture of the radial effects about the ion track, as pointed out by a
number of authors, is of a highly fragmented inner region at very high
excitation densities and a much larger expansion region from which large
organic molecules are ejected. Whole bio-ions are ejected from a fraction of
the expansion region just outside the highly fragmented area. Further, it is
also possible that there is a damaged region lying outside the expansion area
1471, though this is less certain and may be caused by mobile radicals. In
describing the expansion volume, the nature of the apparent (d E/dx)z
dependence for the ejection of neutral leucine was not clear, although a
number of possibilities were discussed which could be tested experimentally.
However, the rough size of the yield was understandable using the initial
critical area ( nr2)o and the fact that the expansion speed into the vacuum
and the radial expansion (transport) speed are initially proportional as they
are both a result of the same energy density gradient. The neutral yields
should also exhibit a strong “threshold” dependence when the critical area,
( w-2)o, approaches L* and should vary less steeply with (dE/dx),.
APPENDIX
Elements
of spike
catcdation
Cylindrically symmetric activation models have a simple general form
[48,67]. In these, the z dependence in Fig. 2 is ignored and the transport of
385
deposited energy density, C, can be described by the diffusion equation
ac
(A-1)
VKVC = at
with K(C) the diffusivity.
K(C) = K()P,
Analytic .solutions to this have been given for
(A-2)
where r is the radial variable about the track and r,, accounts for the initial
width [67]. The standard normalization was used to obtain Eq. (A.2)
$cd% =f(dE/dx),
(A.3a)
where f is the fraction of the energy deposited [see Eq. (3b)]. This assumes
an initial energy distribution with
q)(r) = q)(o) 1 {
[ *]K-,‘)‘”
(A.3b)
(A.3c)
(Note: for (Y+ 0, co(r) = ~~(0) exp[ -(~-/r~)~].) Now v in Eq. (A.2) describes the change in the radial width as a function of time
v2(l+a)
_
[4K4)1t + 1
ro2
(A.3d)
Based on the discussion in the text, f in Eq. (A.3a) may approach unity
for large organic molecule ejection. The activated yield is now calculated as
in Eq. (la)
r;. = /~@&)P,(E)
d2r dt
(A.4a)
with Q)M the equivalent “whole” molecule flux ejected and Pi( 6) is the
survival (production) probability of species i. This flux is often expressed in
the Arrhenius [45,47] form (or equivalently, as a Maxwell-Boltzman distribution of escaping particles [46,67] for atom or small molecule ejection) and
Pi can also have such a form [17,47] but with a different activation energy.
When the initial width, r,, is small (i.e. 7~02- (Un,) 4 f(dE/dx),)
then,
from Eq. (A.l), t scales with r* and from Eq. (A.3c) r* scales with
f(dE/dx),, so
Yaf2(dE/dx)t
(A.4b)
386
This is the form predicted [see Eq. (3a)] beyond the import~t “threshold”
region in which the form of the initial distribution matters. For the case
Pi = 1, Q = A exp( - U/e) [45,47], then, as given in Eq. (3b)
when the initial width is small and the quantity C is a function of material
properties only 1671 ( i.e. diffusivity and a).
For desorption, Lucchese [47] writes
YDi = (~~~)~~
dr2Pi(r,
a)
similar to the result in Eq. (2a). [This is based on the assumption of ion
ejection from the first molecular layer, otherwise a form like Eq. (A.4a)
would be used.] He further writes Pi = pi P, where pi is an ionization
efficiency and P, is the sputter removal of whole neutrals. He then solves P,
from rate equations which describe the l~e~ood
of bond dis~ption vs.
time. These have rate constants of the Arrhenius form, K = A exp( - &/e),
which vary with Y and t via E. Here, U, is an individual bond activation
energy. Solving the rate equations gives the probability of an ejection, P,( r,
co), at each r for use in Eq. (A.6a). The simplest single site rate equation,
without damage, is
dP
-2
dt
= -kp8
which gives
P,(r, co) = 1 - exp [J
exp( - U/c) dt
(A.5b)
where U is the activation energy of this site, presumably the material
cohesive energy. At small P,, i.e. P, + / exp( - U/c)dt, Eq. (A.5a) becomes
identical in form to Eq. (A.4a). Rather than evaluate the yield, we note that,
at high energy densities, P, --) 1 out to some increasing value of r after
which it decays rapidly. (This is examined in the last section of the
Appendix.) This provides an effective cut-off, r,,,
in the integral in Eq.
(ASa). If a damaged region is also assumed below some rti, then Eq (A.5a)
becomes
Yni = (~~~)~~~~~~~
- TV&.&)
(A .5c)
As vrr2 scales with (dE/dx),,
then YDi above also varies as (dE/dx),
at
high (dE/dx) e. Lucchese [47] also considers a model in which thermally
labile molecules may be destroyed beyond some large value of Y, giving a
387
somewhat different value of the effective r,,.
scaling, however.
This would exhibit the same
Elements of the track model for desorption
This is most easily expressed by Eq. (lb). When describing desorption of
a trace species in the general ejection of mass, the yield can be written
Y = n,/Pi(c,,,z) dV
(A.6a)
where z is the depth of origin of the material and only the initial energy
density is taken as cont~buting to ejection. Assuming, to first order, that
only the total amount of material ejected has a depth profile but P, is
independent of z, then the form in Eq. (2a) is obtained
(A.6b)
(Note: Save et al. [60] have recently shown that the ions also exhibit a slow
variation of N with (dE/dx),.)
The probability can be expressed as
Pi = P,(l - P,)(l
- PN)
64.7)
where P, is the production (sputtering) probability of the species in the
general mass flow of molecules, P, is the damage probability and, when
describing ions, P, is the neutralization probability. The first two quantities
involve breaking two different types of bond, as pointed out by a number of
authors. The average bond-breaking probability can be written as
where IV is the average energy required for breaking the bonds (activation)
which is different for the sputter (s, external) or damage (D, internal) bonds,
and the molecular volume is V, = rrl;;r’. Neutralization must be treated
separately and is determined by the availability of electrons at the surface
and the escape time.
If n or more hits are required for ejection f17]
(A.8a)
P, =pS 5 s? e4-17sVm!
IPI=?
and if one or more damage hits lead to fragmentation,
p, = 1 - exp( -vu)
then
(A.8b)
Assuming neutralization depends on the ejection time, At in Eq. (2a), then
the expression in Eq. (A.6b) can be evaluated. At large values of (dE/dx).,
388
a simple analytic expression can be obtained using the fact that co(r) 53
c,f(d E/dx ) J vrr2 over a large range of r. For n 2 2
yn = NC. [l
-
PN@Ql P&3 V(dVdxJ/n,W,J
x (P-l)-‘: (1 + ~/~~)-~+l/~(~
- 1)
(A.9a)
m=R
[
I
This exhibits the linear dependence in (dE/dx),
discussed in the text.
Writing, instead, an activated form for P, based on the initial excitation
density [17], P, =“pSexp[ -n,U/r,(r)],
then
4dWl Psc,[fw/we/~M~l
03
yn = NL[l-
x
l-
[ j
exp( --x - cu/x)dx
0
1
(A.lOa)
with a = U/W,. This has the same form as Eq. (A.9a). Here, the sputter
activation energy U may be the material cohesive energy.
At low (dE/dx).,
the finite value of +,(r) at small r is important when
the molecules are large. In this limit [L(dE/dx),/II$,
GC11, so that for the
hit model
Yi,aN(I -pN)~s[Lf(dE/dx)JW,f~
and, for the activated yield
YnaN(l
-G&J,
expi-
(A.9b)
VLf(dQ’dx),l
(ASOb)
= N(l - P&,fexp[
- ~/~~(dE/dx)~~}’
That is, this is the “threshold” region so that 7rr2 of Eq. (2b) becomes - L2,
the molecular cross-sectional size. Therefore, in EZq.(2b) and the above, one
has (?rr’n,L = 1). The dependence on (dE/dx),
is very different in these
models and, therefore, can be tested expe~ment~ly. However, whether one
uses the sputter activation energy U (which, for n bonds each having energy
U-,, is nU,) or an excitation IV,, a product of probabilities is always involved.
The “threshold” regions above are described for the desorption (fixed
depth) process. “Thresholds” will also occur for neutral whole-molecule
ejection. If, as discussed in the text AtaM a (dE/dx),,
then the above
equations can be roughly multip~ed by (dE/dx).
in order to obtain the
form for the neutral yield dependence for point particles. For large molecules [e.g. Eq. (lb)], the limiting depth to be used is L, giving similar
“threshold” variation to that of the ions.
Radial scales
In cylindrical spike models, the radial extent of the material affected
scales simply with (dZZ/dx),. If U is the net activation energy for the
removal of a molecule of volume nil,
effective area [see Eqs. (A.3)] of
hr2)s=
then the region participating has an
csf(dE/dx)e
n,U
where c, is obtained from Eq. (A.2) by setting c = n,U
(A.lla)
at the largest r
(A.llb)
c, = (1 + +l’a
The result in Eq. (A.lla) applies, of course, only beyond the “threshold”
region, (9~~)~ 3 L 2. The value for ( 7rrL)s above may be a reasonable
estimate for rr& in EQ. (A.%).
Track models also give the same general form, as the electronic energy
density deposited by the secondary electrons decays roughly as rv2. The
quantity BQz, is the critical energy density for induced desorption [17,57].
Therefore, in the initial track, the radius at which the critical energy density
is reached is obtained from
br2)cJ
=
cof(dE/dx)e
n,W,
(A-12)
with the zero indicating that the estimate depends on the initial distribution
in deposited energy and cO is determined from the track parameters. This
also emphasizes that U and W,, although defined differently, appear as
similar parameters.
Although the scaling in these models is the same, one model involves
transport and the other does not. Because of the steep gradient in the energy
deposition profile (see Fig. 2), it is important to know, when calculating the
yield, whether transport of energy radially from the track core can contribute to ejection. The models can be distinguished quantitatively in the
“ threshold” region for the ejection. Below, however, we consider the relative
radial scales. We first note that the forms for 6 in Eq. (A.2) are restrictive for
describing the initial distribution once OLis specified. Therefore non-analytic
solutions corresponding to the true initial distribution must be calculated.
Because the case ar = - 1 + 8, where 6 is a small positive number, has a
form close to that of the initial distribution, we can use that solution in Eq.
(A.2) for purposes of discussion below.
At any r in the track of diffusing energy, the maximum energy density
occurs at time
t,=O
t,=
r2 < i-02
[(r2/r~)1+u-+02
r2 > t-02
+A0)1
(A.13)
390
obtained from Eq. (A.3b). If ( 7~‘)~ from Eq. (A.lla) is less than or equal to
rri, then the scaling of the yield does not depend on energy transport. In
this case, the two models are essentially equivalent. [Using the value of t, to
determine (vv~)~ above, then one obtains c, = (1 + ~y)-i/~ in Eq. (A.llb);
for 1y-+ 0, c, = e-l.1 Therefore, in order to distinguish clearly between these
models, one should arrange experimentally that ( w2)s x=- (qf).
This is
equivalent to the narrow spike criterion [67]
(A.14a)
where r, is obtained by fitting to the distribution using the appropriate form
in Eq (A.3b). Note, however, for the case ar = - 1 + 6, with delta small,
which describes the initial distribution reasonably well (see Fig. 2), the
transport is unfavorable so that very large (dE/dx),
may be required for
such transport to be involved. The criterion in Eq. (A.14a) is also equivalent
to
40) z+
n,U
(1 +
cry
(A.14b)
ACKNOWLEDGEMENT
The author would like to acknowledge many helpful ~nversations about
the ideas discussed here with G. Save, B.U.R. Sundqvist, and P.J. Derrick,
comments from R. Lucchese and M. Salehpour, the support of the University of Uppsala where much of the manuscript was written, and also the
support of the National Science Foundation Astronomy Division under
grant AST-85-11391 and the NSF Foreign Travel Division.
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