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Elsevier Editorial System(tm) for Nuclear Inst. and Methods in Physics Research, B Manuscript Draft Manuscript Number: IISC18-19R2 Title: Characterization of the Ne-Al scattering potential using low energy ion scattering maps Article Type: Proceedings: IISC-18 Keywords: scattering; channeling; ion-surface interactions; LEIS; aluminum Corresponding Author: Dr. Robert David Kolasinski, Corresponding Author's Institution: Sandia National Laboratories First Author: Robert David Kolasinski Order of Authors: Robert David Kolasinski; Josh A Whaley; Richard A Karnesky; Christopher W San Marchi; Robert Bastasz Manuscript Region of Origin:
18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18)
September 26 – October 1, 2010, Gatlinburg, Tennessee, USA
Nuclear Instruments and Methods in Physics Research, Section B.
MANUSCRIPT COVER PAGE
Title of Paper :Characterization of the Ne-Al scattering potential using low energy
ion scattering maps
Corresponding Author :Robert D. Kolasinski
E-mail :[email protected]
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Cover Letter
α
θ
φ
Fig. 1
Figure 1
Fig. 2
0.01
0.1
1
10
100
sign
al in
tens
ity (c
ount
s/nC
) ARIES ion energy spectrum3 keV Ne+Al(111)α=67.0° / θ=45° / ϕ=0°
Al(s++)
Al(ss++) Al(s) Al(ss)
(a)
0.01
0.1
1
10
1.00.80.60.40.20.0
relative energy (E/E0)
ARIES ion energy spectrum3 keV Ne+Al(111)α=67.0° / θ=30° / ϕ=0°
(b)
H(r)
Al(s++)
Al(ss++)
Al(s)Al(r)
Figure 2
0.08
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0.25
0.33
0.42
0.50
0.58
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1.00
signal intensity(normalized)
Es=0.85
θ=30°
(r,φ)r = radius (0-8 Å)φ = azimuth
MARLOWE
(b)
signal intensity(normalized)
Es=0.82
θ=30°
(r,φ)r = radius (0-8 Å)φ = azimuth
ARIES
(a)
Fig. 3
0.08
0.17
0.25
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0.50
0.58
0.67
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Figure 3
EXPERIMENT
SIMULATIONS
Fig. 4
0.50.40.30.20.10.0
1.00.80.60.40.20.0
f=1.2(b)
1.00.80.60.40.20.0
8765432
radial distance (Å)
0.50.40.30.20.10.0
(d) f=0.5scat
terin
g in
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ity (n
orm
aliz
ed)
0.50.40.30.20.10.0
error (yi -m
ai ) 2
1.00.80.60.40.20.0
f=0.85BEST FIT
(c)
1.00.80.60.40.20.0
8765432radial distance (Å)
(a) ARIES polar scan3 keV Ne+Al(111)θ=30° / ϕ=0°
scat
terin
g in
tens
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(n
orm
aliz
ed)
Figure 4
0.4
0.3
0.2
0.1
0.0
R-fa
ctor
1.21.00.80.60.4
screening length multiplier (f)
3 keV Ne+Al(111)
Moliére potential fit
Fig. 5
Figure 5
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 1
Characterization of the Ne-Al scattering potential using low energy ion scattering maps
R. D. Kolasinski1, J. A. Whaley, R. A. Karnesky, C. San Marchi, and R. Bastasz
Sandia National Laboratories, Hydrogen and Metallurgical Science Department, Livermore, CA 94551, USA
Abstract – In this study, we examine the scattering of inert-gas ions from Al(111) using low
energy ion scattering (LEIS). These techniques, because of their high surface specificity, provide
structural and compositional information from the first atomic layer of the surface and can be used
to determine the configuration of low-Z adsorbates. Extracting structural information embedded in
LEIS data presents many challenges, given the complex collision processes which ultimately
contribute to the detected scattering and recoil signals. To aid in the interpretation of these data,
we map scattered Ne+ ion signals over a wide range of crystal orientations with respect to the
incident beam in order to investigate a variety of scattering geometries. The signals are also
simulated using a modified version of the MARLOWE binary collision code and related to the
surface structure. We make quantitative comparisons between the simulated results and the
experimental data using reliability factors, and are able to show how the interatomic potential can
be calibrated.
Keywords: scattering, channeling, ion-surface interactions, LEIS, aluminum
PACS numbers: 34.50.-s, 61.05.Np
1 Mailing address: Sandia National Laboratories, P.O. Box 969, MS 9161, Livermore, CA 94551
Phone: (925) 294-2872 / Electronic Mail: [email protected]
Manuscript (Including Page Numbers)Click here to view linked References
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 2
I. Introduction
Low energy ion scattering (LEIS) and direct recoil spectroscopy (DRS) enable the structure and
composition of the outermost atomic layer of surfaces to be determined. The compositional
information provided by these techniques is reasonably straightforward to interpret, since the
scattered and recoiled particle energies can be directly related to the mass of the collision partner
on the surface using basic kinematic relationships [1]. On the other hand, accurate surface
crystallography using LEIS can be more elusive. The established procedure for determining surface
structure involves calculating shadow cone shapes for the ion-target pairs of interest and
determining the angles of incidence (α) and azimuths (φ) where these shadow cones intersect
neighboring atoms. (See Fig. 1 for angle definitions.) However, this approach can lead to
considerable errors in interpreting scattering data, since the conditions where shadow cone
intersections occur do not necessarily correlate exactly with maxima in scattering intensity. For a
more comprehensive overview of the challenges associated with LEIS surface crystallography, we
refer the reader to Ref. [2].
To circumvent these difficulties, we previously developed a technique where different surface
structures are simulated using binary collision models and are then compared to experimental data
[3]. This involved using reliability factors (R-factors) to make an unbiased, quantitative evaluation
of the best fit between the experiment and model. To make such comparisons, it is useful to
consider which data contain the most information about the surface structure. For this purpose, we
used a mapping technique previously developed by Agostino et al. [4] to acquire scattering signals
over wide ranges of α and φ. A special feature of these maps is that they can be conveniently
rendered in real-space, enabling one to identify important scattering mechanisms and making the
local atomic structure easily recognizable upon inspection.
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 3
In this study, we focus on an alternate application of the aforementioned scattering maps to
cases where the surface structure is already known. One can then apply R-factor analysis in a
similar manner to calibrate the interatomic potential for a surface, a particularly valuable exercise if
the configuration of adsorbed atoms is of interest. This is especially true where the adatoms are
much lighter (e.g. lower Z) than the substrate and have only a minor role in determining how
incident ions are focused along the surface. In this case, adjusting the potentials for the ion-
substrate interaction would clearly enhance the accuracy of adsorbate structural measurements as
well.
We apply the mapping techniques and R-factor analysis described above to the model system 3
keV Ne+→Al(111). This surface has been widely studied, particularly because its interaction with
hydrogen leads to the formation of hydride species [5,6]. In this article, we begin with a description
of our experimental instrumentation, as well as a discussion of our LEIS measurements. We
present ion energy spectra for Ne+→Al(111), and briefly characterize the inelastic losses. A
description of ion scattering maps for the Al(111) surface follows, and a discussion of the R-factor
analysis, which is used to refine the scattering potential, concludes the paper.
II. Experimental and modeling approach
For the measurements described herein, we used an angle-resolved ion energy spectrometer
(ARIES) which has been optimized for detailed LEIS and DRS characterization of low-Z adsorbates
(particularly hydrogen.) A Colutron source produces ions by electron bombardment of a source gas,
and electrostatically accelerates them to a specified energy between 0.5-5 keV. The beam passes
through an E×B filter to remove undesired impurities and is then deflected through a mechanical
bend to remove neutral particles. The beam finally enters an analysis chamber, which is
maintained at a base pressure of 5×10-10 torr. (During operation, this increases to 10-7 torr due to
source gas leakage through the ion gun.) We configured the beam to raster over a 2 mm × 2 mm
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 4
area on the target, adjusting the deflection voltages to maintain an analysis region that is
independent of incidence angle.
An electrostatic analyzer (ESA) collects scattered and recoiled particles over a 2 mm dia.
aperture. The entire detector is mounted within the chamber on a rotatable platform, enabling the
observation angle to be varied between (see Fig. 1 for angle definitions). Our system
is equipped with a 5-axis sample manipulator, which allows for precise alignment of the polar and
azimuthal angles with respect to the incident beam. The polished surface of the Al crystal (MaTecK
GmbH) was aligned to within 0.1° of the (111) plane. We cleaned and ordered the surface by
following previously established procedures [7], which included repeated cycles of sputtering with
Ne+ and annealing to 600 °C.
Aluminum quickly forms an oxide layer when exposed to small amounts of impurities. While
LEIS and DRS enable identification of surface-adsorbed species, Ne+ does not provide a strong
scattering signal from lighter elements such as C and O. To supplement these measurements, we
used Auger electron spectroscopy (AES), which offers high sensitivity to both species. By
monitoring the amplitudes of the O, C, and Al KLL transition peaks in the derivative AES spectrum,
we verified that surface contaminants were reduced to negligible levels during the preparation of
the surface.
For situations where high computational speed is required (i.e. to simulate complete scattering
maps), the binary collision code MARLOWE [8] is particularly well suited. Our modeling approach
was designed to enable analyses of scattered ion trajectories and collision partners; further details
may be found in Ref. [3]. For Al(111), we incorporated a surface binding energy of 3.36 eV as well
as random, non-correlated thermal displacements using a Debye temperature of 428 K [9]. At least
2×106 particle trajectories (initialized uniformly over a single unit cell on the surface) were needed
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 5
for adequate scattering statistics. The interatomic potentials are used in our simulations are
discussed later in Sections III and IV.
III. Ion energy spectra and real-space scattering maps
Ion energy spectra for 3 keV Ne+→Al(111) are presented in Fig. 2, where the energies of the
scattered particles (E) have been normalized to the incident beam energy, E0. We calibrated the Ne+
beam by passing it directly into our hemispherical analyzer and found the FWHM energy spread to
be <1 eV at E0=3 keV. The largest peak in the spectrum depicted in Fig. 2(a) is indicated with the
notation “Al(s)”, and arises from Ne+ undergoing single elastic collisions with the Al surface atoms.
For a scattering angle corresponding to θ=45°, one would expect the Al(s) peak to occur at
E/E0=0.62; however, inelastic losses shift this to a lower energy. The high-energy peak occurring at
E/E0≈0.75 arises from Ne+ ions undergoing multiple in-plane scattering (hence losing less energy
than a single in-plane collision.) Note that we apply the notation (ss) to contributions arising from
multiple in-plane scattering. An ESA-type detector readily detects multiply-charged particles, as is
evident by the Al(s++) and Al(ss++) signals present in Fig. 2(a). Since double ions pass through an
ESA at half the voltage as their single ion counterparts, Ne2+ scattering from the surface appear as
distinct peaks in the ion energy spectrum.
The prominence of signals arising from Ne2+ is rather striking, as the survival probability for
noble-gas ions scattering from surfaces is typically quite small. However, a small subset of
materials (Mg, Al, and Si) appears to be an exception [10-12]. Also of note in the ion energy
spectrum is the presence of a small broad feature at E/E0=0.49. Both recoiling Al and O can be
detected at this energy. However, based on the AES data discussed previously, we can eliminate
surface-adsorbed O as a possibility.
The remaining measurements discussed in this study were acquired at an observation angle of
θ=30°; an ion energy spectrum for this angle is shown in Fig. 2(b). The main effect of using a
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 6
smaller scattering angle is a shift of the main scattering peaks to higher energies, better revealing
light adsorbates which recoil at low energies. For example, a signal from recoiling hydrogen atoms,
labeled as H(r), is clearly evident in Fig. 2(b). The presence of this hydrogen signal is surprising,
especially given the strong barrier to dissociative chemisorption of H2(g) on Al. However, upon
more careful consideration we found this signal to be from residual H2 which had been fragmented
by the various filaments in our vacuum system. A disadvantage of using a small scattering angle is
that the Al(ss) is now incorporated into the high energy shoulder of the Al(s) peak and is no longer
easily distinguishable. However, the superposition of these peaks is taken into account in our
simulations, and should therefore not affect the quantitative comparisons discussed later in this
paper.
As previously discussed, real-space ion scattering maps reveal the structure of single crystal
surfaces, and can be used to identify important scattering processes. The approach described
herein was initially developed by Agostino et al. [4], and has many similarities to the scattering and
recoiling imaging spectrometry (SARIS) maps pioneered by Rabalais and co-workers. (For further
details on SARIS, refer to Ref. [13].) One key difference is the SARIS maps involve collecting
forward-scattered particles over a wide range of observation angles (θ), making “blocking” effects
easily observable. Agostino’s approach, on the other hand, involves varying the incidence angle (α),
allowing ion focusing along atom rows to be easily visualized. Since each mapping style emphasizes
different scattering mechanisms, one could envision choosing whichever better reveals the
structural information of interest.
Fig. 3(a) portrays an experimental scattering map for 3 keV Ne+→Al(111) acquired using our
ARIES instrument. We collected ion signals over complete 360° rotations in azimuth (φ) in 2° steps,
while incrementing the polar angle between 59.94°≤α≤81.46°. This was sufficient to sweep the
shadow cones over an 8 Å radius within the first layer surface plane in 0.25 Å steps. In total, each
map consists of 4887 individual measurements, with the intensity patterns rendered using a first-
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 7
order interpolation between these points. All scattering signals were collected at a constant
observation angle of θ=30°. Once a complete data set has been acquired, the maps are transformed
from a (α,φ) phase space into real-space coordinates by considering where the shadow cone at a
particular incidence angle intersects the first surface plane of atoms. The map coloration indicates
the intensity of the Al(s) peak (E/E0=0.82), corresponding to single in-plane scattering. Our
experimental data are reproduced satisfactorily by MARLOWE, as illustrated in Fig. 3(b). This set of
calculations incorporates a Molière potential [14] using a Firsov screening length [15] adjusted
using a multiplicative factor of 0.85. (Details regarding the calculation of the screening length
which best fit the experimental data appear in the following section.) Note that we have taken
advantage of the surface symmetry by simulating only 0°≤φ≤120° and assembling the complete
map by reflection. Since the second layer of atoms may contribute to the scattering intensity at
lower angles of incidence, it was necessary to consider a 120° domain, rather than 60°.
The intensity patterns in the scattering maps arise depending on how adjacent atoms are
shadowed. Immediately evident is the six-fold symmetry of the patterns, which conform to the
parabola-shaped lines included in the Fig. 3(a) overlay. Each of these lines represents the angular
coordinates where the shadow cone from a reference site (located at the center of the map)
intersects its nearest neighbors. A more complete explanation of the mechanisms which contribute
to the intensity patterns can be found in Ref. [3]. To determine the intersection conditions, we used
the Oen shadow cone formula discussed in Ref. [16].
One benefit of the maps is that atom positions can be roughly assigned to the apex of each of the
red parabolic curves, as illustrated in the Fig. 3(b) overlay. Accurate atom positions can be
determined through more detailed comparisons between the MARLOWE simulations and ARIES
data. The rendering of the map in real space is mainly a convenience, but is also beneficial in
interpreting other features in the maps. This is especially true at the map periphery, where a
strong increase in scattering intensity is evident where the shadow lines converge.
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 8
While every effort was made to minimize the ion dose during the acquisition of the scattering
map (each data point required 100 nC total dose), the accumulation of damage to the surface over
time remains a concern. Strikingly, we did not observe any degradation of our scattering signals
with ion fluence. There are several plausible explanations as to why this would be the case. First, it
is important to recognize that LEIS is not strongly sensitive to surface damage. Scattering from
atoms in non-crystalline regions should only add a uniform background rather than destroy the
structural variation in intensity generated by scattering from the crystalline portions. Also, the
activation energy for Al adatom migration on Al(111) has been observed to be rather low [17],
suggesting that some reordering of the surface is possible. In addition, it is likely that the
sputtering rate of the material from the incident beam is sufficiently fast so as to prevent damage
accumulation in the material.
To further address this issue, we improved the experimental procedure discussed in Ref. [3] by
monitoring only the scattered ion energies of interest, rather than acquiring a full spectrum at each
(α, φ) position. This lowers the fluence needed to acquire a map by a factor of five. Further
reductions could be realized by using a time of flight system (with a MCP), which would have a
much higher detection efficiency than our present ESA. While there is some variation of the
intensity patterns with azimuth, this is likely due to a slight misalignment of the crystal surface,
rather than damage accumulation.
IV. Interatomic potential calibration using R-factors
Accurately modeling low energy ion-surface collisions requires the selection of an appropriate
interatomic potential. Unless detailed sputtering or recoil calculations are of interest, the repulsive
portion of the potential typically dominates the ion-solid interaction [18]. It is common practice to
model the short-range repulsion with a screened Coulomb potential, and in the absence of prior
knowledge of the surface structure the ZBL empirical fit is generally suitable for this purpose [19].
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 9
However, one may wish to calibrate the interatomic potential for a specific ion-target combination.
This is typically accomplished by adjusting the screening length (a) to control how quickly the
potential decays as a function of distance (r) away from the scattering center.
The approach we pursue here is to calibrate the potential by simulating scattering intensities
along a representative subset of Al(111) azimuths using MARLOWE and adjusting the screening
length by a simple multiplicative factor. We then perform a quantitative comparison between the
experiment and model using R-factors:
In the expression above, yi and ai are individual points within the experimental and simulated
scattering maps, respectively. The simulated data are scaled by a single multiplicative factor
which is determined by a weighted least squares scheme so that the error between the two data
sets is minimized. N refers to the number of points in each data set.
Consider Fig. 4, which illustrates the effect of calibrating the interatomic potential. Here we
have simulated the variation in scattering intensity as a function of α for 3 keV Ne+ scattered along
the <100> azimuth on the Al(111) surface. In effect, these conditions correspond to a radial cross
section of the scattering maps shown in Fig. 3 along φ=0°. Case (a) illustrates the experimental data,
whereas cases (b-d) are MARLOWE simulations which have been performed for different potential
screening lengths. For this purpose, we used the Molière theoretical potential used in conjunction
with the following screening length (developed by Firsov [15]):
In the above expression, a0 is the Bohr radius, whereas Z1 and Z2 are the atomic numbers of the
incident particle and target atoms. It is important to note that the Moliere potential is theoretically
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 10
derived, in contrast to the ZBL formulation which is an empirical fit to many pair potentials. A more
thorough discussion of the theoretical underpinnings can be found in Ref. [19].
Fig. 4(a) shows the Ne+ scattering intensity along the <100> direction on the Al(111) surface as
a function of incidence angle. For a better comparison with the scattering maps in Fig. 3, α has been
transformed to radial distance d, based on the shadow cone intersection along the surface. The
lower panels portray scattering signals simulated using a screening factor that has been adjusted by
scalar multipliers of f=1.2 (b), 0.85 (c), and 0.5 (d). For each set of simulations, the dashed curve
plots the error term, . To better clarify the differences between each of the simulated
cases, we have normalized each data set to its maximum value.
Several important points may be extracted from the data presented in Fig. 4. First, the figure
clearly shows the sensitivity of the scattering signals to changes in the screening length. This is not
unexpected, as any modification effectively alters the strength of the potential, and by extension the
shadow cone shape. This affects both the broadness of the various features observed in polar scans,
as well as the incidence angle where these signals occur. In addition, the error curves illustrate
how the R-factor technique outlined here emphasizes the quality of the alignment between the
different features of the experimental and simulated scattering maps. A misalignment is captured
in an especially prominent manner in case (b), which corresponds to f=1.2. In this situation, the
leading edge prior to the maximum in scattering intensity is not reproduced well by the simulation.
This discrepancy is ameliorated by decreasing the screening length multiplier to f=0.85, as in case
(b), whereas further decreases produce unrealistic scattering behavior at grazing incidence,
illustrated by case (c).
While considering R-factor calculations along a single azimuth provides some insight into which
simulations best fit the experimental data, incorporating a larger data set improves the accuracy of
the fitting procedure dramatically [3]. A complete R-factor comparison for a range of screening
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 11
length scaling factors appears in Fig. 5. Here we have compared experimental and simulated
scattering signals along 18 azimuths on the crystal surface for 8 different screening lengths. The
best fit between the experiment and model is indicated by the lowest R-factor value, which in this
case corresponds to f=0.85 and represents a fairly mild correction to the potential. (Further
refinement of this estimate could be obtained by considering a series of additional screening
lengths close to this value.) It is worth comparing this result with the findings of O’Connor and
Biersack [20], who performed a detailed evaluation of the Molière potential. Based on potential
calculations and experimental data for a wide range of ion-target combinations, the authors suggest
the following generalized correction to the screening length for the Molière potential:
where μ=0.045 and β=0.54. For specific case of Ne+→Al, fopt=0.84, which is comparable to the value
obtained through our analysis.
V. Concluding remarks
We have demonstrated how the Ne-Al interatomic potential can be calibrated using low energy
scattering maps. The basic procedure involves first using LEIS to collect ion signals over a wide
range of shadowing geometries. In this specific case we considered the model system 3 keV
Ne+→Al(111). Using MARLOWE allowed us to efficiently simulate scattering for different potential
screening lengths, and R-factor analyses made it possible to accurately compare these results with
the experimental data. For the Molière potential, a mild correction to the screening length provides
the best match with the experimental data.
When confronted with the task of modeling low energy ion scattering from surfaces, several
different options are available. The ZBL fit or Molière potential (coupled with O’Connor and
Biersack’s correction factor) are known to work well for many ion-target combinations, and could
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 12
generally be expected to provide a satisfactory first approximation to the scattering potential.
However, if one wishes to calibrate the interatomic potential for a particular surface, the R-factor
analysis we describe here appears to be a reasonable approach. The R-factor analysis avoids many
of the problems associated with calibrating potentials based upon a more rudimentary shadow
cone analysis, where maxima in scattering intensity do not necessarily correlate well with the
conditions where shadow cones intersect neighboring atoms. With this in mind, application of the
analysis techniques described in this paper to more complex systems (including adsorbates)
appears particularly promising.
Acknowledgements
We express our appreciation to Dorian Balch, Rion Causey, Dean Buchenauer, and William
Wampler for helpful discussions regarding this work. Sandia is a multiprogram laboratory
operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of
Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.
References
[1] W. Eckstein and R. Bastasz, Nucl. Instrum. Meth. B 29 (1988) 603.
[2] H. Niehus, W. Heiland, and E. Taglauer, Surf. Sci. Rep. 17 (1993) 213.
[3] R. D. Kolasinski, J. A. Whaley, and R. Bastasz, Phys. Rev. B 79 (2009) 075416.
[4] R. G. Agostino, R. Aebi, J. Osterwalder, J. Hayoz, and L. Schlapbach, Surf. Sci. 384 (1997) 36.
[5] R. Stumpf, Phys. Rev. Lett. 78 (1997) 4454.
[6] E.P. Go, K. Thuermer, J.E. Reutt-Robey, Surf. Sci. 437 (1999) 377.
[7] H. Brune, J. Wintterlin, J. Trost, G. Ertl, J. Wiechers, and R.J. Behm, J. Chem. Phys. 99 (1993)
2128.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 13
[8] M. T. Robinson, Phys. Rev. B 40 (1989) 10717.
[9] W. Eckstein, Computer Simulations of Ion-Solid Interactions (Springer-Verlag, Berlin, 1991).
[10] R. Souda, K. Yamamoto, W. Hayami, T. Aizawa, and Y. Ishizawa, Surf. Sci. 363 (1996) 139.
[11] F. Ascione, G. Manico, A. Bonanno, A. Oliva, F. Xu, Surf. Sci. 394 (1997) L145.
[12] M.J. Gordon, J. Mace, K. P. Giapis, Phys. Rev. A 72 (2005) 012904.
[13] V. Bykov, L. Houssiau, and J.W. Rabalais, J. Phys. Chem. B 104 (2000) 6340.
[14] G. Molière, Z. Naturforsch A2 (1947) 133.
[15] O.B. Firsov, JETP 5 (1957) 1192.
[16] O.S. Oen, Surf. Sci. 131 (1983) L407.
[17] J.V. Barth, H. Brune, B. Fischer, J. Weckesser, and K. Kern, Phys. Rev. Lett. 84 (2000) 8.
[18] D.M. Danailov, D.J. O’Connor, and K.J. Snowdon, Surf. Sci. 347 (1996) 215.
[19] J.F. Ziegler, J.P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids
(Pergamon, New York, 1985).
[20] D.J. O’Connor and J.P. Biersack, Nucl. Instrum. Meth. B 15 (1986) 14.
Figure Captions
Fig. 1: Schematic of LEIS scattering geometry, illustrating the angle of incidence (α),
observation angle (θ) and azimuth (φ). Note that φ=0° has been aligned with the <100> close-
packed surface directions.
Fig. 2: Ion energy spectra for 3 keV Ne+→Al(111) at scattering angles of θ=45° (a) and θ=30°
(b). Peaks due to in-line single (s) and double (ss) scattering are indicated for both Ne+ and
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18th International Workshop on Inelastic Ion-Surface Collisions (IISC-18) / R. D. Kolasinski 14
Ne2+ (++). In panel (b), the location of a peak due to recoiling hydrogen (r) is also noted. Note
that we have used a logarithmic scale to emphasize the location of the H(r) peak in case (b).
Fig. 3: Experimental (a) and simulated (b) ion scattering maps for the Al(111) surface. All
measurements were obtained at an observation angle of θ=30°. Overlay: red lines indicate
shadow line positions, circular markers indicate atom positions. Atoms indicated in light blue
contribute to the scattering intensity; dark blue indicates a given atom is shadowed from the
incident beam.
Fig. 4: Polar scans along the <100> direction on Al(111), where the incidence angle (α) has
been transformed to a real-space distance along the surface (d). Case (a) shows experimental
ARIES data, whereas cases (b-d) are MARLOWE calculations for different screening lengths.
The dashed line indicates the error term at each point.
Fig. 5: Comparison of R-factors for a range of screening length scaling factors. (The curve is
intended only to guide the eye.)
Response to referee comments
R. Kolasinski
12 November 2010
We appreciate the fast response of the referee, along with the insightful comments. To address the
concern about damage to the crystal surface, we considered the surface diffusion mechanism
suggested by the referee. We found published values for activation energies for Al adatom
migration on different crystal surface planes in a review paper by Kellogg [Surf. Sci. Rep. 21 (1994)
1]. Assuming the diffusion exhibits Arrhenius-type behavior, the diffusion coefficient will be:
For most Al surfaces, a pre-factor of D0=10-3 cm2/s and diffusion activation energy of Ed≈0.43 eV are
typical. This value of Ed is based upon field ion microscope measurement and estimated from an
“onset” temperature, where surface migration is first visible. Onset for single atom migration on
Al(110) has been observed at T≈154 K, and the Al(111) surface appears to be a special case where
the migration activation energy is especially low [Barth, Phys. Rev. Lett. 84 (2000) 1732]. In any
case, these data show atom migration (and therefore some level of reordering) at room
temperature is possible. Of course, these values may change depending on the presence of steps or
other surface effects.
Another explanation is that the sputtering rate of the material is sufficiently fast so as to prevent
damage accumulation in the material. The referee mentions that, assuming a sputtering yield of 1,
the incident beam wears away 100 monolayers of surface material. However, for the grazing angles
of incidence considered in this study, most of the surface damage will be concentrated in the first
15 monolayers or so. The shallow depth of damage makes it easier for the incident beam to sputter
away regions of the surface which contain damage.
An additional possibility as to why surface damage effects are not observed is that LEIS is just not
very sensitive to surface damage. Scattering from atoms in non-crystalline regions should only add
a uniform background rather than destroy the structural variation in intensity generated by
scattering from the crystalline portions. If the signal carries structural information in direct
proportion to the number of surface atoms existing in locally ordered areas, then structural
information could be obtained even on a significantly damaged surface.
We do not have enough information to definitively claim which of these mechanisms predominates,
and an in-depth discussion of each is probably beyond the scope of this work. However, we
reorganized the discussion of surface damage at the end of Section 3, bringing the above points to
the reader’s attention.
Finally, we emphasize that the methods applied here could also be implemented in a time-of-flight
detection system (using an MCP detector), which would reduce the needed dose by orders of
magnitude. This would make acquiring the maps essentially “dose-free”, thereby circumventing
some of the limitations of our ESA setup.
*Response to Reviewers