The Paths of Plurally Scattered Ions in Heavy Ion Elastic
Recoil Detection Analysis
R.D. Franich, P.N. Johnston, I.F. Bubb
Department of Applied Physics, Royal Melbourne Institute of Technology, GPO Box 2476V, Melbourne 3001,
Australia.
Abstract. HIERDA spectra are complicated by the pronounced broadening and tailing effects that arise from the
frequent plural and multiple scattering undergone by swift heavy ions in solids. The quantitative evaluation of these
spectra is dependent on a clear understanding of the contribution of plurally scattered ions. A TRIM based Monte Carlo
ion transport code has been shown to reproduce all features of HIERDA spectra and is used here to study the ion paths.
The large number of scattering events that each ion undertakes makes the handling of the full scattering histories
unwieldy, but the second and subsequent largest scattering angles from individual ion paths may be used to characterise
plural scattering. The paths of scattered incident ions and recoiled target atoms have been modelled for 60 MeV I ions
incident on Au, as well as other projectile-target combinations. The plural and multiple scattering contributions to
HIERDA spectra are quantified and frequency distributions of large deflection scattering events are presented.
Simulation results are compared with experimental measurements conducted on the ToF-E HIERDA facility at Lucas
Heights.
small deflections along its path. Multiple scattering is
well described by the theory of Sigmund and
Winterbon [1] and the resultant spectrum broadening
effects are satisfactorily incorporated into several
analytical simulation codes such as RUMP. The output
spectra of techniques such as Heavy Ion Elastic Recoil
Detection Analysis (HIERDA) contain a significant
contribution from plurally scattered ions and recoil
atoms [2-4]. The analysis of these spectra is critically
dependent upon their accurate simulation and requires
a quantitative understanding of the plural scattering
contribution to the spectra.
INTRODUCTION
Ion beam analysis techniques using energetic heavy
ions are becoming more widely used for depth
profiling of thin layered structures and near surface
regions. The high scattering cross sections of heavy
ions, while responsible for enhancing sensitivity, also
reduce the probing depth of the beam. Probing depth is
recovered by increasing the incident beam energy. The
high cross section results in a higher probability of an
ion having more than one significant scattering event
in the sample. Ions reaching the detector following two
or more large direction changes in the sample are
termed plurally scattered. The detected energy of these
ions will generally not be simply related to their origin
within the sample. Energy lost to elastic collisions may
indicate a deeper origin if assumed to be electronic
stopping. It is also possible for plurally scattered ions
to be detected with higher energy than would result
from a single scatter occurring in the surface
monolayer.
To study plural scattering, we have developed a
Monte Carlo (MC) HIERDA spectrum simulation
program [4] based on a fast FORTRAN version of the
well known TRIM ion transport code [5]. The program
allows for the identification of plurally scattered ions
and recoiled atoms, and enables their contribution to
the output spectra to be isolated and quantified. A
record is kept of the number and magnitude of
significant direction changes in the scattering history
of all ions reaching the detector. This information is
used to characterise the paths of plurally scattered
counts contributing to the output spectra.
Plural scattering is here distinguished from the
multiple scattering process by which the direction of
an ion is continuously changed by a series of very
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
385
substrate does not contribute to the output spectra for
this experimental configuration [3].
EXPERIMENT
All simulation outputs have been compared with
experimental measurements conducted on the
ANTARES 8 MV FN Tandem Accelerator at the
Lucas Heights Research Laboratories of the Australian
Nuclear Science and Technology Organisation. This
HIERDA facility employs a TOF-E detector telescope
with a flight path length of 495mm between C timing
foils of 25.3 µg/cm2 as described in [6]. The detector
is positioned at a scattering angle of 45˚ to the incident
beam direction.
The output file of atoms scattered and recoiled
from the target is post-processed to simulate detection
by a virtual TOF-E telescope with an enlarged
acceptance angle to improve efficiency [2,3]. Energy
loss in the timing foils is accounted for and time
spectra are generated using the bin width and offset
obtained from the experimental calibration.
Recorded with the species, direction, and energy of
each detected ion is a list of the 10 largest direction
changes in its scattering history. The history of a
recoiled target atom incorporates the incident ion’s
history prior to generation of the recoil.
The samples were (i) a well characterised 60 nm
Au layer on a Si substrate irradiated at 67.5˚ to the
surface normal and (ii) a 91.3/326 nm Ta2O5 layer on
Si manufactured at KRISS1 irradiated at 65˚. Incident
beams used were 40, 60, 77, and 97.5 MeV 127I.
RESULTS
Time spectra were extracted from the experimental
data using PAW and a purpose written code developed
at RMIT. Time of flight spectra are used as they
exhibit better depth resolution than the energy spectra
[7] and are readily calibrated using a simple direct
calibration procedure [6].
Figure 1 shows a frequency distribution of the
largest and 2nd, 3rd, 4th and 10th largest direction
change for each scattered I ion and recoiled Au atom
reaching the detector.
100
(a)
2nd largest scatter
SIMULATION
detected ions (%)
10
The simulated HIERDA spectra are generated
using a program based on the TRIM Monte Carlo ion
transport code. The advantage of MC modelling is that
the simulated paths of individual ions are known.
Analytical techniques attempt to predict the statistical
distribution of ion paths and energies. However it is
the atypical ion paths which include plural scattering
events that give rise to many of the characteristic
features in the HIERDA spectrum. MC modelling of
heavy ion recoil spectrometry is only viable subject to
substantial improvements in efficiency described
previously [4] designed to reduce the amount of time
spent processing ion and recoil paths which will not
result in detector events. The secondary particle
enhancement technique used by Arstila [8] is not
employed here, so that the scattered ion spectra may
also be generated and are in turn used to normalise the
output to experimental data. The 60 nm Au layer is
modelled as 75 nm to correct for a deficiency in
theoretical stopping power [2,4]. To improve
efficiency, only the first 10 nm of the Si substrate is
modelled as it has been shown previously that the
1
Largest scatter
3rd
"
"
4th
"
"
10th
"
"
1
0.1
0.01
0
10
20
30
40
50
60
70
80
90
angle (degrees)
100
Largest scatter
2nd largest scatter
(b)
3rd
detected recoils (%)
10
"
"
4th "
10th "
"
"
1
0.1
0.01
0
10
20
30
40
50
angle (degrees)
60
70
80
90
FIGURE 1. Angular distribution of the Largest and 2nd, 3rd,
4th, and 10th largest scattering deflections in the paths of (a)
scattered 60 MeV I ions and (b) recoiled Au atoms.
Korean Research Institute of Standards and Science
386
The distribution of largest deflections shows the
expected single scattering distribution around 45˚,
broadened by the small angular contribution from
multiple scattering. Also present is the distribution
below 40˚ and the long tail beyond 50˚ corresponding
to the plurally scattered counts. The distribution of
second largest deflections exhibits a long tail
extending beyond 60˚ and a local maximum near 20˚.
This local maximum together with the corresponding
feature in the largest scatter data, describe the double
scatters – those having two nearly equal deflections to
reach the detector. The product of kinematic factors
for these two events is greater than that for a single 45˚
scatter, and the ions are detected with an energy
greater than that from a single scatter occurring in the
surface layer. This gives rise to the characteristic high
energy ‘knee’ on the surface edge of the HIERDA
spectrum. The separation of these two local maxima is
due to there being a pair of events, the larger of which
is counted in the first distribution.
The isolation of plurally scattered counts requires
the choice of a threshold value of the second largest
deflection angle, beyond which the ion will be deemed
plurally scattered. The distinction is somewhat
arbitrary, and constitutes the differentiation between
large angle plural and small angle multiple scattering.
The small angle end of the second largest deflection
data corresponds to those counts whose largest
direction change was near 45˚. The half-height of this
edge is approximately at 3˚, and this is chosen to
denote a plural scatter
Figure 2 shows the simulated output spectra with
separated contributions from ions that have had n=1, 2,
…,5 scatters greater than 3˚. The single scattered data
sets, i.e. n=1, show the shape of the spectra that would
be generated by a conventional analytical ‘slab’
analysis technique with only a multiple scattering
correction applied. The high energy (i.e. low ToF)
double scatter feature and the plural scatter tailing
would not be predicted. There is also a plural
scattering contribution to the yield in the main body of
the spectrum which is not easily seen due to the log
scale.
Figure 1(b) shows similar distributions for the
recoiled Au data although the double scattering is not
well defined and the single scattering peak is skewed
substantially towards larger angles.
10000
10000
5 scatters > 3 deg
(a)
"
3
"
"
4
"
"
5
"
3
"
2
1
1000
100
10
1
100
10
1
0.1
0.1
60
70
80
90
100
60
Time of Flight (ns)
70
80
90
100
Time of Flight (ns)
10000
10000
5 scatters > 3 deg
(b)
1000
1 scatter > 3 deg
(b)
2
"
3
"
"
4
"
"
5
"
4
"
3
"
2
1
1000
100
counts
counts
1 scatter > 3 deg
(a)
2
"
counts
counts
1000
4
10
1
100
10
1
0.1
0.1
80
90
100
110
120
130
140
80
Time of Flight (ns)
90
100
110
120
130
140
Time of Flight (ns)
FIGURE 2. Simulated spectra showing contributions to
spectral shape from ions having 1, 2, …,5 scattering events
for (a) scattered 60 MeV I ions and (b) recoiled Au atoms.
FIGURE 3. Simulated spectra showing ToF distributions of
ions having 1, 2, …,5 scattering events for (a) scattered 60
MeV I ions and (b) recoiled Au atoms.
387
Figure 3 shows the same data re-ordered to show
this contribution and the Time of Flight distributions
of the plurally scattered ions. Analytical simulations
are unlikely to correctly predict the total yield
throughout the spectrum if plural scattering is not
accounted for.
deflections in the scattering history of each ion
reaching the detector are recorded and used to
characterize the paths. The contribution to the output
spectra of plurally scattered ions may be separated and
quantified subject to a definition of large angle
scattering. This contribution may be segregated into
those ions having 2,3,4,… etc events.
Figure 4 illustrates the varying degrees of
complexity of the paths of plurally scattered ions
reaching the detector. The 10 largest scattering angles
are shown for each of 100 randomly chosen ion
histories. Each curve represents the data for a single
ion. The majority of paths resemble our idealisation of
a singly scattered ion, having a 45˚ scatter with the
remainder of the path slightly perturbed by the
multiple scattering process. The point P marks the
plural scattering condition i.e. a second direction
change of 3˚ or greater. The curves which pass above
P are the plurally scattered paths. There are 28 such
curves in this sample. Several of these appear as
double scatters having the third and subsequent events
down in the small angle multiple scattering region.
Most exhibit a complex plural scattering history with
some having up to 10 or more significant direction
changes. In the simulated spectra shown in figures 2
and 3, 27% of scattered I ions detected with a Time of
Flight < 100 ns, and 40 % of recoiled Au atoms having
a ToF < 140 ns, satisfied the 3˚ plural scattering
condition.
The degree of complexity of plural scattered paths
leading to the detector has been shown for a simple
case of a thin layer of Au on Si, analysed with a 60
MeV I beam. There is a significant number of plurally
scattered ions reaching the detector, and their paths
frequently have several large deflections, with some
observed having up to 10 deflections greater than 3˚.
Future work in this area will include an analysis of
the effectiveness of simulation methods which include
a double scattering correction to improve the
correlation with experimental output.
ACKNOWLEDGMENTS
This work is supported by the Australian Institute
of Nuclear Science and Engineering.
REFERENCES
deflection angle (degrees)
50
1. P. Sigmund and K.B. Winterbon, Nuclear Instruments
and Methods 119, 541-547 (1974).
40
2. P.N. Johnston, I.F. Bubb, M. El Bouanani, D.D. Cohen
and N. Dytlewski, AIP Conf. Proc. 475, AIP Press, New
York (1999), Ed. J.L. Duggan and I.L. Morgan, p.517.
30
3. P.N. Johnston, R.D. Franich, I.F. Bubb M. El Bouanani,
D.D. Cohen, N. Dytlewski, R. Siegele, Nucl. Instr. and
Meth.B 161-163, 314-317 (2000).
20
10
4. R. D. Franich, P. N. Johnston, I. F. Bubb, N. Dytlewski,
D.D. Cohen, Nucl. Instr. and Meth.B 190 , 252 (2002).
P
0
1
2
3
4
5
6
7
8
9
10
th
n largest scatter
5. J.F. Ziegler, J.P. Biersack, and U. Littmark, Stopping and
Range of Ions in Solids, Published by Pergamon Press,
New York, NY, USA, ISBN 0 08 021603 X (1985).
FIGURE 4. The 10 largest scattering angles in the paths of
100 randomly selected ions reaching the detector. The point
P indicates the plural scattering condition of a second scatter
greater than 3˚.
6. W.B. Stannard, P.N. Johnston, S.R. Walker, I.F. Bubb,
J.F. Scott, D.D. Cohen, N. Dytlewski, J.W. Martin, Nucl.
Instr. and Meth.B 99, 447-449 (1995).
CONCLUSION
7. P. N. Johnston, M. El Bouanani, W. B. Stannard , I.F.
Bubb, D.D. Cohen, N. Dytlewski, R. Siegele, Nucl. Instr.
and Meth.B 136-138, 669-673 (1998).
We have developed a Monte Carlo code for the
simulation of HIERDA spectra which allows for the
analysis of the plural scattering contribution to the
output spectra. The magnitudes of the largest angular
8. K. Arstila, T. Sajavaara, and J. Keinonen, Nucl. Instr.
and Meth.B 174, 163-172 (2001).
388