Measurements Of Electronic Stopping Power Of Swift
Heavy Ions
Yanwen Zhang and Göran Possnert
Division of Ion Physics, Ångström Laboratory, Uppsala, Sweden
Abstract. High-precision measurement of heavy ion stopping power is becoming increasingly important, as
stopping power is a critical parameter in a multitude of applications. Recent experimental approaches are
reviewed with a focus on an analysis procedure that employs time of flight spectrometry to determine energy
loss using standard elastic recoil detection analysis geometry. This procedure eliminates the calibration
problem for Si detectors when used with heavy ions and, therefore, improves the accuracy associated with
simultaneous measurements of the electronic stopping powers of a continuous energy spectrum. This
approach is demonstrated by measuring the stopping powers of a number of heavy ions in amorphous targets
over a continuous range of energies with an absolute uncertainty of less than 3%. The results exhibit good
agreement with limited existing data but indicate some deviations from the predicted theoretical values.
INTRODUCTION
EXPERIMENTAL
With rapidly expanding applications of swift heavy
ions in ion beam analysis, materials modification,
device fabrication, and radiation therapy, heavy-ion
stopping in matter is attracting renewed interest.1-10
Due to lack of experimental data, theoretical values
extrapolate analytically from higher or lower energy
data. Accurate experimental data on energy loss and
stopping powers for swift heavy ions are, therefore,
highly desired to improve predictive theory.
Silicon p-i-n diode energy detector
Removable stopping foil
Carbon foil time detectors
L
φ
Experimental study of the stopping power using
Time of Flight (ToF) techniques can be traced back to
the 1970s.11,12 A significant advantage is achieved
recently to simultaneously measure the stopping
powers over the continuous range of energies, rather
than single energy, and several groups are employing
different techniques (e.g., recoil of atoms, scattering
target) to produce a broad continuous range of particle
energies.5-8 The present paper employs an approach,6
which takes advantage of the continuous energy
spectra, to determine energy loss in the stopping
medium based on ToF data in the ToF-E ERDA
configuration. The precision of obtained stopping data
is demonstrated by a number of heavy ions in
amorphous C, Al and Au.
Sample
θ2
Collimator
θ1
Ion
Vacuum
FIGURE 1. Schematic illustration of the experimental
configuration.
A modified ToF-E ERDA set-up, as shown in Fig.
1, was utilized for the stopping measurements. The
system consists of two carbon-foil time detectors
separated by a 437.5mm flight length (LToF) that is
followed by a Si p-i-n charged particle detector.5
Stopping foils, 101 µg cm-2 C, 150 µg cm-2 Al and 300
µg cm-2 Au, were mounted on a push-rod that can be
reproducibly moved into and out of the ion path
between the second time detector and the Si detector.
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
90
ToF (channel)
8000
Br in C
Without
foil
6000
RESULTS AND DISCUSSION
Without foil
T2
Figure 2 shows the ToF versus energy diagram of
Br particles that are registered in the ToF-E system
with and without the amorphous carbon stopping foil.
A schematic illustration of the analysis procedure is
shown as an insert. The energy of individual recoils
prior to impingement on the stopping foil, Ein, is
determined using the ToF data, T1(ch) from the lower
curve shown as an insert in Fig. 2(a). The exit
energies, Eout, is determined from the corresponding
ToF data without the stopping foil present, T2(ch) from
the upper curve in Fig. 2(a), based on particles that
have been tagged as having the same signal response,
E, in the Si detector as those passing through the
stopping foil in the lower curve. Taking M as the
particle mass, the impinging and exit energies (keV)
are given by:
With foil
T1
E
4000
(a)
With foil
2000
0
2000
4000
6000
Electronic energy loss (keV)
Energy (channel)
5000
Br in C
4000
3000
2000
(b)
1000
0
10000
20000
30000
Energy (keV)
Ein (keV ) =
40000
2
1
L
M ×  ToF 
T1 

2
dE/dx (MeV/(mg cm-2))
60
50
Eout (keV ) =
Br in C
40
(1)
2
1
L
M ×  ToF 
T2 

2
(2)
30
20
SRIM
This study
database
10
0
10
100
6
Be in C
(c)
4
1000
Energy (keV/nucleon)
2
FIGURE 2. (a) The time versus energy spectra of Br ions
with (lower curve) and without (upper curve) the carbon
stopping foil. The data analysis procedure is illustrated
schematically as an insert. (b) The energy loss data of Br in
C determined from the two ToF-E curves of (a) together with
the trend line (white dashed line). (c) Comparisons of the
stopping powers of Br (dashed lines) with the literature
values (diamonds), as well as the SRIM predictions (solid
lines).
dE/dx (MeV/(mg cm-2))
0
The Uppsala 6 MV EN-tandem van de Graaff
accelerator was used to produce 48 MeV 79Br8+ ions as
projectile beams. Elemental bulk samples and simple
compounds were used as targets to create broad range
of energetic target recoils (Be, C, N, O and Si). Bulk
Au was used to forward scattered Br ions. Target
recoils and scattered projectiles were detected with the
stopping foil both in and out in a forward direction at
φ = 43.5° to the primary beam direction. The data
analysis procedure is described using Br in amorphous
C, which illustrates the general behavior for the other
ions.
Be in Al
3
2
1
0
Be in Au
1.0
0.5
0.0
10
SRIM
This study
database
100
1000
Energy (keV/nucleon)
FIGURE 3. Comparisons of the stopping powers of Be in C,
Al and Au with the literature values taken from the H. Paul’s
database, as well as the SRIM predictions.
91
cm-2) of the second time detector that produced the
same pulse height, E, in the Si detector with and
without the stopping foil. The stopping data shown in
Fig. 2(c) for Br in carbon provide new data on the low
energy side are in reasonable agreement with other
experimental values and the SRIM values.
The mean energy loss versus the mean energy for
Br in C is shown in Fig. 2(b). The width of the energyloss distribution is associated with the energy
straggling in the stopping foil, counting statistic, the
energy resolution of the detectors, as well as the foil
thickness variation. The total error (<3%) arises from
the uncertainties in the stopping foil thickness (2%),
the finite resolution of the Si detector (<1%) and the
ToF spectrometer (<1%). It is found that the mean
energy loss is described well over the range of
energies in the present study by fitting to a sixth order
polynomial as indicated in Fig. 2(b).
The stopping power of heavy ions of Be, C, O, and
Si in amorphous C, Al and Au have been studied.
Summaries of the experimental data are shown in Figs.
3-6, using the fitted trend lines from a sixth order
polynomial regression. Also included in Figs. 3-6 are
the calculations from SRIM200013 and other literature
data.14
10
C in C
8
15
6
12
4
9
2
6
O in C
5
3
C in Al
0
dE/dx (MeV/(mg cm-2))
dE/dx (MeV/(mg cm-2))
0
4
3
2
1
0
C in Au
1.5
4
2
0
O in Au
1.0
2
SRIM
This study
database
0.5
0.0
10
100
1
0
10
energy, E , are obtained by scaling to the stopping foil
thickness (∆x):
) (
The stopping data shown in Fig. 3 for Be provides
new data not previously available. The stopping data
in C are in good agreement with the SRIM predictions.
However, some deviations can be observed for the
stopping data in Al and Au. The stopping power of C
ions is relatively well studied, and more data exist for
comparison in the energy region studied as shown in
Fig. 4. The mean stopping powers are in agreement
with the available literature data. The SRIM
predictions are also in good agreement with the results
of this study. The deviation up to 10% in some region
is, however, obvious. In the case of O ions, the
literature data are quite scattered and do not agree to
)
d E Ein − ∆E foil in − Eout − ∆E foil out
(3)
=
dx
∆x
Ein + Eout − ∆E foil in − ∆E foil out
2
1000
FIGURE 5. Comparisons of the stopping powers of O in C,
Al and Au with the literature values taken from the H. Paul’s
database, as well as the SRIM predictions.
The mean stopping power, d E / dx , and the mean
(
100
Energy (keV/nucleon)
FIGURE 4. Comparisons of the stopping powers of C in C,
Al and Au with the literature values taken from the H. Paul’s
database, as well as the SRIM predictions.
The parameters,
SRIM
This study
database
1000
Energy (keV/nucleon)
E=
O in Al
6
(4)
∆E foil in and ∆E foil out , are the
energy-loss of the particles in the carbon foil (5 µg
92
each other within the stated experimental uncertainty.
Furthermore, the data are not always in agreement
with SRIM2000 predictions. As shown in Fig. 5, the
stopping data from this study are in reasonable
agreement with other experimental values, but higher
than the SRIM predictions around stopping peak. The
Si data shown in Fig. 6 are in reasonable agreement
between the present data, other experimental data and
the values determined by SRIM2000 in the limited
energy region covered by this study. The stopping
power of Si in C is determined for the first time over
most of the energy region. There is a tendency for
faster increases in the stopping power with increasing
particle energies for Si in Au compared to the SRIM
prediction.
ACKNOWLEDGMENTS
We are grateful to the staff at the tandem
accelerator laboratory for always keeping the machine
ready to go. We are also thankful to Prof. Harry J.
Whitlow and Erik Langereis for helping with some of
the measurements.
REFERENCES
24
20
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P. Sigmund and A. Schinner, Nucl. Instr. and Meth. B195
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Si in C
16
12
8
4
dE/dx (MeV/(mg cm-2))
0
Si in Al
12
8
4
0
5
Si in Au
4
3
2
SRIM
This study
database
1
0
10
100
1000
Energy (keV/nucleon)
FIGURE 6. Comparisons of the stopping powers of Si in C,
Al and Au with the literature values taken from the H. Paul’s
database, as well as the SRIM predictions.
CONCLUSIONS
The method, based on ToF data, is an effective way
for determining the stopping power of a wide range of
elements over a broad continuous energy regime. This
approach eliminates much of the problems of the
nonlinear response resulting from the Si detector
calibration and improves the precision of stopping
power measurements.
14
93
H. Paul, Stopping Power for Light Ions; Collection of
Graphs, Data and Comments. http://www.uni-inz.ac.at/
fak/TNF/atomphys/STOPPING/welcome.htm.