high-precision measurement of electronic stopping powers for heavy ions using high-resolution...

High-precision measurement of electronic stopping powersfor heavy ions using high-resolution time-of-flight

spectrometry

Yanwen Zhang *

Division of Ion Physics, �AAngstr€oom Laboratory, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden

Received 14 March 2002

Abstract

A new technical and analysis approach based on using time-of-flight (ToF) to determine energy loss has been de-

veloped and used to improve the precision of measuring heavy-ion electronic stopping powers from a continuous energy

spectrum of particles provided by a typical elastic recoil detection analysis geometry. The particle energies entering and

exiting the stopping foil are determined using ToF spectrometry data, with and without the stopping foil. The Si de-

tector is only used to tag identical energies and screen out the extraneous components from the spectrum. This ap-

proach, which is applicable to continuous energy measurements, eliminates the well-known calibration problem of Si

detectors associated with heavy ions that is shown to lead to a clear deviation in the measured stopping power.

Consequently, the stopping powers and the energy dependence are determined with higher precision. In this study, the

stopping powers of a number of heavy ions (3P atomic number6 53) in amorphous C, Al and Au have been deter-

mined with an absolute uncertainty of less than 2.5%. In some energy regimes, data are provided for the first time. In

other energy ranges, the present data exhibit good agreement with most existing data. SRIM stopping power values

show a reasonable agreement with experimental data in most cases; however, some deviations from the measured

values, up to 15%, are observed around stopping maximum.

� 2002 Elsevier Science B.V. All rights reserved.

PACS: 61.85; 34.50.Bw; 29.40.Wk; 29.30.Ep

Keywords: Energy-loss; Stopping power; Elastic recoil detection analysis; Time of flight; Si detector

1. Introduction

With rapidly expanding applications in ion-

beam-based materials analysis, materials modifica-

tion, device fabrication, implantation technology,

nuclear physics, radiation damage and radiation

therapy, heavy-ion stopping in matter is currently

attracting renewed interest [1–15]. For many ions,

no stopping power data exist for many energy re-

gimes of interest, and theoretical values come from

an extrapolation of analytical fits of higher or lower

energy data. Available theories produce stop-

ping powers with varying levels of agreement withexperimental data. In some cases, widely used

Nuclear Instruments and Methods in Physics Research B 196 (2002) 1–15

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E-mail address: [email protected] (Y. Zhang).

0168-583X/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0168-583X(02 )01246-6

mail to: [email protected]

stopping power predictions are in error, e.g. Li [3].

An improved predictive theory is highly desired,

but advances in theory demand accurate experi-

mental data on energy loss and stopping powers forswift heavy ions, which makes this a important area

for renewed research [8–15].

Experimental study of the stopping power using

time-of-flight (ToF) techniques can be traced back

to the 1970s [16,17]. The standard ToF approach is

to directly measure the energy loss of monoener-

getic particles with a ToF spectrometry that is

placed after the stopping medium [15–17]; such amethod provides only a single data point for each

energy and particle type. Moreover, as scattering

foils are normally used to divert the monoenergetic

beam, the energy spread of the primary beam, due

to straggling and modification of the scattering

foils, results in uncertainty in the energy of the

impinging monoenergetic ions. There can be a

significant advantage to measure stopping powersover a continuous range of energies, rather than

point by point, and several groups are employing

different techniques (e.g. recoil of atoms, scattering

target) to produce a broad continuous range of

particle energies and simultaneously measure the

stopping powers over the continuous range of

energies [8–11]. In a previous collaborative study

[8], a time-of-flight-energy elastic recoil detectionanalysis (ToF-E ERDA) set-up was modified to

simultaneously measure stopping powers of heavy

particles in the same area of the stopping me-

dium with a ToF spectrometry placed in front of

the stopping medium, and the energy loss of the

particles was measured over a continuous energy

range, which represented a significant advantage

over single-energy ion approaches. A similar ap-proach, but based on a scattering approach to

produce a continuous energy range of particles,

has been recently employed by a Finnish group

[11]. Since Si detectors, which exhibit considerable

error in measuring heavy-ion energies due to a

non-linear response [3,18–20], are generally used in

these and other approaches to measure the particle

energies exiting the stopping media [8,10–13], thestopping powers determined by these methods

have a comparable systematic error.

The present paper employs an approach [21],

which takes advantage of the continuous energy

spectra, to determine energy loss in the stopping

medium based only on ToF data in the ToF-E

ERDA configuration. This approach eliminates

much of the error resulting from the Si detectorsand improves the precision of stopping power

measurements. In this study, the stopping powers

of a number of heavy ions (3P atomic number

6 53) in amorphous C, Al and Au have been de-

termined. In some energy regimes, data are pro-

vided for the first time.

2. Experimental

2.1. Experimental setup

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 detec-

tors separated by a 437.5 mm flight length (LToF)that is followed by a Si p–i–n charged particle de-

tector with a collimator (8 mm in diameter) in front

of it [8]. Stopping foils are 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. Up to four foils can be loaded on

the push-rod, and the energy loss in each foil can be

measured separately. Moreover, the push-rod canbe rotated, so that the thickness of the stopping foil

can be increased [9] and any effect of channeling in

the crystalline foil can be circumvented.

The Uppsala 6 MV EN-tandem van de Graaff

accelerator was used to produce 50 MeV 127I10þ,

48 MeV 79Br8þ and 1.5–4.0 MeV 4Heþ ions as

projectile beams. Elemental bulk samples and

simple compounds were used as targets to create

Fig. 1. Schematic illustration of the experimental configura-

tion. The removable stopping foils can be reproducibly moved

into and out of the ion path and rotated from both directions.

2 Y. Zhang / Nucl. Instr. and Meth. in Phys. Res. B 196 (2002) 1–15

energetic target recoils, and bulk Au was used to

forward scattered the I and Br ions. Target recoils

and scattered projectiles were detected in a for-

ward direction at / ¼ 43:5� to the primary beamdirection with a wide energy distribution. It should

be stressed that the recoil and scattering processes

are only used to generate a secondary beam with a

large energy distribution but low intensity. In such

a way, direct beam exposure of the stopping foil is

avoided; the beam modification to the stopping

foil is, therefore, negligible. Ninety different ion

species (7Li, Be, 11B, C, N, O, F, Na, Mg, Al, Si,Cr, Mn, Fe, Co, Ni, Cu, Br and I) with a contin-

uous range of energies from a few tens to hundreds

keV per nucleon were produced. These ions were

recorded in the system with the stopping foil both

in and out. It is worth noting that most of parti-

cles, which have larger scattering angles after

penetrating the stopping foil, will not be registered

in the Si detector nor considered in the furtheranalysis. Therefore, the effect of low-probability,

large-angle energy-loss straggling in the stopping

foil is negligible. The data analysis procedure is

described using Br in amorphous C, which illus-

trates the general behavior for the other ions.

2.2. Data analysis procedure

Fig. 2(a) shows the time versus energy diagram

for the continuous energy range of Br particles that

are registered in the ToF-E system with and with-

out the amorphous carbon stopping foil (101

lg cm�2). A schematic illustration of the analysis

procedure is shown, as an insert, in the figure. In

the previous approach [8], only the lower curve was

obtained, and the impinging and exiting particleenergies were determined from the ToF data and

the Si detector, respectively. The novel aspect of the

present approach over the previous procedure [8] is

that, instead of using the Si detector, the ToF data

obtained without the stopping foil present is used

to determine the exit energies. As shown in Fig.

2(a), the energy of individual recoils prior to im-

pingement on the stopping foil, E1 is determinedusing the ToF data, T1(ch) from the lower curve,

and the exit energy is tagged by the Si detector as E

(channel). The exit energy, E2 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 de-

tector as those passing through the stopping foil in

the lower curve. Using the Si detector spectrum to

only tag identical energy with and without the

stopping foil present, allows the energy of theparticles exiting the stopping foil to be accurately

determined from the ToF data (without the stop-

ping foil). This approach is conceptually different

from another approach [11] that also uses contin-

uous ToF versus Si detector energy curves but in-

stead relies on spectrum fits and Si detector

calibration to determine the energy difference with

and without a stopping medium. The impingingand exit energies in keV are given by

Fig. 2. (a) The time (from ToF spectrometry) versus energy

(from Si detector) spectra of Br ions with (lower curve) and

without (upper curve) the carbon stopping foil (101 lg cm�2).

The insert is a schematic illustration for the data analysis pro-

cedure. (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) using the sixth-order polynomial fit (Eq. (8)).

Y. Zhang / Nucl. Instr. and Meth. in Phys. Res. B 196 (2002) 1–15 3

E1ðkeVÞ ¼1

2M ½LToF=T1ðnsÞ�2; ð1Þ

E2ðkeVÞ ¼1

2M ½LToF=T2ðnsÞ�2; ð2Þ

with

T ðnsÞ ¼ a1T ðchÞ þ a0; ð3Þwhere M is the particle mass, a1 and a0 are the time

calibration parameters. The time slope is measured

from a time calibration modular. In order to cali-

brate the time offset a0 the high-energy edge posi-

tions of different elements from the sample surface

are determined by fitting an error function to

the high-energy edge, Tedge(ch), (shortest time) inthe time spectra. The corresponding time in nano-

second for each element, Tedge(ns), is calculated as

TedgeðnsÞ ¼M1

2ðEedge � DEdetÞ

� �1=2

LToF; ð4Þ

where

Eedge ¼ E0

4M0M1

ðM0 þM1Þ2cos2 /; ð5Þ

E0 and M0 represent the energy and mass of the

primary ions from the accelerator, respectively, M1

is the recoil mass, and /ð¼ 43:5�Þ is the scatteringangle shown in Fig. 1. A correction DEdet for the

small energy-loss in the carbon foil of the first time

detector is applied. This is taken to be the product

of the foil thickness (5 lg cm�2) and the stopping

power from Ziegler et al�s SRIM2000.40 code

[22,23]. The time calibration parameters, a0 and a1were determined by Eqs. (3)–(5); the resulting a1has the same value as the measured time slope

from the time calibration modular, which shows

good system consistency.

The average energy loss in the stopping foil, DE,and the mean energy, E, is determined from Eqs.

(1) and (2) by

DE ¼ ðE1 � DEfoil inÞ � ðE2 � DEfoil outÞ; ð6Þ

E ¼ E1 þ E2 � DEfoil in � DEfoil out

2; ð7Þ

where E1 and E2 are the mean energy determined

from the mean ToF data for a certain response in

the Si detector (Fig. 2(a)). The parameters, DEfoil in

and DEfoil out, are the energy-loss of the particles in

the carbon foil (5 lg cm�2) of the second time de-tector that produce the same pulse height in the Si

detector with the stopping foil in and out.

The mean energy loss, DE, versus the mean en-

ergy, E, for Br in amorphous C (101 lg cm�2) is

shown in Fig. 2(b). The width of the energy-loss

distribution, which will not be considered further,

is associated with the energy straggling in the

stopping foil, counting statistic, the energy resolu-tion of the detectors, as well as the foil thickness

variation. The increased broadening of the stop-

ping data at higher energies is mainly attributed to

lower counting statistic. It is found that for all el-

ements, DE is described well over the range of en-

ergies in the present study by fitting the energy loss

(in keV) to a sixth-order polynomial in energy E,

DE ¼X6i¼0

kiEi: ð8Þ

The fitted trend line (white dashed line) for Br in C

data is indicated in Fig. 2(b). Since the registered

events for each element range from 105 to 2� 106

in the present study, the sixth-order polynomialregression as shown in Fig. 2(b) is used to repre-

sent the result over the corresponding energy re-

gion in the remainder of this paper.

The mean stopping power, dE=dx, is extracted

by scaling to the thickness, Dx, of the stopping foil

according to the expressions

dEdx

¼ DEDx

cos h

¼E1 � DEfoil in

� �� E2 � DEfoil out

� �Dx

cos h; ð9Þ

where h is the angle between the foil normal and theincoming beam. Several stopping foils with differ-

ent thickness (listed in Table 1) have been investi-

gated. The thickness, Dx, is determined, using the

same experimental configuration, by measuring the

energy loss of forward scattered He at the exact

position as the heavy-ion beam on the stopping

foils and comparing with the known stopping value

of alpha particles [23]. Measuring the stopping datawith the same ion species after several hours of ion-

beam irradiation is used to evaluate the effect of


beam modification to the stopping foils. No no-

ticeable effect of beam modification is detected;

thus, impact on stopping power measurements is

negligible. The small energy corrections, DEfoil in

and DEfoil out, due to different particle energies

passing through the second time detector are de-

termined by applying Eqs. (6)–(9) iteratively, be-

ginning where DEfoil in and DEfoil out are assumed tobe zero. The average ratios of the energy loss,

DEfoil in and DEfoil out, to the particle energies for

different stopping foil are also listed in Table 1, and

the ratios are on the order of 1%.

2.3. Experimental uncertainties

Discarding of the small corrections resultingfrom the different energy loss in the second time

detector, Eq. (10) can be rewritten:

dEdx

¼12M1L2

ToF1

Tfoil inðnsÞ

� �2� 1

Tfoil outðnsÞ

� �2� �Dx

cos h:

ð10ÞThe uncertainty in the mass stopping power is

d dEdx

� �dEdx

¼d 1

Tfoil inðnsÞ

� �2� 1

Tfoil outðnsÞ

� �2� �1

Tfoil inðnsÞ

� �2� 1

Tfoil outðnsÞ

� �20BB@

1CCA

226664

þ 2dLToF

LToF

� �2

þ dDxDx

� �2

37775

1=2

: ð11Þ

The main uncertainty of the mean energy loss, DE,is contributed from the uncertainties of energy E1

and E2 measured from the ToF in the currentsetup. A unique property of such a measurement is

that the systematic uncertainties in the energies

resulting from the ToF signals tend to, but not

completely, be cancelled out. The contributions to

the uncertainty of energy E1 and E2 are from time

calibration, geometrical variation of the flight

length, recoil angle due to the solid angle, beam

energy governed by the magnet calibration, andcounting statistic. Due to the higher scattering

cross section at lower energies (/ 1=E2) and the

large number of data points for each stopping

curve, the absolute error in the time spectrum,

dT (ch), resulting from statistical error ranges from

less than �1 to �3 ch, which results in uncertainty

<1% to the energy determination. The maximum

error is observed at the high-energy end of eachcurve. Since the slope of the time calibration (a1) ismeasured by the time calibration modular, it is

separated to the determination of the offset (a0).Taking all the variations into account, the contri-

bution of different uncertainties to the energy loss

is given by the following expressions:

d1

Tfoil inðnsÞ

� �2

¼ d1

a1Tfoil inðchÞ þ a0

� �2 !

¼2 Tfoil inðchÞda1ð Þ2 þ a1dT ðchÞð Þ2 þ da0ð Þ2h i1=2

a1Tfoil inðchÞ þ a0ð Þ3;

ð12Þ

d1

Tfoil outðnsÞ

� �2

¼2 Tfoil outðchÞda1ð Þ2 þ a1dT ðchÞð Þ2 þ da0ð Þ2h i1=2

a1Tfoil outðchÞ þ a0ð Þ3;

ð13Þ

where a1 � da1 ¼ 0:0480� 0:0001 ns/ch, a0 � da0 ¼ �3:13� 0:13 ns. The uncertainty in energy

loss from the ToF spectrometry is <1%, much

lower than the several percent associated with the

previous method [8], which employs Si detectorcalibration.

Assuming that the variation of the flight length

is 1 mm, the relative change in length is below

Table 1

The stopping foil thickness and the average ratio of the energy

loss when the particles pass through the thin carbon foil in the

second time detector

Foil Thickness

(lg cm�2)

DEfoil in=E1

(%)

DEfoil out=E2

(%)

C 101 <1.1 <1.1

C 167 <1.1 <1.2

Al 130 <0.96 <1.05

Al 150 <0.95 <1.04

Al 210 <0.96 <1.04

Al 240 <0.97 <1.05

Au 330 <1.01 <1.1


0.5%. From Eq. (11), the dominant contribution to

the total uncertainty arises from the uncertainty in

the stopping foil thickness, which is determined

from known stopping power of alpha particles. Ifit is assumed that the uncertainty in the alpha

stopping [23] is 2%, the total uncertainty (Eq.

(11)) from the foil thickness, the flight length and

the energy-loss determinations is <2.5%.

3. Results and discussions

3.1. Deviation of electronic stopping using Si

detector

The novel aspect of the present approach overthe previous procedure [8], as described recently

[21], is that, instead of using the Si detector in-

formation, the ToF data obtained without the

stopping foil is used to determine the exit energies.

In the previous procedure, the energy calibration

of the Si-detectors was established individually for

each element by fitting the energy in keV, E2(keV),

derived from the ToF (Eq. (2)) to the energy sig-nals E(ch) from the Si detector (Fig. 2(a)). As the

atomic number of particles increases, energy de-

tection becomes more problematic due to the pro-

gressive degradation of the resolution. The energy

response of the detector is affected by the surface

dead layer and non-ionizing processes [3,18–20]

which lead to a non-linear response of several

percent divergence in energy per channel for agiven particle. It was found that for light recoils

with Z1 6 7 and energies >200 keV per nucleon,

the data could be described by a linear relationship

[8] given by

E2ðkeVÞ ¼ b1EðchÞ þ b0: ð14ÞHowever, due to the non-linear response of the

Si detector for heavy recoils with Z1 P 8, a second-

order polynomial is needed, which is given by the

expression

E2ðkeVÞ ¼ b2EðchÞ2 þ b1EðchÞ þ b0: ð15ÞThe deviations of the measured data points from

the best-fits of Eqs. (14) and (15) for 27Al recoils

are shown in Fig. 3. The trends of the deviations

from the linear and polynomial fits are indicated as

white lines. Evaluation of the results in Fig. 3(a),

where Eq. (14) is applied, indicates that the devi-

ation occasionally exceeds 3% and the spread in

uncertainty is several percent. Moreover, the de-

viation indicates a strong trend (indicated by the

white line) that would result in additional systemicuncertainty in the energy-loss determination and

seriously modify the shape of the stopping power

curve and its energy dependence. This additional

trend could, however, be corrected to a certain

extent by using the second-order polynomial fit

(Eq. (15)) that is shown in Fig. 3(b). Although the

central trend of the deviations indicated by the

white line does not exceed by more than �0.5%,the spread in uncertainty for individual data points

is still several percent.

Using F and Si ions in amorphous C as exam-

ples, the stopping powers obtained by the present

procedure and the previous procedure [8], using

the same ERDA configuration and carbon foil

(101 lg cm�2), are shown in Fig. 4. Also included

are the literature data [24] and the results ob-tained from SRIM calculations [23]. In general, the

Fig. 3. Deviations of particle energy from the energy calibra-

tion of the Si detector based on (a) a linear (Eq. (14)) fit and (b)

a second-order polynomial (Eq. (15)) calibration.


experimental data agree well with SRIM predic-

tions. Most stopping values from the database lieon the low energy side. The stopping powers de-

termined from the previous procedure [8], where

the Si detector is used to measure the exit energy,

are considerably less than the present stopping

powers over much of the energy range because of

the particle-dependent non-linear calibration re-

sponse of the Si detector. The curvature of the

previous data in Fig. 4 is also attributed to thenon-linear response of the Si detector [19,20],

which was calibrated using a second-order poly-

nomial fit (Eq. (15)), shown as the white line in

Fig. 3(b). As the non-linear response of the de-

tector modifies the magnitude of the stopping

power curve, the energy dependence of the stop-

ping curve indicates a systematic error. The new

approach avoids the complexities of Si detectorcalibration that are associated with heavy ions

[3,19,20]. Since only the ToF signals, which have

much higher energy resolution compared to Si

detectors, are used to obtain the energy loss of ions

in the stopping foil, the stopping power and its

energy dependence are determined more accu-

rately. The new data procedure overcomes the

major difficulties with Si detectors in terms of (i)improved precision through dramatic reduction of

the uncertainty in the determination of exit energy,

(ii) insensitivity to irradiation-induced damage in

the Si detector and (iii) extended range of appli-

cation to lower energies, as the energy resolution

at low exit energies is much better for a ToF

measurement than with a Si detector. Further-

more, the uncertainty due to the carbon foil in thefirst time detector is eliminated. Likewise, as the

incident beam is composed of recoiled or scattered

particles with a relatively low beam density, the

modification of the stopping medium is negligible

[9]. As an additional benefit, the energy loss of

several elements can be measured simultaneously

with high precision using compound targets in the

ERDA geometry. As the ERDA is a well-estab-lished technique in most accelerator laboratories

and the measurement time for one stopping curve

is only about 30 min, similar type measurements

can be easily carried out for a large range of ion/

target combinations.

3.2. Analysis of raw data

Stopping data for Al ions in amorphous foils of

C, Al and Au over a continuous range of energies

are shown in Fig. 5. While only the results for a

single C or Au foil of given thickness are shown,

the results for four Al foils of different thickness

are provided to evaluate the effect of foil thickness.

Also included in Fig. 5 are other experimental data

taken from H. Paul�s database [24] and SRIM-2000 predictions [23]. The registered Al particles in

each plot shown in Fig. 5 are between 2 and

4� 105. The relative scatter of the data points is

representative of the general behavior of the

stopping data for the other ion species. Inspection

of the Al stopping data in Fig. 5 indicates that the

scatter in the data is relatively small due to the low

experimental errors.It is clear in Fig. 5 that for Al ions in amorphous

C (Al in C), the present data is higher than the

SRIM predictions, especially at energies from 220

to 460 keV per nucleon. The maximum deviation

Fig. 4. Comparison of the trend fits for the stopping power

data for F and Si ions in amorphous carbon (101 lg cm�2)

obtained from the ToF spectrometry (�) and the previous

procedure [8] (}). Also included the literature values (M) taken

from the H. Paul�s database as well as the SRIM predictions

(––).


of the SRIM values from the measured stopping

values is on the order of 5%. In the case of the

different Al stopping foils, similar stopping power

data and energy dependence for each thickness are

observed in Fig. 5. The effect of foil thickness isnegligible over energy range and foil thickness

studied. This observation holds for all other ion

species in the present study. The mean stopping

powers for Al in Al from this study are in good

agreement with the available literature data. The

SRIM predictions are, however, overestimated by

up to 8%. The stopping data for Al in Au, as

shown in Fig. 5, are in reasonable agreement withother experimental values and the SRIM values,

with the highest deviation being about 8% around

500 keV per nucleon.

3.3. Effect of target atomic number

The stopping cross section is a measure of the

mean energy loss of ions in various materials andis dependent on the density of the material. The

stopping cross sections for different targets,

therefore, change with the target atomic number,

Z2. The dependence of the electronic stopping

cross section on Z2 for Al ions with energies of 102

and 400 keV per nucleon has been calculated using

SRIM2000 [23] under the assumptions of bulk

density for the targets, and the results indicate theZ2-oscillations of stopping cross sections as shown

in Fig. 6. The experimental results for Al (Fig. 6) at

corresponding energies agree with the SRIM pre-

diction. The foil densities used in converting the

Fig. 5. Comparison of the experimentally determined Al stopping power data (}) with the literature values ( ) taken from the H. Paul�sdatabase as well as the SRIM predictions (––). The corresponding stopping foil and its thickness are indicated in the

plots.


stopping power to stopping cross section are 2.253,2.70 and 19.311 g/cm3 for C, Al and Au stopping

foils, respectively.

3.4. Comparison with published stopping data and

SRIM predictions

To demonstrate the approach, the stopping of

heavy ions (7Li, Be, 11B, C, N, O, F, Na, Mg, Al,Si, Cr, Mn, Fe, Co, Ni, Cu, Br and I) in amor-

phous C, Al and Au have been studied. Summaries

of the experimental data are shown in Figs. 7–9,

using the fitted trend lines from a sixth-order

polynomial regression to represent the results from

this study. For the stopping data in amorphous C

and Al, where more than one stopping foil is em-

ployed in the study, the curves shown are the bestfit to the data from all foils. Also included in Figs.

7–9 are the calculations from SRIM2000 and other

literature data. Over most of the energy regimes in

this study, as shown in Figs. 7–9, previous exper-

imental data are not available in the literature. In

some energy regimes, the present data are com-

parable with the existing literature data. It should

be stressed that the mean energy-loss is investi-gated under the assumption of equilibrium charge

conditions; no evidence of a dependence on the

charge state of the particle could be detected

within the current experimental setup. From the

results in Figs. 7–9, a number of interesting general

observations can be drawn. The stopping power

increases with atomic number as expected. For thelight ions, the measured stopping power in this

study begins near the maximum and decreases

slowly with increasing particle energy. For the

medium and heavy ion in all targets, the stopping

power measured in the present study begins sig-

nificantly below the maximum and increases with

increasing energy. In most cases, there is reason-

able consistency between the experimental dataand the SRIM-predicted values. At the lower en-

ergies, the SRIM calculations for the heavier ions

in all foils are in good agreement with the values

measured here.

From the results for the stopping power of Li in

C (Fig. 7), the experimentally determined values

exceed the SRIM values in the stopping peak re-

gion by up to 15%. Moreover, the stopping peakfrom this study and other literature data appears

to be shifted to lower energies compared with the

SRIM prediction. In comparing with the literature

data, the present data have similar energy depen-

dence, but the absolute values of the present re-

sults are lower. There is no clear explanation for

this anomalously large departure [3] at this time. It

is known that studies of the Z1 and energy de-pendence of the second moment (straggling) of the

energy-loss distribution have shown deviations of

up to 200% for Li projectiles [25]; however, further

analysis and discussion of this observation re-

quires consideration of the charge state, polariza-

tion and leading-term effects [6], which is beyond

the scope of the present paper. For stopping values

of other ion species in amorphous C, the presentresults in Fig. 7 are in good agreement with most

of previous experimental data. In the case of O, F

and Al in amorphous C, different experimental

results from the literature are not always in

agreement to each other or with SRIM2000 values.

For stopping power of heavy ions (Z1 PMg) in

amorphous C (Fig. 7), the present data are in fair

agreement with the SRIM prediction curves overmost of the energy region, except for particle en-

ergies near 300 keV per nucleon, where the present

results indicate deviations of SRIM2000 values on

the order of 8%.

Fig. 6. The target (Z2) dependent stopping cross section oscil-

lation. The dependence of electronic stopping cross sections of

102 and 400 keV per nucleon Al ion in different targets simu-

lated by SRIM2000 is indicated by the solid and dashed

lines, respectively. The experimentally determined values are

shown as diamonds for the correspond energies and stopping

foils.


As seen from Fig. 8, the stopping powers of C,N, O and Si in Al are relatively well studied, and

much more data exist for comparison. However,the literature data are quite scattered (e.g. N in Al

Fig. 7. Comparisons of the stopping powers in amorphous C (- - -) with the literature values (}) taken from the H. Paul�s database, aswell as the SRIM predictions (––).


and Si in Al), and do not agree within the statedexperimental uncertainty. The SRIM values are

much closer to the stopping powers determined in

this studied. For Al in Al, the present data agree

well with the literature data; however, the SRIM

values appear to overestimate the stopping power

in the energy region studied here. For ions of Be,

Mg, Cr, Mn, Fe, Co, Ni, Cu and I, the stopping

data are determined for the first time over most ofthe energy region, and agree, within several per-

cent, with the SRIM values, except a larger dif-

ference is observed for Be (up to 9%).

The stopping data in amorphous Au is shownin Fig. 9. There is reasonable agreement be-

tween the present data, other experimental data

and the values determined by SRIM2000. How-

ever, there is a tendency for faster increases in the

stopping power with increasing particle energies

for the present data compared to the SRIM pre-

diction. At lower ion energies, as shown in Fig. 9,

the SRIM curve overestimates the stopping power,but the SRIM predictions increase slower than

the present results with increasing energy. For the

higher energy range covered in this study, the

Fig. 7 (continued)


SRIM values underestimate the electronic stop-ping power for heavy ions. In comparing with the

literature data shown in Fig. 9, the experimen-tal data from the literature are quite scattered,

Fig. 8. Comparisons of the stopping powers in amorphous Al (- - -) with the literature values (}) taken from the H. Paul�s database, aswell as the SRIM predictions (––).


and more than 20% broadening can be seen inthe cases of C, N and O ions. The experimen-

tal stopping powers for C, N, O, Mg, Al and

Si are in good agreement with the literature

data in the limited energy region covered by

this study. The stopping powers of Be and Cr in

Au provide data that are not previously avail-

able.

4. Conclusions

The present study has demonstrated a new ap-

proach to determine high-precision stopping

powers, based on a ToF spectrometry, for a wide

range of elements in the energy region where most

ion beam analysis (IBA) techniques are employed.This simple analysis procedure takes advantage of

the continuous energy spectra to eliminate the

calibration uncertainties associated with the use of

Si detectors, and greatly improves the precision of

the stopping power measurements. The key im-

provement and novelty of the present approach is

to use the ToF spectrometry placed in front of the

stopping medium to obtain ToF data that is tag-ged by the Si detector with and without the stop-

ping foil present. By using the analysis approach

described in this paper, it is possible to obtain

high-precision stopping power data without rely-

ing on any energy calibration of the Si detector.

The stopping powers of some heavy ions (3Patomic number6 53) in amorphous C, Al and Au

have been determined. In some energy regimes,new data are provided for the first time. The ex-

perimental data are in reasonable agreement with

SRIM stopping powers in most cases; however,

SRIM values exhibit some deviation from the

measured values, up to 15%, around stopping

maximum.

By simply replacing the stopping foil with any

self-supporting foil, stopping power in elemental orcompound, amorphous or crystalline targets can be

investigated with high precision in terms of energy

and atomic number dependence. This approach

can measure the stopping power of a few ele-

ments simultaneously and be easily applied to a

great majority of ion-target combinations over a

wide continuous energy range. These provide much

Fig. 8 (continued)


needed experimental data for the development of

improved predictive theory, high resolution IBA,and precise implantation.

Acknowledgements

The author is grateful to Dr. W.J. Weber for

helpful discussions and many important sugges-

tions.

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