electronic stopping powers for heavy ions in silicon

Nuclear Instruments and Methods in Physics Research B 215 (2004) 48–56

www.elsevier.com/locate/nimb

Electronic stopping powers for heavy ions in silicon

Yanwen Zhang a,*, William J. Weber a, Harry J. Whitlow b

a Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USAb Division of Nuclear Physics, Lund Institute of Technology, P.O. Box 118, Se-221 00 Lund, Sweden

Received 11 March 2003; received in revised form 24 August 2003

Abstract

The stopping powers in silicon of heavy ions, with atomic numbers ranging from 4 to 29, have been determined using

a time-of-flight elastic recoil detection analysis (TOF ERDA) set-up. In transmission geometry, the energy loss of heavy

elastic recoils in the self-supporting silicon foil of known thickness is measured over a continuous range of recoil en-

ergies using time-of-flight (TOF) spectrometry. By essentially calibrating the Si detector for each channel over the

measured energy region using the TOF spectrometer, an uncertainty of less than 4% is achieved. The stopping powers

are parameterized using a sixth order polynomial and compared with the limited experimental data in the literature. In

the energy regimes where experimental data exist, the present data exhibit good agreement with most data. Stopping

powers predicted by SRIM (the stopping and range of ions in matter) are in reasonable agreement with much of the

experimental data, and SRIM-2003 predictions are in somewhat better agreement than SRIM-2000. There are, how-

ever, still some discrepancies between SRIM predictions and the experimental data.

� 2003 Elsevier 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

The energy loss of particles in matter is of

considerable interest in several areas of physics,

such as ion-beam modification, ion-beam-based

materials analysis, nuclear physics, radiationdamage and radiation therapy. With rapidly ex-

panding applications for heavy ions, heavy-ion

stopping in matter is attracting renewed interest

* Corresponding author. Tel.: +1-509-376-3429; fax: +1-509-

376-5106.

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

0168-583X/$ - see front matter � 2003 Elsevier B.V. All rights reser

doi:10.1016/j.nimb.2003.09.005

[1–15]. For many heavy ions, no stopping power

data exist for many energy regimes of interest, and

values predicted from the extrapolation of ana-

lytical fits of higher or lower energy data often

have considerable error. Available theories predict

stopping powers that are in varying levels ofagreement with experimental data. Improvements

in stopping theories and predictive models demand

accurate experimental data on energy loss and

stopping powers for heavy ions, which makes this

an important area for renewed research [7–15].

Silicon is one of the most studied targets ma-

terials because of its predominant use in semi-

conductor technology. New applications evolving

ved.

mail to: [email protected]

First time detector Si detector

Targets

127I10+

L ToF

Removablesilicon foil

Second time detector

φ

Fig. 1. Schematic illustration of the experimental configura-

tion. The removable silicon stopping foil can be reproducibly

moved into and out of the recoil path.

Y. Zhang et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 48–56 49

from silicon-based integrated circuit technologies

are still quite challenging, such as the ultra-high

resolution, low-temperature, polysilicon thin film

transistor, liquid crystal display and the siliconquantum computer [16]. As silicon-integrated cir-

cuit technology enters the sub-100 nm realm,

continued progress will depend on a fundamental

understanding of the physics of materials pro-

cessing, including ion implantation and highly

accurate stopping powers. Because of the some-

what limited database on stopping powers for

some elements in Si, a wider range of data is nee-ded to confirm or validate the stopping power

models currently employed.

The present paper employs a unique approach

previously reported [8,9] to determine energy loss

in polycrystalline silicon based on a modified time-

of-flight elastic recoil detection analysis (TOF

ERDA) set-up. The energy loss of heavy recoil

particles in the same area of the stopping foil overa continuous range of energies is simultaneously

measured by TOF spectrometry. This approach

eliminates much of the error resulting from the

normal Si detector calibration procedures when

applied over a wide energy range to determine the

small energy loss in stopping foils and, as a result,

reduces the uncertainty of the stopping power

measurements. The method has been validated bythe studies of stopping power of heavy ions in

targets of carbon, aluminum and gold [8,9]. In this

study, the stopping powers of a number of heavy

ions (4 6 atomic number 6 26) in a self-support-

ing foil of silicon have been determined. In some

energy regimes, experimental data are provided for

the first time. The measured data are compared

with previous existing data and the predicted val-ues obtained from the stopping and range of ions

in matter program, both the newly released version

SRIM-2003 and an earlier version SRIM-2000

[17,18].

2. Experimental

A modified TOF ERDA set-up, as shown in

Fig. 1, was utilized for the energy loss measure-

ments. The system consists of two carbon-foil time

detectors separated by a 437.5 mm flight length

(LTOF) that is followed by an ORTEC Si ion-im-

plantation detector. The polycrystalline silicon

stopping foil is mounted on a push-rod that can be

reproducibly moved into and out of the particle

path, between the second time detector and the Si

detector (Fig. 1). A projectile beam of 44 MeV127I10þ ions, produced from a 5 MV NEC tandemaccelerator at the Uppsala Tandem Laboratory,

Sweden, was used to create energetic target recoils

from elemental bulk samples or simple com-

pounds. Using the recoil method, fourteen differ-

ent ion species (Be, 11B, C, N, O, F, Mg, Al, Si, Cr,

Mn, Fe, Co and Cu) over a continuous range of

energies, from a few tens to hundreds of keV per

nucleon, were produced. As shown in Fig. 1, thetarget recoils were detected by the TOF-energy

spectrometer in a forward direction at / ¼ 43� tothe primary beam direction. These ions were re-

corded with the stopping foil both in and out. It is

worth noting that there is a very low probability

that particles passing through the Si foil will un-

dergo some nuclear stopping and be scattered into

the limited solid angle of the Si detector. However,those particles that do undergo nuclear stopping

and are registered in the Si detector will be ex-

cluded from the analysis by the mass window se-

lected [19]. Thus, the effect of low-probability

nuclear scattering events is negligible, and only the

energy loss due to electronic stopping is considered

further.

The recoil energies were determined by the TOFspectrometer that was calibrated using an ORTEC

Model 462 Time Calibrator [9]. As an example, the

time spectra for energies detected by the Si detec-

tor at channel number 300, 500 and 700 are shown

Time (channel)

600 800 1000 1200 1400 1600

Yie

ld

0

20

40

60Be in Si

E = 300

E = 700

T1 T2

E = 500

Fig. 2. Time spectra (from TOF spectrometry) of Be ions at

different energies (channel at 300, 500 and 700) registered by the

Si detector. The peaks indicated by the dashed lines are the time

spectra with the silicon stopping foil present and the peaks in-

dicated by the solid lines are the time spectra without the silicon

stopping foil present.

50 Y. Zhang et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 48–56

in Fig. 2 for Be target recoils, which illustrates the

general behavior for other heavier particles. As

described previously [8,9], the energy loss of par-ticles in the polycrystalline silicon foil is deter-

mined by measuring the TOF information with the

stopping foil both in and out of the recoil path,

and the Si detector is only used to tag particles of

identical energies, with and without the stopping

foil present. Therefore, for the same energy signal

(channel 300, 500 or 700) recorded by the Si de-

tector, as shown in Fig. 2, there are two TOFspectra, one, T1, with the silicon foil in (the dashed

line) and the other, T2, with the foil out of the

recoil path (the solid line), respectively. Using

particles detected by the Si detector at the energy

channel of 300 as an example, the energy of indi-

vidual recoils prior to impingement on the silicon

stopping foil, E1, is determined from T1 (time

channel 1280), as measured by the TOF spec-trometer. Instead of using the Si detector to de-

termine the exit energy, the TOF spectra, T2 (time

channel 1393), without the stopping foil present is

used to determine the exit energy, since the energy

has been tagged by the Si detector to be identical

to that exiting the stopping foil. Thus the exit en-

ergies, E2, are determined from the corresponding

TOF data, T2, without the stopping foil present,based on the tagging of particles that have the

same signal response in the Si detector as those

passing through the stopping foil. By using the Si

detector to only tag identical energies with and

without the stopping foil present, the energies of

the particles exiting the stopping foil are moreaccurately determined by the TOF spectrometer,

which has much better resolution and linear re-

sponses to the heavy elements over the energy re-

gion studied. This approach essentially calibrates

the Si detector using the TOF spectrometer for

each channel over the whole measured energy re-

gion and eliminates the error resulting from

nominal energy calibration of the Si detector,where parameterization of a simple function is

generally used to convert measured channel num-

ber to energy. Since nominal Si detector calibra-

tion is not used in the present approach, pulse

height defects and other calibration problems as-

sociated with heavy particles in Si detectors

[12,20–22] do not cause additional error in the

energy loss determination, as in a previous study[23]. Using this unique approach, the energy loss in

the stopping foil, DE, and the mean energy, E, aredetermined from the following expressions:

DE ¼ ðE1 � DEfoil;inÞ � ðE2 � DEfoil;outÞ ð1Þ

and

E ¼ E1 þ E2 � DEfoil;in � DEfoil;out

2; ð2Þ

where E1 and E2 are the energies determined from

the peak position of the corresponding TOF data(e.g. time channel of 1280 and 1393) for the same

pulse height in the Si detector (e.g. energy channel

of 300), as shown in Fig. 2. The parameters,

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

particles in the carbon foil of the second time de-

tector that produced the same pulse height in the

Si detector with and without the stopping foil.

These small energy-loss in the second time detector(a few percent of the particle energy) are taken to

be the product of the carbon foil thickness (7

lg cm�2) and the stopping powers of the corre-

sponding ions in carbon, which were recently

measured in a previous study [8,9].

The thickness of the silicon foil, Dx, was deter-mined by measuring the energy loss of 5.48 MeV

alpha particles at different positions over the foiland using the stopping powers for alpha particles


in Si, which are accurately known. The foil thick-

ness varies between 102.4 and 109 lg cm�2, with

the mean thickness of 105.5 lg cm�2 [23].

The stopping power, �dE=dx, is determined byscaling to the foil thickness, Dx, according to the

expression

� dEdx

¼ DEDx

¼ ðE1 � DEfoil;inÞ � ðE2 � DEfoil;outÞDx

: ð3Þ

Since the number of registered events for each el-

ement range from 4 · 104 to 2 · 105 in the present

study, the counting statistics are generally good,and a polynomial regression is used to represent

the results over the corresponding energy region. It

is found that for all elements, the mean stopping

power, �dE=dx (MeVmg�1 cm2), is described well

over the range of energies (keV/nucleon) by fitting

to a sixth order polynomial:

� dEdx

¼X6

i¼0

kiEi: ð4Þ

An average energy approximation, E, determinedfrom the impinging and the exit energies (Eq. (2))

is used to represent the particle energy on the

stopping curve. The validation of using this energy

approximation, instead of the impinging energy

(E1) or the exit energy (E2), was discussed else-

where [24].

The dominant contribution to the total uncer-

tainty in the mean stopping power, �dE=dx, arisesfrom the uncertainty in the stopping foil thickness,

which was determined from the known stopping

powers of alpha particles. Other uncertainties, re-

sulting from the time calibration, the drift of the Si

detector response due to the radiation damage and

beam heating, the finite resolution of the Si de-

tector, geometrical variation of the flight length,

recoil angle due to the solid angle, and countingstatistics, will, to a small extent, contribute to the

uncertainties in the energy loss measurements. A

detailed discussion on experimental uncertainties

can be found elsewhere [9]. The total uncertainty

in the mean energy loss from the current set-up is

less than 1%. If it is assumed that the uncertainty

in the alpha stopping is �2%, and the total un-

certainty from the foil thickness determination,

including the thickness variations, is �3.5%, the

total uncertainty of the mean stopping power,

�dE=dx, in the current study is less than 4.0%.

3. Results and discussion

The experimentally determined stopping pow-

ers, �dE=dx, versus particle energy for Be, C, Si

and Cu recoils in polycrystalline silicon, which

cover the mass range of this study, are shown inFig. 3. Stopping predictions from SRIM-2003 [18]

and the existing data taken from Paul�s database

[25] are also shown for comparison. In Fig. 3, the

scatter of the measured stopping data, �dE=dx, isassociated with the energy straggling in the silicon

stopping foil and time detectors, counting statis-

tics, the energy resolution of the detectors, as well

as the foil thickness variation. It can be seen thatthe scatter of the data points increases as the ion

mass increases, which is primarily attributed with

the increase of the energy straggling with ion

mass. The increased broadening at higher ener-

gies for the same ion species is observed as a

general behavior, and this is primarily attributed

to lower counting statistics as the scattering cross

section for the target recoils decreases propor-tional to 1=E2, as shown in Fig. 2 by the decrease

of the registered events (integrated peak insensi-

tivity) with increases energy. An increase of peak

width at lower energies in Fig. 2 is also obvious,

which is attributed to the increase of the energy

straggling through the stopping foil at lower en-

ergies.

The stopping power of Be in silicon over thecontinuous energy range from �140 to 620 keV/

nucleon is shown in Fig. 3(a). There are no other

data in the literature on Be stopping power in

silicon. The results, as shown in Fig. 3(a), indicate

that the current data are in good agreement with

the prediction of SRIM-2003 only at higher ener-

gies. SRIM-2003 overestimates the stopping power

at lower energies, and deviation is more than 10%at energies near the stopping peak (�210 keV/nu-

cleon). For the case of C in silicon in Fig. 3(b), the

current data show excellent agreement with both

the existing data and the SRIM-2003 prediction,

Energy (keV/nucleon)0 100 200 300 400 500 600 700

0

1

2

3

4

5

6

7

C in Si

(b)Energy (keV/nucleon)100 200 300 400 500 600 700

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

0

1

2

3

4

Be in Si

(a)

Data Database SRIM 2003

Energy (keV/nucleon)0 100 200 300 400 500

0

4

8

12

16

Si in Si

(c) Energy (keV/nucleon)0 100 200 300

0

5

10

15

20

25

Cu in Si

(d)

Fig. 3. Comparison of the experimentally determined stopping power data, �dE=dx (diamonds), of particles (a) Be, (b) C, (c) Si and

(d) Cu, together with the literature values (triangles) taken from the Paul�s database as well as the SRIM-2003 predictions (solid lines).


within the experimental uncertainty. As shown in

Fig. 3(c), general agreement is observed for Si

stopping in silicon; however, the present data is

slightly higher than previous data over the entire

energy region of this study. The current Si data are

consistent with the SRIM predictions only at

higher energies; at lower energies, SRIM-2003

overestimates the stopping power of Si in siliconby up to 7%. Data from this study for Cu stopping

in silicon are provided in Fig. 3(d). As in the case

of Be stopping, there are no other data on Cu

stopping in silicon for comparison. SRIM-2003

underestimates the stopping power of Cu in silicon

at low energies (�100 keV/nucleon) by as much as

�12%; however, smaller deviations (�5%) exist at

high energies (�250 keV/nucleon).Summaries of the mean stopping data, �dE=dx,

determined in this study are shown in Figs. 4 and 5

together with some existing experimental data

from the literature [25]. A sixth order polynomial

regression (Eq. (4)) is used to represent the mean

stopping power from this study over the corre-

sponding energy region, and the parameters are

listed in Table 1 for convenient implementation

into other applications. Because the recoil tech-

nique is used in the current set-up to produce en-

ergetic particles, the energy range for light

elements (up to F) encompasses the stoppingmaximum, as shown in Fig. 4. For heavier ions

(heavier than Mg), the energy range in the present

study is on the low energy side of the stopping

peak. The energy coverage can be easily increased

by using a higher energy projectile beam or using a

gold bulk target to forward scatter high energy

ions, in which case the energy loss of the forward

scattered projectile particles in silicon is measured.SRIM, as one of the most accepted simulation

programs, is widely used for calculating stopping

power and range of ions in matter [18]. In the past

few years, improvements in SRIM have focused on

0

1

2

3

4

Be in Si

This study

SRIM 2000

Database SRIM 2003

0

1

2

3

4

511B in Si

0

1

2

3

4

5

6

7

C in Si

0

2

4

6

8

N in Si

0

2

4

6

8

O in Si

0

2

4

6

8

10

F in Si

Energy (keV/nucleon)

10 100 10000

4

8

12

16

Mg in Si

Energy (keV/nucleon)

10 100 10000

4

8

12

16

Si in Si

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

dE/d

x (M

eV/(

mg

cm-2

))

Fig. 4. Comparisons of the mean stopping powers, �dE=dx, of Be, 11B, C, N, O, F, Mg and Si ions in silicon using the polynomial fit

(diamonds) with the literature values (triangles) taken from the Paul�s database, as well as the predictions by SRIM-2003 (thick solid

lines) and SRIM-2003 (thin solid lines).


the stopping of relativistic light ions with energies

above 1 MeV/nucleon. In 1998, improvements to

SRIM were made to account for the Barkas effect

and the theoretical stopping of Li ions [18]. More

recent efforts have emphasized the stopping of

heavy ions at lower energies. In the newly releasedversion SRIM-2003 [18], the average accuracy of

the stopping powers is stated to be about 5%

overall and 6% for heavy ions. The predictions of

the two most recent versions, SRIM-2003 and

SRIM-2000, are compared to the experimental

data in Figs. 4 and 5.

From the results for the stopping powers of Be

and 11B in silicon (Fig. 4), the experimentally de-termined values are lower than the SRIM values in

the stopping peak region by over 10%. In the case

0

4

8

12

16Al in Si

0

5

10

15

20

25

30Cr in Si

0

8

16

24

32Mn in Si

0

5

10

15

20

25

30

35Fe in Si

Energy (keV/nucleon)10 100 1000

0

5

10

15

20

25

30

35Co in Si

Energy (keV/nucleon)10 100 1000

0

10

20

30

40Cu in Si

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

dE/d

x (M

eV/(m

g cm

-2))

Data

SRIM 2000

Database SRIM 2003

Fig. 5. Comparisons of the mean stopping powers, �dE=dx, of Al, Cr, Mn, Fe, Co and Cu ions in silicon using the polynomial fit

(diamonds), as indicated in the plots, with the literature values (triangles) taken from the Paul�s database, as well as the predictions bySRIM-2003 (thick solid lines) and SRIM-2003 (thin solid lines).


of 11B, the current data appear to be in good

agreement with the previous literature data, but

both data sets indicate an overestimation by

SRIM-2003, although a reduction in the predicted

stopping power for Be and 11B by the newer SRIMversion is obvious, as compared with SRIM-2000.

Moreover, the experimental data for Be and 11B

data exhibit a similar dependence on energy that is

not well predicted by SRIM. There is no clear

explanation for this large departure at this time.

The stopping powers for C, N and O in silicon

have been studied more thoroughly, and there

exist more experimental data, obtained by differentgroups with different techniques [25], for compar-

ison. The results at the present study are in good

agreement with most of the previous experimental

data and, in general, with the SRIM-2003 predic-

tions. For N and O ions, the absolute values of the

present experimental results are slightly higher

than the SRIM-2003 predictions, and in some

energy regimes, closer to the SRIM-2000 predic-tions. In the case of F ions, previous data are

available at lower energies, and the present study

provides new data in the energy region shown. By

comparing the experimental data for F in silicon

with the different SRIM versions over the energy

region from 10 to 530 keV/nucleon, improvements

in both the energy dependence and the absolute

values predicted by SRIM-2003, over those ofSRIM-2000, are clearly evident. For Mg ions,

previous data show a tendency for higher stopping

force and more rapid increases in stopping power

Table

1

Polynomialfitto

thestoppingdata

forthecorrespondingvalidatingenergyregion

Particles

Emin

(keV

/nucleon)

Emax

(keV

/nucleon)

j0

j1

j 2j 3

j 4j5

j6

Be

150

625

2.222E+00

1.252E)02

)9.423E)05

3.550E)07

)7.077E)10

7.100E)13

)2.841E)16

11B

201

567

)4.831E+00

1.491E)01

)1.049E)03

3.842E)06

)7.733E)09

8.120E)12

)3.478E)15

C119

587

1.898E+00

5.378E)02

)3.408E)04

1.048E)06

)1.699E)09

1.391E)12

)4.509E)16

N150

566

5.116E+00

)1.071E)02

3.068E)04

)1.953E)06

5.456E)09

)7.163E)12

3.615E)15

O138

520

3.742E+00

2.062E)02

1.372E)04

)1.513E)06

5.036E)09

)7.348E)12

4.020E)15

F97

530

1.373E+00

8.657E)02

)4.424E)04

1.068E)06

)9.974E)10

)2.428E)13

6.733E)16

Mg

66

483

1.033E+00

1.149E)01

)7.284E)04

2.739E)06

)5.710E)09

5.816E)12

)2.098E)15

Al

76

467

)9.947E)01

1.556E)01

)9.809E)04

3.541E)06

)7.079E)09

7.095E)12

)2.668E)15

Si

59

430

9.971E)01

1.242E)01

)6.975E)04

2.468E)06

)5.277E)09

6.352E)12

)3.413E)15

Cr

49

323

3.272E+00

1.534E)01

)1.280E)03

9.861E)06

)4.591E)08

1.085E)10

)1.007E)13

Mn

49

318

)4.738E+00

4.289E)01

)5.007E)03

3.737E)05

)1.603E)07

3.586E)10

)3.227E)13

Fe

39

328

)1.619E+00

2.886E)01

)2.486E)03

1.509E)05

)5.641E)08

1.146E)10

)9.622E)14

Co

45

319

)2.671E+00

3.538E)01

)3.892E)03

2.969E)05

)1.329E)07

3.096E)10

)2.885E)13

Cu

42

295

1.314E+00

1.786E)01

)5.684E)04

)2.450E)06

3.422E)08

)1.283E)10

1.632E)13


with increasing particle energy, as compared with

the current results, which are in better agreement

with SRIM predictions. The stopping power of Si

ions is relatively well studied, and much more dataexist for comparison. However, the literature data

are quite scattered, especially in the stopping peak

region, and do not agree within the reported ex-

perimental uncertainties. While the SRIM values

for Si are closer to the stopping powers determined

in this study, the predicted values are higher than

any of the experimental data. The stopping powers

for Al, Cr, Mn, Fe, Co and Cu ions in silicon areshown in Fig. 5, which represent the only available

data for these ions. In general, the results are in

reasonable agreement with SRIM-2003 prediction;

however, there is a trend for better agreement with

SRIM-2000 at lower energies for Fe, Co and Cu

ions.

An overall reduction of the stopping power in

SRIM-2003 comparing to SRIM-2000 is observedover the energy region in this study, as shown in

Figs. 4 and 5. In general, there is improved

agreement of SRIM-2003 with the experimental

data in the stopping peak region. For heavier ions

at low energies, SRIM-2000 may provide slightly

better predictions. For the case of N, O and Cu,

the current data lie between the SRIM-2003 and

SRIM-2000 predictions.It should be noted that, except for Cr, Co and

Cu ions for which the stopping values are provided

for the first time, the stopping powers for other

ions in Si were previously measured [23]. Despite

the careful calibration of the Si detector in previ-

ous work [23], differences in the measured stopping

between the current study and the previous study

[23] suggest that the Si detector calibration with asecond order polynomial over a wide energy range

leads to a significantly increase in uncertainty from

the error propagation in measuring small energy

loss in the stopping foil. By calibrating the Si de-

tector for each channel based on the TOF spec-

trometer over the measured energy region, the

present approach eliminates much of the error

associated with pulsed height defects and other Sidetector calibration problems, and provides more

reliable stopping data. The stopping values from

this study should be considered to supersede the

previous results [23].


4. Conclusions

The stopping powers in silicon have been de-termined for a wide range of ions over an energy

region where most ion implantation is employed.

Based on TOF spectrometry to determine the

stopping powers, the simple analysis approach

takes advantage of the continuous energy spectra

to calibrate the Si detector for each channel over

the measured energy region, and the uncertainty in

the energy determination reduces significantly. Thestopping powers of heavy ions in polycrystalline Si

determined in the current study have been para-

meterized, which enables easy implementation in

other applications. In some energy regimes and for

some ions, data are provided for the first time. In

energy regimes where other experimental data ex-

ist, reasonable agreement can be observed in most

cases. Improvement in the prediction of Si stoppingpower for SRIM-2003, compared with SRIM-

2000, is observed. Except for the light elements of

Be and 11B, SRIM-2003 predicted stopping values

are in good agreements (within a few percent) with

the current data and most other previous data.

Acknowledgements

We are grateful to the staff at the Tandem

Laboratory, Uppsala University, Sweden for ac-

celerator operations and experimental assistance.

This work was partially supported by Division of

Materials Science and Engineering, the Office of

Basic Energy Sciences, US Department of Energy.

Pacific Northwest National Laboratory is oper-ated by Battelle for the US Department of Energy

under contract no. DE-AC06-76RLO 1830.

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electronic stopping powers for heavy ions in silicon

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