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Determination of excitation functions for carbon detection by charged particle activation analysis
Nuclear Instruments and Methods in Physics Research B36 (1989) 7-13 North-Holland, Amsterdam
DETERMINATION OF EXCITATION FUNCTIONS FOR CARBON BY CHARGED PARTICLE ACTIVATION ANALYSIS V. LIEBLER,
K. BETHGE,
J. KRAUSKOPF,
J.D. MEYER,
DETECTION
P. ~ISAELID~S
* and G. WOLF
Institut f6r Kemphysik, Universitiit Frankfurt am Main, FRG Received 31 August 1988
The excitation fictions of the reactions ‘2C(3He, a)“C and 12C(3He, d)13N have been measured in 100 to 200 keV steps in the energy region between 0.4 and 14.0 MeV considering all perceptible sources of errors. The absolute cross sections have been determined by measuring the annihilation radiation of positron emitting nuclei produced during the irradiation. The precision of the determination is in the order of 10%.
1. Introduction Nuclear reactions have been applied very successfully to the determination of light element impurities in different host matrices. In particular the amount of carbon impurities in semiconductors as silicon and gallium arsenide can be determined. The presence of carbon is of importance for the development of highly integrated semiconductor circuits, e.g. carbon in gallium arsenide acting as a shallow acceptor. There are only a few suitable chemical methods with high sensitivity for the determination of traces of carbon in semiconductor materials. Among them, the burning of the sample in an oxygen atmosphere and measuring carbon dioxide gives a sensitivity in the order of 0.1 pg/g [l]. The physical methods applied, like infrared absorption spectroscopy, give good results only when an accurate calibration is available. The charged particle activation analysis (CPAA) is an absolute method and can be used as a calibration of nonabsolute physical techniques. For this purpose very precise absolute cross sections of nuclear reactions are required. The nuclear reaction i*C( 3He, cu)“C is suitable for the determination of carbon by charged particle activation analysis because of its high cross section values up to 330 mb [2,3] and its zero threshold energy (Q, = 1.856 MeV 141). The reaction 12C(3He, d)r3N can be used as an alternative reaction to detect carbon, in e.g. materials containing boron leading to the nucleus “C by the reaction ‘“B(3He, d)“C too. The maximum cross section of the r*C( 3He, d)13N reaction amounts to 140 mb [2,3,5] and the threshold energy is 4.44 MeV (Q, = -3.55 MeV IS]). The determination of traces of nitrogen by the reaction 14N(‘He, (u)13N also requires the
knowledge of the excitation function of the reaction 12Ct3He, d)t3N, because both reactions lead to the same final nucleus. A number of authors published excitation functions for the nuclear reactions induced on carbon by 3He ions. But these data measured in wide energy steps show large uncertainties of the cross section as well as the reaction energy ]2,3,5]. The unpub~shed data of Fack [7] and Kohlhase f8] are also not reliably accurate. They are not sufficient for the purpose of analysis. In the present work the excitation functions of ‘*(J3He, ol)“C and l2 C( 3He, d)13N nuclear reactions were measured in the energy region between 0.4 and 14.0 MeV in energy steps of 100 to 200 keV. We tried to eliminate or at least to determine all sources of errors in order to achieve a high precision [9]. 2. Experimental method The total cross sections of the reactions ‘2C(3He, ol)“C and 12C(3He, d)13N were measured using 3He ion beams from the two Van de Graaff accelerators (2.5 and 7 MV) of the Institut fir Kernphysik of the University of Frankfurt. The cross section was determined by irradiating the samples and measuring the activity of the *‘C and r3N nuclei produced during the activation afterwards. “C and 13N are positron emitting nuclei with half-lives of 20.3 min [4] and 9.96 min [6] respectively. The accuracy of the determination of the cross section depends on the error minimization of the quantities in the following formula. The cross section o(E) given by u(E)
* Present address: Department of General and Inorganic Chemistry, Aristotelian University, Thessaloniki, Greece. 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holiand Physics abusing Division)
=
ear,A rqcDN,/3
AZ( tb) _(l At
_e-%)-’
includes the following two groups of quantities:
8
V. Liebler et al. / Carbon excitation functions
(1) constants taken from the literature: e elementary charge [lo], A atomic mass Ill], c isotope abundance 1111, NA Avogadros number [lo], ,8 probability of e+ decay compared to competing processes (for “C 99.8% [4], “N 100% [6]), X decay constant of the activated nucleus [4,6]; (2) parameters which have to be measured independently: charge of the projectile, determined by the maga netic deflection of the accelerated beam, c efficiency of the measuring system, total charge accumulated during the activation q period Ib, D target thickness in g/cm’, A Z( tb)/Aht counting rate. In the following sections the details of the measurement are described. 2. I. Targets The carbon targets were produced by evaporating carbon onto a glass plate, floating the foil off and mounting it on an aluminium frame. The thickness of each foil was then measured by the energy loss in the foil of 01 particles emitted from an 241Am-source. The statistical error included in this measurement is less than 2%. Rutherford backscattering of 3 MeV 4He+ ions was also used to control the thickness independently and determine the lateral homogeneity using the peak width in the spectrum. Due to the beam diameter of about 2 mm only a rough lateral resolution could be achieved. The measured values, however, deviate from the average value by less than 5% as shown in fig. 1. The stopping power values with an error of 5% were taken from ref. [12]. From the kinematics of the nuclear reaction i2C( 3He 9 cu)“C is known that the kinetic energy trans-
1
600
I
5 .OMeV
3He -+“t
in C
400-
200-
3He o- e)
beam
axis
zoo400-
x[%I Fig. 2. Averaged range distribution of “C nuclei in carbon calculated at a bombarding energy of 5 MeV from the kinematics of the ‘2C(3He, a)“C reaction (Q = 1.856, 0.144, - 2.463 and - 2.952 [4]).
fered allows the product nuclei to be ejected from carbon foils of 20 to 50 ug/cm* thickness. The ranges of “C nuclei produced by 5 MeV ‘He projectiles in a carbon target are shown as a two dimensional plot in fig. 2. This figure also indicates the Q values for the four possible excitation states in “C. From this figure it is obvious that a large fraction of the “C nuclei is lost unless a catcher foil in forward and backward direction is used. To stop all “C nuclei in forward direction a 2 mm tantalum foil was used. The maximum range of “C in
400
15.0MeV 3He .+
3He
‘*C in Al
overagedrange PI: I
----_
beam OXIS
0
3
6
9
12
15
X-Axis lmml
Fig. 1. Lateral thickness distribution of a carbon foil measured by RBS in comparison to the energy loss measurement (shaded).
Fig. 3. Straggling
of recoiling “C nuclei into aluminium bombarding energy of 5 MeV.
at a
9
V. Liebler et al. / Carbon excitation functions
tantalum in the energy range covered in this work is approximately 6 pm [12]. In backward direction an alu~~urn foil of 220 pg/cm* was used. This alu~nium foil is thick enough to stop all “C nuclei leaving the target in this direction, taking also in account the transversal u1 and longitudinal straggling u,, (fig. 3). For the determination of the reaction energy the energy loss of the 3He ions (50 to 300 kev) in the aluminium catcher foil has been taken into account. No aluminium catcher foils are required for the measurement of the cross section of the endothermal t* C( 3He, d)t3 N reaction, because the produced 13N nuclei are ejected in an angular range up to a maximum angle of 42*. Both catcher materials contain carbon and other light elements that can be activated during the bombardment. The surface impurities in the tantalum foil were reduced by removing 7 Frn of the surface by etching 2 min in a solution of one volume 40% HF and one volume 65% HNO, before each irradiation. The catcher foils were irradiated at different energies in order to correct the total activity induced in the target arrangement. The carbon content of the tantalum foil was about 0.6 ug/cm*, whereas the corresponding carbon concentration in aluminium amounted to 3 tLg/cm*. 2.2. Beam current ~e~~e~e~t The irradiation chamber was carefully insulated from the rest of the equipment. Thus the whole chamber could be used as Faraday cup. At the entrance of the chamber a 3 cm diameter aperture is mounted so that secondary electrons cannot escape. The production rate of the electrons is proportional to the electronic stopping power of the projectiles in the target material [13]. For 4 MeV 3He ions in carbon (electronic stopping power: 200 keV/um [12]) and a proportionality factor of 0.012 pm/keV 1131one obtains 2.4 secondary electrons per projectile. Taking into account that the maximum of the electron distribution, showing a cosine square shape, appears at 180° [14] one predicts, that less than 1% of the emitted secondary electrons can escape out of the Faraday cup. The precision of the current measurement including the quality of the current integrator and the insulations of the Faraday cup is about 3%.
corrections due to the absorption of the 511 keV yquanta in the tantalum catcher foil were made. A sufficient reduction of the background radiation from natural sources (@K etc.) could be achieved by sufficient lead shielding (0.007 s-t in coincidence). 2.4. Initial counting rates The absolute cross sections were deter~ned measuring the decay curve of the activated sample as a function of time. The important figure is the initial counting rate AZ( tb)/At at the end of the activation which can be extrapolated from a semilogarithmic plot of the actual counting rate. If, as a rule, several nuclei are activated during the irradiation, the initial costing rates have to be determined separately for each species in successive stages. Since the cross sections of the nuclear reactions studied increase with increasing bombarding energies in the low energy region under consideration, the errors are larger for the lower energies. Using the measured counting rates and the iterative procedure of the decay curve analysis for the “C decay we estimated errors of 0.5% for the energy region above 1.5 MeV and about 50% at bombarding energies around 400 keV. The corresponding errors in the case of 13N are about 5% above 6 MeV and about 50% at energies around 5.5 MeV respectively.
3. Results The errors of the cross sections for the ‘*C( 3He, e)‘*C reaction in the energy region above 1.5 MeV and the ‘2C(3He, d)13N reaction are 10% and 12% respectively. The experimental results for the reaction of ‘*C ( 3He, ,)I1 C are presented in fig. 4 and for the reaction l2 C( “He, d)t3N in fig. 5. The open and the full symbols
2.3. Efficiency After activation the target was positioned between two 4 x 4 in. NaI(Tl) detectors in order to measure in coincidence the ~n~iation radiation of the positrons emitted by the product nuclei. The precision of the efficiency determination is dependent on the absolute activity of the 22Na calibration source. All necessary
0
2
G 6 a IO Projectile Energy IMeVl
12
34
Fig. 4. Excitation function of the reaction “C(‘He, a)“C. Full symbols represent measurements with and open symbols without aluminium catcher.
V. Liebler et al. / Carbon excitation functions
10
Table 1 Cross section values of the reaction 12Cf3He, a)“C Energy [MeVj Cross section [mb]
for low energies
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.003
0.008
0.013
0.21
0.90
2.2
8.8
are presenting the results of measurements without and with an ahuninium foil respectively. The results obtained with both target arrangements show good agreement. The cross section values of ‘2C(3He, cu)“C for energies below 1.8 MeV are given in table 1. Since the excitation function is needed for the material analysis the shape of an averaging polynomial fit is important (see figs. 4 and 5). A few resonances in the excitation function of the reaction “C( 3He, cu)“C can be seen corresponding to excitation states in the compound nucleus I50 at Ecom = 14.4, 16.6, 17.4 and 21.2 MeV (Et,, = 2.8, 5.6, 6.7 and 11.4 MeV). These states obviously possess large a-widths. The experimental widths are 0.6, 0.3, 0.4 and
L_”
0 E
200
‘2C(3He,d)‘3N 0 C/la l
Al /C tTa
6
0 Projectile
Fig.
5. Excitation
10 12 Energy IMeVl
function of the reaction Symbols as in fig. 4.
Projectile
Energy
‘2C(3He,
< 0.2 MeV respectively. These values are given with uncertainties of 0.1 MeV. Spin assignments to these states are not well known [6] which prevents further conclusions regarding the structure of these states. A detailed representation of the cross sections in the neighbourhood of one of these resonances is given in fig. 6. After background subtraction using a linear fit the shape of the resonance is fitted to a Gaussian function. From this fit a center position at 2.84 k 0.04 MeV (EGO,,,= 14.35 f 0.03 MeV) and a FWHM of 0.66 + 0.05 MeV are deduced which is in good agreement with values taken from ref. [6] ( Ecom = 14.34 MeV and FWHM = 0.24 MeV). The fits to the other resonances are of nearly similar quality except that at 21.2 MeV, for which an upper FWHM value of 0.2 MeV can be given. The excitation function of the reaction ‘2C(3He, d) 13N shows one resonance at Elab = 8.22 + 0.05 MeV with a width of 0.43 & 0.07 MeV. The corresponding excitation state in “0 appears at 18.65 MeV. From previous measurements a state at 18.65 ]6] is known. The cross section values below 6 MeV bombarding energy are smaller than 10 mb and are difficult to determine accurately because of the interfering relative high “C activity produced simultaneously by the “CJ3He, a)“C reaction.
14
4. Discussion d)13N
The excitation functions of the two reactions investigated can be used for the analysis of carbon contaminations in semiconductor (e.g. silicon and gallium arsenide) and metal matrices. Using thick samples the projectiles penetrate the material, lose energy and come to rest. The trends of the projectile energy with sample depth as well as the change of the cross section with the depth are shown in fig. 7. In this case an averaged cross section O( E, Emin) taken between the projectile energy E and a minimum energy Emin which is, as a rule, the threshold energy of the nuclear reaction is of interest to determine unknown carbon concentrations [15]. The b( E, E,,,) is given by:
i MeVl
Fig. 6. Gaussian fit of the resonance at the 14.35 MeV state in I50 (E,,, = 2.84 MeV) of the excitation function of ‘2C(3He, cu)“C.
Therefore the averaged cross section depends on the matrix because of the material depending stopping
11
V. Liebler et al. / Carbon excitation functions
360
a
_ -
this work
-..---
HahnlRicci Brill
Si -Matrix t
Depth
turn1
Fig. 7. Dependence of projectile energy and cross section on the penetration depth in silicon and gallium arsenide at a bombarding energy of 14 MeV.
d E/dx. The integral over the excitation function is essential for the precision and the detection limits of the charged particle activation analysis. To obtain this integral it is however sufficient to use an averaged curve produced by a least square fit procedure. The measured resonances do not affect the integrated excitation function drastically. Figs. 8 and 9 represent the fit curves compared to those of previous measurements [2,3,5,7,8]. Deviations can be observed over certain energy regions.
power
LOO
‘2C(3He,a)“C -this work 300
z .-6
2
Ln 200
3 100
0 0
LO
120
80
40
0
”
-
&
8
Projectile
Energy
12
J
IMeVI
Fig. 8 Polynomial fit to the excitation function of the reaction ‘2C(3He, a)“C compared to those by other authors (Mahony [2], Hahn and Ricci [3], Fack [7] and Kohlhase [S]).
C
1
6 Projectile
,
10 Energy
I
11, [MeVI
Fig. 9. Polynomial fit to the excitation function ‘2C(3He, d)13N compared with the literature Hahn and Ricci [3] and Brill[5]).
of the reaction (Mahony [2],
Mahony [2] used for the measurement of the excitation function of the t* C( 3He, ,)I1 C reaction plastic foils of 2 mg/cm* thickness with a content of 93% carbon. Several of these foils were sandwiched between gold foils. The stack was irradiated by 30.7 MeV 3He ions. The corresponding energy of each plastic foil was estimated from the beam energy lost in the previous foils. In this way the energy determination was not very accurate. This fact might explain some of the deviations from the present data. Hahn and Ricci [3] activated a sandwich-target of three 0.01 mm teflon foils, but measured only the activity of the central foil. The results show a slight deviation of the peak position from the present work. Fack [7] used a catcher foil on which a carbon film was evaporated. The determination of the thickness of the carbon film introduced large errors. Kohlhase [8] measured integrated cross sections by activating thick samples. The results show at energy regions above 8 MeV large deviations from values obtained in this work. The comparison of the excitation function of the ‘*C( 3He, d)13N reaction with the previously published data shows good agreement (Hahn and Bicci [3], Brill [5]). The earlier data published by Mahony [2] deviate considerably due to the reason mentioned above. Considering the feasibility of these nuclear reactions for determination of carbon by CPAA, one has to check the possible interference with other competing nuclear reactions leading to the same product nucleus. The possible interference due to the matrix activation should also be taken into account.
K Liebler et al. / Carbon excitation functions
12
“C
5
-
SI- Matrlx
---
GaAs-
Table 2 Detection limits of the reaction bombarding energies
Matrw
Si [at.
6
\L--c 0
i
2
ProJectile
10 14
10
a
b
Energy
12
lr,
1
lMeV
Fig. 10. Averaged cross section ratio of the interference reactions ‘ZC(3He, cu)“C and “B(jHe, d)“C in silicon and gallium arsenide.
If boron and carbon are present in the sample the same final nucleus “C is produced by the 12q3He, cw)“C as well as by the ‘“B(3He, d)“C reaction. The excitation function of the second reaction was published before [15]. To estimate the feasibility of a carbon determination we plot the ratio of the averaged cross sections Z( E,Emi,) for the reaction ‘2C(3He, a)“C to that of ‘“B(3He, d)13N as function of the projectile energy E {fig. IO). For a silicon and a gallium arsenide matrix an almost constant value of that ratio is found in the energy range under consideration. The figure shows that a determination of carbon with the reaction ‘2C(3He, a)“C would be connected with large uncertainties, if a sample contains boron in about the same or larger quantities than carbon. In this case it would be more appropiate to use different reactions producing final nuclei with different half-lives for the analysis, e.g. 12C(d,n)13N and “B(d,n)“C.
r lb -_
;j_/ / /
/’
1’
---
//
6
or)“C
at different
CU
GaAs
Au
Pb
41 13 7
43 13 8
74 23 13
82 24 13
ppbl
30 8 4
Interference with the nuclear reaction ‘ZC(3He, d)13N can occur if nitrogen is present in the material because of the “N(3He, a)13N reaction leading to the same final nucleus. The excitation function of the reaction “N(3He, (r)13N is published in ref. 1161. The ratio of the averaged cross sections of the 12C(jHe, cu)“C and “N(3He, a)13N reaction as a function of the projectile energy is shown in fig. 11. In this case the ratio exceeds a factor of 2 at bombarding energies above 9 MeV so that the possible interference is reduced. The limits of the determination of carbon in various matrices by the reaction ‘2C(3He, (Y)“C can be estimated making the following assumptions. In order to keep the irradiation time in reasonable limits we assume three half-lives of the product nucleus which is about 87.5% of the maximum accessible activity. If an initial count rate of 0.1 s- ’ is sufficient for the determination one can obtain with an efficiency of the detector arrangement of 12% and a 3He2+ ion beam current of 400 nA the detection limits at different projectile energies given in table 2. The calculated values do not consider the possibility of producing positron emitting nuclei from interfering reactions induced on the matrix or other impurities. In this case a chemical separation (e.g. hot extraction) should be performed to obtain low detection limits.
5. Conclusions
13N
,tF
‘*Cf3He,
a Projectde
SI- Matrix GaAs - Mohx
70 Energy
12
I MeV
14
1
Fig. 11. Averaged cross section ratio of the interference reactions ‘*C(‘He, d)13N and 14N(“He. ~u)‘~N in silicon and gallium arsenide.
The excitation function of the reaction ‘2C(3He, ol)“C shows a reasonably smooth shape allowing the use of this reaction for the determination of low carbon concentrations in the bulk of matrix materials, since the resonances do not affect drastically the integration of the fitted excitation function. The reaction I2 C( 3He, d)13N could be used as an alternative in those cases were the presence of interfering elements limit the application of the 12C( “He (Y)“C reaction. The different half-life of 13N offers &e possibility of distinguishing between the final nuclei “C and 13N. The cooperation stitut fiir Kernphysik
of the accelerator staff of the Inof the University of Frankfurt and
V. Liebler et al. / Carbon excitation functions
the financial support from the Federal Ministry of Research and Technology (BMFT) and the Stiftung Volkswagenwerk is gratefully acknowledged.
References
PI J.K. Hirvonen and G.K. Htibler, Proe. Conf. Ion Beam Surface Layer Analysis (Plenum Press, New York 1975). PI J.D. Mahony, UCRL 11780 (1965) [31 R.L. Hahn and E. Rieci, Phys. Rev. 146 (1966) 650. [41 F. Ajzenberg-Selove, Nucl. Phys. A433 (1984) 1. [51 O.D. Brill, Soviet J. Nucl. Phys. [Engl. transl.] 1 (1965) 37. [61 F. Ajzenberg-Selove, Nucl. Phys. A449 (1986) 1. 171 W. Fack, Diploma thesis, University of Frankfurt. Institut fttr Kemphysik (1978).
13
[S] R. Kohlhase; Diploma thesis, University of Frankfurt, Institut fiir Kernphysik (1982). (91 V. Liebler; Diploma thesis, University of Frankfurt, Institut ftir Kemphysik (1988). [lo] E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59 (1987) 1121. iIll CM. Lederer and VS. Shirley, Table of Isotones, 7th ed. (Wiley, New York 1978). [12] J.F. Ziegler, J.P. Biersack and U. Littmark, PRAL, The Stopping and Range of Ions in Solids (Pergamon, 1985). [13] D. Hasselkamp, Habilitation, University of Giessen/FRG /19x5\ \&,.,‘,. [14] R. Rothat&, communication. [15] P. Misaelides, J. Krauskopf, G. Wolf and K. Bethge, Nucl. Instr. and Math. B18 (1987) 281. [16] R.L. Hahn and E. Ricci, Nucl. Phys. Al01 (1967) 353.
DETERMINATION OF EXCITATION FUNCTIONS FOR CARBON BY CHARGED PARTICLE ACTIVATION ANALYSIS V. LIEBLER,
K. BETHGE,
J. KRAUSKOPF,
J.D. MEYER,
DETECTION
P. ~ISAELID~S
* and G. WOLF
Institut f6r Kemphysik, Universitiit Frankfurt am Main, FRG Received 31 August 1988
The excitation fictions of the reactions ‘2C(3He, a)“C and 12C(3He, d)13N have been measured in 100 to 200 keV steps in the energy region between 0.4 and 14.0 MeV considering all perceptible sources of errors. The absolute cross sections have been determined by measuring the annihilation radiation of positron emitting nuclei produced during the irradiation. The precision of the determination is in the order of 10%.
1. Introduction Nuclear reactions have been applied very successfully to the determination of light element impurities in different host matrices. In particular the amount of carbon impurities in semiconductors as silicon and gallium arsenide can be determined. The presence of carbon is of importance for the development of highly integrated semiconductor circuits, e.g. carbon in gallium arsenide acting as a shallow acceptor. There are only a few suitable chemical methods with high sensitivity for the determination of traces of carbon in semiconductor materials. Among them, the burning of the sample in an oxygen atmosphere and measuring carbon dioxide gives a sensitivity in the order of 0.1 pg/g [l]. The physical methods applied, like infrared absorption spectroscopy, give good results only when an accurate calibration is available. The charged particle activation analysis (CPAA) is an absolute method and can be used as a calibration of nonabsolute physical techniques. For this purpose very precise absolute cross sections of nuclear reactions are required. The nuclear reaction i*C( 3He, cu)“C is suitable for the determination of carbon by charged particle activation analysis because of its high cross section values up to 330 mb [2,3] and its zero threshold energy (Q, = 1.856 MeV 141). The reaction 12C(3He, d)r3N can be used as an alternative reaction to detect carbon, in e.g. materials containing boron leading to the nucleus “C by the reaction ‘“B(3He, d)“C too. The maximum cross section of the r*C( 3He, d)13N reaction amounts to 140 mb [2,3,5] and the threshold energy is 4.44 MeV (Q, = -3.55 MeV IS]). The determination of traces of nitrogen by the reaction 14N(‘He, (u)13N also requires the
knowledge of the excitation function of the reaction 12Ct3He, d)t3N, because both reactions lead to the same final nucleus. A number of authors published excitation functions for the nuclear reactions induced on carbon by 3He ions. But these data measured in wide energy steps show large uncertainties of the cross section as well as the reaction energy ]2,3,5]. The unpub~shed data of Fack [7] and Kohlhase f8] are also not reliably accurate. They are not sufficient for the purpose of analysis. In the present work the excitation functions of ‘*(J3He, ol)“C and l2 C( 3He, d)13N nuclear reactions were measured in the energy region between 0.4 and 14.0 MeV in energy steps of 100 to 200 keV. We tried to eliminate or at least to determine all sources of errors in order to achieve a high precision [9]. 2. Experimental method The total cross sections of the reactions ‘2C(3He, ol)“C and 12C(3He, d)13N were measured using 3He ion beams from the two Van de Graaff accelerators (2.5 and 7 MV) of the Institut fir Kernphysik of the University of Frankfurt. The cross section was determined by irradiating the samples and measuring the activity of the *‘C and r3N nuclei produced during the activation afterwards. “C and 13N are positron emitting nuclei with half-lives of 20.3 min [4] and 9.96 min [6] respectively. The accuracy of the determination of the cross section depends on the error minimization of the quantities in the following formula. The cross section o(E) given by u(E)
* Present address: Department of General and Inorganic Chemistry, Aristotelian University, Thessaloniki, Greece. 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holiand Physics abusing Division)
=
ear,A rqcDN,/3
AZ( tb) _(l At
_e-%)-’
includes the following two groups of quantities:
8
V. Liebler et al. / Carbon excitation functions
(1) constants taken from the literature: e elementary charge [lo], A atomic mass Ill], c isotope abundance 1111, NA Avogadros number [lo], ,8 probability of e+ decay compared to competing processes (for “C 99.8% [4], “N 100% [6]), X decay constant of the activated nucleus [4,6]; (2) parameters which have to be measured independently: charge of the projectile, determined by the maga netic deflection of the accelerated beam, c efficiency of the measuring system, total charge accumulated during the activation q period Ib, D target thickness in g/cm’, A Z( tb)/Aht counting rate. In the following sections the details of the measurement are described. 2. I. Targets The carbon targets were produced by evaporating carbon onto a glass plate, floating the foil off and mounting it on an aluminium frame. The thickness of each foil was then measured by the energy loss in the foil of 01 particles emitted from an 241Am-source. The statistical error included in this measurement is less than 2%. Rutherford backscattering of 3 MeV 4He+ ions was also used to control the thickness independently and determine the lateral homogeneity using the peak width in the spectrum. Due to the beam diameter of about 2 mm only a rough lateral resolution could be achieved. The measured values, however, deviate from the average value by less than 5% as shown in fig. 1. The stopping power values with an error of 5% were taken from ref. [12]. From the kinematics of the nuclear reaction i2C( 3He 9 cu)“C is known that the kinetic energy trans-
1
600
I
5 .OMeV
3He -+“t
in C
400-
200-
3He o- e)
beam
axis
zoo400-
x[%I Fig. 2. Averaged range distribution of “C nuclei in carbon calculated at a bombarding energy of 5 MeV from the kinematics of the ‘2C(3He, a)“C reaction (Q = 1.856, 0.144, - 2.463 and - 2.952 [4]).
fered allows the product nuclei to be ejected from carbon foils of 20 to 50 ug/cm* thickness. The ranges of “C nuclei produced by 5 MeV ‘He projectiles in a carbon target are shown as a two dimensional plot in fig. 2. This figure also indicates the Q values for the four possible excitation states in “C. From this figure it is obvious that a large fraction of the “C nuclei is lost unless a catcher foil in forward and backward direction is used. To stop all “C nuclei in forward direction a 2 mm tantalum foil was used. The maximum range of “C in
400
15.0MeV 3He .+
3He
‘*C in Al
overagedrange PI: I
----_
beam OXIS
0
3
6
9
12
15
X-Axis lmml
Fig. 1. Lateral thickness distribution of a carbon foil measured by RBS in comparison to the energy loss measurement (shaded).
Fig. 3. Straggling
of recoiling “C nuclei into aluminium bombarding energy of 5 MeV.
at a
9
V. Liebler et al. / Carbon excitation functions
tantalum in the energy range covered in this work is approximately 6 pm [12]. In backward direction an alu~~urn foil of 220 pg/cm* was used. This alu~nium foil is thick enough to stop all “C nuclei leaving the target in this direction, taking also in account the transversal u1 and longitudinal straggling u,, (fig. 3). For the determination of the reaction energy the energy loss of the 3He ions (50 to 300 kev) in the aluminium catcher foil has been taken into account. No aluminium catcher foils are required for the measurement of the cross section of the endothermal t* C( 3He, d)t3 N reaction, because the produced 13N nuclei are ejected in an angular range up to a maximum angle of 42*. Both catcher materials contain carbon and other light elements that can be activated during the bombardment. The surface impurities in the tantalum foil were reduced by removing 7 Frn of the surface by etching 2 min in a solution of one volume 40% HF and one volume 65% HNO, before each irradiation. The catcher foils were irradiated at different energies in order to correct the total activity induced in the target arrangement. The carbon content of the tantalum foil was about 0.6 ug/cm*, whereas the corresponding carbon concentration in aluminium amounted to 3 tLg/cm*. 2.2. Beam current ~e~~e~e~t The irradiation chamber was carefully insulated from the rest of the equipment. Thus the whole chamber could be used as Faraday cup. At the entrance of the chamber a 3 cm diameter aperture is mounted so that secondary electrons cannot escape. The production rate of the electrons is proportional to the electronic stopping power of the projectiles in the target material [13]. For 4 MeV 3He ions in carbon (electronic stopping power: 200 keV/um [12]) and a proportionality factor of 0.012 pm/keV 1131one obtains 2.4 secondary electrons per projectile. Taking into account that the maximum of the electron distribution, showing a cosine square shape, appears at 180° [14] one predicts, that less than 1% of the emitted secondary electrons can escape out of the Faraday cup. The precision of the current measurement including the quality of the current integrator and the insulations of the Faraday cup is about 3%.
corrections due to the absorption of the 511 keV yquanta in the tantalum catcher foil were made. A sufficient reduction of the background radiation from natural sources (@K etc.) could be achieved by sufficient lead shielding (0.007 s-t in coincidence). 2.4. Initial counting rates The absolute cross sections were deter~ned measuring the decay curve of the activated sample as a function of time. The important figure is the initial counting rate AZ( tb)/At at the end of the activation which can be extrapolated from a semilogarithmic plot of the actual counting rate. If, as a rule, several nuclei are activated during the irradiation, the initial costing rates have to be determined separately for each species in successive stages. Since the cross sections of the nuclear reactions studied increase with increasing bombarding energies in the low energy region under consideration, the errors are larger for the lower energies. Using the measured counting rates and the iterative procedure of the decay curve analysis for the “C decay we estimated errors of 0.5% for the energy region above 1.5 MeV and about 50% at bombarding energies around 400 keV. The corresponding errors in the case of 13N are about 5% above 6 MeV and about 50% at energies around 5.5 MeV respectively.
3. Results The errors of the cross sections for the ‘*C( 3He, e)‘*C reaction in the energy region above 1.5 MeV and the ‘2C(3He, d)13N reaction are 10% and 12% respectively. The experimental results for the reaction of ‘*C ( 3He, ,)I1 C are presented in fig. 4 and for the reaction l2 C( “He, d)t3N in fig. 5. The open and the full symbols
2.3. Efficiency After activation the target was positioned between two 4 x 4 in. NaI(Tl) detectors in order to measure in coincidence the ~n~iation radiation of the positrons emitted by the product nuclei. The precision of the efficiency determination is dependent on the absolute activity of the 22Na calibration source. All necessary
0
2
G 6 a IO Projectile Energy IMeVl
12
34
Fig. 4. Excitation function of the reaction “C(‘He, a)“C. Full symbols represent measurements with and open symbols without aluminium catcher.
V. Liebler et al. / Carbon excitation functions
10
Table 1 Cross section values of the reaction 12Cf3He, a)“C Energy [MeVj Cross section [mb]
for low energies
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.003
0.008
0.013
0.21
0.90
2.2
8.8
are presenting the results of measurements without and with an ahuninium foil respectively. The results obtained with both target arrangements show good agreement. The cross section values of ‘2C(3He, cu)“C for energies below 1.8 MeV are given in table 1. Since the excitation function is needed for the material analysis the shape of an averaging polynomial fit is important (see figs. 4 and 5). A few resonances in the excitation function of the reaction “C( 3He, cu)“C can be seen corresponding to excitation states in the compound nucleus I50 at Ecom = 14.4, 16.6, 17.4 and 21.2 MeV (Et,, = 2.8, 5.6, 6.7 and 11.4 MeV). These states obviously possess large a-widths. The experimental widths are 0.6, 0.3, 0.4 and
L_”
0 E
200
‘2C(3He,d)‘3N 0 C/la l
Al /C tTa
6
0 Projectile
Fig.
5. Excitation
10 12 Energy IMeVl
function of the reaction Symbols as in fig. 4.
Projectile
Energy
‘2C(3He,
< 0.2 MeV respectively. These values are given with uncertainties of 0.1 MeV. Spin assignments to these states are not well known [6] which prevents further conclusions regarding the structure of these states. A detailed representation of the cross sections in the neighbourhood of one of these resonances is given in fig. 6. After background subtraction using a linear fit the shape of the resonance is fitted to a Gaussian function. From this fit a center position at 2.84 k 0.04 MeV (EGO,,,= 14.35 f 0.03 MeV) and a FWHM of 0.66 + 0.05 MeV are deduced which is in good agreement with values taken from ref. [6] ( Ecom = 14.34 MeV and FWHM = 0.24 MeV). The fits to the other resonances are of nearly similar quality except that at 21.2 MeV, for which an upper FWHM value of 0.2 MeV can be given. The excitation function of the reaction ‘2C(3He, d) 13N shows one resonance at Elab = 8.22 + 0.05 MeV with a width of 0.43 & 0.07 MeV. The corresponding excitation state in “0 appears at 18.65 MeV. From previous measurements a state at 18.65 ]6] is known. The cross section values below 6 MeV bombarding energy are smaller than 10 mb and are difficult to determine accurately because of the interfering relative high “C activity produced simultaneously by the “CJ3He, a)“C reaction.
14
4. Discussion d)13N
The excitation functions of the two reactions investigated can be used for the analysis of carbon contaminations in semiconductor (e.g. silicon and gallium arsenide) and metal matrices. Using thick samples the projectiles penetrate the material, lose energy and come to rest. The trends of the projectile energy with sample depth as well as the change of the cross section with the depth are shown in fig. 7. In this case an averaged cross section O( E, Emin) taken between the projectile energy E and a minimum energy Emin which is, as a rule, the threshold energy of the nuclear reaction is of interest to determine unknown carbon concentrations [15]. The b( E, E,,,) is given by:
i MeVl
Fig. 6. Gaussian fit of the resonance at the 14.35 MeV state in I50 (E,,, = 2.84 MeV) of the excitation function of ‘2C(3He, cu)“C.
Therefore the averaged cross section depends on the matrix because of the material depending stopping
11
V. Liebler et al. / Carbon excitation functions
360
a
_ -
this work
-..---
HahnlRicci Brill
Si -Matrix t
Depth
turn1
Fig. 7. Dependence of projectile energy and cross section on the penetration depth in silicon and gallium arsenide at a bombarding energy of 14 MeV.
d E/dx. The integral over the excitation function is essential for the precision and the detection limits of the charged particle activation analysis. To obtain this integral it is however sufficient to use an averaged curve produced by a least square fit procedure. The measured resonances do not affect the integrated excitation function drastically. Figs. 8 and 9 represent the fit curves compared to those of previous measurements [2,3,5,7,8]. Deviations can be observed over certain energy regions.
power
LOO
‘2C(3He,a)“C -this work 300
z .-6
2
Ln 200
3 100
0 0
LO
120
80
40
0
”
-
&
8
Projectile
Energy
12
J
IMeVI
Fig. 8 Polynomial fit to the excitation function of the reaction ‘2C(3He, a)“C compared to those by other authors (Mahony [2], Hahn and Ricci [3], Fack [7] and Kohlhase [S]).
C
1
6 Projectile
,
10 Energy
I
11, [MeVI
Fig. 9. Polynomial fit to the excitation function ‘2C(3He, d)13N compared with the literature Hahn and Ricci [3] and Brill[5]).
of the reaction (Mahony [2],
Mahony [2] used for the measurement of the excitation function of the t* C( 3He, ,)I1 C reaction plastic foils of 2 mg/cm* thickness with a content of 93% carbon. Several of these foils were sandwiched between gold foils. The stack was irradiated by 30.7 MeV 3He ions. The corresponding energy of each plastic foil was estimated from the beam energy lost in the previous foils. In this way the energy determination was not very accurate. This fact might explain some of the deviations from the present data. Hahn and Ricci [3] activated a sandwich-target of three 0.01 mm teflon foils, but measured only the activity of the central foil. The results show a slight deviation of the peak position from the present work. Fack [7] used a catcher foil on which a carbon film was evaporated. The determination of the thickness of the carbon film introduced large errors. Kohlhase [8] measured integrated cross sections by activating thick samples. The results show at energy regions above 8 MeV large deviations from values obtained in this work. The comparison of the excitation function of the ‘*C( 3He, d)13N reaction with the previously published data shows good agreement (Hahn and Bicci [3], Brill [5]). The earlier data published by Mahony [2] deviate considerably due to the reason mentioned above. Considering the feasibility of these nuclear reactions for determination of carbon by CPAA, one has to check the possible interference with other competing nuclear reactions leading to the same product nucleus. The possible interference due to the matrix activation should also be taken into account.
K Liebler et al. / Carbon excitation functions
12
“C
5
-
SI- Matrlx
---
GaAs-
Table 2 Detection limits of the reaction bombarding energies
Matrw
Si [at.
6
\L--c 0
i
2
ProJectile
10 14
10
a
b
Energy
12
lr,
1
lMeV
Fig. 10. Averaged cross section ratio of the interference reactions ‘ZC(3He, cu)“C and “B(jHe, d)“C in silicon and gallium arsenide.
If boron and carbon are present in the sample the same final nucleus “C is produced by the 12q3He, cw)“C as well as by the ‘“B(3He, d)“C reaction. The excitation function of the second reaction was published before [15]. To estimate the feasibility of a carbon determination we plot the ratio of the averaged cross sections Z( E,Emi,) for the reaction ‘2C(3He, a)“C to that of ‘“B(3He, d)13N as function of the projectile energy E {fig. IO). For a silicon and a gallium arsenide matrix an almost constant value of that ratio is found in the energy range under consideration. The figure shows that a determination of carbon with the reaction ‘2C(3He, a)“C would be connected with large uncertainties, if a sample contains boron in about the same or larger quantities than carbon. In this case it would be more appropiate to use different reactions producing final nuclei with different half-lives for the analysis, e.g. 12C(d,n)13N and “B(d,n)“C.
r lb -_
;j_/ / /
/’
1’
---
//
6
or)“C
at different
CU
GaAs
Au
Pb
41 13 7
43 13 8
74 23 13
82 24 13
ppbl
30 8 4
Interference with the nuclear reaction ‘ZC(3He, d)13N can occur if nitrogen is present in the material because of the “N(3He, a)13N reaction leading to the same final nucleus. The excitation function of the reaction “N(3He, (r)13N is published in ref. 1161. The ratio of the averaged cross sections of the 12C(jHe, cu)“C and “N(3He, a)13N reaction as a function of the projectile energy is shown in fig. 11. In this case the ratio exceeds a factor of 2 at bombarding energies above 9 MeV so that the possible interference is reduced. The limits of the determination of carbon in various matrices by the reaction ‘2C(3He, (Y)“C can be estimated making the following assumptions. In order to keep the irradiation time in reasonable limits we assume three half-lives of the product nucleus which is about 87.5% of the maximum accessible activity. If an initial count rate of 0.1 s- ’ is sufficient for the determination one can obtain with an efficiency of the detector arrangement of 12% and a 3He2+ ion beam current of 400 nA the detection limits at different projectile energies given in table 2. The calculated values do not consider the possibility of producing positron emitting nuclei from interfering reactions induced on the matrix or other impurities. In this case a chemical separation (e.g. hot extraction) should be performed to obtain low detection limits.
5. Conclusions
13N
,tF
‘*Cf3He,
a Projectde
SI- Matrix GaAs - Mohx
70 Energy
12
I MeV
14
1
Fig. 11. Averaged cross section ratio of the interference reactions ‘*C(‘He, d)13N and 14N(“He. ~u)‘~N in silicon and gallium arsenide.
The excitation function of the reaction ‘2C(3He, ol)“C shows a reasonably smooth shape allowing the use of this reaction for the determination of low carbon concentrations in the bulk of matrix materials, since the resonances do not affect drastically the integration of the fitted excitation function. The reaction I2 C( 3He, d)13N could be used as an alternative in those cases were the presence of interfering elements limit the application of the 12C( “He (Y)“C reaction. The different half-life of 13N offers &e possibility of distinguishing between the final nuclei “C and 13N. The cooperation stitut fiir Kernphysik
of the accelerator staff of the Inof the University of Frankfurt and
V. Liebler et al. / Carbon excitation functions
the financial support from the Federal Ministry of Research and Technology (BMFT) and the Stiftung Volkswagenwerk is gratefully acknowledged.
References
PI J.K. Hirvonen and G.K. Htibler, Proe. Conf. Ion Beam Surface Layer Analysis (Plenum Press, New York 1975). PI J.D. Mahony, UCRL 11780 (1965) [31 R.L. Hahn and E. Rieci, Phys. Rev. 146 (1966) 650. [41 F. Ajzenberg-Selove, Nucl. Phys. A433 (1984) 1. [51 O.D. Brill, Soviet J. Nucl. Phys. [Engl. transl.] 1 (1965) 37. [61 F. Ajzenberg-Selove, Nucl. Phys. A449 (1986) 1. 171 W. Fack, Diploma thesis, University of Frankfurt. Institut fttr Kemphysik (1978).
13
[S] R. Kohlhase; Diploma thesis, University of Frankfurt, Institut fiir Kernphysik (1982). (91 V. Liebler; Diploma thesis, University of Frankfurt, Institut ftir Kemphysik (1988). [lo] E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59 (1987) 1121. iIll CM. Lederer and VS. Shirley, Table of Isotones, 7th ed. (Wiley, New York 1978). [12] J.F. Ziegler, J.P. Biersack and U. Littmark, PRAL, The Stopping and Range of Ions in Solids (Pergamon, 1985). [13] D. Hasselkamp, Habilitation, University of Giessen/FRG /19x5\ \&,.,‘,. [14] R. Rothat&, communication. [15] P. Misaelides, J. Krauskopf, G. Wolf and K. Bethge, Nucl. Instr. and Math. B18 (1987) 281. [16] R.L. Hahn and E. Ricci, Nucl. Phys. Al01 (1967) 353.