Nuclear Reaction Analysis (NRA)

Nuclear Reaction Analysis (NRA) M. Mayer Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching, Germany Lectures given at the Workshop on Nuclear Data for Science and Technology: Materials Analysis Trieste, 19-30 May 2003 LNS0822004 Matej.Mayer@ipp.mpg.de

Abstract Nuclear Reaction Analysis (NRA) is a widely used method for the quantitative determination and depth profiling of light isotopes. This lecture gives a brief introduction into the method. Reaction kinematics, experimental methods, cross section data sources, and computer simulation codes are discussed. Useful nuclear reactions using incident protons, deuterons, 3 He and 4 He ions are presented.

Contents 1 Introduction 85 2 Radiation Safety 85 3 Reaction Kinematics 86 4 Cross Section Data 88 5 Resonant and Non-resonant NRA 89 6 Filtering Methods of Unwanted Particles 91 7 Useful Nuclear Reaction 92 7.1 Proton induced reactions..................... 92 7.2 Deuteron induced reactions................... 92 7.3 3 He induced reactions...................... 96 7.4 α induced reactions........................ 98 7.5 Nuclear reactions for hydrogen analysis............ 98 8 Computer Simulation Codes 99 References 100

1 Introduction Nuclear Reaction Analysis (NRA) 85 Nuclear Reaction Analysis (NRA) is a nuclear method for the quantitative determination and depth profiling of selected light elements and isotopes. As it has many similarities with Rutherford Backscattering Spectrometry (RBS), detailed information about basic physical processes like energy loss of charged particles in solids and energy loss straggling can be found in many textbooks about RBS like [1]. While RBS is the method of choice for the detection and depth profiling of medium mass and heavy elements, it has major disadvantages for the detection of light elements: When a layer of a light element is positioned on top of a heavy substrate, then the RBS spectrum of the light element will overlap with the spectrum of the heavy element, which forms a huge background. In these cases, NRA can provide additional information which is not available by RBS. As nuclear reactions are isotope specific, they can easily be used for isotopic tracing. However, because a measurement at a specific energy and with a specific incident ion species detects only one (or maximum a few) different isotopes, the composition of a target cannot usually be determined by one measurement, but requires measurements at different energies and/or different incident ion species. The required equipment for RBS and NRA is basically the same. However, there are some differences in the required detectors, mainly due to the filtering of unwanted particles in NRA and smaller reaction cross sections compared to backscattering, which requires larger detectors. NRA with deuterium beams requires special radiation shielding, see section 2. Particle-particle reactions, particle-γ reactions, and particle-neutron reactions can be used for NRA. This report focuses on particle-particle reactions, for other types of reactions see e.g. [1]. 2 Radiation Safety Caution has to be observed when using beam energies exceeding the Coulomb barriers of elements present in the target or beam particles. Wanted and unwanted nuclear reactions will occur, and there can be radiation hazards from prompt or induced radiation. The extent of radiation depends on the beam, beam current, sample material, and facility layout and shielding. Deuterium beams have to be used with special care due to the D(d,n) 3 He reaction. Deuterium is implanted into parts of the accelerator and beam transport system

86 M. Mayer Figure 1: Schematic representation of a nuclear reaction. like apertures, and into the target, where it will react further with incident beam deuterons. As this reaction has no threshold, it may already occur at low beam energies, and the use of deuterium beams usually requires special shielding of the accelerator, beam transport system, and target chamber. Another notorious reaction is 9 Be( 4 He,n) 12 C, which has a high cross section at energies above about 2 MeV. Always consult your radiation safety professional before undertaking measurements involving nuclear reactions. 3 Reaction Kinematics The kinetics of a nuclear reaction is shown schematically in Fig. 1, the quantities used for nuclear reactions kinematics calculations are listed in table 1. We define the following quantities: A 13 = A 14 = A 23 = A 24 = M 1 M 3 (M 1 + M 2 )(M 3 + M 4 ) M 1 M 4 (M 1 + M 2 )(M 3 + M 4 ) M 2 M 3 (M 1 + M 2 )(M 3 + M 4 ) M 2 M 4 (M 1 + M 2 )(M 3 + M 4 ) E 1 E T E 1 E T ( 1 + M ) 1 Q M 2 E T ( 1 + M ) 1 Q M 2 E T

Nuclear Reaction Analysis (NRA) 87 Table 1: Quantities used for the calculation of nuclear reactions kinematics. The target nucleus is initially at rest. For exothermic reactions Q > 0, for endothermic reactions Q < 0. Mass Energy Incident ion M 1 E 1 Target nucleus M 2 0 Light product M 3 E 3 Heavy product M 4 E 4 Energy released in reaction Q Total energy E T = E 1 + Q = E 3 + E 4 The energy E 3 of the light product created in the nuclear reaction is then given in the laboratory system by ( ) ] 1/2 2 A24 E 3 = E T A 13 [cos θ ± sin 2 θ (1) A 13 θ is the emission angle of the light product in the laboratory system. For A 13 < A 24 only the plus sign in eq. 1 applies. If A 13 > A 24 then eq. 1 has two solutions, and the maximum possible emission angle θ max of the light product is ( ) 1/2 A24 θ max = arcsin (2) The energy E 4 of the heavy product created in the nuclear reaction is given in the laboratory system by A 13 ( ) ] 1/2 2 A23 E 4 = E T A 14 [cos Φ ± sin 2 Φ (3) A 14 Φ is the emission angle of the heavy product in the laboratory system. For A 14 < A 23 only the plus sign in eq. 3 applies. If A 14 > A 23 then eq. 3 has two solutions, and the maximum possible emission angle Φ max of the heavy product is ( ) 1/2 A23 Φ max = arcsin (4) Usually only nuclear reactions with positive Q-values are used for NRA, because the energy of the reaction products is higher than the energy of A 14

88 M. Mayer the incident beam and backscattered particles are well separated from the reaction products in the spectrum. This enables the use of the absorber foil technique for filtering of backscattered particles, see section 6 Some reactions with light target elements, like D(d,p)T, D( 3 He,p) 4 He, and D( 3 He, 4 He)p, result in reverse kinematics at backward angles: If the energy of the incident ion decreases, the energy of the emitted reaction product increases. These reactions therefore require special detection geometries for depth profiling. The energy of protons created in nuclear reactions may be very high. These high energetic protons are only partly stopped in typical solid state detectors, and the detection of these particles may require special detectors with large sensitive depths. 4 Cross Section Data Usually there is no analytical theory of nuclear reaction cross sections, and experimental data have to be used. As most nuclear reaction cross sections were measured in the years 1950 1970 for nuclear physics research and not materials analysis (usually to obtain information about the nuclear levels in the nuclei), they are only sometimes available at optimal angles, and they are often not precise enough for NRA. Many data were published only in graphical form, resulting in additional errors if these data are digitized from the original publications. A few reactions with light nuclei, like D(d,p)T and 3 He(d,p) 4 He, were re-measured or re-analyzed during the last two decades for nuclear fusion or astrophysical reasons [2], thus obtaining a higher accuracy. Graphical representations of many reaction cross sections can be found in [1, 3, 4]. Graphical representations and numerical values can be obtained from SigmaBase [5, 6], or with the program NRABASE [7]. The spectrum simulation program SIMNRA [8] contains many data files with cross section data, which can be used directly for computer simulations. Nuclear reaction cross sections are usually much smaller than backscattering cross sections. This requires higher beam currents or larger detector solid angles to obtain sufficient data statistics, which may cause large pulse pile up and background by backscattered particles. High fluxes of backscattered particles will also limit the detector lifetime. As the energy of reaction products is usually higher than the energy of backscattered particles, these particles can be eliminated by a filtering technique, e.g. by an absorber foil. See section 6 for details.

Nuclear Reaction Analysis (NRA) 89 Often more than one reaction is possible on a certain nucleus (especially in deuteron and 3 He induced reactions), resulting in different emitted particles or particles emitted at different energies if the target nucleus has several excited states close to the ground state. In these cases the spectra may be difficult to interpret because different peaks originating from different target isotopes may overlap. A proper choice of absorber foil and detector thickness may help to overcome this problem. In some cases narrow resonances exist, which allow high resolution depth profiling. See section 5 for details. Due to the uncertainty or unavailability of cross section data it is often necessary to use reference targets, which contain a well known amount of the detected element. Reference targets should be sufficiently thin to avoid significant change of the cross section due to energy loss of the incident beam, should be uniform over the beam area, and must have long term stability in air, vacuum, and under ion bombardment. Stability under ion bombardment can be a problem, and has to be checked carefully. The use of reference targets requires a reproducible beam current measurement. 5 Resonant and Non-resonant NRA Flat (or slowly) varying portions of the reactions cross section can be used for the determination of the overall near-surface content or depth profiling of a specific isotope. This is called non-resonant NRA. The depth resolution depends on the stopping powers of incident and emerging ions and the energy resolution of the detector. If sharp resonances (with a typical width of some kev) are used, this is called resonant NRA. In resonant NRA a high reaction yield is obtained only in a shallow depth region corresponding to the region of resonant cross section, see Fig. 2. By changing the incident beam energy the depth of the resonant region is changed. The beam energy can be changed either manually, or (better) by a fully automated system. Resonant reactions with charged particles in the exit channel or particle-gamma reactions can be used. An example of a cross section with resonant and non-resonant portions is shown in Fig. 3. The overall near-surface content ρ of a thin layer of an isotope can be determined in surface energy approximation from N = N 0Ωσ(E 0 )ρ, (5) cos(α)

90 M. Mayer Figure 2: Schematic representation of resonant NRA depth profiling. In the top part of the figure, the incident beam is resonant in a layer of the selected isotope. Increase of the beam energy shifts the resonant region deeper into the material. where N is the number of counts in the reaction product peak, N 0 the number of incident particles 1, Ω the detector solid angle, σ(e 0 ) the reaction cross section at incident energy E 0, ρ the number of nuclei per cm 2, and α the angle of incidence. This approximation is valid if the energy loss in the layer is small enough that the reaction cross section σ(e) is almost constant, i.e. σ(e) σ(e 0 ). For thicker layers the variation of the cross section cannot be neglected, and computer simulation codes like SIMNRA are necessary for data evaluation. See section 8 for details. In resonant depth profiling the depth scale is given by x = E 0 E Res S(E)/cos α, (6) where x is the depth in which the resonance occurs, E Res the resonance energy, and S(E) the averaged stopping power of the incident beam. The mean energy E, at which the stopping power is calculated, can be obtained from E = E 0 + E Res. (7) 2 1 For singly charged ions N 0 = Q/e, where Q is the total collected charge and e the nuclear charge.

Nuclear Reaction Analysis (NRA) 91 This is a linear approximation to the stopping power which can be used if the energy change is not too large. 6 Filtering Methods of Unwanted Particles Backscattered particles from the incident beam may cause large unwanted background count rates. The easiest method to stop unwanted backscattered particles is to place an absorber foil in front of the detector. Usually Mylar foils are used because they are pinhole free and show good thickness homogeneity, although aluminum foils can be used as well. The energy E of the particles after passing the foil is D E = E 0 S(E(x))dx, (8) 0 where E 0 is the initial particle energy, S(E) the stopping power of the absorber, and D the absorber thickness. For exothermal reactions the energy of light reaction products is higher than the energy of backscattered particles, and it is always possible to find an appropriate foil thickness which stops backscattered particles and transmits reaction products. The absorber foil technique can also be used to separate overlapping α and proton peaks due to the different stopping powers. The major disadvantage of this method is the degraded depth resolution due to additional energy loss straggling in the absorber foil. Nevertheless, it is the mostly used filtering method due to its simplicity and cheapness. Other filtering methods include: Electrostatic or magnetic deflection. This method gives better depth resolution than the absorber technique, but is rarely used due to the complicated setup. Time-of-flight (TOF) technique. This technique is based on the simultaneous measurement of energy and velocity of the particles, which allows to deduce the mass of the detected particles. This method gives a better depth resolution than the absorber foil technique, but may suffer from small detector solid angles and requires sophisticated electronics and a two dimensional multichannel analyzer. Another disadvantage is that large fluxes of backscattered particles may reach the detector, which may severely limit the detector lifetime.

92 M. Mayer Coincidence technique. Both reaction products are detected in coincidence in two different detectors at the appropriate angles. This technique is limited to thin foils in transmission geometry, as one of the reaction partners has to be detected in the forward direction. As in the TOF technique, the flux of backscattered particles may be high, thus limiting detector lifetime. Thin detector technique. This technique can be used if α- and protonpeaks overlap to separate the two peaks. This technique can be combined with the absorber foil technique. 7 Useful Nuclear Reaction 7.1 Proton induced reactions Although there are proton induced reactions with almost all light elements, many of the reactions suffer from low Q-values and are only of limited use. The most useful proton induced reactions are: Reaction Q-value [MeV] 7 Li(p,α) 4 He 17.347 11 B(p,α) 8 Be 8.582 18 O(p,α) 15 N 3.9804 19 F(p,α) 16 O 8.1137 All of these reactions can be used for depth profiling. The most frequently used proton induced reaction is 18 O(p,α) 15 N, which cross section is shown in Fig. 3 at θ = 165 [1, 9]. The natural abundance of 18 O is about 0.2%. The cross section varies slowly at about 750 kev incident energy, and this energy range can be used for non-resonant depth profiling. There is a resonance with a width of 2.1 kev at 629 kev, which can be used for resonant depth profiling. 7.2 Deuteron induced reactions Almost all light elements have deuteron induced reactions with positive Q- values. Most reactions are (d,p), but (d,α) and (d, 3 He) can also be used. Often there are many excited states of the created nucleus, resulting in many groups of emitted particles, like 14 N(d,p 0 6 ) 15 N or 19 F(d,p 0 15 ) 20 F.

Nuclear Reaction Analysis (NRA) 93 Figure 3: Cross section for the 18 O(p,α) 15 N reaction at 165. From [1]. This results in complicated spectra and interference of emitted particles from different elements. Caution has to be observed when using deuterium beams due to the D(d,n) 3 He reaction, which may result in high levels of radiation. See section 2 for details. Useful and often used deuterium induced reactions with protons in the exit channel are: Reaction Q-value [MeV] 2 D(d,p) 3 T 4.033 3 He(d,p) 4 He 18.352 12 C(d,p) 13 C 2.722 14 N(d,p 0 6 ) 15 N 8.610 (p 0 ) 16 O(d,p 0,1 ) 17 O 1.917 (p 0 ) 19 F(d,p 0 15 ) 20 F 4.247 (p 0 ) These reactions are usually not suitable for depth profiling due to the small stopping powers of incident deuterons and exit protons, but allow to measure easily the overall near-surface content. For depth profiling reactions with α s in the exit channel should be used, see below.

94 M. Mayer Figure 4: Total cross section for the 2 D(d,p) 3 T reaction. From [1]. The total cross section for the D(d,p)T reaction is shown in Fig. 4 [1, 2]. This reaction is always present if a deuteron beam is used. The reaction has no threshold and occurs already at low energies. It is always accompanied by the D(d,n) 3 He reaction with a branching ratio of 50%. The cross section for the 12 C(d,p) 13 C reaction is shown in Fig. 5 [1, 10]. The cross section has a plateau at around 0.9 MeV, which can be used for overall surface carbon content measurements. The cross sections for the 16 O(d,p 0 ) 17 O and 16 O(d,p 1 ) 17 O reactions are shown in Fig. 6 [1, 4]. These are the most frequently used reactions for detection of 16 O. Because the p 0 peak may overlap with protons from the D(d,p)T reaction, and also due to the higher cross section, usually the p 1 peak is used at deuteron energies of 0.8 0.9 MeV (typically 0.83 MeV). The measured spectrum with 834 kev deuterons on a SiO 2 /Si sample is shown in Fig. 7. There is an extra peak due to the 12 C(d,p) 13 C reaction. The carbon originates from hydrocarbon layer formation at the sample surface during ion bombardment due to poor vacuum conditions. Deuterium is implanted into the surface as a result of the deuterium bombardment, resulting in protons from the D(d,p)T reaction. The following reactions can be used for depth profiling with high depth

Nuclear Reaction Analysis (NRA) 95 Figure 5: Cross section for the 12 C(d,p) 13 C reaction at 165. From [1]. Figure 6: Cross sections for the 16 O(d,p 0) 17 O and 16 O(d,p 1) 17 O reactions at 135. From [1].

96 M. Mayer Figure 7: Measured spectrum of 834 kev deuterons on a SiO 2/Si sample. From [1]. resolution: Reaction Q-value [MeV] 3 He(d,α) 1 H 18.352 9 Be(d,α) 7 Li 7.153 10 B(d,α) 8 Be 17.818 16 O(d,α) 14 N 3.11 An absorber foil cannot be used, because an absorber that would stop backscattered deuterons would also stop the α-particles. Therefore these reactions cannot be used with high Z targets. 7.3 3 He induced reactions 3 He induced reactions are available for many light elements and offer an alternative if deuteron beams cannot be used. Often there are many excited states of the created nucleus, resulting in many groups of emitted particles. This results in complicated spectra and interference of emitted particles from different elements. Useful 3 He induced reactions are:

Nuclear Reaction Analysis (NRA) 97 Figure 8: Total cross section for the D( 3 He,p) 4 He reaction. From [1]. Reaction Q-value [MeV] D( 3 He,p) 4 He 18.352 D( 3 He,α) 1 H 18.352 12 C( 3 He,p 0 11 ) 14 N 4.7789 (p 0 ) 12 C( 3 He,α) 11 C 1.8563 16 O( 3 He,p 0 7 ) 18 F 2.0321 (p 0 ) 16 O( 3 He,α) 15 O 4.9139 The D( 3 He,p) 4 He and D( 3 He,α) 1 H are often used for the determination of the overall near surface content and depth profiling of deuterium. The total cross section for this reaction is shown in Fig. 8 [1, 2]. The cross section maximum is at about 640 kev incident energy. The energy of the emitted protons is about 12.4 MeV, resulting in a range in silicon of almost 1 mm. These protons are only partly stopped in silicon detectors with a typical thickness of about 100 µm and may overlap with other peaks. The use of this reaction requires thick detectors with a thickness of > 500 µm to avoid peak overlap. The proton spectrum using 2.5 MeV 3 He from a sample containing a thick layer of D, Be and C is shown in Fig. 9. The proton peaks from the D( 3 He,p) 4 He, 9 Be( 3 He,p 0,1 ) 11 B, and 12 C( 3 He,p 0,1 ) 14 N reactions are clearly

98 M. Mayer Counts (arbitrary value) 400 300 200 100 0 p 1 C p 0 Be p1 p 0 D 0 1000 2000 Channel number Figure 9: Proton spectrum from a sample containing a thick layer of D, Be and C, bombarded with 2.5 MeV 3 He at 135. A Mylar absorber was used to stop backscattered 3 He. The three curves were measured at different sample positions. separated. 7.4 α induced reactions Only a few light elements have α induced reactions with positive Q-values. The cross sections are high enough only at rather high energies (E > 2 MeV) and contain many narrow resonances. α induced reactions are rarely used for NRA, and usually better alternatives using incident deuterons or 3 He ions are available. 7.5 Nuclear reactions for hydrogen analysis Besides elastic recoil detection analysis (ERDA) resonant reactions are used for hydrogen depth profiling. The most often used reaction is 15 N + 1 H 12 C + 4 He + γ (4.43 MeV) (9) This reaction has a large cross section at a resonance energy of 6.385 MeV with a width of only about 5 kev. The γ is observed, not the charged particles. Other reactions using 7 Li or 19 F exist, but have either smaller cross

Nuclear Reaction Analysis (NRA) 99 sections (resulting in smaller sensitivity) or a larger width (resulting in decreased depth resolution). For a discussion of advantages and disadvantages see [1]. Like all resonant reactions (see section 5) these techniques require a change of the incident beam energy. 8 Computer Simulation Codes There are only few computer simulation codes available for NRA data analysis. SIMNRA by M. Mayer, Max-Planck-Institute for Plasma Physics, Garching, Germany, [8], is a spectrum simulation code for Rutherford backscattering (RBS) and NRA. It allows to simulate backscattering and NRA spectra for a given target structure. The program already contains a large number of cross section data files, and the cross section data base can easily be extended. SENRAS by G. Vizkelethy, Idaho State University, USA [11] is another spectrum simulation program for NRA. NRABASE by A. Gurbich, Institute of Physics and Power Engineering, Obninsk, Russia [7], is a database for nuclear reactions cross sections, Q-values and references. Cross section data can be obtained in graphical and numerical form. Acknowledgments The spectra shown in Fig. 9 were measured by M. Rubel, Royal Inst. of Technology, Stockholm, Sweden.

100 M. Mayer References [1] J.R. Tesmer and M. Nastasi, Eds. Handbook of Modern Ion Beam Materials Analysis. Materials Research Society, Pittsburgh, Pennsylvania, 1995. [2] H.-S. Bosch and G.M. Hale. Nucl. Fusion 32 (1992) 611. [3] R. Jarjis. Nuclear Cross-section Data for Surface Analysis, vol. 1. University of Manchester, England, 1979. [4] R. Jarjis. Nuclear Cross-section Data for Surface Analysis, vol. 2. University of Manchester, England, 1979. [5] G. Vizkelethy. SigmaBase: Data base and data server for ion beam analysis. http://ibaserver.physics.isu.edu/sigmabase/. [6] G. Battistig. SigmaBase (European mirror): Data base and data server for ion beam analysis. http://www.mfa.kfki.hu/sigmabase/. [7] A. Gurbich. NRABASE: Nuclear reaction data for ion beam analysis. Can be obtained from the SigmaBase Web Site. [8] M. Mayer. SIMNRA: Simulation of RBS, ERD and NRA spectra. http://www.rzg.mpg.de/ mam/. [9] G. Amsel and D. Samuel. Anal. Chem. 39 (1967) 1689. [10] M.T. McEllistrem, K.W. Jones, R. Chiba, R.A. Douglas, D.F. Herring, and E.A. Silverstein. Phys. Rev. 104 (1956) 1008. [11] G. Vizkelethy. SENRAS: Simulation program for nuclear reaction analysis. Can be obtained from SigmaBase.