Nuclear Engineering

Nuclear reaction Analysis (NRA)

In nuclear reaction analysis presence of any element (particularly low mass elements, like C, N, O) is detected through the nuclear reactions emitted almost instantaneously from nuclear reactions produced in the target by the irradiating beam. One advantage of this analysis is combining it with backscattering spectrometry, highly sensitive depth profiling of elements particularly distributed in the surface and near-surface region of a material can be done. The characteristics of the emitted radiations from various depths depend on the energy loss of the incident ions as they go into the sample and also the charged particles emitted from the reactions as they come out from the sample. The primary emphasis of this lecture is to discuss how to determine concentration depth profile of various trace element impurities by analyzing some nuclear reactions. First let us see the basic methodologies:


Basic Methodology

For depth profiling using NRA, two different methods are generally adopted, namely the energy-analysis method and the resonance method.⁵ In the first case the energy of the analyzing beam is kept fixed and during analysis, the energy spectra of the particles from which the depth profiles are derived, are recorded. The second method known as resonance is used when a sharp peak (resonance) as a function of energy is obtained. In this case, the depth profile is derived from a measurement of the nuclear reaction yield as a function of the energy of the analyzing beam


Let us first discuss the energy analysis method.

In this technique both neutrons and charged particles are used as probes. Let me begin with the following neutron induced reaction ¹⁰B(n,α)⁷Li. The energy of emitted alpha particles is ~1.5 MeV and the reaction cross section is ~4000 barns.⁶ The charged particles (alpha and Li), which are emitted isotropically due to this reaction start travelling to the outward path and leave the sample and detected in a suitable detection system. The energy of the detected particle depend on the energy loss of the particle in the outward path and the depth (from the surface) where the nuclear reaction takes place. The energy difference (ΔE) of the alpha particle from the surface and from a layer at a depth t is given by:


A quantitative analysis of the elemental distribution with depth, i.e. depth profile is generated directly from the charged particle spectrum. The range which can be considered the distance the particles can travel after creation and still exit the surface varies with composition.


*Let us now see the nuclear reactions induced by charged particles:*

In charged particles induced reactions the incident particle energy is high enough so that it can penetrate through the Coulomb barrier resulting in various nuclear reactions. For example, a deuteron of ~1.7 keV when bombarded on aluminium nitride target results in following nuclear reactions:⁷ ²⁷Al (d,p)²⁸Al, ¹⁴N(d,p)¹⁵N, ¹⁴N(d,α)¹²C. The schematic of the geometry and the reactions associated with this specific example is shown in Fig. m5.9.

FIGURE m5.9 Schematic of deuterium induced reaction and basic arrangement from depth profiling of Al_xN/Ni
The elastically scattered particles are stopped in a thin absorber to prevent count rate saturation of the detector and electronic system. Let us now see the basic equations those govern the layer composition and depth profile using this nuclear reaction process. Similar to RBS The number of detected particles Y_D is proportional to the areal concentration (atoms/cm²) N_t and is given by the following equation:

where σ(θ) is the differential cross section, Q is the number of incident particles, and Ω the detection solid angle. However, the cross section in this process cannot be represented by a simple analytical formula. This can be obtained from the nuclear physics literature. For depth profiling, the energy difference between the detected particles originating from the surface and from a depth d depends on the energy losses in inward and outward path.

The difference between this and RBS is that the kinematic factor K of RBS is replaced by reaction factor a.6 If the cross section of a reaction is known, the concentration profile can be deduced from the shape of the experimental spectrum.

Nuclear Engineering

Nuclear Engineering

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Nuclear reaction Analysis (NRA)

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