Keywords

67.1 Principle

Nuclear reaction analysis is a method to quantitatively determine the concentration versus depth distribution of light elements in the near-surface region of solids. To detect a specific nucleus A, the analyzed material is bombarded with a beam of projectile ions (a) at a high energy (100 keV–20 MeV) that is sufficient to overcome the Coulomb repulsion barrier to fuse the nuclei of a and A. Conserving the total energy, the resulting nuclear reaction A(a,b)B forms a new nucleus B and emits secondary particles (b: protons (p), neutrons (n), 4He ions (‘α particles’) and/or γ-photons) with well-defined high (keV–MeV) energies. The presence of nucleus A in the target is then proven by registering such secondary particles (b) or the reaction product (B) with a suitable detector. The reaction yield (Y) is proportional to the efficiency (‘cross section,’ σ) of the nuclear reaction, to the number of incident ions (Qa), and to the content of A (cA) in the target: Y ∝ σ·Qa·cA. An unknown cA in a sample is thus quantified by normalizing the reaction yield to the number of incident beam ions and by relating this to a measurement of a reference target (standard) with a well-known content of A under identical conditions.

The depth information on the target nucleus location obtained through NRA is based on the energy loss (or ‘stopping’) that the charged particles (the projectile ions going into and/or the emitted secondary particles or products exiting from the target) suffer inside the analyzed material due to electronic friction. This energy loss (ΔE) is proportional to the traveled distance (z) of the respective particle inside the target, i.e., ΔE = zS, where S = dE/dz (keV/nm) is the so-called stopping power of the material.

Many nuclear reactions between light elements can occur in the MeV regime [1]. They are insensitive to the chemical bonding state of the target nucleus and—due to different neutron numbers—not only element- but also isotope-specific, i.e., reactions of 1H, 2D, 14N, 15N, and 16O, 18O, for example, are distinctly different. The cross section of each nuclear reaction has its own unique dependence on the collision energy (E): The σ(E) variation can be strong or smooth in certain ranges, and some nuclear reactions have narrow resonances at certain energies (Eres), where σ is strongly enhanced over the neighboring non-resonant regions.

Such narrow resonances in σ(E) are highly versatile for depth profiling, because the stopping effect makes the depth in the target at which the nuclear reaction occurs selectable through the incident ion beam energy (Ei). For Ei = Eres, the beam reacts with target nuclei on the sample surface, whereas for an initial Ei larger than Eres, the energy loss below the surface reduces the projectile energy so that it meets the narrow energy window of the resonant reaction at a well-defined probing depth d = (Ei−Eres)/S (Fig. 67.1a). By measuring the reaction yield (Y) as Ei is incrementally scanned across and beyond Eres (Y(Ei), an ‘excitation curve’) the depth distribution of the target nucleus in the sample is thus revealed. Notable reactions for narrow-resonance NRA are 18O(p,α)15N (Eres = 150 keV, 50 eV width) for 18O profiling with proton beams [2] and 1H(15N,αγ)12C (Eres = 6.385 MeV, 1.8 keV width) for 1H NRA with 15N beams [3].

Fig. 67.1
figure 1

(a) Principle of narrow-resonance NRA. Due to energy loss by stopping in the target the projectile energy reaches Eres in a probing depth d = (Ei-Eres)/(dE/dz), (b) 1H depth profiling with the 1H(15N,αγ)12C reaction. Surface hydrogen reacting with 15N incident at Ei = Eres is distinguished from H buried inside the material, which reacts at Ei = Eres + ΔE

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In the following, we focus exemplarily on 1H NRA with 15N, as it has found a very large number of applications for the analysis of H at surfaces and interfaces [4]. 1H NRA via 1H(15N,αγ)12C is particularly elegant as the reaction emits highly penetrating γ-rays of 4.43 MeV that can be registered with a detector outside of the analytic vacuum chamber, and the energy loss of the 15N projectile alone defines the probing depth (Fig. 67.1b). In general, the near-surface depth resolution in resonant NRA is roughly defined by the resonance energy width divided by S, but it decreases in larger probing depths due to the ‘straggling’ effect that broadens the energy distribution of the projectiles due to random scattering in the analyzed material. For 15N near 6.4 MeV, S = 1–4 keV/nm, and including an additional Doppler broadening effect due to H-vibration, 1H(15N,αγ)12C NRA provides for a resolution of a few nm near the surface before straggling becomes the dominating limitation for the depth resolution from depths of 10–20 nm [4].

Also, nuclear reactions with smoothly varying or plateau-like cross sections (and even with rather broad resonances such as the large, ~350 keV wide resonance at 630 keV in the 2D(3He,p)4He reaction cross section widely utilized for D analysis with 3He beams [5]) are useful for depth profiling. In such non-resonant NRA, Ei is kept constant while the energy distribution of the outgoing particles is analyzed with a surface barrier detector near the target. Such a detector typically has to be protected from scattered beam ions by a filter foil, which causes additional energy loss and reduced depth resolution due to straggling. Because heavier particles have larger stopping powers, it is advantageous for 2D(3He,p)4He to detect the product 4He atoms (rather than the protons) to obtain better depth resolution (10 nm near the surface have been demonstrated [6]).

67.2 Features

  • Quantitative light element depth profiling

  • Quasi nondestructive (for many conductive target materials)

  • For 1H-15N NRA via 1H(15N,αγ)12C: (near-surface) depth resolution: 2–5 nm (surface-normal beam incidence); <1 nm (surface-grazing incidence)

  • Sensitivity for surface-H coverages: a few % of a monolayer (~1013 cm−2)

  • Sensitivity for volume (‘bulk’) H concentrations: ~100 ppm (~1018 cm−3)

  • Direct zero-point vibration energy measurement of H in adsorption layers.

67.3 Instrumentation

The principle and practice of NRA measurements via the resonant 1H(15N,αγ)12C reaction have been described in detail [4, 7]. The high energy 15N ion beam near 6.4 MeV (up to ~10 MeV, 15N2+) is generated with an electrostatic accelerator. Typically, a Faraday cup upstream of the target measures the ion beam current. Removing it from and inserting it into the beam path can be used to define the acquisition time during which the sample is irradiated by the ion beam at a given 15N energy. The targets are held electrically insulated in (ultra) high vacuum on manipulation stages, which allows for incidence angle and position alignment. To detect the γ-rays from the 1H(15N,αγ)12C reaction, lead-shielded bismuth germanate (Bi4Ge3O12, BGO) scintillation crystals coupled to photomultiplier tubes are placed closely to the sample outside the vacuum chamber. The 4.43-MeV γ-rays are identified through pulse height analysis with a multichannel analyzer. The number of incident 15N projectiles can be evaluated from the sample charge acquired through a current integrator. Quantitative (absolute) H concentrations are obtained through background subtraction, normalizing the γ-counts to the number of incident 15N ions, and calibrating the sensitivity of the γ-detection system with a standard sample of precisely known H content (such as Kapton® foil).

67.4 Applications

Two major purposes of 1H NRA with 15N are to quantify the H coverage on surfaces and to determine the depth location and quantity of hydrogen at buried interfaces; analytical tasks difficult to accomplish with other methods. Figure 67.2a exemplifies for H-terminated Si(111)-(1 × 1) that a single layer of surface-H atoms appears in the NRA γ-yield profile as a peak at Eres with a FWHM of several (here: 12.7 ± 0.4) keV. A Doppler effect in the 15N–1H collisions due to H-Si zero-point vibration broadens the profile substantially beyond the nuclear reaction resonance width, which causes the nearly Gaussian shape. The profile width allows extracting the zero-point vibrational energy (123.4 ± 4.6 meV for H-Si) [8]. The profile integral is proportional to the H coverage, in this case 1.0 monolayer (ML).

Fig. 67.2
figure 2

NRA γ-ray yield profiles from (a) bare Si(111)(1 × 1)–H and after deposition of 4.5 nm Pb at (b) 360 K, and (c) at 110 K. (d) and (e): illustrations of Pb growth on Si(111)(1 × 1)–H at 360 K and 110 K, respectively. The solid curves are fits to Gaussian forms [a sum of two Gaussians for (b)]. Adapted with permission from Ref. [9]. Copyright (1999) by the American Physical Society

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After depositing 4.5 nm Pb at 110 K, the integral γ-yield of profile (c) is the same, but it broadens (to 21.3 ± 1.3 keV), and its center shifts (by 10.3 ± 0.4 keV) above Eres. As neither Si nor Pb dissolve H, this indicates conservation of the full initial Si(111)-(1 × 1)-H coverage underneath a uniform (~4.4 nm thick) Pb overlayer (Fig. 67.2e), which causes energy straggling and stopping of the 15N ions before they react with H at the Pb/Si interface. Depositing 4.5 nm Pb at 360 K splits the γ-yield curve (b) into a surface component at Eres and a second (24.0 ± 8.5 keV wide) peak at 23.5 ± 3.5 keV above Eres (holding 0.4 ML H). Here, the interfacial H is shaded by thicker Pb islands of 10.1 nm height, between which 0.6 ML surface-H on the Si substrate remain directly accessible to the incident 15N beam (Fig. 67.2d), revealing a change in the Pb growth mode between 110 and 360 K.

Another important application of 1H(15N,αγ)12C NRA is the direct observation of the dynamical behavior of hydrogen in the near-surface region of H-absorbing materials (such as Pd) during desorption from and diffusion into the target, which can be achieved by evaluating the thermal stability of surface-adsorbed and material-absorbed H species in a depth-resolved fashion. In the following example, this technique is applied to identify the two peaks in the H2 thermal desorption spectrum (TDS) (Fig. 67.3a) from H2-exposed Pd(100) that are difficult to interpret without additional information. The NRA profile of identically prepared Pd(100) (Fig. 67.3b) has a dominant peak at Eres indicating 1.0 ML of surface-H and additional γ-yield due to ~2.6 at. % of H in a few nm wide region below the surface. Probing the surface and the Pd-absorbed H selectively with NRA at two fixed Ei values (arrows in Fig. 67.3b) while raising the sample temperature (T) in increments yields T-dependent NRA signals of the respective H species. These signals drop sharply at temperatures that coincide with the peak positions in the H2 TDS (Fig. 67.3a). The comparison clearly assigns the peak at 180 K to desorption of the Pd-absorbed hydrogen and the one at 330 K to desorption of surface-H.

Fig. 67.3
figure 3

(a) H2 TDS trace and (b) NRA profile of Pd(100) exposed at 100 K to 300 L H + H2 (1 L = 1.33 × 10−4 Pa s). Temperature-dependent NRA signals of the surface (d = 0 nm) and near-surface absorbed (d = 6 nm) H (arrows in (b)) are superimposed in (a). Adapted with permission from Ref. [10]. Copyright (2008) by the American Physical Society

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Finally, Fig. 67.4 illustrates NRA under a surface-grazing incidence angle (αi), which—by virtue of increasing the depth resolution - accomplishes the observation of hydrogen inside Pd nanocrystals that measure merely 1–2 nm in height. For such small particles, the width of the Doppler-broadened resonance peak (~10 keV, cf. Figure 67.3b) would preclude discriminating Pd-absorbed H from H on the surface under surface-normal 15N incidence. The grazing incidence geometry (inset in Fig. 67.4, αi = 75°), however, elongates the 15N ion path in the Pd by a factor of 1/cos(αi) which expands the ‘apparent depth’ axis of the NRA profiles (~4 times). On this enlarged scale, the γ-yield profile can be broken down into a surface peak (red) and a component for the H absorbed in the interior of the Pd nanocrystals (blue). Raising the H2 pressure (Fig. 67.4b, c) causes the amount of Pd-absorbed H to increase, whereas the surface-H remains saturated [11]. This NRA-based insight into the pressure-dependent H-breathing of Pd nanocrystals has been instrumental in assigning the role of the reactive species in the Pd-catalyzed hydrogenation of 2-butene (C4H8, an olefin with an unsaturated C=C double bond) to Pd-absorbed hydrogen [12]. The example highlights that NRA is even useful to study the behavior of near-surface hydrogen in chemical reactions.

Fig. 67.4
figure 4

Grazing incidence NRA γ-ray yield profiles from h = 1–2 nm high Pd nanocrystals exposed to (a) 2 × 10−5 Pa, (b) 6 × 10−4 Pa, and (c) 2 × 10−3 Pa H2 at 90 K. Components of surface-H (red shaded) and of H absorbed inside the nanocrystals (blue curves) are indicated. Inset Grazing incidence NRA geometry and schematic morphology of Pd nanocrystals supported on a thin H-free Al2O3 film on a NiAl(110) backing. Adapted with permission from Ref. [11]. Copyright (2008) by the American Physical Society

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