Optimization of the depth resolution for deuterium depth profiling up to large depths

doi:10.1016/j.nimb.2016.09.004

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Volume 387, 15 November 2016, Pages 103-114

https://doi.org/10.1016/j.nimb.2016.09.004 Get rights and content

Abstract

The depth resolution of deuterium depth profiling by the nuclear reaction D(³He,p)α is studied theoretically and experimentally. General kinematic considerations are presented which show that the depth resolution for deuterium depth profiling using the nuclear reaction D(³He,p)α is best at reaction angles of 0° and 180° at all incident energies below 9 MeV and for all depths and materials. In order to confirm this theoretical prediction the depth resolution was determined experimentally with a conventional detector at 135° and an annular detector at 175.9°. Deuterium containing thin films buried under different metal cover layers of aluminum, molybdenum and tungsten with thicknesses in the range of 0.5–11 μm served as samples. For all materials and depths an improvement of the depth resolution with the detector at 175.9° is achieved. For tungsten as cover layer a better depth resolution up to a factor of 18 was determined. Good agreement between the experimental results and the simulations for the depth resolution is demonstrated.

Introduction

The nuclear reaction D(³He,p)α is commonly used to determine the depth profile of deuterium in solids [1], [2], [3]. The total cross section of this reaction has a broad maximum around 630 keV with a cross-section maximum of about 850 mb: This relatively high cross-section allows high detection sensitivity and a low detection limit below 100 ppm. Differential cross sections for various reaction angles have been measured by a number of authors [3], [4], [5]. Nocente et al. derived a fit formula for the differential cross section, thus allowing to interpolate differential cross-section data for any angle [6]. The reaction has a high Q-value of 18.4 MeV resulting in high energetic protons of 11–14 MeV and α’s of 4.4–7.4 MeV using incident energies of 0.5–6 MeV. This high Q-value is advantageous in nuclear reaction analysis as the backscattered ³He particles can be easily stopped by a foil installed in front of the detector. Hence the signal of the high-energetic protons is usually background free.

By utilizing the energy spectrum of the emitted α-particles the deuterium depth profile can be derived with a depth resolution of several nm within the near-surface layer. This requires a special detector geometry with normal incidence and grazing exit angle, resulting in reaction angles close to 100° [1]. The analyzed depth, however, is limited to a near surface layer of several hundred nanometers: For many applications, such as the study of hydrogen isotope diffusion in metals [7], [8] or the determination of the amount of trapped deuterium in wall materials of nuclear fusion experiments [9], this shallow analyzed depth range is largely insufficient.

The deuterium depth profile can be reconstructed up to much larger depths from the proton energy spectra by using multiple incident energies: Analyzed depths up to about 40 μm in low-Z materials and up to about 8 μm in heavy materials such as tungsten have been demonstrated [2]. Main disadvantage of this method is the limited achievable depth resolution because of angular spread caused by the finite size of the detector aperture and by multiple small-angle scattering in the sample [2]. In [2] it is shown that for low-Z elements geometrical straggling dominates the deterioration of the depth resolution. This problem can be overcome by decreasing the width of the detector aperture (at the cost of detector solid angle and thus sensitivity). For samples containing high-Z elements multiple scattering is the dominant process limiting the depth resolution, see [2]: This process cannot be avoided.

For samples containing high-Z elements a possible available optimization parameter with respect to depth resolution is the reaction angle. At many experimental facilities the proton detector is situated at a reaction angle in the vicinity of 135°. This angle is usually used due to the technical limitation that angles around 100° are blocked by an α-detector for high-resolution, near surface D depth profiling and angles in the range 150–170° are blocked by Rutherford backscattering (RBS) detectors, while reaction angles around 135° are usually unused and offer enough space for (typically large) proton detectors. This technical solution, however, does not mean that this angle is optimal in any respect and the question arises if there exists a reaction angle which optimizes the depth resolution for deuterium depth profiling up to large depths.

General kinematic considerations for the D(³He,p)α reaction are presented in Section 2. It is shown that the optimum depth resolution for this reaction is achieved at reaction angles of 0° and 180°. These reaction angles are optimal for all materials at all depths and at all incident energies up to at least 9 MeV. In order to confirm this theoretical prediction the depth resolutions at 135° and at 175.9° were determined experimentally. As sample we used deuterium containing thin films buried under aluminum as low-Z, molybdenum as medium-Z and tungsten as high-Z materials. The experimental results are presented and compared with simulations in Section 3.

Section snippets

Optimum reaction angle for depth profiling

To find the best reaction angle for deuterium depth profiling we need to consider the change of the proton energy with respect to the reaction depth. The energy $E_{p}$ of the proton after the nuclear reaction is given by the equation for the energy of the light product of an inelastic collision [10]: $E_{p} = B {[\cos θ + \sqrt{[D / B - \sin^{2} θ}]}^{2} (E_{3 He} + Q),$ which is valid for $B ⩽ D$ . It was calculated that $B ⩽ D$ holds for all energies used.

Following abbreviation were used:

$B = \frac{M_{3 He} M_{p}}{(M_{3 He} + M_{D}) (M_{p} + M_{α})} (E_{3 He} / (E_{3 He} + Q)),$
$D = \frac{M_{D} M_{α}}{(M_{3 He} + M_{D}) (M_{p} + M_{α})}$

Experimental set-up

To check this theoretical prediction and to measure the depth resolution, the energy spread for two detectors at 135° and at 175.9° was measured. The energy spread was then divided by the calculated effective stopping power to derive the depth resolution.

All measurements were performed in the ion beam analysis laboratory of the E2M division at the Max-Planck-Institut für Plasmaphysik. The ion beam was generated by a 3 MV tandem accelerator. The accelerator terminal voltage was calibrated using

Summary

Kinematic considerations show that the best depth resolution for depth profiling with the D(³He,p)α reaction is achieved at angles of 0° or 180°. In order to confirm this theoretical prediction the depth resolution of an annular proton detector at 175.9° and a proton detector at 135° were determined experimentally and compared with simulations.

For determination of the energy spread at different energies proton energy spectra from the D(³He,p)α nuclear reaction were recorded at reaction angles

Acknowledgments

The technical assistance with ion beam measurements by J. Dorner and M. Fußeder and scanning electron microscopy investigations by G. Matern are gratefully acknowledged.

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Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Abstract

Introduction

Section snippets

Optimum reaction angle for depth profiling

Experimental set-up

Summary

Acknowledgments

References (15)

Depth distribution profiling of deuterium and ³He

J. Nucl. Mater.

Quantitative depth profiling of deuterium up to very large depths

Nucl. Instrum. Methods Phys. Res., Sect. B

Differential cross-section of the D(³He, p)α nuclear reaction and depth profiling of deuterium up to large depths

Nucl. Instrum. Methods Phys. Res., Sect. B

Cross section data for the D(3He, p)4He nuclear reaction from 0.25 to 6 MeV

Nucl. Instrum. Methods Phys. Res., Sect. B

Theoretical approximations for depth resolution calculations in IBA methods

Nucl. Instrum. Methods Phys. Res., Sect. B

Improved formulas for fusion cross sections and thermal reactivites

Nucl. Fusion

Cross section of the D+3He→α+p reaction of relevance for fusion plasma applications

Nucl. Fusion

Cited by (13)

Cross-section data for the reactions <sup>12</sup>C(<sup>3</sup>He,p<inf>0</inf>)<sup>14</sup>N to <sup>12</sup>C(<sup>3</sup>He,p<inf>6</inf>)<sup>14</sup>N at energies up to 6 MeV

Dynamic equilibrium of displacement damage defects in heavy-ion irradiated tungsten

3D deposition patterns of deuterium retention and impurities in the COMPASS divertor: a data-driven root cause analysis and prediction approach

Comparison experiment on the sputtering of EUROFER, RUSFER and CLAM steels by deuterium ions

Tritium measurements by nuclear reaction analysis using <sup>3</sup>He beam in the energy range between 0.7 MeV and 5.1 MeV

Experiments and modelling of multiple sequential MeV ion irradiations and deuterium exposures in tungsten