Absolute cross section for forward recoiling hydrogen with 1.0–12.5 MeV ⁴He

Abstract

The differential cross-section for forward recoiling hydrogen with ⁴He ions has been determined for the energy range of 1.0–12.5 MeV at a laboratory angle of 30°. Relative measurements of the cross-section were determined from a magnetron sputtered diamond-like carbon thin film deposited on a polished molybdenum substrate. Polystyrene (C₈H₈) thin films were used as a standard to re-normalize the relative cross-section measurements through the Rutherford cross-section of carbon. This technique allowed the determination of all data points to 5% absolute error over the entire energy range. A polynomial fit of the absolute cross section is also presented.

Introduction

The detection and quantification of hydrogen in materials is important to the fundamental understanding of the properties of many material systems. In diamond-like carbon [1], [2], [3], [4] it is known to dramatically alter the optical, electrical and mechanical properties of the material and in semi-conductor devices it is a necessary dopant used to passivate the dangling bonds at the Si–SiO₂ interface [5]. Further, profiling and quantification of hydrogen is commonly used in metallurgical science [6], [7], nuclear fusion technology and polymeric science [8] for material process analysis.

Many techniques exist for hydrogen determination: secondary ion mass spectroscopy (SIMS) [9], [10], [11], microcombustion analysis [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], nuclear magnetic resonance (NMR) [13], Fourier transform infrared spectroscopy (FTIR) [13], [14], nuclear reaction analysis (NRA) [15] and elastic recoil spectroscopy (ERS) [16], but few are absolute and most are destructive. ERS, however, is a technique that is non-destructive in many materials, and provides both elemental quantification and depth profiling capabilities. When used in conjunction with helium Rutherford backscattering spectroscopy (RBS), full element detection and profiling is feasible. However, quantitative measurements require accurate knowledge of the cross-sections. Previous measurements of the forward recoiled hydrogen cross-section measurements with helium at low energies ¹H(⁴He,¹H)⁴He [17], [18], [19], [20], [21], [22], [23], [24] show large variance between each other and span energies from 0.6 to 5.0 MeV. Measurements at higher energies [25], or using the inverse reaction of protons scattered from ⁴He [26], [27], [28] are limited to ⁴He energies above 6 MeV. In this work, we have measured the hydrogen recoil cross-section at energies spanning over a decade, from 1.0 to 12.5 MeV, and implemented a measurement technique which reduces common systematic errors.

Two types of hydrogen bearing samples were used to determine the absolute hydrogen cross-section at a laboratory angle of 30°. A series of thin, ∼1000 Å, polystyrene films spin coated on silicon substrates were used as the standard for the hydrogen cross-section determination at 2.0 and 3.04 MeV.² These samples, however, were impractical for the full series of measurements performed. This is due to high degree of ion induced hydrogen loss observed in these samples, which would mandate frequent sample substitution for accurate carbon/hydrogen ratios. Moreover, the carbon/silicon cross sections become strongly non-Rutherford above ∼2.5 MeV which would have resulted in errors due to background subtraction. Therefore, the use of these samples would require carbon/hydrogen calibration at low energy for each sample as well as the determination of hydrogen loss rates at the measurement energy. These difficulties were circumvented by using ‘radiation hard’ [29] diamond-like carbon (DLC) thin films deposited on highly polished molybdenum substrates. After an initial ≃10% decline of the original hydrogen signal during the first 30 particle μC of bombardment, no further decrease in the hydrogen yield was observed. This allowed repeated, high fluence measurements with no significant deviation in the hydrogen ERS signal. However, since the carbon/hydrogen ratio was not known apriori for the DLC films, only relative variations of the hydrogen ERS signal with energy were made. The relative DLC hydrogen cross-section measurements were converted to absolute values through the polystyrene cross-section measurements.