Rutherford backscattering spectrometry

Rutherford backscattering spectrometry (RBS) is also called high-energy ion backscattering spectrometry and is used for compositional depth profiling. A collimated beam of light ions (usually H+_{, He}+ _{or He}++_{) is accelerated towards}

the sample with energies in the order of 1 MeV. At these energies, electronic stopping will dominate and only about one in 106 _{ions will undergo a nuclear}

collision [42]. Some of the backscattered ions are detected and their energy distribution is analysed to deduce the elements present in the sample, up to a few µm from the surface. This is a quantitative and somewhat non-destructive technique, which can also determine areal density and crystalline structure. The collision between a probe ion and a stationary target atom can be classically modelled as an elastic collision. This means that the total energy in both the parallel and perpendicular directions, as well as the total momentum must be conserved. These conditions yield three equations, which can be rearranged into a ratio of the probe atom velocities after and before the collision [43]. It is assumed that the mass of the projectile, M₁ is much less than the mass of the target atom, M₂. In terms of the projectile energies,

K = E1 E₀ = " M₁cosθ+ (M₂2−M₁2sin2θ) 1 2 M₁+M₂ #2 . (2.10)

In this relation,θ is the scattering angle and the energies of the probe atom before and after the collision are E₀ and E₁, respectively. The energy ratio is named the kinematic factor (K) and this will be most sensitive to a difference in target masses ∆M₂ for θ = 180◦. So the backscatter detector is usually positioned at about 170◦ in order to accurately distinguish between substrate elements.

The backscattering yield (Y) is given by the number of detected backscattered particles. This depends on the density of target atoms, the amount of charge collected and the scattering cross-section. The yield is also influenced by the solid angle Ω subtended by the detector, which can be approximated by Ω =A/l2 for a detector that is a distance l from the target and has a small area A. The average

Figure 2.11: The mechanisms of energy loss when a particle is backscattered below the sample surface at depthT, reproduced from [43]. Continuous electronic stopping occurs as the probe ion enters (∆E_in) and exits (∆E_out) the sample. The energy loss (∆E_S) is attributed to the nuclear scattering event.

scattering cross-section,σ(θ) is defined as [43]

σ(θ) = 1 Ω Z Ω dσ dΩ dΩ. (2.11)

Generally Ω in RBS is on the order of 10−_{2 sr. For an ideal detector, the yield can}

be expressed asY =σ(θ)ΩQNs, where Ns is the areal atomic density of the target and Q is the total number of incident particles. Tables of differential scattering cross sections (dσ/dΩ) are available for common probe ions.

Although (2.10) is an adequate description of a collision at the sample surface, it is not accurate for events below the surface. When a light ion passes through the substrate matrix, electronic stopping occurs. This is due to the excitation and ionisation of substrate electrons. These are discrete inelastic collisions, but electronic stopping can be modelled as a continuous process. The rate of energy loss due to electronic stopping through a distance dx can be described as dE/dx. Alternatively, the electronic stopping cross section can be defined in terms of the volume atomic density (N) as = 1/N(dE/dx). As shown in figure 2.11, a backscattered particle will lose energy while travelling through the sample, then during the nuclear scattering event, and finally further electronic stopping occurs as the ion exits the sample at angleθ. So the final energy (E₁) of a detected particle that has been backscattered at depth T, and the signal energy width (∆E) due to a series of these collisions in a film of thickness ∆T, can be respectively written as

E₁ = KE₀ −T[S], (2.12) ∆E = ∆T[S], (2.13) where [S] = K dE dx _in + 1 |cosθ| dE dx _out. (2.14)

[S] is known as the backscattering energy loss factor. For films thinner than about 100 nm, the surface energy approximation for (2.13) can be used to determine ∆E₀, where dE/dx ‘in’ and ‘out’ are evaluated at E₀ and KE₀, respectively [43]. These equations form the basis for fitting experimental RBS spectra, and hence extracting the thin film parameters measured in this thesis. In some measurements, samples can be specifically oriented such that the probe ions are travelling parallel to the crystal axes in the substrate. These channelling measurements can provide information about sample crystallinity, but were not used for this thesis.

Note that the finite width ∆E means that a continuum of energies E < E₀ are seen for thick substrates, and these may overlap with the energy of ions backscattered from light elements on the surface. This means that the substrate signal can decrease the sensitivity to small concentrations of these light elements. This situation occurs when measuring the stoichiometry of SiOxNy films on Si substrates. To overcome this, the films characterised in chapter 6 were deposited on Si substrates that had been pre-coated with 1.1 µm of diamond-like carbon (DLC). Since M_C is less than M_O and M_N, and the DLC film is thick enough to shift the Si substrate backscatter energies, the signals were energetically separated and x, y could be accurately extracted.

The RBS system in the Department of Electronic Materials Engineering uses a National Electrostatics Corporation (NEC) Alphatross charge-exchange ion source to deliver H+_{, He}+ _{or He}++ _{ions, however only He}+ _{was used for the experiments}

in this thesis. During operation, He gas is slowly delivered to the glass source bottle, which is maintained at about 10−_{6 Torr. An RF field is applied through}

two electrodes around the bottle, which ionises the source gas. The Ta exit canal is surrounded by a solenoid magnet to concentrate the plasma there. A bias voltage drives the He+ _{ions from the bottle and into the charge exchange chamber. Here,}

a 300 ◦_{C oven provides Rb vapour, which donates electrons to the helium and}

produces He− _{ions. Up to 4 µA of these particles can be produced from the source,}

which then pass through a velocity steerer to select the correct species [45]. Before entering the accelerator, the beam is focussed with an einzel lens set to 50 kV.

Figure 2.12: Schematic of the Rutherford backscattering spectrometry system, including an RF charge-exchange ion source. The inset shows the inside of the 5SDH tandem pelletron accelerator, adapted from [44].

An NEC 5SDH tandem pelletron accelerator is used to accelerate the ions towards the target chamber and is shown schematically in figure 2.12. In this accelerator, steel pellets are linked with nylon brushes to form a chain, and this is charged by a 10 kV power supply. The spinning chain charges the terminal, which can hold up to 1.7 MV but was set to 0.95 MV for these experiments. At the terminal, N2 stripper gas is bled into the system, also at around 10−6 Torr. This removes

electrons from the He− _{ions, which again become positively charged. They are now}

accelerated away from the terminal, and this two-stage process to achieve high ion energies gives rise to the name tandem accelerator.

After leaving the accelerator, the He+ _{ions are collimated with a set of quadrupole}

magnets. The beam-line pressure here is about 3×10−_{7 Torr and is maintained by}

a turbomolecular pump. A switching magnet then selects between the 2 MeV He+

and 3 MeV He++_{species, and also directs the beam into one of two target chambers.}

For these experiments with Line 1, the switching magnet was driven with about 19.2 A, producing a field of about 4400 G. Finally, the beam passes through a set of 1–2 mm apertures and is incident on the sample. A surrounding shield to minimise secondary electrons is biased with a suppression voltage and can also be connected to a liquid-nitrogen-immersed cold finger. The chamber is evacuated by another turbomolecular pump, to at least 2×10−_{6 Torr during measurements. Depending}

on the performance of the source and which apertures are selected, 10–50 nA He+

is usually available at the target.

The sample is mounted on a goniometer that has two degrees of translation and two degrees of rotation. The backscatter detector is an Ametek UltraTM _{Si surface-}

barrier detector that is biased at 50 V. When a backscattered ion enters the depletion region of the detector, electron-hole pairs are created and collected as a pulse. The size of this pulse is proportional to the ion energy, so each pulse is directed into a voltage bin called a channel. The backscatter detector used in these experiments is fixed atθ = 168◦ and another detector is available for glancing-angle measurements. The data is collected using in-house written software named DEI, which runs on OS/2. This software also allows the goniometers to be controlled, and a randomise function was generally used. This function performs periodic changes in the sample orientation during a measurement, to ensure that any channelling effects do not affect the final averaged data. Only small tilt angles are required, and the data is not compromised by this process. The results were matched to simulated spectra using the Rutherford universal manipulation program (RUMP) software [46]. A linear relationship between the channel and energy was calibrated using a set of standards, or with a known compound superficial layer, such as SiOx.

The depth resolution in RBS is usually limited to about 10 nm, due to straggling effects and the resolution of the detector.