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Laboratory of Nuclear Analytical Methods
RBS - Rutherford Backscattering Spectrometry:

General facts
Theory of RBS
Non-Rutherford scattering
Example of investigated systems
    (Plasma deposited layers)

For any information or collaboration contact :
Vratislav Peřina (perinanonameujf.cas.cz)
Anna Macková (mackovanonameujf.cas.cz)

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The general facts

RBS is most commonly used non-destructive nuclear method for elemental depth analysis of nm-to-mm thick films. It involves measurement of the number and energy distribution of energetic ions (usually MeV light ions such He+) backscattered from atoms within the near-surface region of solid targets. From such measurement it is possible to determine, with some limitations, both the atomic mass and concentration of elemental target constituents as a function of depth below the surface.

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Theory of RBS
Sample is irradiated with light ions (usually 2-3 MeV α-particles or protons) and the elastically backscattered projectiles at large angles are detected. The mass of the target atoms could be identified from the energy of the backscattered projectile.
collision and backscattering
Fig.1: Schematics of an classic collision and backscattering of a lighter projectile of mass M1 with a heavier target particle of mass M2, innitially at rest in the laboratory. The recoil of the target is not plotted.

The backscattered particles are detected by the semiconductor detectors Si(Au), the accessible depth 2-10 mm. The heavy element detection limit in the light matrix is up to 1mg/g. The lower mass causes higher transferred energy. The mass resolution is given by detector energy resolution, the energy and projectile mass. The ussage of heavier ions enables us to reach the mass resolution DM<2.

The Rutherford differential cross-section is described by following equation (1911):

Rutherford equation, where
dσ/dΩ - differential cross-section of solid angle unit, characterize an elastic scattering;
Z1e, Z2e - electric charge of particles;
E - collision energy;
Θ - backscattering angle
backscattering event resulting spectrum
Fig.2: Schematic of backscattering event form a thick elemental sample and a resulting spectrum
ΔE - the energy difference observed for ions scattered from the surface and from depth x;
E0, E1 - incident and exit energies;
ε - is a stopping cross section factor.

Fig.3: Kinematic factor K for 170 o angle backscattering of various ions as a function of target mass (after [1]).

Equation for K

SSD resolution for various ions
Fig.4: The detector resolution of standard silicon surface barrier detector (SSD) for various ions as calculated from the parameters of [2] (after [1]).
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Non-Rutherford scattering
The resonant cross-section for light elements is increased significantly in case of used proton beam during RBS measurement. High sesitivity for C, N, O, Si elements is observed in case of proton beam 2,4 MeV and for O in case of alpha particle beam 3,06 MeV.
Non-Rutherford cross-section
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Example of investigated systems
Plasma deposited layers
The Alumina Oxide layers are prepared by plasmatic oxidation. These layers are designed for hardcoating, optics elements or transparent insulators.

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[2] Hinrichsen, P.F., Hetherington, D.W., Gujrthi, S.C., and Cliche, L., Nucl. Instrum and Methods, B45, 275, 1990