Rutherford Backscattering Spectrometry

Rutherford Backscattering Spectrometry (RBS), German Rutherford backscattering spectrometry , is a method for investigating thin layers close to the surface with the help of ion beams . It is therefore closely related to other methods of ion scattering spectroscopy , such as low-energy and medium-energy ion scattering spectroscopy (LEIS and MEIS).

The process is named after Ernest Rutherford , who was the first to explain the backscattering of alpha particles observed in the so-called gold foil experiment and who developed his atomic model from this.

functionality

For a measurement, high-energy ions (0.1 to 4  MeV ) of low mass ( hydrogen or helium ) are shot at a sample. A detector measures the energy of the backscattered ions. Their energy depends on the original amount of energy, on the mass of the respective sample atom hit and on the angle at which the detection is made. The ratio of the energy of the backscattered ions ( ) to the incident ion beam ( ) is known as the k-factor. The k-factor depends on the backscatter angle ( ) and the ratio of the projectile mass ( ) to the sample atomic mass ( ). In general, the momentum and energy conservation for the k-factor result: ${\displaystyle E_{\mathrm {R} }}$ ${\displaystyle E_{0}}$ ${\displaystyle \Theta }$ ${\displaystyle m_{1}}$ ${\displaystyle m_{2}}$

RBS spectrum with layer structure

${\displaystyle k=\left[{\frac {\cos(\Theta )+{\sqrt {[{\frac {m_{2}}{m_{1}}}]^{2}-\sin ^{2}(\Theta )}}}{1+{\frac {m_{2}}{m_{1}}}}}\right]^{2}}$

Typically, the detector is set up at an angle close to 180 °, since the energy loss during scattering is maximum here and the mass resolution is therefore higher.

Furthermore, the ions continuously lose energy on their way through the sample. The energy of the detected particle after a scattering results from:

${\displaystyle E_{2}(z)=k\left[E_{0}-\int \limits _{0}^{a_{1}}\left({\frac {\mathrm {d} E}{\mathrm {d} z}}\right)\mathrm {d} z\right]-\int \limits _{0}^{a_{2}}\left({\frac {\mathrm {d} E}{\mathrm {d} z}}\right)\mathrm {d} z}$

The term in the square brackets corresponds to the injection energy minus the energy loss until the depth is reached in which the scattering is carried out, multiplied by the k-factor results in the energy after the scattering. The energy loss as it leaves the sample is then deducted from this. Here, and are the distances to the surface, which depend on the specific test arrangement. The so-called braking capacity results from the Bethe formula and depends on the energy of the particle and the sample composition. ${\displaystyle a_{1}}$ ${\displaystyle a_{2}}$ ${\displaystyle \left({\tfrac {\mathrm {d} E}{\mathrm {d} x}}\right)}$

Due to this depth dependence of the energy of the backscattered particles, the measurement of the composition by means of RBS is also depth-resolved. Depending on the test parameters, depths from a few hundred nanometers to a few micrometers can be investigated. This great penetration depth is possible because the scattering cross-section for high-energy ions (a few MeV ) is much smaller than for low-energy ion spectroscopy (e.g. LEIS , energies up to 10  KeV , only suitable for surface analysis ) and the braking capacity is typically several 100 eV / nm is located (for bombardment with He ions). Accordingly, the depth that can be analyzed is primarily dependent on. The higher the higher the analyzable depth, but the lower the depth resolution. For higher depths, the depth resolution also decreases due to so-called straggling (broadening of the energy distribution of the ion beam when passing through the sample), which occurs due to the statistical nature of the energy loss when passing through the sample. ${\displaystyle E_{0}}$ ${\displaystyle E_{0}}$

For energies that are not too high, the scattering potential corresponds (almost) to the Coulomb potential and thus the probability of backscattering ( scattering cross section ) is known and given by the Rutherford scattering cross section . For higher energies there may be deviations from the Rutherford scattering cross-section.

The composition of a binary alloy can be determined iteratively from the following formula (add and calculate a starting value for . Then use Bragg's rule to determine the correct values and recalculate them): ${\displaystyle A_{\mathrm {x} }B_{\mathrm {y} }}$ ${\displaystyle {\frac {\epsilon _{\mathrm {B} }(E,x)}{\epsilon _{\mathrm {A} }(E,y)}}:=1}$ ${\displaystyle x=1-y}$ ${\displaystyle \epsilon }$

${\displaystyle {y \over x}={\frac {Q_{\mathrm {B} }\sigma _{\mathrm {A} }(E,\theta )\epsilon _{\mathrm {B} }(E,x)}{Q_{\mathrm {A} }\sigma _{\mathrm {B} }(E,\theta )\epsilon _{\mathrm {A} }(E,y)}}}$

with as the measured backscatter yield of the respective element and as the differential effective cross-section , the stopping power cross-section (braking cross-section). Stopping power values ​​can be determined with the SRIM software. For an approximation of the formula, use appropriately averaged braking cross-sections; the complete neglect of the braking cross-sections leads in most cases to large errors. ${\displaystyle Q}$ ${\displaystyle \sigma }$ ${\displaystyle \epsilon }$

The formula results from the yield equation:, with the number of projectiles and the solid angle of the detector. ${\displaystyle Q_{\mathrm {A} }=x\cdot \sigma _{\mathrm {A} }\cdot n_{\mathrm {P} }\cdot \Omega _{\mathrm {Det} }\cdot \mathrm {N} _{0}\Delta x=x\cdot \sigma _{\mathrm {A} }\cdot n_{\mathrm {P} }\cdot \Omega _{\mathrm {Det} }\cdot {\frac {\Delta \mathrm {E} }{\epsilon _{\mathrm {A} }}}}$ ${\displaystyle n_{\mathrm {P} }=}$

See also

• Surface chemistry

literature

• Joseph R. Tesmer, Michael Anthony Nastasi: Handbook of Modern Ion Beam Materials Analysis. Materials Research Society , Pittsburgh, PA 1995, ISBN 1-55899-254-5 .
• Leonard C. Feldman, James W. Mayer: Fundamentals of Surface and Thin Film Analysis . Prentice Hall, 1986, ISBN 0-13-500570-1 .
• G. Götz, K. Gärtner: High Energy Ion Beam Analysis of Solids . Akademie Verlag Berlin, 1988.
• AG Fitzgerald: Quantitative microbeam analysis . SUSSP Publ., 1993, ISBN 0-7503-0256-9 .