RBS Theory: Kinematics

For scattering at the sample surface the only energy loss mechanism is momentum transfer to the target atom. The ratio of the projectile energy after a collision to the projectile energy before a collision is defined as the kinematic factor.

There is much greater separation between the energies of particles backscattered from light elements than from heavy elements, because a significant amount of momentum is transferred from the incident particle to a light target atom. As the mass of the target atom increases, less momentum is transferred to the target atom and the energy of the backscattered particle asymptotically approaches the incident particle energy. This means that RBS is more useful for distinguishing between two light elements than it is for distinguishing between two heavy elements. RBS has good mass resolution for light elements, but poor mass resolution for heavy elements.

For example, when He++ strikes light elements such as C, N, or O, a significant fraction of the projectile's energy is transferred to the target atom and the energy recorded for that backscattering event is much lower than the energy of the beam. It is usually possible to resolve C from N or P from Si, even though these elements differ in mass by only about 1 amu.

However, as the mass of the atom being struck increases, a smaller and smaller portion of the projectile energy is transferred to the target during collision, and the energy of the backscattered atom asymptotically approaches the energy of the beam. It is not possible to resolve W from Ta, or Fe from Ni when these elements are present at the same depths in the sample, even though these heavier elements also differ in mass by only about 1 amu.

An important related issue is that He will not scatter backwards from H or He atoms in a sample. Elements as light as or lighter than the projectile element will instead scatter at forward trajectories with significant energy. Thus, these elements cannot be detected using classical RBS. However, by placing a detector so that these forward scattering events can be recorded, these elements can be quantitatively measured using the same principles as RBS.

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