Mon 11 December, 2017

Medium Energy Ion Scattering: Scattering Details

Fig 1
Fig 1: An example MEIS spectrum. The higher energy signal is due to ions scattered from Ho, whereas the lower energy signal is due to ions scattered from the lighter Si.

As mentioned in the description of the technique, MEIS may be considered as a series of kinematic collisions. As such the equations describing the ion scattering are simple to derive.

Considering elastic scattering between two bodies the energy of the scattered ion is easily seen to be given by

E=E0*[((m2^2-m1^2*sin(theta)^2)^0.5+m1*cos(theta))/(m1+m2))^2=k^2*E0

where E0 is the intital ion energy and m1 and m2 are the ion and target masses. θ is the scattering angle.

The factor K2 is known as the kinematic factor and has important consequences for the technique. If there are two different target masses (i.e. two elements within the crystal) then k2 becomes increasingly different with increasing scattering angle. For sufficiently high scattering angles this means that the scattered ions from two different target masses may be distinquished. Also, for a given target mass, the ion energy decreases with increasing scattering angle. Both of these effects can be clearly seen in the MEIS spectrum of holmium silicide shown in figure 1. The Ho and Si signals are clearly seperated and there is a fall off in energy with scattering angle.

As MEIS deals with Rutherford scattering there is also a fall off in the number of scattered ions with increasing scattering angle due to the Rutherford scattering cross-section.

Another important effect in medium energy ion scattering is the energy loss due to inelastic scattering. The rate of energy loss is known as the stopping power. Although the stopping power is dependent upon the ion energy, which is of course changing due to inelstic losses, the layers in MEIS are thin enough to consider the ion energy as a constant (and as another constant once scattered). An ion scattered from a depth, d, will therefore have a characteristic energy,

E=k^2E0-[(k^2d/cos(theta1)(dE/dx){E0}+d/cos(theta2)(dE/dx){k^2E0}]

This means that the energy scale is both a mass scale (due to the kinematic factor) and a dept scale(due to the inelastic losses).

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