# User:Norcimo/Medium energy ion scattering

Medium Energy Ion Scattering (or MEIS) is an analytical technique offering surface and near surface sensitive crystallographic structural information. Ions (usually H+ or He+) are accelerated to around 100 keV and focused onto the surface. Those scattered from the surface are detected over a range of angles and energies. In this way MEIS is an enhancement of Rutherford backscattering (RBS) but it offers improved angular and energy resolution. It is also related to the techniques of HEIS in which the ions are of much higher energy (about 2 MeV) and somewhat less so to LEIS which involves energies of only a few keV. MEIS can distinguish between elements which are well separated in mass but is not very sensitive to lighter elements. The technique can be used in depth profiling and structural analysis on the atomic scale.

## Surface Structure Determination

MEIS generally gains its surface sensitivity from the practice of shadowing. The ionic beam is aligned along a major direction (in practice by means of rotating the crystal about the fixed beam). This shadows atoms deeper in the crystal, further along the atomic row. The shadowed volume forms a cone, the radius of which increases with distance from the atom casting the shadow. Shadowing has the overall effect that the illumination of the crystal is restricted to a certain depth, although thermal vibrations mean that the shadowing is not ideal and deeper layers do provide some contribution to the backscattered yield. This restriction means that the scattered ions are surface sensitive, with the added advantage that buried interfaces close to the surface can still be probed. Careful selection of scattering geometry can be used to dictate the number of layers exposed.

### Double Alignment

Although shadowing is useful, further information about the crystal under investigation can be gained by the use of double alignment. This combines shadowing with blocking. Blocking is basically the same process as shadowing but acting on the scattered ions (i.e. those atom nearer the surface block the exit of ions scattered from deeper atoms. This blocking results in a drop in scattering yield at characteristic scattering angles where the scattered beam intersects with atoms on its way out of the crystal. The angular positioning, number and character of these blocking dips yields structural information. For instance a relaxation of the surface layer will produce a change in the scattering angle of a blocking feature and additional blocking features may also be present due to reduced shadowing of deeper layers.

## Depth Profiling

Because ion scattered from deeper within the crystal suffer greater inelastic energy losses the energy scale of the detected scattered ions can act as a depth scale, as it does in RBS. By concentrating on the number of total number of ions scattered over an angular range as a function of energy the distribution of an element as a function of depth can therefore be studied.

## Theory

As the scattered ions have energies of around 100 keV their speed is much greater than the atomic movement due to crystal phonon vibrations, so the ions essentially see a frozen snapshot of the crystal. This allows the scattering to be considered as a sequence of kinematic scattering events between ion and crystal atomic nucleus. The energy of an ion of mass ${\displaystyle m_{1}}$ elastically scattered from an atom of mass ${\displaystyle m_{2}}$ is given by

${\displaystyle E=\left[{\frac {{\sqrt {m_{2}^{2}-m_{1}^{2}\sin ^{2}\theta }}+m_{1}\cos \theta }{m_{1}+m_{2}}}\right]^{2}E_{0}=k^{2}E_{0}\qquad (1)}$

where ${\displaystyle E_{0}}$ is the intitial energy of the ion and ${\displaystyle \theta }$ is the scattering angle.

As already mentioned inelastic losses result in the energy scale beign a depth scale. However, Equation 1 shows that the energy scale is also a mass scale. Ions scattered from atoms with lower mass will emerge with less energy than those scattered from atoms of higher mass. In MEIS a sufficiently sensative detector can therefore distinguish scattering from different elements within a crystal, provided the mass separation of those elements is large enough. This allows the dependance on scattering angle to investigated independently for each element and depth profiling to be performed for each element.

It can also be seen from Equation 1 that the energy of the scattered ions decreases as the scattering angle increases. Of course the scattering cross section means that the number of ions scattered at a given angle also decreases as the scattering angle increases.

The radius ${\displaystyle R}$ of the shadow cone a distance ${\displaystyle l}$ from the shadowing atom and for a Coulomb potential is given by

${\displaystyle R=2{\sqrt {\frac {Z_{1}Z_{2}e^{2}l}{E}}}\qquad (2)}$

where ${\displaystyle Z_{1}}$ and ${\displaystyle Z_{2}}$ are the atomic numbers of ion and target atom and ${\displaystyle E}$ is the ion energy.

The angular width of the blocking dips seen in the scattered ion yield is given by

${\displaystyle \psi =2\left({\frac {nAc}{Es^{n}}}\right)^{1/(n+1)}\left(1+{\frac {1}{n}}\right){\mbox{radians}}\qquad (3)}$

${\displaystyle s}$ is the distance between the scattering target and the blocking atom, ${\displaystyle n}$ the power of the potential,

${\displaystyle c={\sqrt {\pi }}{\frac {\Gamma (1/2n+1/2)}{\Gamma (1/2n)}}\qquad (4)}$

and A is the potential parameter, which for a Coulomb potential is

${\displaystyle A={\frac {Z_{1}Z_{2}e^{2}}{4\pi \epsilon _{0}}}\qquad (5)}$

Thus for a Coulomb potential Equation 3 reduces to

${\displaystyle \psi =4{\sqrt {\frac {A}{Es}}}\qquad (6)}$

## Computer Simulations

To use MEIS as a truely quantitative surface structure technique it is necessary to simulate the scattering of ions from a number of trail structures and compare these simulations with the experimental data. Hence it is normal to perform computer simulations using Monte Carlo methods of the ion scattering from trail structures.