Channelling (physics)

[1][2][3] Many physical phenomena can occur when a charged particle is incident upon a solid target, e.g., elastic scattering, inelastic energy-loss processes, secondary-electron emission, electromagnetic radiation, nuclear reactions, etc.

All of these processes have cross sections which depend on the impact parameters involved in collisions with individual target atoms.

When the target material is homogeneous and isotropic, the impact-parameter distribution is independent of the orientation of the momentum of the particle and interaction processes are also orientation-independent.

When the target material is monocrystalline, the yields of physical processes are very strongly dependent on the orientation of the momentum of the particle relative to the crystalline axes or planes.

Or in other words, the stopping power of the particle is much lower in certain directions than others.

The channelling effect was first discovered in pioneering binary collision approximation computer simulations in 1963[1][3] in order to explain exponential tails in experimentally observed ion range distributions that did not conform to standard theories of ion penetration.

The simulated prediction was confirmed experimentally the following year by measurements of ion penetration depths in single-crystalline tungsten.

[4] First transmission experiments of ions channelling through crystals were performed by Oak Ridge National Laboratory group showing that ions distribution is determinated by crystal rainbow channelling effect.

[5] From a simple, classical standpoint, one may qualitatively understand the channelling effect as follows: If the direction of a charged particle incident upon the surface of a monocrystal lies close to a major crystal direction (Fig.

2), it is much more likely to undergo large-angle scattering and hence its final mean penetration depth is likely to be shorter.

Channelling usually leads to deeper penetration of the ions in the material, an effect that has been observed experimentally and in computer simulations, see Figures 3-5.

[6] Negatively charged particles like antiprotons and electrons are attracted towards the positively charged nuclei of the plane, and after passing the center of the plane, they will be attracted again, so negatively charged particles tend to follow the direction of one crystalline plane.

Because the crystalline plane has a high density of atomic electrons and nuclei, the channeled particles eventually suffer a high angle Rutherford scattering or energy-losses in collision with electrons and leave the channel.

So positively charged particles tend to follow the direction between two neighboring crystalline planes, but at the largest possible distance from each of them.

Therefore, the positively charged particles have a smaller probability of interacting with the nuclei and electrons of the planes (smaller "dechannelling" effect) and travel longer distances.

The same phenomena occur when the direction of momentum of the charged particles lies close to a major crystalline, high-symmetry axis.

At low energies the channelling effects in crystals are not present because small-angle scattering at low energies requires large impact parameters, which become bigger than interplanar distances.

Channelling effects can be used as tools to investigate the properties of the crystal lattice and of its perturbations (like doping) in the bulk region that is not accessible to X-rays.

The channelling method may be utilized to detect the geometrical location of interstitials.

The channelling may even be used for superfocusing of ion beam, to be employed for sub-atomic microscopy.

[12] At higher energies (tens of GeV), the applications include the channelling radiation for enhanced production of high energy gamma rays,[13][14] and the use of bent crystals for extraction of particles from the halo of the circulating beam in a particle accelerator.

[15][16] The classical treatment of channelling phenomenon supposes that the ion - nucleus interactions are not correlated phenomena.

The first analytic classical treatise is due to Jens Lindhard in 1965,[17] who proposed a treatment that still remains the reference one.

He proposed a model that is based on the effects of a continuous repulsive potential generated by atomic nuclei lines or planes, arranged neatly in a crystal.

is feasible, since we consider a good alignment between ion and crystallographic axis.

The channelling condition can now be considered the condition for which an ion is channeled if its transverse energy is not sufficient to overcome the height of the potential barrier created by the strings of ordered nuclei.

Further considerations can be made by considering the thermal vibration motion of the nuclei: for this discussion, see the reference.

Typical critical angles values (at room temperature) are for silicon <110> 0.71 °, for germanium <100> 0.89 °, for tungsten <100> 2.17 °.

Planar channelling has critical angles that are a factor of 2-4 smaller than axial analogs and a

A complete discussion of planar channelling can be found in references.

Fig. 3. Map of channelling crystal directions for 10 keV Si ions in Si. [ 7 ] The red and yellow colors indicate directions with deeper mean ion penetration depth, i.e. directions where the ions are channeled.
Fig. 4. Experimentally determined penetration depth profiles for 15 keV B ions in Si along the 100 and 110 crystal channels, as well as in a non-channelling direction. The data is scanned in with smoothing from. Ref. [ 8 ]
Fig. 5. Computer simulations of the mean penetration depth of 80 keV Xe ion penetration in single crystal Au, considering a tilting of the implantation profile off the main direction. These simulations were made with the MDRANGE code [ 9 ] for a study of Xe irradiation of Au nanowires. [ 10 ] Also shown are simulations using the binary collision approximation SRIM code which does not take into account the crystal structure and thus does not describe channelling at all. The order of the strength of channelling, i.e. that 110 has the strongest effect, 100 is intermediate and 111 has the weakest, agrees with experimental observations in face-centered cubic metals. [ 11 ]