Box 1. Stopping of energetic particles in solids

From the following article

Engineering of nanostructured carbon materials with electron or ion beams

A. V. Krasheninnikov & F. Banhart

Nature Materials 6, 723 - 733 (2007)



The slowing down of an energetic ion moving in a solid target can be separated into two different channels2, 104: electronic and nuclear stopping. The nuclear stopping originates from collisions between the ion and the nuclei of atoms in the target, so that the ion's kinetic energy is partly transmitted to a target atom as a whole resulting in its translatory motion. The energy loss is determined by screened Coulomb interactions. A common feature for all ions is that the nuclear stopping is important only for relatively slow and heavy ions. The electronic stopping is governed by inelastic collisions between the moving ion and the electrons in the target, which can be either bound or free. Many different physical processes contribute to the electronic stopping: ionization of the target atoms, generation of phonons through the electron–phonon coupling, collective electronic excitations such as plasmons, and so on. Electronic stopping dominates at high ion energies. The crossover between the nuclear and electron stopping depends on the ion mass (in the case of a carbon target, 100 keV for Ar ions, and 1 MeV for Xe). For hydrogen ions (protons), electronic stopping always prevails.

Energetic electrons interact with the nuclei and the electron system in the target31. For reasons of momentum conservation, only a tiny fraction of the impinging electron energy can be transferred to a nucleus, so a rather high electron energy ('threshold energy') is needed to displace an atom (this occurs via electron–nucleus scattering). For example, an electron energy of 100 keV is needed to transfer approximately 20 eV to a carbon atom; this is the threshold for displacing the atom permanently in a graphitic structure. Electron–electron scattering, on the other hand, is possible at low electron energies and may cause ionization or bond breaking. This kind of energy transfer normally does not lead to atom displacements but may damage the target because of local reactions. The cross-section of both nuclear and electron scattering decreases with increasing electron energy; however, electron–nucleus scattering only leads to observable effects if the displacement threshold energy is exceeded.

Many structural modifications of nanosystems were first carried out in electron microscopes where the irradiation of specimens with energetic electrons is unavoidable and radiation effects were often seen accidentally as a by-product of structural characterization. For defect generation the most important mechanism of energy transfer from electrons to the target atoms is the ballistic collisions of the electrons with the nuclei. The electron energies in TEMs range typically between 100 and 300 keV and in a few high-voltage instruments may exceed 1 MeV. Hence, the electrons may have enough momentum to displace atoms permanently from their positions31, 105. The advantage of carrying out irradiation experiments in a TEM is that all structural modifications under the electron beam can be monitored in real time and at the full lateral resolution of the instrument. Modern electron microscopes achieve point resolutions of 1 Å or even better and can focus the electron beams onto spots of less than 1 nm diameter (in some instruments 1 Å spots are achievable). Enormous beam current densities can be achieved when the electron beams are focused onto a spot (approximately 300 A cm-2 in beams from thermal electron guns and up to 105 A cm-2 from field emission guns). Because irradiation effects are governed by the temperature of the material under the beam, high-temperature specimen stages (with an adjustable specimen temperature up to 1,000 °C or more) have to be used in such in situ experiments.