In materials science, the threshold displacement energy (Td) is the minimum kinetic energy that an atom in a solid needs to be permanently displaced from its site in the lattice to a defect position.
In a crystal, a separate threshold displacement energy exists for each crystallographic direction.
In amorphous solids, it may be possible to define an effective displacement energy to describe some other average quantity of interest.
Threshold displacement energies in typical solids are of the order of 10-50 eV.
that an irradiating particle can transfer in a binary collision to an atom in a material is given by (including relativistic effects)
In order for a permanent defect to be produced from initially perfect crystal lattice, the kinetic energy that it receives
[1] The reason for this apparent discrepancy is that the defect formation is a complex multi-body collision process (a small collision cascade) where the atom that receives a recoil energy can also bounce back, or kick another atom back to its lattice site.
An additional complication is that the threshold displacement energy for a given direction is not necessarily a step function, but there can be an intermediate energy region where a defect may or may not be formed depending on the random atom displacements.
Hence theoretical study of the threshold displacement energy is conventionally carried out using either classical [6] [7] [8] [9][10] [11] or quantum mechanical [12] [13] [14] [15] molecular dynamics computer simulations.
The animation shows how a defect (Frenkel pair, i.e. an interstitial and vacancy) is formed in silicon when a lattice atom is given a recoil energy of 20 eV in the 100 direction.
The data for the animation was obtained from density functional theory molecular dynamics computer simulations.
[15] Such simulations have given significant qualitative insights into the threshold displacement energy, but the quantitative results should be viewed with caution.
The classical interatomic potentials are usually fit only to equilibrium properties, and hence their predictive capability may be limited.
Even in the most studied materials such as Si and Fe, there are variations of more than a factor of two in the predicted threshold displacement energies.
[7][15] The quantum mechanical simulations based on density functional theory (DFT) are likely to be much more accurate, but very few comparative studies of different DFT methods on this issue have yet been carried out to assess their quantitative reliability.
The threshold displacement energies have been studied extensively with electron irradiation experiments.
Electrons with kinetic energies of the order of hundreds of keVs or a few MeVs can to a very good approximation be considered to collide with a single lattice atom at a time.
Since the initial energy for electrons coming from a particle accelerator is accurately known, one can thus at least in principle determine the lower minimum threshold displacement
Particular care has to be taken when interpreting threshold displacement energies at temperatures where defects are mobile and can recombine.
Since low-energy recoils just above the threshold only produce close Frenkel pairs, recombination is quite likely.
Hence the net effect often is that the threshold energy appears to increase with increasing temperature, since the Frenkel pairs produced by the lowest-energy recoils above threshold all recombine, and only defects produced by higher-energy recoils remain.
In a wide range of materials, defect recombination occurs already below room temperature.
E.g. in metals the initial ("stage I") close Frenkel pair recombination and interstitial migration starts to happen already around 10-20 K.[18] Similarly, in Si major recombination of damage happens already around 100 K during ion irradiation and 4 K during electron irradiation [19] Even the stage A threshold displacement energy can be expected to have a temperature dependence, due to effects such as thermal expansion, temperature dependence of the elastic constants and increased probability of recombination before the lattice has cooled down back to the ambient temperature T0.
The threshold displacement energy is often used to estimate the total amount of defects produced by higher energy irradiation using the Kinchin-Pease or NRT equations[20][21] which says that the number of Frenkel pairs produced
[4] The threshold displacement energy is also often used in binary collision approximation computer codes such as SRIM[22] to estimate damage.
However, the same caveats as for the Kinchin-Pease equation also apply for these codes (unless they are extended with a damage recombination model).
Moreover, neither the Kinchin-Pease equation nor SRIM take in any way account of ion channeling, which may in crystalline or polycrystalline materials reduce the nuclear deposited energy and thus the damage production dramatically for some ion-target combinations.
For instance, keV ion implantation into the Si 110 crystal direction leads to massive channeling and thus reductions in stopping power.
[23] Similarly, light ion like He irradiation of a BCC metal like Fe leads to massive channeling even in a randomly selected crystal direction.