Threshold Displacement Energy - Temperature Dependence

Temperature Dependence

Particular care has to be taken when interpreting threshold displacement energies at temperatures where defects are mobile and can recombine. At such temperatures, one should consider two distinct processes: the creation of the defect by the high-energy ion (stage A), and subsequent thermal recombination effects (stage B).

The initial stage A. of defect creation, until all excess kinetic energy has dissipated in the lattice and it is back to its initial temperature T₀, takes < 5 ps. This is the fundamental ("primary damage") threshold displacement energy, and also the one usually simulated by molecular dynamics computer simulations. After this (stage B), however, close Frenkel pairs may be recombined by thermal processes. Since low-energy recoils just above the threshold only produce close Frenkel pairs, recombination is quite likely.

Hence on experimental time scales and temperatures above the first (stage I) recombination temperature, what one sees is the combined effect of stage A and B. 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. Since thermal recombination is time-dependent, any stage B kind of recombination also implies that the results may have a dependence on the ion irradiation flux.

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. Similarly, in Si major recombination of damage happens already around 100 K during ion irradiation and 4 K during electron irradiation

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. These effects, are, however, likely to be much weaker than the stage B thermal recombination effects.