Thermalization of sparse collision cascades in metals: simultaneous relaxation of nonequilibrium electron and ion distributions

Thermalization of ion bombardment induced large and sparse cascades in metals is studied. We introduce a model where nonequilibrium electron and ion distributions relax simultaneously, and coupling between the thermal ions and valence electrons allows heat exchange between electronic and ionic systems. This model takes into account the competing time scales of the relaxation processes and the heat outdiffusion from the cascade zone. Nearly free conduction electron bands are assumed, which restricts the applicability of the model to simple metals only. It is shown that in cascades with an extent of about 10 nm or more, a considerable part of the energy, residing initially in the electronic system, may reappear in the ionic system in the cascade zone. Ions in cascades with radius larger than 20 nm take up nearly all of the energy available in the cascade zone. Due to this energy transfer, the ionic system may experience appreciable additional heating in large cascades.