Cascade structure and overlap effects in ion-beam mixing experiments

General considerations about ion-beam mixing are reviewed: we show that the cascade structure, i.e., the distribution of spikes in the cascade volume, can have a strong influence on the ion-beam mixing efficiency. We first give an analytical expression of mixing rate versus the thermodynamic parameters and the spike distribution function in the case where the spikes are distributed randomly in the cascade and no overlap is taken into account. When several spikes occur in the same volume at the same time, it is shown that the temperature field is modified, and the jump frequency and diffusion rate change. This problem cannot be solved analytically, and we introduce a basic Monte Carlo calculation, where diffusion in the spikes in the case of overlap is treated. This calculation allows us to describe what happens when the substrate temperature is increased: starting from the hypothesis that the spike volume increases with temperature following an Arrhenius law, we find expressions for the activation energy in the thermally activated regime and the values of onset temperatures for thermally assisted diffusion under irradiation. The values found are in good agreement with experimental results published in the literature.

Cascade structure and overlap effects in ion-beam mixing experiments Academic Article