Model for compound formation during ion-beam mixing

Abstract

We propose an ion-beam-mixing model that accounts for compound formation at a boundary between two materials during ion irradiation. It is based on Fick's law together with a chemical driving force in order to simulate the chemical reaction at the boundary. The behavior of the squared thickness of the mixed layer, ${\mathit{X}}^{2}$, with the irradiation fluence, \ensuremath{\Phi}, has been found in several mixing experiments to be either quadratic (${\mathit{X}}^{2}$\ensuremath{\alpha}${\mathrm{\ensuremath{\Phi}}}^{2}$) or linear (${\mathit{X}}^{2}$\ensuremath{\alpha}\ensuremath{\Phi}), a result which is qualitatively reproduced. Depending on the fluence range, compound formation or diffusion is the limiting process of mixing kinetics. A criterion is established in terms of the ratio of the diffusion coefficient D due to irradiation to the chemical reaction rate squared which allows us to predict quadratic or linear behavior. When diffusion is the limiting process, D is enhanced by a factor which accounts for the formation of a compound in the mixed layer. Good agreement is found between the calculated mixing rates and the data taken from mixing experiments in metal/Si bilayers.