Alloy sputtering at high fluence: preferential sputtering and competing effects

Abstract

This work addresses composition profiles and partial sputter yields of an alloy under ion bombardment. The effects of preferential sputtering, mixing, and Gibbsian segregation have been modelled. The theoretical basis is an integro-differential equation derived previously, into which a feasible expression for a segregation current has been included. A dependence on composition of pertinent input parameters like relocation cross sections and atomic volumes has been allowed for but has not been explored explicitly. In the limit of high fluence, a stationary state may be reached with a composition profile that shows more or less pronounced deviations from bulk stoichiometry. Two methods have been designed for direct determination of such stationary solutions. An iterative scheme for numerical solution of the nonlinear balance equation is very efficient and accurate. An approximate scheme, assuming weakly preferential behavior and thus based on a linearized balance equation, turns out to be quite accurate even in case of strongly preferential sputtering. An explicit analytical solution is given for a particular example. On the basis of simple, schematic input, it is seen that the deviation of a stationary composition profile from bulk stoichiometry may be very strong, even when the sputter cross section is only weakly or moderately preferential. This difference is most pronounced in the absence of substantial feeding by mixing and segregation. In case of a nonzero depth of origin of sputtered atoms, composition profiles depend sensitively on the depth dependence of the sputter cross section, even in cases where consideration of only the partial sputter yields would suggest stoichiometric sputtering. A few examples illustrate explicitly the competition between preferential sputtering on the one hand and mixing or segregation on the other.