A phenomenological theory of ion-beam synthesis of ternary compound in silicon

Abstract

A model for the annealing stage of ion-beam synthesis of a buried layer of a ternary phase in silicon coimplanted with a relatively low dose of chemically active ions is presented. Physically, the system under investigation is a mixture of precipitates of two binary phases which are formed in the subsurface region of silicon as a result of chemical reaction between each implanted impurity and matrix atoms. During annealing, the precipitates of each binary phase function as alternative sinks for the solutes. Therefore, the ensemble of new phase inclusions is regarded as a superposition of precipitate pairs. Each pair involves the nuclei of both binary phases. The incorporation of an impurity atom into a binary phase inclusion is assumed to be controlled by the corresponding kinetic parameter. During annealing, binary phase inclusions play the role of seeds for ternary phase formation. Mathematically, the redistribution and chemical segregation of implanted species are described by a set of diffusion equations. The sink terms of the equations have been derived in the two-particle approximation which reflects the competitive growth of two phases. Generally, this set of equations is solved numerically; however, two assumptions allow the analytic solution: there are (i) chemical segregation of the reagent is a predominant mechanism of phase formation; (ii) the phases formed have a constant chemical composition. The model is successfully applied to the description of silicon oxynitride synthesis by silicon implantation with a substoichiometric dose of oxygen and nitrogen ions. The computer simulation showed that nitrogen atoms, collected on the oxide surface, change the interface mechanism of oxide growth into that of bulk diffusion, which eventually facilitates the ternary phase formation.