Profile of tracer Si in silicide when Si diffuses by vacancy mechanism

Abstract

A mathematical model is constructed to interpret the profiles of radioactive Si tracers during silicide formation. This model assumes that only Si moves in the silicide during silicide formation and that the moving Si diffuses in the Si sublattice of the silicide in terms of vacancy mechanism. Analytical solutions of the model for long-time annealing (i.e., asymptotic profiles) are given. The analytical asymptotic profiles are very accurate for the annealing period generally used in experiments. It is shown that the profiles of the Si tracer in the silicide are almost flat. This thus proves that self-diffusion of the tracer atoms cannot be neglected as assumed in some published papers. In fact, several experimental tracer profiles are found to be flat in the silicide. Some numerical solutions for short-time annealing are also given to show how the tracer profile evolves. The result given here can also be used for many intermetallic reactions.