Diffusion at a planar interface using continuous distribution of sources

Many investigations of films grown on planar substrates at higher temperatures are accompanied by interdiffusion of atomic species across the planar interface from the substrate into the film and from the film into the substrate. In the present work, a new analysis is presented so that the concentration profiles of the diffusing species with different diffusion coefficients are determined. The analysis is carried out using the mathematical method of continuous distribution of diffusing sources in the two phases. The two boundary conditions in the form of continuity of flux and concentration at the interface are used to solve for the two distribution functions. These results are used to solve for the concentration profiles resulting from the mass diffusion in the two-phase medium. Application of the solution to a bilayer system with a planar interface and different diffusion coefficients in the adjoining phases is provided to illustrate the use of this method to several situations.