Diffusion through a polycrystalline thin film

Analytical solutions to Fick’s second law of diffusion have been simultaneously derived without the restrictions of parabolic profiles along the x-axis in grain boundaries and expressed in a series for both grain interior and grain boundary diffusing through a polycrystalline thin film. The analysis takes segregation of diffusion species at grain boundaries into account. The analytic solutions lead to the concentration profiles in the grain interior and in the grain boundary, to the average-integrated amount of diffusion species at the exit surface, and to the time lag, which can be technologically used for depth profile studies and kinetic accumulation measurements.