A novel grain-boundary diffusion model was developed by using the transmission-line matrix method. Together with a 2-dimensional Monte Carlo thin-film growth simulation, this model could be used to analyze impurity diffusion in thin-film diffusion barriers with realistic microstructures. In this model, an impurity at the upper surface of the barrier layer could diffuse through rapid and irregularly shaped grain-boundary diffusion paths in order to reach the bottom surface. Calculations of the impurity concentration and out-diffusion flux, as a function of elapsed diffusion time and position, permitted the effectiveness of the barrier layer to be evaluated at the microstructural level. As a result, the diffusion process could be described by using fewer assumptions, and more precisely, than was possible using previous approaches.

X.Gui, L.J.Friedrich, S.K.Dew, M.J.Brett, T.Smy: Journal of Applied Physics, 1995, 78[7], 4438-43