Grain-boundary diffusion modeling and efficiency evaluation of thin-film diffusion barriers considering microstructure effects

Abstract

We have developed a novel grain-boundary diffusion model using the transmission-line matrix method. In conjunction with a two-dimensional Monte Carlo thin-film growth simulator, this model can be employed for the analysis of impurity diffusion in thin-film diffusion barriers with realistic microstructures. In the model, the impurity at the upper surface of the barrier layer may diffuse through rapid and irregularly shaped grain-boundary diffusion paths to reach the bottom surface. Calculations of the impurity concentration and out-diffusion flux as a function of elapsed diffusion time and position enable the evaluation of the effectiveness of the barrier layer at a microstructure level. Consequently, the diffusion process is depicted with less assumptions and more precisely than previously available approaches. This paper details the grain-boundary diffusion modeling method outlined above, with the emphasis on the treatment of various boundary conditions. A representative application to titanium nitride (TiN) thin-film diffusion barriers is also demonstrated, as befits the high level of interest in this particular material for very large scale integrated devices.