Positronium diffusion in porous methylsilsesquioxanethin films

Depth profiled positronium (Ps) annihilation lifetimespectroscopy (PALS) is an extremely useful probe of the porecharacteristics in nanoporous low-dielectric (low-k) constant thinfilms. PALS has also been considered as a potential probe toinvestigate diffusion barrier integrity and the structural changesof porous low-k films during their integration with Cu. Hence, itis essential to understand the diffusion behaviour of positronium/Cuatoms in the films. In this work, based on the fact that porousmaterials possess characteristics of statistical self-similarity, afractal model, the Menger sponge model, has been applied to simulate thestructure of a promising dielectric, porous methylsilsesquioxane(MSQ) films. The diffusion behaviour of Ps out of the fractal model andinto the surrounding vacuum is studied by means of the diffusionequation and traditional advective--diffusive theory. Predictiveresults from our model show good agreement with measurement data.