Modeling and Simulation of Cu Diffusion in Porous low-k Dielectrics

A modeling and simulation study of metal atom diffusion in porous dielectrics is presented using elementary jump frequencies for a random walk in 2D and 3D. The simulation is calibrated with experimental data from Cu/porous SiCOH/W structures. The effective Cu diffusivity is shown to depend not only on the level of porosity but also on the pore morphology. Other important factors: i) surface diffusion on the inner pore surfaces vs diffusivity in the bulk matrix material, ii) the rate of Cu dissolution into the dielectric vs the rate of transport by diffusion, and iii) the degree of the contact area of the Cu electrode with the porous dielectric surface, are also taken into account. The large multitude of porosity effects on diffusivity can be consistently and intelligibly explained in terms of "channeling" and "trapping" effects based on perturbation of local vertical and lateral concentration gradients imparted by the pore morphology.