Time minimization for a three-step cyclic process of deposition and diffusion

The optimal layer thickness for minimizing the total time to build a layer with a three-step cyclic process of deposition and diffusion, or "annealing," is determined. Deposition and diffusion processes scale rather differently according to time. This analysis, for the building of a TiN barrier layer, quantifies those times in a model and is then used to find the thickness that minimizes a total time function across more than one process. This model would apply equally to the doping of SiO₂ strata.