Fick's law of diffusion was used to model the diffusion of Cu into TaN barrier materials. From the matching with the experimental results, the Cu diffusion coefficients could be described by:

D (cm2/s) = 2.4 x 10-14 exp[-0.1395(eV)/kT]

Using the calculated results, a 24nm TaN layer was expected to block O transmission rate diffusion at 500C.

Study of Copper Diffusion into Ta and TaN Barrier Materials for MOS Devices. S.W.Loh, D.H.Zhang, C.Y.Li, R.Liu, A.T.S.Wee: Thin Solid Films, 2004, 462-463, 240-4