Fick's law of diffusion was used to model the diffusion of Cu into Ta barrier material. By matching experimental results, the Cu diffusion coefficient was found to be described by:

D(cm2/s) = 2.870 x 10−14exp[−0.1457(eV)/kT]cm2/s

By using the calculated results, a 25nm Ta layer was found to be sufficient to stop Cu from diffusing through it during annealing (600C, 0.5h).

S.W.Loh, D.H.Zhang, C.Y.Li, R.Liu, A.T.S.Wee: Thin Solid Films, 2004, 462-463, 240-4