Size effects in electrodiffusion in thin films

Abstract

The effective ion charge and the electrodiffusion activation energy in thin films are analysed as a function of the film thickness. The effective ion charge Z ef f in electrodiffusion in thin films is shown to depend on the ratio of the film thickness d to the electron free path length λ e, the specular scattering factor p and a coefficient K which is proportional to the increase in the resistivity ρ a due to the activated ions. Values of p of 0, 0.25, 0.5, 0.75 and 1.0 were considered. Z ef f was found to be unaffected by the ratio d/λ e for p = 1.0. At other values of p there is a marked dependence of Z ef f on d/λ e for d λ e < 10 . If it is assumed that the coefficient K f for thin films is equal to the coefficient K ∞ for bulk specimens, Z ef f = Z ef ∞ at p = 1.0. If K f ⪡ K ∞ then Z ef f < Z ef ∞, and if K f > K ∞ then Z ef f > Z ef ∞. The decrease in the electrodiffusion activation energy with thickness can be explained if grain boundary diffusion is replaced by surface diffusion. Calculations showed that the size effect is least for electrodiffusion in thin films of metals with high melting points.