Correlation between resistivity and diffusion in thin films

Abstract

Empirical equations have been derived that relate resistivity to diffusivity and activation energies for thin films. Results for the Cr/Au structure agree with published data on the interdiffusion of Cr and Au thin films at temperatures ranging from 350 to 450 °C. The following relationships were determined: Δρ/ρ0C=λ exp(−Q/kT); Δρ/ρ0C=nDt/χ2; Δρ/ρ0C=ψ exp(−χ2/4Dt) and D=Nχ2 /t exp(−Q/kT), where Nχ2/t=D0(cm2/s) is the frequency factor; Δρ is the change in resistivity; ρ0 is the room temperature resistivity; χ is film thickness; T is temperature; t is time; C is concentration; k is Boltzman’s constant; D is diffusion coefficient; and n, ψ, N, and λ are constants. Analysis of the Cr/Au resistivity data using these equations gives D0=1.2×10−7 cm2/s and Q=1.00 eV for Cr diffusion in Au; and D0=1.0×10−7 cm2/s and Q=1.06 eV for Au diffusion in Cr. These values were verified by analysis using Rutherford backscattering spectroscopy and, they are consistent with those reported for grain boundary diffusion.