An exact analytical solution to metal diffusion in a triplet stack consisting of a barrier material layer, an interlayer dielectric, and a semiconductor substrate has been developed. The solution shows how the diffusive behavior of the metal depends on the material properties of the entire system. The resistance of the interconnect system to contamination is not linearly dependent on the material and geometrical properties and some properties, such as the barrier diffusivity and solubility, are significantly more important than others. The model was able to match the copper diffusion data of Shacham-Diamand [J. Electrochem. Soc., 140(8), 2427 (1993)] very well using material properties consistent with the available experimental data.