A model is developed for estimating effects due to electron scattering from grain boundaries, occurring simultaneously with background scattering. Since grain-boundary effects are negligible in bulk materials, the model is particularly relevant to polycrystalline metal films in which a very fine-grained structure is often found. It is shown by solution of the appropriate Boltzmann equation, that the total resistivity can be strongly dominated by grain-boundary scattering. If grain size increases with film thickness, a marked dependence of resistivity on thickness exists, even when scattering from external surfaces is negligible or is completely specular.
A model was constructed for electromigration failure where both Fickian diffusion and mass transport due to the electromigration driving force are considered concurrently. The solution to the resulting diffusion equation yields a current exponent of 2 and an activation energy consistent with grain-boundary self-diffusion. A modification of the standard median time to failure equation first proposed by Black is suggested.
A mechanism describing the incipient stages of intrinsic dielectric breakdown is formulated for the case of a wide-band-gap insulator with a low hole mobility. Dielectric instability results from the tunnel injection of electrons from the cathode contact and the subsequent impact ionization and field distortion which lead to dielectric breakdown. The model, evaluated for the parameters of SiO2, predicts an intrinsic breakdown voltage which approaches a lower limit of V=9+φ for very thin films, where φ is the cathode contact barrier in volts. As a result, both the electric field at breakdown and the critical current density increase rapidly as the film thickness is reduced below 200 Å.
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