A model for the specific grain-boundary resistivity of metallic bamboo conductor lines was developed and was compared with other theoretical treatments and with experimental data. The grain boundary was modelled as an array of scatterers on a plane. The scatterers were termed so-called vacancy-ion complexes; in which the vacancy represented the boundary free-volume and the ion was an atom which was adjacent to the vacancy. Three cases were investigated: non-interfering scatterers, continua of interfering scatterers and discrete interfering scatterers. The approximations which were used led to a specific grain-boundary conductivity of about 10-16S/m2 for Al (in agreement with experiment) for the first 2 cases. In the non-interfering case, the specific resistivity was independent of the grain-boundary area. In the continuum interfering case, it was found that the grain-boundary resistivity was only weakly dependent upon the grain-boundary area. The grain boundary had a high probability of exhibiting perfect reflection or transmission of incident electrons. The source of the resistivity was the reflection of electrons. This behavior was independent of the exact interaction potential between the incident electrons and the defects which comprised the grain-boundary free-volume. The discrete interfering case produced specific resistivities which were several orders of magnitude too large, and exhibited a strong dependence upon the grain-boundary area. A relationship was established between the grain-boundary resistivity and the electromigration wind force.

Behavior of Grain Boundary Resistivity in Metals Predicted by a Two-Dimensional Model. R.Dannenberg, A.H.King: Journal of Applied Physics, 2000, 88[5], 2623-33