Theory of the resistivity of inhomogeneous conducting "fine lines"

The mechanisms contributing to the resistivity of the AlSingle Bond signCu thin-film conducting stripes used as connections on chip microcircuitry are analyzed. The excess resistivity due to the presence of copper in the stripe, both in solution and as a precipitated compound, is studied here by a general theory of mixtures and by computer simulations. Consequences of the finite size of a strip are predicted, leading to systematic increases in resistivity and variations of the resistance within populations of similarly prepared stripes. We obtain some quantitative estimates of the conditions under which such size effects became significant, and analyze the role of different preparation techniques on these size effects.