Modeling and simulation of resistivity of nanometer scale copper

A highly versatile simulation program was developed and used to examine how the resistivity of thin metal films and lines is increased as their dimensions approach and become smaller than the mean free path of electrons in metals such as copper and aluminum. The simulation program is flexible in that it can include the effects of surface and grainboundary scattering on resistivity either separately or together, and it can simulate the effect on resistivity where each surface of a film or line has a different value for the scattering parameter. The simulation program (1) provides a more accurate calculation of surface scattering effects than that obtained from the usual formulation of Fuchs theory, (2) calculates grain-boundary effects that are consistent with the theory of Mayadas and Shatzkes, (3) shows that surface and grain-boundary scattering effects are interdependent, and (4) shows that the change in resistivity with temperature begins to increase as dimensions approach the bulk mean free path of the electrons in the metal. 2005 Elsevier Ltd. All rights reserved.