Piezoresistance and electrical resistivity of Pd, Au, and Cu films

Electrical resistivity and piezoresistance of some metal films, such as the Pd, Au, and Cu films, were measured. Surface features of a few characteristic films, used in this study, were revealed by using an atomic force microscope. The electrical resistivity p is plotted as a function of the film thickness t, and the strain gauge factor gamma is plotted as a function of the sheet resistivity R-sq. Two parameters are found useful: i.e. h/lambda and 2h/t, where h is the amplitude of undulations of the surface roughness and lambda is the electron mean free path at room temperature. By taking the Cu film as an example, the area-distribution function of island-like humps on the specimen surface is also analyzed. Two models, namely the surface roughness and the electron tunneling models, are employed to explain the electrical resistivity and piezoresistance data observed. It is found that (1) if h/lambda less than or equal to 0.3 and 2h/t < 0.5, the films are continuous, and the former model is effective, and (2) if 0.5 < 2h/t < 1, the films are critically coalesced, and the latter model is important. Finally, from the area-distribution plot, we can show indirectly that if the film is at the coalescence stage, the average separation Deltad between two neighboring humps is wider than if the film is at the continuous stage. (C) 2003 Elsevier Science B.V. All rights reserved.