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Resistivity and the Hall effect in polycrystalline Ni-Cu and Ta-Cu multi-layered thin films

The dependences of the resistivity rho and the Hall voltage UH of polycrystalline Ni-Cu and Ta-Cu multi-layered thin films on the layer thickness dl are discussed. The thickness dependence of rho and UH can be well understood using a simple model in which the layers are considered as parallel resistors, whereby the resistivity of a single layer is enhanced via surface scattering described by the well known Fuchs-Namba size theory. The Hall coefficients are independent of the layer thickness, although the measured Hall voltage varies with dl owing to the enhancement of the individual layer resistivities. For very thin layers, i.e. if the layer thickness becomes smaller than the layer roughness, the experimental data on both rho and UH indicate a breakdown of the multi-layered structure to an island-like clustered film structure. For Ni-Cu a crossover from ferroparamagnetic to superparamagnetic behaviour was observed at this critical thickness.