New experimental results concerning basic electronic properties of fine grained metallic films call for theoretical models differing from standard theories: 1) The d.c. conductivity depends on the number of electrons crossing the grain boundary potentials along their background scattering length. An intrinsic scattering length for the whole polycrystal cannot be defined. 2) The Hall coefficient depends on the grain size. Below a “cut-off grain size”, electrons with p-symmetry are virtually confined within the grains. Consequently a virtual free electron value is observed. 3) The work function shows a long ranging thickness dependence. For film thicknesses comparable with electronic scattering lengths, the film’s surfaces start to interact.
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J. Vancea (1989) studied this question.