What do these two measurements actually imply? Please make the answer brief.
I think there is no such direct relationship but the work function should not show any statistical deviation across the film's surface during any transition (due to band bending at the boundaries of a small domains) as the local work function corresponded closely to the resistance of that small area.
Both have more or less nothing to do with each other: The work function gives somehow the boundary, how much ENERGY do I need to transport a conducting electron from the conduction (or valence) band to the vacuum in front of the surface. The conductivity is simply related to the transport of the electrons WITHIN the conduction bands, here the NUMBER of charge carriers as well as their MOBILITY are the most important properties - and these properties have (more or less) nothing to do with each other, at least, they can be manipulated independently.
If films are thin, it should be related as in semiconductor thin films.
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