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The resistivity of an interface region (ρsurface) with a thickness of λ is different from that of a bulk region (ρbulk) with a thickness ofd− 2λ, where the film thickness isd. With these notations, the additive rule of serial resistance can be applied. Here,Ais the area of the top electrode of the sandwich structure. ρfilm(d/A) = 2ρsurface(λ/A) + ρbulk(d− 2λ)/A. Therefore, ρfilm= ρbulk+ 2(ρsurface− ρbulk)(λ/d). Thus, it is possible to show with this simple argument that the resistivity varies linearly with the reciprocal thickness.
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