In this article we investigate the electron-phonon interaction in metals in the system strongly reduced in one dimension. The Fermi sphere which represents the free-electron structure of a bulk metal was replaced by a discrete set of the Fermi disks. Using the variational expression for resistivity the temperature and film thickness dependences of the resistivity were derived and compared with experimental data.
We present new formula which describes the change of electrical resistivity of a monoatomic metallic layer with temperature. The results are compared with those given by the Bloch-Grüneisen formula for bulk metals. Our calculated values compared with those for bulk materials are significantly higher at low temperatures (T<0.1θ) and apparently lower at the remaining range of temperatures. Both effects can be explained by the low dimensionality of the sample.
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