Quantum theory of the effect of grain boundaries on the electrical conductivity of thin films and wires
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2015Metadata
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Moraga, Luis
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Quantum theory of the effect of grain boundaries on the electrical conductivity of thin films and wires
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Abstract
We calculate the electrical conductivity of a metallic sample under the effects of distributed impurities
and a random distribution of grain boundaries by means of a quantum mechanical procedure based on
Kubo formula. Grain boundaries are represented either by a one-dimensional regular array of Dirac delta
potentials (Mayadas and Shatzkes model) or by its three-dimensional extension (Szczyrbowski and
Schmalzbauer model). We give formulas expressing the conductivity of bulk samples, thin films and thin
wires of rectangular cross-sections in the case when the samples are bounded by perfectly flat surfaces.
We find that, even in the absence of surface roughness, the conductivity in thin samples is reduced from
its bulk value. If there are too many grain boundaries per unit length, or their scattering strength is high
enough, there is a critical value Rc of the reflectivity R of an individual boundary such that the electrical
conductivity vanishes for R > Rc . Also, the conductivity of thin wires shows a stepwise dependence on R.
The effect of weak random variations in the strength or separation of the grain boundaries is computed
by means of the method of correlation length. Finally, the resistivity of nanometric polycrystalline
tungsten films reported in Choi et al. J. Appl. Phys. (2014) 115 104308 is tentatively analyzed by means of
the present formalism.
General note
Artículo de publicación ISI
Patrocinador
FONDECYT
1120198
Fondo lnterno de Investigacion, Universidad Central
project Conicyt CENAVA
791100037
Identifier
URI: https://repositorio.uchile.cl/handle/2250/132243
DOI: doi: 10.1016/j.physb.2015.04.034
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Physica B 470-471 (2015) 39–49
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