Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires |
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Authors: | R I Boughton J E Neighbor |
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Affiliation: | (1) Department of Physics, Northeastern University, Boston, Massachusetts |
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Abstract: | Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, ![Delta](/content/u1x06243n0605r6m/xxlarge916.gif)
d
(T)![equiv](/content/u1x06243n0605r6m/xxlarge8801.gif)
d
(T)–
d
(0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, ![Delta](/content/u1x06243n0605r6m/xxlarge916.gif)
d(T)
increases logarithmically with
d(0); (2) for a cylindrical Fermi surface, ![Delta](/content/u1x06243n0605r6m/xxlarge916.gif)
d
(T) increases essentially linearly with
d
(0). In each case the qualitative dependence of
d(0) on /d is, for practical purposes, linear. However, the correct value of the product ![rgr](/content/u1x06243n0605r6m/xxlarge961.gif) ![infin](/content/u1x06243n0605r6m/xxlarge8734.gif) in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of
d
(0) vs.d
–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior. |
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Keywords: | |
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