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TCR of thin ilms Consider Matthiessen's rule applied to a thin film. Show that, very approximately, the product of the thermal coefficient of resistivity (TCR) aiim and the resistivity piim is...

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TCR of thin ilms Consider Matthiessen's rule applied to a thin film. Show that, very approximately, the product of the thermal coefficient of resistivity (TCR) aiim and the resistivity piim is equivalent to the product of the bulk TCR and resistivity:

 

Answered 133 days After May 13, 2022

Solution

Amar Kumar answered on Sep 24 2022
60 Votes
To solve the issue, quantitative models for the temperature dependence of metallic nanowires or thin films are essential. At the moment, there is no reliable, practical model for the temperature dependency of the resistivity in nanowires. Although ab initio methods have been effective in demonstrating quantum effects in very thin nanowires, they are restricted to low temperatures or only work at a small range of temperatures. More quantitative evidence is still required to support semi classical motions. The resistance of small films has traditionally been illustrated using semiclassical models, such as the one that Mayadas and Shatzkes initially deduced from the early work of Fuchs in addition to Sondheimer and quantum models for surface dispersion. The semiclassical model by Mayadas and Shatzkes has the benefit of simultaneously handling surface roughness and grain limit dissipation...
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