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  • ward-jphysd2021

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The heat equation for nanoconstrictions in 2D materials with Joule self-heating

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Article number475303
<mark>Journal publication date</mark>25/11/2021
<mark>Journal</mark>Journal of Physics D: Applied Physics
Issue number47
Number of pages10
Publication StatusPublished
Early online date10/09/21
<mark>Original language</mark>English


We consider the heat equation for monolayer two-dimensional materials in the presence of heat flow into a substrate and Joule heating due to electrical current. We compare devices including a nanowire of constant width and a bow tie (or wedge) constriction of varying width, and we derive approximate one-dimensional heat equations for them; a bow tie constriction is described by the modified Bessel equation of zero order. We compare steady state analytic solutions of the approximate equations with numerical results obtained by a finite element method solution of the two-dimensional equation. Using these solutions, we describe the role of thermal conductivity, thermal boundary resistance with the substrate and device geometry. The temperature in a device at fixed potential difference will remain finite as the width shrinks, but will diverge for fixed current, logarithmically with width for the bow tie as compared to an inverse square dependence in a nanowire.

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This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics D. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/0957-4484/26/21/215201.