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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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In: Journal of Physics D: Applied Physics, Vol. 54, No. 47, 475303, 25.11.2021.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

### Author

Ward, Oliver ; McCann, Edward. / The heat equation for nanoconstrictions in 2D materials with Joule self-heating. In: Journal of Physics D: Applied Physics. 2021 ; Vol. 54, No. 47.

### Bibtex

@article{203d65e2ee524c34983910703ebda931,
title = "The heat equation for nanoconstrictions in 2D materials with Joule self-heating",
abstract = "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.",
author = "Oliver Ward and Edward McCann",
note = "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. ",
year = "2021",
month = nov,
day = "25",
doi = "10.1088/1361-6463/ac21fe",
language = "English",
volume = "54",
journal = "Journal of Physics D: Applied Physics",
issn = "0022-3727",
publisher = "IOP Publishing Ltd",
number = "47",

}

### RIS

TY - JOUR

T1 - The heat equation for nanoconstrictions in 2D materials with Joule self-heating

AU - Ward, Oliver

AU - McCann, Edward

N1 - 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.

PY - 2021/11/25

Y1 - 2021/11/25

N2 - 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.

AB - 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.

U2 - 10.1088/1361-6463/ac21fe

DO - 10.1088/1361-6463/ac21fe

M3 - Journal article

VL - 54

JO - Journal of Physics D: Applied Physics

JF - Journal of Physics D: Applied Physics

SN - 0022-3727

IS - 47

M1 - 475303

ER -