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首页> 外文期刊>International Journal of Heat and Mass Transfer >Transient Joule heating of graphene, nanowires and filaments: Analytical model for current-induced temperature evolution including substrate and end effects
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Transient Joule heating of graphene, nanowires and filaments: Analytical model for current-induced temperature evolution including substrate and end effects

机译：石墨烯，纳米线和细丝的瞬态焦耳加热：电流诱导的温度演化的分析模型，包括衬底和最终效应

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摘要

Transient Joule heating of graphene or nanowires, supported by substrates, is an important and complex heat transfer problem to be solved in the context of nanoscale electronic devices. We formulate here an analytical model that allows the examination of the effects of input power, heat transfer through substrate and the end contacts on the transient temperature evolution. An exact analytical solution is obtained here by the superposition of the Joule heating, the substrate heat transfer and the temperatures at the ends of contacts, within the Fourier formalism, through Laplace transformations. The transient solution explicitly relates temperature profile to the input power, size and the thermal properties of the element, and the heat transfer properties of the substrate. The transient solution naturally reduces to steady state solution. The solutions can be useful for the thermal design of devices made of graphene or nanowires or electrically heated filaments. Experimental steady-state temperature distribution data, obtained by 2D phonon band spectroscopy, are used to confirm the accuracy of the solution. It is found that the time to achieve steady-state temperatures in graphene is of the order of nanoseconds and is a strong function of substrate heat transfer. Further, the maximum temperature and the gradient in steady state profile temperature profile are greatly affected by heat transfer to the substrate.
机译：受衬底支撑的石墨烯或纳米线的瞬时焦耳加热是重要且复杂的传热问题，需要在纳米级电子设备的背景下解决。在这里，我们制定了一个分析模型，该模型可以检查输入功率，通过基板的热传递以及端接点对瞬态温度变化的影响。在这里，通过拉普拉斯变换，通过傅立叶形式主义中的焦耳热，基板传热和接触端温度的叠加，可以获得精确的分析解决方案。瞬态解决方案明确地将温度曲线与输入功率，元件的尺寸和热特性以及基板的传热特性相关联。瞬态解自然会还原为稳态解。该解决方案可用于石墨烯或纳米线或电加热丝制成的设备的热设计。通过2D声子带光谱法获得的实验稳态温度分布数据用于确认溶液的准确性。发现在石墨烯中达到稳态温度的时间约为纳秒，并且是衬底传热的强函数。此外，最高温度和稳态曲线温度曲线中的梯度受传至基板的热量的影响很大。

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