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Non-linearity and dimensionality in optical heating Chang, Hung Chao Mike

Abstract

One of the most important hurdles in electron-beam technologies such as thermionic energy conversion and parallel-beam lithography is having a high-performance electron source (cathode) material. Both of these applications, directly or indirectly, would benefit from a material’s ability to be heated efficiently through localized optical heating. Similarly, the main objective of thermoelectrics research is to maintain a high temperature gradient without hindering electrical conductivity, in order to increase the energy conversion efficiency. For this, many researchers have been pursuing the development of complex crystals with a host-and-rattling compound structure to reduce thermal conductivity Recently, localized heating with a temperature rise of a few thousand Kelvins has been induced by a low-power laser beam (< 50 mW) on the side-wall of a vertically-aligned carbon nanotube (CNT) forest. Given the excellent thermal conductivity of CNTs, such localized heating is very counterintuitive, and proper understanding of this phenomenon is necessary in order to use it for applications in thermionics and thermoelectrics. Here, an analytical formulation for solving the associated non-linear inhomogeneous heat problem through a Green’s function-based approach will be introduced. The application of this formulation to bulk metals, semiconductors, and different allotropes of carbon will be discussed. In particular, a systematic investigation will be presented on the effect of the material dimensionality and non-linear dependence of thermal conductivity on temperature. It will be shown that, if thermal conductivity is assumed to be constant, the peak temperature is proportional to the linear power density up to temperatures where radiative loss becomes significant. On the other hand, if the thermal conductivity falls with temperature, a significantly higher peak temperature and temperature gradient can be achieved. Furthermore, reducing the dimensionality of a material (going from a three-dimensional to a one-dimensional form) can lead to a significant peak temperature and temperature gradient.

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Attribution-NonCommercial-NoDerivs 2.5 Canada

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