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International Heat Transfer Conference 12

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

Advances in Computational Modeling of Nano-Scale Heat Transfer

Cristina H. Amon
Office of the Dean, University of Toronto

DOI: 10.1615/IHTC12.3130
14 pages


Over the last decade, heat transfer at extremely small length and time scales has come to play an increasingly important role in nano-scale material processing, in ultra-fast laser processing, and in the design of microelectronics, superlattices and thin film structures. In designing microelectronics, for example, it is crucial to consider the thermal performance of sub-micron thin films and composites, the effect of nano-scale heat sources and the rapid transient energy releases. Additionally, thermally-induced failure and reliability at nano scales is hindering further miniaturization of electronic devices. Therefore, understanding, predicting and controlling thermal energy transport at extremely short time and length scales in dielectrics and semiconductors is critical to a host of emerging technologies. However, the well known thermal diffusion equation based on the Fourier’s law fails to predict accurately the thermal response at nano-scale characteristic lengths because it does not resolve the actual energy carrier mechanisms and the phonon ballistic behavior. For thermal systems requiring consideration of phonons transport, when the characteristic dimension becomes comparable to the phonon mean free path, a more general equation, such as the Boltzmann transport equation (BTE), must be employed. Since solving the BTE is time intensive, even for simple geometries, several modeling approaches and numerical methods have been proposed. This lecture presents a comprehensive review of state-of-the-art techniques used in the computational modeling of sub-micron and nano-scale heat transfer with the Boltzmann transport equation, its simplified models (hyperbolic heat equation, equation of phonon radiative transfer, ballistic-diffusive heat conduction equation, and phonon energy density approach), Monte Carlo technique and molecular dynamics approach. It also outlines the challenges to model nano-scale thermal transport and to integrate solutions across multiple length scales ranging from nanometers to macro scales. Relevant thermal behavior in thin films, superlattices and silicon on insulator hot spots are discussed as well.

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