Modal decomposition of thermal conductance

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Gordiz, Kiarash
Henry, Asegun
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Reliably and quantitatively calculating the conductance of phonons across an interface between two materials has been one of the major unresolved questions in thermal transport physics for the last century. Theories have been presented in this regard, but their predictive power is limited. In this thesis, a new formalism to extract the modal contributions to thermal interface conductance, termed interface conductance modal analysis (ICMA) is developed. ICMA can fully include the temperature dependent anharmonicity and atom level topography around the interface in the calculations. In addition, compared to all the previous techniques that are based on the phonons gas model (PGM) and can only be applied to crystalline interfaces, ICMA is not based on preexisting assumptions; thus, it can be applied to the interface of disordered/amorphous solids as well. The obtained results indicate that when two materials are joined a new set of vibrational modes are required to correctly describe the transport across the interface. The new set of vibrational modes is inconsistent with the physical picture described by the PGM, because some of the most important modes are localized and non-propagating and therefore do not have a well-defined velocity nor do they impinge on the interface. Among these new modes, certain classifications emerge, as most modes extend at least partially into the other material. Localized interfacial modes are also present and exhibit a high conductance contribution on a per mode basis by strongly coupling to other types of vibrational modes. ICMA formalism is applied to different interfaces to present thermal interface conductance accumulation functions, two-dimensional cross-correlation matrices, and a quantitative determination of the contributions arising from inelastic effects. Moreover, the results show that ICMA present a physical explanation for interfacial heat transafer that is based on correlation and that is different and independent of the dominant scattering viewpoint followed by the PGM. The provided new perspective on interface thermal transport can open new gates towards deeper understanding of phonon-phonon and electron-phonon interactions around interfaces.
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