Theory of Thermal Conductivity of Micro- and Nano-structured Materials
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1172-T08-07
Theory of Thermal Conductivity of Micro- and Nano-structured Materials
Gyaneshwar P. Srivastava School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
ABSTRACT We provide a brief discussion of the Boltzmann equation derived Callaway-Debye relaxation time theory of lattice thermal conductivity of micro- and nano-structured materials (of size greater than 20 nm). Incorporated in the theory is a comprehensive treatment of three-phonon scattering events. Using numerical results from this theory, we present a quantitative investigation of the magnitude and temperature variation of the conductivity of CVD polycrystalline diamond films, suspended GaAs nanostructures, Si nanowires, and AlN micro- and nano-ceramics. INTRODUCTION Phonons, quanta of atomic vibrational energies, are the main carriers of heat in nonmetallic solids. Consider a hypothetical crystal that is infinitely long, is isotopically pure, has no imperfections or defects, and is characterised by purely harmonic atomic vibrations. Phonons in such an idealised crystal will be infinitely long lived, and would transport all heat from the hot end to the cold end upon the application of a temperature gradient. However, real solids are of finite size, contain impurities and defects, and their atomic vibrations are characterised with anharmonicity. These realities limit the life time of phonons, which in turn results in finite values of temperature-dependant thermal conductivity of solids. Numerical values and temperature variation of thermal conductivity of solids can be determined from experimental measurements. However, quantitative ascertaining the roles of individual phonon scattering mechanisms in limiting thermal transport can only be done with the help of well-developed theoretical models. The role of theory is even more important in confidently predicting the most important phonon scattering processes, and how to control their contribution to the heat transport process, in a given system. In this article we provide a brief discussion of the Boltzmann equation derived CallawayDebye-Srivastava relaxation-time theory of lattice thermal conductivity [1, 2]. We apply this theory to provide numerical results for the thermal conductivity of micro- and nanostructured nonmetallic materials. Using our numerical results, we present a quantitative investigation of the magnitude and temperature variation of the conductivity of CVD polycrystalline diamond films, suspended GaAs nanostructures, Si nanowires, and AlN microand nano-ceramics.
CALLAWAY-DEBYE-SRIVASTAVA THEORY OF HEAT TRANSPORT Conductivity expression Two fundamentally different microscopic approaches have been developed for lattice thermal conductivity (see, e.g. [2]). These are rooted in (i) linear-response methods based upon the Green-Kubo formalism, and (ii) methods based upon solving the phonon Boltzmann equation. Linear-response methods employ quantum statistical approaches to evaluate a correlation function involving the phonon number-density operator. On the other hand
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