Theory of Thermal Conductivity of Micro- and Nano-structured Materials

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.

Improved transparent thermal insulation using nano-spaces

“…The sol-gel derived silica shell has many defects, and that situation induces phonon scattering between phonon-phonon and phonon-intraparticle defects, especially at room temperature [21]. A low q shell indicates that the silica shell contains many defects, which according to Callaway-Debye-Srivastava relaxation-time theory [22] might be barrier for phonon transmission. The dispersibility of HSNPs in PU film was observed by using a scanning electron microscope (SEM).…”

Tuning phonon properties in thermoelectric materials

“…It has been argued [160] that in order to explain the conductivity of the nanowire of diameter 22 nm it is important to employ a theoretical model that combines incoherent surface scattering for short-wavelength phonons with nearly ballistic longwavelength phonons. However, a later theoretical attempt [157] employing the Callaway-Debye-Srivastava relaxationtime model (i.e. using equations ( 102), ( 104), ( 105), ( 107) and ( 125)) was found to successfully explain the results for all diameter sizes, including 22 nm.…”

“…Several theoretical attempts have been made to explain the experimental results obtained by Li et al, including the semi-classical Boltzmann-type approach [158], a semiempirical molecular dynamics approach [159], and the quantum Landauer formalism [160]. All these models are [156] and the figure is reproduced with permission from [157]. capable of explaining the measured thermal conductivity results for the nanowires of all diameters, except 22 nm.…”

“…using equations ( 102), ( 104), ( 105), ( 107) and ( 125)) was found to successfully explain the results for all diameter sizes, including 22 nm. The theoretical results from [157] are shown by the solid curves in figure 23.…”

“…Lattice thermal conductivity of Si nanowires. The experimental data is read from[156] and the figure is reproduced with permission from[157].…”