SP Hepplestone's Cv

Thesis

Abstract

In the following Thesis, the physics of phonons in silicon nanostructures and carbon nanotubes has been discussed. The fundamental quantity, the phonon dispersion curves, which are necessary for considering any thermal property, have been obtained. The phonon dispersion relation results for nanostructures of various sizes have been discussed and the effects of dimensionality on their lattice dynamics has been presented. Based upon these phonon dispersion relations, the specific heat capacity of carbon nanotubes has been calculated. The change over from one-dimensional behaviour to two-dimensional behaviour has been explained and a relationship for this occurence, which is dependent on the nanotube size and temperature, has been expressed. Using the dispersion relations obtained in this Thesis, detailed calculations of the lifetime of phonon modes in nanostructures have been performed using an approach based on Fermi's Golden Rule. The lifetime of the low-lying zone-center optical modes has been calculated and shown to be comparable with that of bulk acoustic modes. Hence, it has been shown that these modes must be included for accurate calculations of the lifetime of phonon modes undergoing phonon-phonon interactions. Upon this basis the lifetime of phonon modes in carbon nanotubes were calculated and this lifetime has been shown to be of the order of nanoseconds. A correct one-dimensional model was described for the carbon nanotube, which considered the important angular momentum conditions which limit phonon-phonon interactions that had not been noted before. This model was adapted using Debye dispersion relations to provide analytic expressions for the relaxation rate of phonon modes. This analytic expression was shown to be in good agreement with numerical calculations based upon fully dispersive phonon dispersion relations. It is shown that the thermal conductivity is linearly dependent on temperature for between 75 K and 225 K. It was also shown that mass-defect scattering has substantially less effect in one-dimensional systems than in three-dimensional systems. Using the theory for boundary scattering, the reason for the vast number of different theoretical results is described as being a result of the ballistic free-path distance. These results are expected to be of great use to anyone who is researching into the theory or applications of nanotubes or semiconducting nanostructures.

A copy of my thesis is available for download here.