ABSTRACT
In this dissertation, lattice thermal conductivity (LTC) is computed numerically using a Modified-Debye-Callaway model, in the temperature range 2-300 K, under a hydrostatic pressure in the range 0-10GPa, for bulk silicon, naofilms (NFs) in the thickness range 20-3000 nm and nanowires (NWs) in the diameter range of 22-115 nm.
The bulk silicon is included as a reference and for comparison purposes. Both longitudinal and transverse modes are explicitly considered within the model. The parameters needed in the calculation, such as group velocity, melting-temperature, Debye-temperature, Grüneisen-parameter, bulk-modulus, surface-roughness, dislocation-density and impurity density, were scaled, when it was necessary, for size-dependency and/or pressure-dependency, using proper formulas. The calculated LTC values at zero-pressure were fitted to experimental data when such data was available. The best fit is used to deduce the appropriate value of the parameter. For pressures up to 10 GPa scaling the parameter was used when it was necessary.
In this regard, Murnaghan and Clapeyron equations for pressure-dependent lattice volume and melting-temperature were employed. The respective applications of the two equations in the modified Debye-Callaway model produce results that tend to be systematically applicable in this model. The confinement and size effects of phonons and the role of pressure in the reduction of LTC are investigated to reduce the change in the peak value bell-shape of LTC from zero pressure to 10 GPa in Si NWs, whilst the certain temperature at which the LTC obtains maximum values for this range decreases with pressure as the NWs diameter is decreased.
The LTC curves have the usual bell-shape in the temperature range 2-300K. The low temperature range is attributed to boundary-scattering and phonon-electron scattering. The medium temperature range is attributed to phonon-phonon scattering, dislocation and impurity scattering, and the high temperature range is attributed to multi-phonon Umklapp scattering.
The bell-shape LTC curve shifts to lower value as the diameter of the NWs and the thickness of the NFs decrease. Additionally, the maximum LTC for NFs shifts to the lower temperatures, and the larger the thickness, the greater is the shift in (LTC)max towards the lower temperature. Generally, the pressure decreases the value of LTC across the whole temperature range. The results show that pressure reduces the unit cell volume. The difference Δ(LTC) in LTC value between 10GPa and zero pressure, increases with increasing diameter of the NWs and with increasing thickness of the NFs.