Thermal management is one of the main issues which must be overcome in order to maintain the continued reduction of feature sizes in silicon microelectronics. The new materials and device architectures which are used to achieve better performance have had a detrimental effect on thermal management due to higher thermal resistances and\ud additional thermal interfaces. Current thermal models, based on diffusive continuum flow, are inaccurate at nanoscale dimensions and a model which considers the microscopic nature of heat generation and heat tansport must be used.\ud \ud \ud On the microscale, heat transport can be described by the Boltzmann transport equation for phonons. The complexity and quantity of the phonon anharmonic interactions make a direct numerical solution difficult without numerous approximations. The Monte Carlo technique has been established as an accurate approach to the modelling of charge transport in semiconductors and the application of this method to phonon transport is a logical choice.\ud \ud \ud There has been little reported work on Monte Carlo simulations of phonon transport. This thesis examines previous work on non-momentum conservation Monte Carlo\ud simulations, exposing the shortcomings of this approach and attempting to rectify them with algorithmic changes as well as the use of relaxation times calculated using second\ud and third order elastic constants. These changes result in an improvement of the equilibrium simulation as well as producing more realistic thermal gradients for both large\ud and small temperature differences at steady state. The improved techniques are applied to nanowire geometries and found to provide the correct trends.\ud \ud The work is extended further to produce a momentum conservation Monte Carlo simulation and used to simulate the anharmonic three-phonon processes (both absorption\ud and emission type) for acoustic phonon modes in silicon. Phonon-phonon absorption events are performed by selecting a partner phonon from within the same real space cell that satisfies momentum and energy conservation. In previous derivations of analytical approximations for phonon lifetimes and thermal conductivities, it has been difficult to determine the relative contribution of Normal and Umklapp processes in phonon-phonon interactions; this information can be extracted directly from the Monte Carlo simulation. Some success is achieved with this method at low temperatures and it is shown that with higher computational power, this simulation could provide a very accurate model for heat transport
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