This thesis uses Monte Carlo simulations to investigate electron transport in GaAs, its ternary In0.₅₃Ga₀.₄₇As and GaN. Ensemble Monte Carlo methods are used to determine the effects of a non-equilibrium phonon distribution on the transport properties of bulk In₀.₅₃Ga₀.₄₇As. Hot phonons are shown to reduce the critical field, peak velocity and saturation velocity. The dominant hot phonon effects in In₀.₅₃Ga₀.₄₇As are shown to be diffusive heating and phonon re-absorption. Evidence of the phonon drag effect is not found.A notched GaAs Gunn diode originally modelled by J. Tully in 1983 [1] is then recreated with a finer mesh and more superparticles. The device is shown to operate in accumulation mode with a considerable ‘dead zone’. The model is shown to be consistent with the original to a reasonable estimate considering the uncertainty surrounding material parameters. Significantly less noise is present demonstrating the increased precision offered by a Monte Carlo model with an increased resolution.Characteristics of GaN Gunn diodes are then explored. Results are presented for a device operating in accumulation mode with an operating frequency of 164 GHz. Results are then presented for a device operating in dipole mode with an operating frequency of 119 GHz. The mechanisms surrounding the function of these devices are analysed and shown to be consistent with the literature.Finally, a proof of concept 2-dimensional device simulator is validated through comparison with an equivalent 1-dimensional device. While equivalency is proven a number of obstacles are highlighted surrounding computational efficiency and optimum simulation parameters
