Gallium nitride with its high negative differential mobility threshold is an appealing material for high power millimetre-wave oscillators as a Gunn diode. By means of extensive ensemble Monte Carlo simulations, the dynamics of large-amplitude Gunn domain oscillations from 120 GHz to 650 GHz is studied in detail. Their operations are checked under both impressed single-tone sinusoidal bias and external tank circuit conditions. The width of the doping notch is observed to enhance higher harmonic efficiency at the expense of the fundamental frequency up to a critical value, beyond which sustained Gunn oscillations cease. The degeneracy effects due to the Pauli exclusion principle are also considered, but their effects are seen to be negligible within the realistic bounds of the Gunn diode operation.