Gallium nitride can offer a high-power alternative for millimeter-wave Gunn oscillators. Hence, an ensemble Monte Carlo-based comprehensive theoretical assessment of efficiency and harmonic enhancement in n-type GaN Gunn diodes is undertaken. First, the effects of doping notch/mesa and its position within the active channel are investigated which favors a doping notch positioned next to cathode. It is then observed that the width of the notch can be optimized to enhance the higher-harmonic operation without degrading its performance at the fundamental mode. Next, the effects of dc bias and channel doping density are investigated. Both of these have more significant effects on the higher-harmonic efficiency than the fundamental one. The lattice temperature is observed to have almost no influence up to room temperature but severely degrades the performance above room temperature. As a general behavior, the variations of temperature, channel doping, and the notch width primarily affect the phase angle between the current and voltage wave forms rather than the amplitude of oscillations. Finally, the physical origin of these Gunn oscillations is sought which clearly indicates that the intervalley scattering mechanism is responsible rather than the Γ valley nonparabolicity or the effective mass discrepancy between the Γ and the lowest satellite valleys.