High field transport in wide bandgap semiconductors like GaN is of great technological importance. The negative differential mobility regime at high fields, under suitable conditions, can lead to millimeter-wave Gunn oscillations. Using extensive simulation based an ensemble Monte Carlo technique, the prospects of GaN Gunn diodes are theoretically investigated. The possibility of operating these Gunn diodes at their higher harmonic modes are explored. Main finding of this research is that the carrier dynamics in GaN can be tailored by an optimum choice of doping profile, temperature and bias conditions so that the efficiency of higher harmonic Gunn oscillations can be boosted.