Impact of doping on the morphology, structure and optical properties of c-oriented GaN nanorods

•PAMBE growth of GaN nanorods on Si(111) with Mg and Si doping demonstrated.•Mg doping enhances coalescence while Si doping increases misorientation.•Dopant incorporation confirmed by photoluminescence and cathodoluminescence.•Raman analysis used to measure carrier concentrations from phonon-plasmon modes.•Strain relaxation studied using transmission electron microscopy.