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Heteroepitaxial growth of metal-catalyst-free indium nitride (InN) nanorods on GaN/sapphire substrates by radio-frequency metal-organic molecular beam epitaxy (RF-MOMBE) system was investigated. We found that different N/In flow ratios together with the growth temperatures greatly influenced the surface morphology of InN nanorods and their structural properties. The InN nanorods have been characterized in detail using X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM). Optical property was evaluated by photoluminescence (PL) measurements. At lower growth temperatures, InN nanorods were successfully grown. A pronounced two-dimensional growth mode was observed at higher growth temperature of 500 degrees C, and these films showed preferred orientation along the c-axis. XRD patterns and SEM images reveal that InN nanorods has high quality wurtzite structure with FWHM approaching 900 arcsec, and they have uniform diameters of about 150 nm and length of about 800 nm. Meanwhile, no metallic droplet was observed at the end of the nanostructured InN, and this is strong evidence that the nanorods are grown via the self-catalyst process. The PL peak at 0.8 eV is attributed to the quantum confinement and Moss-Burstein effects. These observations provide some valuable insights into the physical-chemical process for manufacturing InN nanorods devices.