Growth of InN by radio frequency plasma-excited molecular beam epitaxy on (0001) sapphire was systematically studied. To improve the crystalline quality of InN, the following growth conditions were found to be essential: (1) nitridation of sapphire, (2) two-step growth, (3) precise control of V/III ratio, and (4) selection of optimum growth temperature. Results of structural characterization using x-ray diffraction, transmission electron microscopy, and extended x-ray absorption fine structure have clearly demonstrated that InN grown in this study had single crystalline with ideal hexagonal wurtzite structure. It is confirmed, however, that the InN had a threading dislocation density on the order of 10(10)/cm(2) and large twist distribution. Photoluminescence studies on these well-characterized InN clearly demonstrated that band-gap energy of InN should be less than 0.67 eV at room temperature. (C) 2004 American Vacuum Society.