Single-crystalline aluminum nitride (AlN) has successfully been grown on 6H-SiC (0001) substrates by sublimation using an open-system crucible at 2273 K within 30 h. The thickness of the AlN single-crystal layer is about 1 mm. The dislocation density in the vicinity of the crystal surface has been calculated to be less than 107 cm(-2) from transmission electron microscopy observation and etch pit density measurement of the crystal. Single-crystal growth of AlN has been carried out by varying supersaturation of Al vapor and employing on-and off-axis SiC substrates. Supersaturation of Al vapor has critically influenced the crystalline quality and morphology, while it has not affected the growth rate so much. Thus, precise control of supersaturation is a key to ensuring the quality of AlN single crystals. The quality of the crystals grown on off-axis SiC substrates is superior to that grown on on-axis SiC substrates. Moreover, the quality has been improved as the thickness of the crystals has increased. (C) 2008 Elsevier B.V. All rights reserved.