Silicon carbide (SiC) has a range of useful physical, mechanical and electronic properties that make it a promising material for next-generation electronic devices. Careful consideration of the thermal conditions in which SiC [0001] is grown has resulted in improvements in crystal diameter and quality: the quantity of macroscopic defects such as hollow core dislocations (micropipes), inclusions, small-angle boundaries and long-range lattice warp has been reduced. But some macroscopic defects (about 1-10 cm(-2)) and a large density of elementary dislocations (approximately 10(4) cm(-2)), such as edge, basal plane and screw dislocations, remain within the crystal, and have so far prevented the realization of high-efficiency, reliable electronic devices in SiC (refs 12-16). Here we report a method, inspired by the dislocation structure of SiC grown perpendicular to the c-axis (a-face growth), to reduce the number of dislocations in SiC single crystals by two to three orders of magnitude, rendering them virtually dislocation-free. These substrates will promote the development of high-power SiC devices and reduce energy losses of the resulting electrical systems.