The diffusion of deuterium (H-2) in B and Al doped 4H and 6H silicon carbide (SiC) has been studied in detail by secondary ion mass spectrometry. From H-2 depth profiles, following trap limited diffusion with negligible complex dissociation, an effective capture radius for the formation of H-2-B complexes (at 460 degreesC) is determined to R-HB = (21+/-4) Angstrom. This value is in good agreement with that expected for a Coulomb force assisted trapping mechanism. At annealing conditions where dissociation is non-negligible, the H-2 diffusion follows Fick's law with a constant effective diffusivity, from which the complex dissociation frequencies nu are determined. The extracted values of nu cover three orders of magnitude and exhibit a close to perfect Arrhenius temperature dependence for both H-2-B and H-2-Al complexes. The large difference between the extracted complex dissociation energies, E-d(HB)=(2.51+/-0.04) eV and E-d(HA1)=(1.61+/-0.02) eV, suggests that the atomic configurations of the two complexes are significantly different. The corresponding extracted dissociation attempt frequencies, nu (HB)(0)=(1.2+/-0.7) x 10(13) s(-1) and nu (HA1)(0)=(0.7+/-0.3) x 10(13) s(-1), are very close to the characteristic oscillation frequency of the SiC lattice, nu (SiC)(lattice)=1.6 x 10(13) s(-1). This is strong evidence for the assumption of a first order dissociation process. No difference between 4H- and 6H-SiC has been observed.