We investigate the atomic structure and electronic properties of various defect configurations which consist of B and C atoms in Si predoped with C impurities through first-principles density-functional calculations. In the absence of Si self-interstitials ͑I's͒, substitutional B and C atoms interact repulsively with each other, implying that B-C pairs at neighboring substitutional sites do not behave as a trap for B dopants. For I-B-C complexes, which can be formed in the presence of self-interstitials, we find that a C-B split interstitial, where the B and C atoms share a single lattice site along the ͓001͔ axis, is the most stable configuration. For several diffusion pathways, along which the B dopant diffuses from the C-B split-interstitial configuration with the ͓001͔ orientation to nearby tetrahedral and hexagonal sites, we find very high migration energies of about 3 eV. Thus, the diffusing B atom can be easily trapped in the neighborhood of C, resulting in the reduction in the B diffusivity. The range of the C trap potential is estimated to be about 7 Å. We also examine the diffusion of C from the stable C-B split interstitial, leaving the B dopant at a substitutional site, and find the migration energy to be much reduced to 2.16 eV. This result indicates that, as the C atom is dissociated, it acts as a trap for self-interstitials, leading to the reduction in self-interstitials which are available for B diffusion. In this case, the suppression of the B diffusivity is still expected, without degrading the electrical activity of the B dopants.