Mechanistic reaction paths for the heteroepitaxial growth of 3C-SiC on carbonized Si(001) were investigated using a combination of molecular dynamics (MD) simulations, molecular beam epitaxy (MBE), and chemical vapor deposition (CVD) experiments. MD simulations elucidated possible mechanisms of carbonization of 3C-SiC/Si(001) as the shrinkage of the [110] row of the Si lattice atoms with C adatoms. The addition of Si adatoms (ad-Si) to the Si-terminated 3C-SiC(001) 2 x 1 surface results in formation of a series of surface reconstructions of h x 2 where h = H,7, 5, 3 with increasing ad-Si coverage. The most energetically stable 3C-SiC(001) surface was found to be 3 x 2. The 'surface-structure-controlled epitaxy', in which in situ RHEED was used as a feedback signal to adjust J(C)/J(Si) during MBE growth to maintain a 3 X 2 surface reconstruction, on miscut Si(001)-[110] 4 degrees enables the formation of single-phase 3C-SiC with very low density of pit formation, Si bonds, surface crystallites and antiphase boundaries. Additional CVD growth of the 'surface-structure-controlled epitaxy' 3C-SiC MBE film on miscut Si(001)-[110] 4 degrees results in the thick single-phase 3C-SiC with smooth surface and little strain at the 3C-SiC/Si interface.