Heteroepitaxial growth of 3C-SiC on Si by chemical vapor deposition has been investigated using the precursor trimethylsilane. To optimize the growth process and to obtain high growth rates, we have investigated the effect of temperature and precursor flow rate on on-axis Si(100) and off-axis Si(111) substrates. High growth rates, in excess of 30 mu m/h, have been obtained. Growth on carbonized Si(111) substrates produces a smoother surface morphology compared to films grown on noncarbonized substrates. Growth of thicker SiC films was carried out on carbonized off-axis Si(111) substrates with a growth rate of similar to 20 mu m/h at 1200 degrees C and 10 seem of trimethylsilane. The resulting SiC films were 6-7 mu m thick, crack-free, and highly crystalline. This reveals the possibility for the application of these SiC films as "pseudosubstrates" and also for SiC-on-Si microelectromechanical structures which can withstand high temperature and corrosive environments.