Single-crystalline 3C-SiC epitaxial layers were grown on on-axis Si (001) substrates by low-pressure hot-wall chemical vapour deposition. Aluminium from a trimethylaluminium (TMA) source was used for p-type doping. The atomic Al and carrier concentrations in the layers were determined as a function of the partial pressure of the TMA source gas. Secondary ion mass spectroscopy (SIMS), Hall-effect measurements at room temperature and four-point electrical resistivity method were applied to measure the atomic and electrically active Al concentrations. The crystalline perfection of the layers was characterized by high-resolution x-ray diffraction (HRXRD). At TMA-partial pressures ranging from 510-7 mbar up to 1.510-4 mbar corresponding aluminium concentrations from 21015 cm-3 up to 1.31019 cm-3 were measured in the epitaxial layers. On increasing the Al concentration from 1x1017 cm-3 to 1x1019 cm-3 the layer electrical resistivity decreases from 17 cm to 0.8 cm, while no influence on the crystalline quality of the layers was observed. The average full width at half maximum (FWHM) of the rocking curve for a 5µm thick 3C-SiC layer is about 500 arcsec. With increasing layer thickness (up to 16 µm) the FWHM of the rocking curve decreases to about 300 arcsec.