We have investigated the unintentional n-type background doping in GaN(0001) layers grown on semi-insulating 4H-SiC(0001) substrate by plasma-assisted molecular beam epitaxy under Ga-rich conditions at growth temperatures from 780°C and 900°C. All layers exhibited very smooth surface morphology with monolayer steps as revealed by atomic force microscopy. Hall-effect measurements showed that the sample grown at 900°C had carrier concentration of 9.8 9 10 17 cm À3 while the sample grown at 780°C had resistivity too high to obtain reliable measurements. Secondary-ion mass spectroscopy revealed O and Si concentrations of <10 17 cm À3 in the sample grown at 900°C but >10 17 cm À3 in the sample grown at 780°C. The trend for the atomic concentrations of O and Si, which are common donor impurities in GaN, was thus contrary to the trend of the carrier concentration. The fullwidth at half-maximum for x-ray rocking curves obtained across the GaN(0002) and GaN(10 15) reflections for the sample grown at 900°C was 62 arcsec and 587 arcsec, respectively. The half-width increased with decreasing growth temperature. The atomic concentrations of O and Si are too low to account for the unintentional background doping levels. A possible explanation proposed in early reports for the background doping is N-vacancies.