Differently doped and undoped silicon was irradiated with electrons to study the formation of nonequilibrium defects and their annealing behavior. The annealing curves, measured by positron lifetime and also partly by the shape parameters of the Doppler-broadened annihilation line, depend strongly on the doping concentration and the oxygen content. In addition, temperature-dependent positron-lifetime measurements starting at 15 K were performed after low-temperature and room-temperature irradiation with different doses and in different annealing states. Shallow positron traps were detected for all conductivity types of irradiated Si. However, the concentration of shallow traps depends on the crystal-growth procedure. Electron-irradiated Czochralski-grown samples contain a higher number of shallow traps than electron-irradiated floating-zonegrown material. Due to the different concentrations of oxygen in these differently grown Si, we conclude that the oxygen atoms are a part of these traps. A possible candidate is the irradiation-induced A center. Correlated infrared-absorption investigations were carried out to support this interpretation.