We investigated the inter-band transition effects in spin generation in semiconductors by measuring the time-resolved differential transmission of the samples. The degree of polarization pumped with the single- photon excitation of electrons was found to decay with a time constant of 210 ps, giving a spin relaxation time of 420 ps, and to be enhanced with decreasing temperature. We also found that the polarization depends strongly on the excitation photon energy. The results are discussed based on the selection rules governing optical transitions from heavy-hole, light-hole and split-off states to conduction band states in a bulk sample.