We study theoretically the propagation and distribution of electron spin density in semiconductors within the drift-diffusion model in an external electric field. From the solution of the spin drift-diffusion equation, we derive the expressions for spin currents in the down-stream (DS) and up-stream (US) directions. We find that drift and diffusion currents contribute to the spin current and there is an electric field, called the drift-diffusion crossover field, where the drift and diffusion mechanisms contribute equally to the spin current in the DS direction, and that the spin current in the US direction vanishes when the electric field is very large. We calculate the drift-diffusion crossover field and show that the intrinsic spin diffusion length in a semiconductor can be determined directly from it if the temperature, electron density and both the temperature and electron density, respectively, are known for nondegenerate, highly degenerate and degenerate systems. The results will be useful in obtaining transport properties of the electron's spin in semiconductors, the essential information for spintronic technology.