We have determined silicon self-diffusivity at temperatures 735-875 degrees C based on the Raman shift of longitudinal optical phonon frequencies of diffusion annealed 28Si/30Si isotope superlattices. The activation enthalpy of 3.6 eV is obtained in such low temperature diffusion annealing. This value is significantly smaller than the previously reported 4.95 eV of the self-interstitial mechanism dominating the high temperature region T>>855 degrees C and is in good agreement with the theoretical prediction for the vacancy-mediated diffusion. We present a model, containing both the self-interstitial and the vacancy terms, that quantitatively describes the experimentally obtained self-diffusivity between 735 and 1388 degrees C, with the clear crossover of the two diffusion mechanisms occurring around 900 degrees C.