The outstanding features associated with Zn and Be diffusion in GaAs substrates and GaAs/AlGaAs superlattices are explained either quantitatively or semiquantitatively using the kick-out mechanism, in which it is assumed that the doubly positively charged Ga self-interstitial governs Ga self-diffusion. These features include (i) the dependence of the Zn solubility upon the pressures of the As and Zn vapor phases, (ii) the square power-law dependence of the Zn diffusivity on its own background concentrations under Zn isoconcentration diffusion conditions, (iii) the different shapes of the Zn in-diffusion profiles, (iv) the much lower diffusivities of Zn and Be under out-diffusion conditions than under in-diffusion conditions, and (v) the tremendous enhancement effect of Zn in-diffusion on GaAs/AlGaAs superlattice disordering and the undetectable effect of Be under out-diffusion conditions. Some useful quantitative information has been obtained. Strictly on a qualitative basis, we have found that the Longini mechanism is also able to explain the above features (i)-(iv) fairly well. The predicted effects of the Longini mechanism on Ga self-diffusion are, however, contrary to experimental results associated with superlattice disordering.