The self-diffusion of Ga and As atoms in GaAs crystal with the zince-blende structure (ZnS) is investigated by using the statistical moment method (SMM). The activation energy $(Q)$, diffusion coefficient $(D)$, and pre-exponential factor ($D_0$) are expressed by analytical closed expressions. The present analytical formulas are including the anharmonic effects of the lattice vibrations. The obtained results are applied to GaAs crystal and the SMM calculations of $Q, D$ and $D_0$ are in agreement with the experimental data.
