  The Ga vacancy mediated microstructure evolution of (Ga,Mn)As during growth
and post-growth annealing is studied using a multi-scale approach. The
migration barriers for the Ga vacancies and substitutional Mn together with
their interactions are calculated from first principles, and temporal evolution
at temperatures ranging from 200 to 350$^\circ$C is studied using Lattice
Kinetic Monte Carlo simulations. We show that at the typical growth and
annealing temperatures (i) gallium vacancies provide the diffusion mechanism
for substitutional Mn and (ii) in 10--20 h the vacancy mediated diffusion of Mn
promotes the formation of substitutional clusters. Clustering reduces the Curie
temperature ($T_C$), and therefore the Mn clustering combined with the fast
interstitial Mn diffusion explains the experimentally observed twofold
annealing behavior of $T_C$.
