We present a first-principles analysis of the strain renormalization of the
cation diffusivity on the GaAs(001) surface. For the example of In/GaAs(00
1)-c(4X4) it is shown that the binding of In is increased when the substrat
e lattice is expanded. The diffusion barrier DeltaE(epsilon) has a nonmonot
onic strain dependence with a maximum at compressive strain values (epsilon
<0), while being a decreasing function for any tensile strain (<epsilon> >
0) studied. We discuss the consequences of spatial variations of both the b
inding energy and the diffusion barrier of an adatom caused by the strain f
ield around a heteroepitaxial island. For a simplified geometry, we evaluat
e the speed of growth of two coherently strained islands on the GaAs(001) s
urface and identify a growth regime where island sizes tend to equalize dur
ing growth due to the strain dependence of surface diffusion.