  Nonlinear evolution of three-dimensional strained islands or quantum dots in
heteroepitaxial thin films is studied via a continuum elasticity model and the
development of a nonlinear dynamic equation governing the film morphological
profile. All three regimes of island array evolution are identified and
examined, including a film instability regime at early stage, a nonlinear
coarsening regime at intermediate times, and the crossover to a saturated
asymptotic state, with detailed behavior depending on film-substrate misfit
strains but not qualitatively on finite system sizes. The phenomenon of island
stabilization and saturation, which corresponds to the formation of steady but
non-ordered arrays of strained quantum dots, occurs at later time for smaller
misfit strain. It is found to be controlled by the strength of film-substrate
wetting interaction which would constrain the valley-to-peak mass transport and
hence the growth of island height, and also determined by the effect of elastic
interaction between surface islands and the high-order strain energy of
individual islands at late evolution stage. The results are compared to
previous experimental and theoretical studies on quantum dots coarsening and
saturation.
