  Heteroepitaxial self-assembled quantum dots (SAQDs) will allow breakthroughs
in electronics and optoelectronics. SAQDs are a result of Stranski-Krastanow
growth whereby a growing planar film becomes unstable after an initial wetting
layer is formed. Common systems are Ge$_{x}$Si$_{1-x}$/Si and
In$_{x}$Ga$_{1-x}$As/GaAs. For applications, SAQD arrays need to be ordered.
The role of crystal anisotropy, random initial conditions and thermal
fluctuations in influencing SAQD order during early stages of SAQD formation is
studied through a simple stochastic model of surface diffusion. Surface
diffusion is analyzed through a linear and perturbatively nonlinear analysis.
The role of crystal anisotropy in enhancing SAQD order is elucidated. It is
also found that SAQD order is enhanced when the deposited film is allowed to
evolve at heights near the critical wetting surface height that marks the onset
of non-planar film growth.
