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.
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