  Epitaxial self-assembled quantum dots (SAQDs) are of both technological and
fundamental interest, but their reliable manufacture still presents a technical
challenge. To better understand the formation, morphology and ordering of
epitaxial self-assembled quantum dots (SAQDs), it is essential to have an
accurate model that can aid further experiments and predict the trends in SAQD
formation. SAQDs form because of the destabilizing effect of elastic mismatch
strain, but most analytic models and some numerical models of SAQD formation
either assume an elastically homogeneous anisotropic film-substrate system or
assume an elastically heterogeneous isotropic system. In this work, we perform
the full film-substrate elastic calculation. Then we incorporate the elasticity
calculation into a stochastic linear growth model. We find that using
homogeneous elasticity can cause errors in the elastic energy density as large
as 26%, and for typical modeling parameters lead to errors of about 11% in the
estimated value of average dot spacing. We also quantify the effect of elastic
heterogeneity on the order estimates of SAQDs and confirm previous finding on
the possibility of order enhancement by growing a film near the critical film
height.
