Effects of elastic heterogeneity and anisotropy on the morphology of self-assembled epitaxial quantum dots

Abstract

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 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 and incorporate it into a stochastic linear model of the initial stages of SAQD formation process for the case of fast deposition followed by annealing. We find that using homogeneous elasticity can cause errors in the elastic energy density as large as 26%. The wavelength corresponding to the fastest growing mode in the linear model is used as an estimate for SAQD spacing. We calculate that homogeneous elasticity can lead to an error of about 11% in the estimated value of average spacing established during the initial stages of SAQD formation process. 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.