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

TL;DR

This paper develops a comprehensive elastic model for self-assembled quantum dots, revealing significant errors in previous homogeneous assumptions and showing how elastic heterogeneity influences dot morphology and ordering.

Contribution

It introduces a full elastic calculation into the modeling of SAQDs, improving accuracy and understanding of how heterogeneity affects their formation and order.

Findings

Homogeneous elasticity assumptions can cause up to 26% errors in elastic energy density.

Elastic heterogeneity impacts the estimated average dot spacing by about 11%.

Growing films near critical height can enhance quantum dot order.

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 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.