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

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 Added by Lawrence Friedman
 Publication date 2008
  fields Physics
and research's language is English




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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.



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Epitaxial self-assembled quantum dots (SAQDs) represent an important step in the advancement of semiconductor fabrication at the nanoscale that will allow breakthroughs in electronics and optoelectronics. In these applications, order is a key factor. Here, the role of crystal anisotropy in promoting order during early stages of SAQD formation is studied through a linear analysis of a commonly used surface evolution model. Elastic anisotropy is used a specific example. It is found that there are two relevant and predictable correlation lengths. One of them is related to crystal anisotropy and is crucial for determining SAQD order. Furthermore, if a wetting potential is included in the model, it is found that SAQD order is enhanced when the deposited film is allowed to evolve at heights near the critical surface height for three-dimensional film growth.
Epitaxial self-assembled quantum dots (SAQDs) are of interest for nanostructured optoelectronic and electronic devices such as lasers, photodetectors and nanoscale logic. Spatial order and size order of SAQDs are important to the development of usabl e devices. It is likely that these two types of order are strongly linked; thus, a study of spatial order will also have strong implications for size order. Here a study of spatial order is undertaken using a linear analysis of a commonly used model of SAQD formation based on surface diffusion. Analytic formulas for film-height correlation functions are found that characterize quantum dot spatial order and corresponding correlation lengths that quantify order. Initial atomic-scale random fluctuations result in relatively small correlation lengths (about two dots) when the effect of a wetting potential is negligible; however, the correlation lengths diverge when SAQDs are allowed to form at a near-critical film height. The present work reinforces previous findings about anisotropy and SAQD order and presents as explicit and transparent mechanism for ordering with corresponding analytic equations. In addition, SAQD formation is by its nature a stochastic process, and various mathematical aspects regarding statistical analysis of SAQD formation and order are presented.
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