Theoretical analysis of strain and strain decay in InAs∕GaAs(001) multilayer quantum dot growth

Abstract

The results of analytically based calculations of the various strain components within and outside InAs quantum dots (QDs) in a GaAs matrix are presented. The calculations performed here take into account cubic crystal strain anisotropy and spatial grading of the indium composition. The assumptions regarding the shape and compositional profile of the QDs have been refined and reflect experimental findings from previous morphological studies. Generally, cone-shaped QDs are modeled with and without truncation, and the composition is either pure InAs or is assumed to change linearly from 50% at the bottom to 100% at the top. The exact QD dimensions—height and base diameter—have been obtained from scanning tunneling microscopy and atomic force microscopy. The first part of the calculation addresses structures containing a single QD layer. Particular emphasis is placed on evaluating the decay of strain in the growth direction, as this is known to affect QD nucleation and growth in subsequent layers. In the second part the calculations are expanded to structures containing two layers of QDs with separations of 10, 20, and 30nm. It is shown that the biaxial strain component decays more rapidly in the case of an isolated QD compared with a QD in the second layer of a structure with 10nm spacing. In this bilayer structure, the hydrostatic strain within the first layer QDs is significantly smaller compared with that in the upper QDs and the implications for the electronic band structure are discussed. Our calculations provide insight into trends in (multilayer) QD structures that are not easily observed experimentally.