Elastic fields in quantum dots arrays: A three-dimensional finite element study

In this paper, a three-dimensional finite element analysis is used to study the strain, stress and stain energy density distributions in quantum dots (QDs) arrays. Two different QD geometries are simulated: truncated-pyramidal and lens-shaped. The effect of the material anisotropy and the cap layer thickness on the elastic fields is studied. The simulation results show that the material anisotropy has significant influence on the strain distribution. The average compressive strain εxx in the QDs increases as the anisotropy ratio A increases from 1.0 to 4.0, while it decreases as A is reduced from 1.0 to 0.25. When the anisotropy ratio A>1, [1 0 0] and [1¯ 0 0] are the “elastic soft” directions with the strain εxx decaying rapidly in these directions. However, these lattice directions become “elastic hard” when A<1. Due to the elastic interaction among the QDs, various distributions of strain energy density can be obtained by changing the material anisotropy and the cap layer thickness, possibly resulting in different vertically ordered QD structures. The distribution of the strain energy minima at the cap layer surface is not sensitive to the two different QD shapes studied, though the strain and stress distributions in the QDs and the matrix are.