Elastic energy release rate (EERR) of a surface quantum dot (QD) near laterally and vertically neighboring seed QDs in a linear anisotropic elastic substrate iscalculated. An efficient boundary element method is used to solve the three-dimensional boundary value problem of anisotropic elasticity, which requires discretization only along the surfaces of the QDs and their interfaces with the substrate. Numerical results are reported for InAs QDs of cuboidal shapes on aGaAs substrate with a free surface along the (001) plane, assuming that the spatial variation of the total change of free energy (including elastic energy, surface energy and edge energy) depends only upon the elastic energy part. The results are used to explore the driving force and favorable location of a new surface QD in the presence of buried and surface seed QDs. It is found that the presence of a surface seed QD inhibits the growth of a new surface QD. The new Q prefers to align with the seed QD in the (1 00) and (01 0) directions. However, this effect is relatively small. In contrast, the effect of a buried seed QD on the growth of a new surface QD can be significant. It is found that the favorable location of a new surface QD may be either vertically above or at an angle to the buried seed QD, depending on the depth of the latter. The driving force for the growth of a new QD at the favorable locations is enhanced by the presence of the buried seed QD. In addition, the theory predicts an optimum depth of the buried seed QD for the driving force for the growth of a new QD at the surface.
Citation: Physical Review B (Condensed Matter and Materials Physics)
Issue: No. 3
Pub Type: Journals
boundary element method, elastic Green's function, energy release rate, InAs/GaAs, quantum dots