Three-dimensional strain field calculations in coupled InAs/GaAs quantum dots

A detailed calculation of the three-dimensional strain field in and around InAs/GaAs quantum dots is presented. The strain field is calculated by minimizing the elastic strain energy on a cubic grid. Surface boundary conditions are incorporated to enable the strain field at the surface of the cap layer to be examined in detail. This has important implications for the vertical and lateral ordering of subsequent layers of dots. Results are presented for a single dot as well as two and four coupled dots. It is found that the elastic energy density at the surface of the epilayer above a layer of seed dots exhibits strong minima directly above the seed dots, facilitating vertical ordering. An intriguing result is that, under certain conditions, satellite minima also occur at interstitial points, raising the possibility that a second layer of dots above the seed layer can have significantly more dots than the seed layer because of lateral ordering.