Stress distributions and energetics in the laterally ordered systems of buried pyramidal Ge/Si(001) islands: An atomistic simulation study

Abstract

Stress distributions in laterally ordered arrays of coherent Ge islands of shallow pyramidal shape buried in a Si(001) matrix are studied via large-scale atomistic simulations, using Stillinger-Weber Ge/Si systems as a vehicle. The existence of tensile hydrostatic stress regions is observed on the spacer surface, above the buried islands. Our previously reported finding [M. A. Makeev and A. Madhukar, Phys. Rev. Lett. 86, 5542 (2001)] that the hydrostatic stress at the spacer layer surface above the island apex is nearly inversely proportional to the spacer layer thickness is validated by a comparison with experimental data. The lateral variations of the hydrostatic stress on the spacer layer surface show ``bell-shape'' profiles, with the effective size of the tensile regions above the island apex varying as a power law with the spacer layer thickness, with the power exponent being greater than 1. Studies of the energetics of twofold stacks of island systems show that the elastic interaction energy between the islands is minimized for the vertically aligned geometry. The spacer layer thickness dependence of the hydrostatic and biaxial stress field distributions in the interior of the Si(001) matrix are presented as these define the behavior of the electron and hole three-dimensional confinement potentials that determine the electronic properties of the pyramidal island quantum dots.