Abstract: A comparative study is made of the strain distribution in cylindrical InAs/GaAs and InP/InGaP self-assembled quantum dots as obtained from isotropic elasticity theory, the anisotropic continuum mechanical model, and from atomistic calculations. For the isotropic case, the recently proposed approach [J. H. Davies, J. Appl. Phys. 84, 1358 (1998)] is used, while the finite-element method, the valence force field method, and Stillinger-Weber potentials are employed to calculate the strain in anisotropic structures. We found that all four methods result in strain distributions of similar shapes, but with notable quantitative differences inside the dot and near the disk-matrix boundary. The variations of the diagonal strains with the height of the quantum dot, with fixed radius, as calculated from all models, are almost linear. Furthermore, the energies of the band edges in the two types of quantum dots are extracted from the multiband effective-mass theory by inserting the strain distributions as obtained by the four models. We demonstrated that all strain models produce effective potentials for the heavy and light holes which agree very well inside the dot. A negligible anisotropy of all normal strains in the (x,y) plane is found, which, providing the axial symmetry of the kinetic part of the multiband effective-mass Hamiltonian, justifies the use of the axial approximation. Strain propagation along the vertical direction is also considered with the aim to study the influence of strain on the electron coupling in stacks of quantum dots. We found that the interaction between the strain fields of the individual quantum dots makes the effective quantum wells for the electrons in the conduction band shallower, thereby counteracting the quantum mechanical coupling. (C) 2002 American Institute of Physics.

Abstract: The electronic structure of disk-shaped InP/InGaP self-assembled quantum dots is calculated within the effective-mass theory. The strain-dependent 6x6 multiband Hamiltonian for the valence band is simplified into an axially symmetric form. Both the continuum mechanical model, discretized by finite elements, and the isotropic model are used to calculate the strain distribution and their results are critically compared. The dependence of the electron and the hole energy levels on the dimensions of the quantum dot is investigated. We found that both the electron and hole energies are underestimated if the strain distribution is calculated by the isotropic elasticity theory. The agreement between the electron energies for the two approaches is better for thinner quantum dots. The heavy holes are confined inside the quantum dot, while the light holes are located outside the disk, but confined by the strain field near the edge of the disk periphery. We found that the (h) over bar /2 hole ground state crosses the 3 (h) over bar /2 ground state when the height of the quantum dot increases and becomes the ground state for sufficiently thick quantum disks. The higher hole levels exhibit both crossings between the states of the different parity and anticrossings between the states of the same parity.