Effect of isotropic versus anisotropic elasticity on the electronic structure of cylindrical $\mathrm{InP}/{\mathrm{In}}_{0.49}{\mathrm{Ga}}_{0.51}\mathrm{P}$ self-assembled quantum dots

The electronic structure of disk-shaped InP/InGaP self-assembled quantum dots is calculated within the effective-mass theory. The strain-dependent $6\times 6$ 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 $ħ/2\mathrm{}$ hole ground state crosses the $3ħ/2\mathrm{}$ 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.