Electronic states inInAsquantum spheres and ellipsoids

Abstract

The eight-band effective-mass Hamiltonian of the free-standing narrow-gap $\mathrm{InAs}$ quantum ellipsoids is developed, and the electron and hole electronic structures as well as optical properties are calculated by using the model. The energies, wave functions and transition probabilities of quantum spheres as functions of the radius of quantum sphere $R$ is presented. It is found that the energy levels do not vary as $1∕{R}^{2}$, which is caused by the coupling between the conduction and valence bands, and by the constant terms correspond to the spin-orbit splitting energy. The blueshifts of hole states depend strongly on the coupling from electron states, so that the order of hole states changes as has been predicted in experiment. The exciton binding energies are calculated, the calculated excitonic gaps as functions of the ground exciton transition energy are in good agreement with the photoluminescence measured spectra in details. Finally, the hole energy levels and the linear polarization factors in $\mathrm{InAs}$ quantum ellipsoids as functions of the aspect ratio are presented. The state $1{S}_{Z\ensuremath{\uparrow}}^{(1∕2)}$ becomes the hole ground state when $e$ is larger than 2.4. The saturation value of the linear polarization factors of the $\mathrm{InAs}$ long ellipsoids of diameter $2.0\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ is 0.86, in agreement with the experimental results.