Size dependence of ground-state energy of the excitons in spherical Y2O3

The exciton energies of rare earth oxides (Ln2O3) have rarely been calculated by the theory. Experimentally, the blue-shift of exciton energy in nanocrystals deviates from the traditional size confinement effect. Herein, the dependence of the ground-state energy of an exciton in Y2O3 spheres on particle radius was calculated by using a variational method. In the model, an exciton confined in a sphere surrounded by a dielectric continuum shell was considered. The ground-state energy of exciton comprises kinetic energy, coulomb energy, polarization energy and exciton–phonon interaction energy. The kinetic and coulomb energy were considered by the effective mass and the dielectric continuum and the exciton–phonon interaction energy was given by the intermediate coupling method. The numerical results demonstrate that the present model is roughly consistent with the experimental results. The confinement effect of the kinetic energy is dominant of the blue-shift of the exciton energy in the region of R < 5 nm, while confinement effect of the coulomb energy is dominant of the blue-shift of the exciton energy in the region of R > 5 nm. The polarization energy contributes largely to the exciton energy as the particle size is smaller than ~ 10 nm, while the exciton–phonon interaction energy takes only a little contribution in all the range.