The correlation energies in a singlet and in a triplet state of a two-electron quantum dot in a finite barrier square well potential are computed. Closed analytical expressions are obtained in the perturbation method. Effects of band non-parabolicity and polaronic correction are included. Effects of hydrostatic pressure on the correlation energies are computed. Our results show that (i) the correlation energies in the triplet state are negative, reflecting the exchange interaction, (ii) both the singlet and triplet state correlation energies approach zero as the dot size approaches infinity, (iii) while the band non-parabolicity and the polaronic effects are not significant in the estimation of correlation energies, they however decrease the total confined energies to a maximum of 43% in the triplet state, and (iv) the hydrostatic pressure affects the confined energies appreciably for narrow dots only. The interesting cross-over behavior of the triplet and the singlet state energies at a particular dot radius is explained physically.
Correlation energies in the (1s-1p) triplet state of a two-electron spherical QD with square-well potential confinement are estimated for dots of different radii. The results are presented taking GaAs dot as an example. Our results show that the correlation energies are i) negative in a triplet state in contrast to the singlet state, ii)approaches zero as the dot size approaches infinity, and iii) the "fictitious crossing" of the singlet and triplet state energies at a particular dot size is explained on the basis of Hund's rules.
Simultaneous effect of hydrostatic pressure and polaronic mass on the binding energies of the ground and excited states of an on-center hydrogenic impurity confined in a GaAs/GaAlAs spherical quantum dot are theoretically investigated by the variational method within the effective mass approximation. The binding energy is calculated as a function of dot radius and pressure. Our findings proved that the hydrostatic pressure led to the decrease of confined energy and the increase of donor binding energy. Conduction band non-parabolicity and the polaron masses are effective in the donor binding energy which is significant for narrow dots not in the confined energy. The maximum donor binding energy achieved by the polaronic mass in the ground and excited states are 2%–19% for the narrow dots. The confined and donor binding energies approach zero as the dot size approaches infinity.
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