It is very interesting to probe the rotational symmetry of semiconductor quantum dots for quantum information and quantum computation applications. We studied the effects of rotational symmetry in semiconductor quantum dots using configuration interaction calculation. Moreover, to compare with the experimental data, we studied the effects of hidden symmetry. The 2D single-band model and the 3D single-band model were used to generate the single-particle states. How the spectra affected by the breaking of hidden symmetry and rotational symmetry are discussed.

The breaking of hidden symmetry splits the degeneracy of electron-hole single-triplet and triplet-singlet states, which can be clearly seen from the spectra. The breaking of rotational symmetry redistributes the weight percentage, due to the splitting of p_x and p_y states, and gives a small brightness to the dark transition, giving rise to asymmetry peaks. The asymmetry peaks of 4X, 5X, and 6X were analyzed numerically. In addition, Auger-like satellites of biexciton recombination were found in the calculation. There is an asymmetry peak of the biexciton Auger-like satellite for the 2D single-band model while no such asymmetry peak occurs for the 3D single-band model. Few-particle effects are needed in order to determine the energy separation of the biexciton main peak and the Auger-like satellite.

From the experiments, it was confirmed that the lower emission energy peak of X^2-spectrum is split. The competed splitting of the X^2- spectra were revealed when temperature dependence was implemented. However, since the splitting is small, we suggest the X^2- peaks are broadened in comparison with other configurations according to single-band models. Furthermore, the calculated excitonic emission patterns were compared with experiments. The 2D single-band model fails to give the correct energy order of the peaks for the few-particle spectra; on the other hand the peaks order from 3D single-band model consistent with experimental data.