Removal of Accidental Degeneracy in Semiconductor Quantum Dots

We present a quantitative analysis of the energy levels and wavefunctions of carriers in a cubic quantum dot of GaAs embedded in GaAlAs with finite confining potential barriers at their interfaces. The energy spectrum has substantially reduced degeneracies compared to the analytically determined energy levels of the infinite-barrier quantum box of the same dimensions. The level degeneracy of states has been explained by group representations of the octahedral point group. Projection operators for the irreducible representations provide a unique way of obtaining the linear combinations of the degenerate wavefunctions which form a basis set for the representations. Energy level splittings in the presence of externally applied electric and magnetic fields are also studied.