Relativistic correction of biexciton fine structure in ellipsoidal quantum dots

In the framework of the effective mass approximation the biexciton states have been investigated in the oblate and prolate ellipsoidal quantum dots. To calculate the ground state energy of the biexciton, three-parameters’ variational trial function was utilized. Based on the non-relativistic energy and wave function the lowest-order relativistic correction to the non-relativistic Hamiltonian have been calculated. The relativistic correction energy of the biexciton fine structure have been found to be the order 10−6meV. The relativistic correction approaches zero with increase of the quantum dot sizes. It has been also revealed that the relativistic correction of the biexciton fine structure increases with the increase of size quantization. As a result, the mentioned effect is more pronounced for the case of prolate ellipsoidal quantum dot in the comparison with oblate one.