Binding energy and stability of charged excitons in a semiconductor cylindrical quantum dot

The binding energy of full three-dimensional (3-D) charged excitons confined in a semiconductor cylindrical quantum dot (QD) is theoretically investigated using a variational procedure within the effective mass approximation. We predicted a trial wave function to not only satisfy the strong confinement regime but also yield the correct results in the weak confinement regime. The trions confinement is described by a finite square potential well. We show that the negatively charged exciton has higher binding energy than the positively charged exciton, when the QD half height is less than the effective Bohr radius (strong confinement regime). At large QD, the negatively charged exciton binding energy crosses down the positively charged exciton binding energy and becomes an unstable system. We have clarified the paradoxes existing in the previous literatures concerning the trions binding energy.