Low-Lying of a Negatively Charged Exciton X^– in Two-Dimensional Quantum Dots

The Hamiltonian of a charged exciton X^– (trion) in a two-dimensional quantum dot with parabolic confinement has been diagonalized to obtain the low-lying eigenenergy values as a function of the dot size and the electron to hole effective mass ratio. The introduction of the transformation bracket for 2D harmonic oscillators facilitates the evaluations of Hamiltonian. By using this method, we have calculated the energies of the low-lying states of the charged exciton as a function of the mass σ and the radius of quantum dots. It is found that a charged exciton X^– in a quantum dot may have more than one bound states. Theoretical explanations derived from the first principles have been formulated.