BOUND AND RESONANT ELECTRON-STATES IN QUANTUM DOTS - THE OPTICAL-SPECTRUM

The energy spectrum and the wave functions of an electron in a quantum dot (QD) are computed using the effective-mass approximation. The cas e of a shallow, hydrogenlike center in a quantum dot is also considere d. We use the spherical shape approximation in the belief that the bas ic results are more sensitive to the dimensions than to the shape of t he confining potential. The wave functions for the discrete bound stat es and for the continuum states are obtained in a dosed form. We show that resonances of the Breit-Wigner type occur in the continuum, due t o the local potential of the microstructures. The lifetimes of the res onant states are computed and their impact on the optical properties o f the QD material is discussed. As an example, we give detailed result s for the GaAs/Ga1-xAlxAs QD, where the basic properties (band mismatc h, effective masses, dielectric constants) are well known. We find tha t the optical excitation spectrum, with or without the impurity center , depends dramatically on the dot radius.