Theory for excitons in type II quantum dot systems

This letter presents the first calculation of the exciton binding energy (Ex) and oscillator strength (os) for quantum dots in type II semiconductor systems. These structures consist of a spherical dot of one semiconductor embedded in a second semiconductor. As in the type II exciton systems in quantum wells, the electron is confined in one semiconductor and the hole in the other due to band line-ups in the two materials which make this arrangement energetically favourable. We use a variational calculation where the wavefunction of the particle confined to the dot is a spherical Bessel function and the wavefunction of the other particle is a generalized Fang-Howard wavefunction allowing correlation with the confined particle. We have considered the GaAs/AlAs system where the electron is confined in the X state in the AlAs while the hole is confined in the GaAs dot which is indirect in both real and k space for a dot radius of less than 56 angstrom. We compare Ex in the type II dot to Er, the binding energy of a bulk hydrogenic impurity in the AlAs. We find that for the case of infinite barriers Ex <Er. For the finite barrier case with wavefunction leakage into the dot, Ex >> Er due to the effect of the overlapping electron and hole wavefunctions within the dot. Although Ex is always smaller for type II than for the corresponding type I systems (using the masses of the type II system) the values for a type II dot system are vastly larger than those for a type II quantum well system due to the extra correlation in the other two confined dimensions. The Ex of the type II GaAs/AlAs system are comparable to the Ex of the type I GaAs/AlxGa1-xAs system (with the electron mass being that of the Γ valley) for a gt; 30 angstrom where a is the radius of the dot.