Excitons in type-II quantum-dot systems: A comparison of the GaAs/AlAs and InAs/GaSb systems

A calculation of the exciton binding energy (${\mathit{E}}_{\mathit{x}}$) and oscillator strength for quantum dots in type-II semiconductor systems is presented. 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 is confined in the other due to band lineups in the two materials which make this arrangement energetically favorable. We have considered the systems (i) GaAs/AlAs where the electron is confined in the X state in the AlAs while the hole is confined in the GaAs dot (for a dot radius of less than 56 Å) and (ii) InAs/GaSb where the electron is confined in the InAs dot while the hole is confined in the GaSb (for a dot of radius less than 87 Å). While both of these systems are indirect in real space the GaAs/AlAs system is also indirect in k space. We compare ${\mathit{E}}_{\mathit{x}}$ in the type-II dot to ${\mathit{E}}_{\mathit{r}}$, the binding energy of a bulk hydrogenic impurity in the bulk barrier. We find that for the case of infinite barriers ${\mathit{E}}_{\mathit{x}}$<${\mathit{E}}_{\mathit{r}}$. For the finite barrier case with wave-function leakage into the dot, ${\mathit{E}}_{\mathit{x}}$≫${\mathit{E}}_{\mathit{r}}$ due to the effect of the overlapping electron and hole wave functions within the dot. The values of ${\mathit{E}}_{\mathit{x}}$ 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 and for the GaAs/AlAs system the values are comparable to the type-I ${\mathit{E}}_{\mathit{x}}$ values for 30<a<70 Å where a, is the radius of the dot.