A calculation of the exciton binding energy (${\mathit{E}}_{\mathit{x}}$) and oscillator strength (OS) for quantum wires in type-II semiconductor systems is presented. These structures consist of a cylindrical wire of one semiconductor embedded in a second semiconductor. In the type-II exciton systems in quantum wells the electron is confined in one semiconductor and the hole in the other is due to band lineups in the two materials, which make this arrangement energetically favorable. We use an approach which initially decouples the ρ and z components. We use a variational approach for motion in the ρ direction which allows for correlation of the free particle, and solve for the one-dimensional exciton in the z direction using an effective Coulomb interaction. The solutions are then coupled self-consistently to produce ${\mathit{E}}_{\mathit{x}}$, where ${\mathit{E}}_{\mathit{x}}$(ρ,z)=E(ρ)+E(z), and a product wave function which is used to calculate the OS. We consider the idealized situation of infinite confining barriers and the more realistic case of finite barriers for the system GaAs/AlAs, where the electron is confined in the X state in the AlAs while the hole is confined in the Γ state in the GaAs wire (for a wire diameter of less than 43 Å). For finite barriers ${\mathit{E}}_{\mathit{x}}$ peaks at 33 meV for a wire diameter of 16 Å, which represents a large enhancement over the infinite-barrier case due to the strong wave-function correlation possible in two dimensions.

• Received 23 May 1994

DOI:https://doi.org/10.1103/PhysRevB.50.8008