Parametrized Equations for Excitons in Quantum Wires

Abstract

A set of analytic equations for calculating the binding energies of excitons in T-shaped and squared quantum well wires are established within the effective mass approximation and the two-band model. The resolution is performed in the framework of the variational method. The projections of the relative movement in a lateral plane (2D exciton) and along the free movement direction (1D exciton) are examined as limiting cases. Binding energies and spatial extensions of the exciton as functions of the size of the wire for both the ground and the first excited states are calculated in the case of GaAs/GaAlAs heterostructures for T-shaped and squared geometries. The method is applied to calculate the effects on the excitons induced by the application of crossed electric and magnetic fields. Comparison between quantum wells, T-wires and squared wires is given.