Excitonic trion $X^{-}$ in semiconductor quantum wells

The ground-state energy of the negatively charged exciton in a semiconductor quantum well is calculated assuming finite band offsets in a two-band model within the envelope-function approximation with isotropic electron and hole masses. A variational 66-term Hylleraas-type wave function has been used. The stability against dissociation into an exciton and a free electron is investigated in the cases of ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ and ${\mathrm{C}\mathrm{d}\mathrm{T}\mathrm{e}/\mathrm{C}\mathrm{d}}_{1-x}{\mathrm{Zn}}_x\mathrm{Te}$ quantum wells with several compositions and different values of the well width. A stable binding is obtained in all cases. The calculated transition energies are in reasonable agreement with the available experimental values. A particular experiment is proposed in order to identify charged excitons and to distinguish them from neutral donor bound excitons.