The ground-state energy of the negatively charged exciton in a semicon
ductor quantum well is calculated assuming finite band offsets in a tw
o-band model within the envelope-function approximation with isotropic
electron and hole masses. A variational 66-term Hylleraas-type wave f
unction has been used. The stability against dissociation into an exci
ton and a free electron is investigated in the cases of GaAs/Ga1-xAlxA
s and CdTe/Cd1-xZnxTe quantum wells with several compositions and diff
erent values of the well width. A stable binding is obtained in all ca
ses. The calculated transition energies are in reasonable agreement wi
th the available experimental values. A particular experiment is propo
sed in order to identify charged excitons and to distinguish them from
neutral donor bound excitons.