Theoretical comparative study of negatively and positively charged excitons in $\mathrm{GaAs}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ semiconductor quantum wells

We compare the binding energies of the singlet ground states of negatively and positively charged excitons in a $\mathrm{GaAs}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ semiconductor quantum well. We found that the binding energies are very close, contrary to what happens in three-dimensional and two-dimensional semiconductors where the positively charged exciton is always more stable than the negatively charged exciton. This result is in agreement with recent experimental observations.