Quantum-confined Stark effects of an exciton bound to an ionized donor in a $\mathrm{GaAs}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum well

We have calculated by a variational procedure the binding energy of an exciton bound to an ionized donor ${(D}^{+},X)$ in a $\mathrm{GaAs}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum well with $x=0.15\mathrm{}$ and $x=0.30\mathrm{}$ as a function of the well width L and an electric field F perpendicular to the well interfaces. The dependence of the correlation energy on the electric field is investigated and compared with those of a shallow donor $D^0$ and an exciton X. It is shown that the correlation energy of the ${(D}^{+},X)$ complex decreases monotonically at increasing F values in the case of large well widths $\left(L\gtrsim 10\hspace{0.5em}\mathrm{nm}\right).\mathrm{}$ However, it is not sensitive to the electric field in narrow QW’s. For all investigated well widths, the ${(D}^{+},X)$ complex remains stable compared to its product of dissociation.