Binding energy of bound excitons $D^{0}X$ in quantum wells

The binding energies of excitons bound to silicon donors in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum-well (QW) structures have previously been investigated experimentally as a function of the well width by several groups. The most comprehensive data show a clear maximum for a well width of about 100 Å, and a steady decrease for widths above this. Existing theories give qualitative agreement with the decrease in binding energy with increasing well width. However, no theory predicts a maximum near 100 Å. Furthermore, the quantitative agreement is poor for all well widths. We develop a theoretical model using a density-functional approach which correctly predicts the maximum in the binding energy at 100 Å. The agreement with the experimental results is significantly better for all well widths than that of existing models. Photoluminescence experiments have also been carried out on samples with a wide range of different doping profiles in order to clarify the previous experimental results and provide additional information on the effect of the position of the impurity in the QW.