Increased screening of the hydrogenic donor due to modulation doping in quantum wells

Screening of the hydrogenic donor at the center of the well in p-type modulation-doped ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs quantum wells was measured by monitoring the free to bound transition, free hole to donor. Undoped, center of the well doped, and center of the barrier doped samples were investigated. The screening increased, as measured by the reduction in the binding energy of the donor, in the sequence undoped, center of the well doped, and center of the barrier doped samples. The screening efficiency increases as the donor ion is moved farther away from the center of the well. The reduction in the donor binding energy, due to screening from carriers introduced by center of the barrier doping, agrees reasonably well with the calculated value for modulation-doped quantum wells of the same carrier density.