Phonon-induced shift in shallow donor levels of semiconductor quantum structures

Using perturbational, variational, and Feynman-path-integral techniques, we have calculated shifts in impurity binding energies of shallow hydrogenic donor levels in two-dimensional semiconductor systems due to the electron–LO-phonon interaction. We find that polaron shifts in donor energy levels are of the order of 1–10 % in weakly polar ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As-GaAs quantum wells, and 10–20 % in a more polar CdTe-HgTe system. We find Lamb-shift corrections due to the electron-phonon interaction to be negligibly small. Different theoretical techniques and their quantitative implications for experimental measurements are critically discussed.