Phonon renormalization effects in quantum wells

We investigate the effects of screening on polaronic corrections to the effective band edge and effective mass in a quasi-two-dimensional GaAs quantum well. We find that both screening and finite well width significantly reduce the polaron energy and thus oppose the polaronic band-gap renormalization. We calculate how this ``counter-renormalization'' depends on the free-carrier density and temperature. We show that static screening overestimates screening in comparison with dynamical screening. We calculate the polaronic effective mass as a function of free-carrier density and temperature and show that the calculated temperature dependence of screening is too small to account for the observed temperature dependence in recent cyclotron resonance measurements of effective mass.