AbstractThe effect of the screening of the electron‐phonon interaction on the polaron binding energy (E) and the polaron mass (m*) is investigated within second order perturbation theory and for different approximations to the two‐dimensional electron gas response (random‐phase approximation, Hartree‐Fock and Thomas‐Fermi approximation). For the electron–phonon contribution to the polaron ground state energy a dynamical screening is applied which takes into account the dielectric response at all frequencies. The influence of the finite width of the electron layer onEandm*is investigated. The results are applied to GaAsAlxGa1–xAs heterostructures and it is found that the mass renormalization forne= 1011cm−2is 0.4% which is a factor of eight smaller than the effective mass of the unscreened