Electric-field effect on spatially dependent screening of impurity states in quantum wells

The binding energy of a shallow acceptor in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells subjected to a longitudinal electric field is calculated with use of a variational method. The spatially dependent screening effect is taken into account with an r-dependent dielectric function to evaluate the acceptor binding energy. The effect of the electric field on the spatially dependent screening of the acceptor states is investigated. It is shown that the electric field affects effectively the difference between the binding energies calculated from a spatially-dependent-screening theory and those from a constant-screening theory. It is also clearly shown that the electric-field effect on the spatially dependent screening depends on the position of the acceptor within a quantum well of finite depth.