In this study, we have investigated theoretically the binding energies of shallow donor impurities in modulation-doped GaAs/Al0.33Ga0.67 As double quantum wells (DQWs) under an electric field which is applied along the growth direction for different doping concentrations as a function of the impurity position. The electronic structure of modulation-doped DQWs under an electric field has been investigated by using a self-consistent calculation in the effective-mass approximation. The results obtained show that the carrier density and the depth of the quantum wells in semiconductors may be tuned by changing the doping concentration, the electric field and the structure parameters such as the well and barrier widths. This tunability gives a possibility of use in many electronic and optical devices. (C) 2009 Elsevier Ltd. All rights reserved.