In this study, we have investigated theoretically the effects of the electric field and doping concentration on the optical transitions in a modulation-doped GaAs-AlGaAs quantum well for different well widths. The binding energies of the donor have also been computed using a trial wave function with two parameters in the framework of an effective-mass approximation. The electronic structure of a modulation-doped quantum well under the electric field is determined by solving the Schrodinger and Poisson equations self-consistently in the effective-mass approximation. The results obtained show that inter-sub-band transitions and the energy levels in the modulation-doped quantum well can be significantly modified and controlled by the well width and donor concentration. The sensitivity to the well widths of the absorption coefficient can be used in various optical semiconductor devices' applications. (C) 2009 Elsevier Ltd. All rights reserved.