We have theoretically investigated the intersubband transition for different doping concentrations and thickness in Si δ-doped GaAs with an applied electric field. The electronic properties such as the δ-potential profile and the subband energy have been calculated by solving the Schrödinger and Poisson equations self-consistently. We show an abrupt drop of the energy differences and the absorption peaks whenever the external electric field reaches a certain value. We can say that the appearance of a second quantum well in the effective potential dependent on the applied electric field creates a rapid change in the subband energies. This critical electric field value changes as dependent on the donor concentration and thickness. Thus, we conclude that the intersubband optical absorption is very sensitive to the donor distribution and thickness as dependent on the applied electric field. This changing in the intersubband transition gives a new degree of freedom in regions of interest semiconductor device applications.