Low temperature spectral photoconductivity measurements were used to obtain the part of the energy spectrum in the absorption edge region connected with the presence of doping donors in single and double Si delta-doped GaAs layers. Experimental results proved that, in delta-doped samples with a high concentration of donors and a thin cup layer under illumination in the band edge region at low temperatures, optical transitions into the bound exciton states prevail. The potential of the donors in the delta-layer and the distance between the layers in double doped layers determine the features of the energy spectrum. The free-electron distribution at low temperatures is given by the classical Poisson equation rather than by the model of free 2D electrons in a V shaped potential.