In this letter we use a Semi-Classical Impurity Band Model and obtain by Monte Carlo simulation the density of states (DOS) and the impurity charge distribution inside a quantum well (QW) of Ga 1−x Al x As/GaAs . We show the existence of a Coulomb gap as has been observed in bulk semiconductors. The DOS is not very sensitive to the QW width close to the Coulomb gap, at least in the range from 1 to 4 times the Bohr radius, and shows a behavior D(E)∝|E−EF| which indicates a two-dimensional signature. We show that the neutral donors concentrate in the center of the well according to a distribution whose width and decay rate depend on the compensation and impurity concentration respectively. Those effects are expected to be observed by infra-red absorption experiments and useful in device diagnosis.