The in-plane profiles of the electron density and potential energy in modulation δ-doped quantum wells with thin spacer layers are studied as a function of the average sheet electron density. With depleting the electron gas, the impurity induced density and potential fluctuations become more and more pronounced, until the lateral electron density profile desintegrates into a set of spatially insulated clusters. This strongly disordered phase of an interacting 2D electron system is analysed by applying and comparing four different theoretical approaches.
In the limit of high average electron density, excellent agreement is found between the selfconsistent potential profiles calculated with the random phase approximation (RPA), with a non-linearized version of the semiclassical Thomas-Fermi approximation (NLTF) and with a full-scale 2D Hartree calculation. For the strongly depleted case the RPA is invalid, while a modified version of the classical theory of weakly doped impurity bands (BEGS) becomes effective. The NLTF model is found to be applicable for all electron densities, thus providing a computationally efficient simulation method for both the linear and non-linear regime of impurity screening.