NONLINEAR IMPURITY SCREENING IN STRONGLY DEPLETED 2D ELECTRON GASES

The in-plane profiles of the electron density and potential energy in modulation delta-doped quantum wells with thin spacer layers are studi ed as a function of the average sheet electron density. With depleting the electron gas, the impurity induced density and potential fluctuat ions become more and more pronounced, until the lateral electron densi ty profile desintegrates into a set of spatially insulated clusters. T his strongly disordered phase of an interacting 2D electron system is analysed by applying and comparing four different theoretical approach es. In the limit of high average electron density, excellent agreement is found between the selfconsistent potential profiles calculated wit h 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 foun d to be applicable for all electron densities, thus providing a comput ationally efficient simulation method for both the linear and non-line ar regime of impurity screening. (C) 1997 Academic Press Limited