A Modified Local Density Approximation. Electron Density in Inversion Layers

In the local density approximation (LDA) the density of a many-electron system is expressed as a function of the spatially varying potential. Here a modified LDA is derived applicable for a potential with a high step at some plane which is e.g. a model for the band edges in an inversion layer at the semiconductor—insulator interface. The local density of states shows oscillations and decreases to zero at the interface as a consequence of quantum mechanical reflection. Simple expressions for the density are obtained for the strongly degenerate and for the non-degenerate system. The comparison with exact results for a model system (triangular potential) shows that the modified LDA yields good results for a wide range of parameters corresponding to real inversion layers.