Modified Local Density Approximation for Potentials with a Finite Step

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Abstract
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 which takes into account a finite potential step at a plane interface so being applicable for semiconductor‐insulator structures and, in many cases, also for semiconductor heterojunctions. Different modifications of the standard LDA are discussed. They are compared with one another and with the exact solution of the Schrödinger equation for a model system. The simplest modification is shown to be also the best one and to give very good results for inversion layers even in the case of relatively small potential jumps and up to field strengths of some 105 V cm−1.