Self‐Consistent Theory of the Electronic Structure of Inversion Layers. I. A New Method Using the Modified Local Density Approximation

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Abstract
A new method is described for the self‐consistent calculation of electron and hole densities, band bending, and subband energies in inversion layers of MIS‐structures. This method makes use of new and simple expressions for carrier densities which take into account the influence of the interface semiconductor–insulator within a modified local density approximation. The method allows for an accuracy which is comparable with that one of explicit self‐consistent solutions of the Schrödinger equation for inversion layers. But it is of the numerical simplicity of the classical method. This gives the possibility to calculate electronic properties of MIS‐structures in much more detail than before. In part I the method is described and its advantages for modelling MIS‐structures are shown. In part II the influence is discussed of quantum effects in inversion layers on electronic properties of MIS‐structures in comparison with classical calculations for various semiconductors in a wide range of temperature and doping concentration.